Illustrating the Phaenomena: Celestial Cartography in Antiquity and the Middle Ages [1 ed.] 0199609691, 9780199609697

Citation preview

ILLUSTRATING THE PHAENOMENA

This page intentionally left blank

ILLUSTRATING THE PHAENOMENA Celestial Cartography in Antiquity and the Middle Ages

Elly Dekker

1

3

Great Clarendon Street, Oxford, ox2 6dp, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Elly Dekker 2013 The moral rights of the author have been asserted First Edition published in 2013 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer British Library Cataloguing in Publication Data Data available ISBN 978–0–19–960969–7 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work.

To Henk

PREFACE AND ACKNOWLEDGEMENT In 1979 Debby Warner published The Sky Explored: Celestial Cartography, 1500–1800.This excellent study on celestial cartography has documented the production of printed celestial maps and the main streams of development in constellation designs since 1500. However the history of celestial cartography starts in Antiquity and I have always felt it as a desideratum to know the achievements of the generations preceding those that could make use of the printing press.The purpose of this study is to fill this gap in our knowledge on celestial cartography. For a proper evaluation it is essential to establish our material heritage of manuscript maps and globes. It is true that the survival of any artefact over centuries is bound to be random, but this has never prevented historians from looking into the history of their subject, regardless of how badly that may have been documented. In selecting material I have limited myself predominantly to artefacts that present the celestial sphere in its entirety. Astrolabes and globes which comprise, say, less than a hundred stars have been left out. Also artefacts such as the celestial hemisphere of the Old Sacristy in Florence—presenting that half of the celestial sky that at a certain time was above the local horizon—and astrological ceiling paintings have been left aside. The globes and maps discussed in the present book have mostly been studied before by philologists and art historians. To provide a suitable framework I have emphasized here especially cartographical aspects. It amounts to a close

examination of the construction details that may be compared with theoretical models or written sources. It also means that constellations in this study are in the first place seen as a means to fix the locations of stars rather than the main figures of mythological drama, although this side of celestial cartography is not completely ignored. Sixteen extant celestial globes made before 1500 have been examined and described individually. In this I was able to build on the work of competent predecessors. Less well documented are the about 40 celestial maps included in this study, the earliest example dates from the early ninth century and the latest from 1503. These maps have never been described collectively before. Next to presenting in depth analyses of the material presented the purpose of this book is giving access to these sources for further study. A vital part of the book is its photographic documentation. Many objects are not easily accessible and this has certainly hampered their study. Besides, there are many details, especially arthistorical ones, for which written descriptions are inadequate. My thanks go to all those libraries, museums, and institutions for their permission to study the instruments and maps in their collections and for their help with photographic material: Aberystwyth, Llyfrgell Genedlaethol Cymru/ The National Library of Wales; Amman, Institut Français du Proche-Orient; Athens, Deutsches Archäologisches Institut; Basle,

Preface and Acknowledgement Universitätsbibliothek; Berlin, Antikensammlung, Staatliche Museen zu Berlin—Preussischer Kulturbesitz; Berlin, Staatsbibilothek zu Berlin—Preussischer Kulturbesitz; Bern, Burgerbibliothek; Bernkastel, St. NikolausHospital/Cusanusstift; Boulogne-sur-Mer, Bibliothèque Municipale; Cologny, Fondation Martin Bodmer; Cracow, Jagiellonian University Museum; Darmstadt, Universitätsund Landesbibliothek; Dresden, Staatliche Kunstsammlungen Dresden-MathematischPhysikalischer Salon Zwinger; El Burgo de Osma, Cabildo Catedral; Florence, Museo Galileo; Gävle, Länsmuseet Gävleborg; Greenwich, National Maritime Museum; Kuwait, The al-Sabah Collection, Dar al-Athar al-Islamiyyah; London, The British Library; London, The Warburg Institute, Photographic Collection; Mainz, Römisch-Germanisches Zentralmuseum; Malibu, The J. Paul Getty Museum; Monza, Museo e Tesoro del Duomo; Munich, Bayerische Staatsbiliothek; Naples, Museo Archeologico; Nuremberg, Germanisches Nationalmuseum; Oxford, Bodleian Library; Oxford, Museum of the History of Science; Paris, Bibliothèque national de France; Paris, Galerie J. Kugel; Philadelphia, University of Pennsylvania; St. Gall, Stiftsbibliothek; Stuttgart, Landesmuseum Württemberg; Trier, Rheinisches Landesmuseum; Utrecht, University Library; Vatican City, Biblioteca Apostolica Vaticana; Veste Coburg, Kunstsammlungen der

vii

Veste Coburg; Vienna, Österreichische Nationalbibliothek. In my quest to clarify all sorts of details I have received the help of many people: Silke Ackermann, Søren Andersen, Alejandro García Avilés, Marcin Banaś, Jim Bennet, Dieter Blume, Sandrine Boucher, Wolfram Dolz, Catherine Hofmann, Patrick McGurk, Allard Mees, Wolfgang Metzger, Marco Mostert, Irmgard Muesch, Barbara Pferdehirt, Martin Rolland, Lawrence J. Schoenberg, Barbara Brizdle, Nancy M. Shawcross, Giorgio Strano, Giancarlo Truffa, Silvia Uhlemann, and ClaudeVibert-Guigue. My thanks go to all these and others who, although unnamed here, lent their aid. The present book, especially Chapter 3, owes much to the encouragement of Kristen Lippincott who introduced me in the field of illustrated astronomical manuscripts.Without her help and instruction I might never have taken up the study of medieval maps. The Arabic language formed another barrier in the study of celestial cartography before 1500. To overcome this problem at least partially in Chapter 4 I have had the help and support of Paul Kunitzsch. His studies of the Ptolemaic star catalogue and its transmission, and his work on Arabic star names are of great value in discussing celestial cartography. I thank him most warmly for his advice on all sorts of matters. For errors of content, including those always possible when transcribing difficult inscriptions, I of course remain responsible.

This page intentionally left blank

CONTENTS 1. Preliminaries 1 1.1 1.2 1.3 1.4 1.5 1.6

The descriptive tradition 1 The geometry of the cosmos 5 The mathematical tradition 10 Signs, conventions, precession, and epochal modes 14 Prerequisites to globe making 26 Hipparchus’s rule 34 Appendix 1.1 Summary of the ancient constellations 38 Appendix 1.2 On sources 41 Appendix 1.3 Locating colures with respect to stars 44

2. Celestial cartography in antiquity 49 2.1 2.2 2.3 2.4 2.5 2.6

The Berlin fragment 52 The Larissa globe 54 Kugel’s globe 57 The Mainz globe 69 Hyginus’s globe 80 The Farnese globe 84 Appendix 2.1 Catalogue of antique celestial globes 102

3. The descriptive tradition in the Middle Ages 116 3.1 3.2 3.3 3.4

Summer and winter hemispheres 118 Planispheres 142 Northern and southern hemispheres 180 Globe making in the Middle Ages 192 Appendix 3.1 Catalogue of medieval hemispheres 207 Appendix 3.2 Catalogue of medieval planispheres 227 Appendix 3.3 Northern and southern medieval hemispheres 249 Appendix 3.4 Medieval pictures of globes 254

4. Islamic celestial cartography 257 4.1 4.2 4.3 4.4

The celestial ceiling of Quṣayr cAmra 260 The Islamic mathematical tradition 278 The Uranography of Abu ’L-Ḥusayn al-Ṣūf ī (903–86) 286 Extant globes made before 1500 307 Appendix 4.1 Islamic globes with constellation images made before 1500 323

Contents 5. The mathematical tradition in medieval Europe 337 5.1 5.2 5.3 5.4

The mathematical tradition: the Islamic legacy 337 Ptolemy’s precession globe 343 Maps in the mathematical tradition 357 Globes in the service of astrology 388 Appendix 5.1 European celestial maps made before 1500 408 Appendix 5.2 European celestial globes made before 1500 420

Epilogue 432 Bibliography 437 Addendum 459 Manuscript Index 463 Author Index 465

x

chapter one

preliminaries

. THE DESCRIPTIVE TRADITION

of 51 star groups and some of their stars as these have become known in the Western World (see Appendix 1.1: Summary of the ancient constelhe appearance of hundreds of stars in the lations for a number of ancient sources). clear night sky is a dazzling sight.The patterns Not all historians are unanimous in their opinformed by the stars appeared to remain fixed in the ion that when writing his Phaenomena Aratus used course of time, and it is therefore not surprising a prose version of the description of the sky by the that in many civilizations specific groups of stars Greek mathematician, astronomer, and geograwere distinguished.The arrangement of stars into pher Eudoxus of Cnidos, who lived in the first constellations served to construct agricultural cal- half of the fourth century BC (400–347 BC). endars, record celestial omens, and create weather Already Hipparchus (fl. 130 BC) had expressed this predictions.1 However, questions concerning the opinion in his Commentary to Aratus. Hipparchus origin of constellations are not easily answered. himself had at his disposal two treatises, one called Many cross-cultural influences, especially from Enoptron and the other Phaenomena, which differ the ancient Near East, are attestable but it is outside very little and which he attributed to Eudoxus.3 the scope of this study to trace the processes After a detailed comparison of the texts, he coninvolved. In the present study we are concerned in cluded that it was the Phaenomena which had served particular with the role of the fixed stars and con- as the model for Aratus poem. This point of view stellations in mapping the celestial sky, as this hap- has been accepted by most science historians.4 pened in Antiquity and the Middle Ages. Classical scholars, on the other hand, are more The earliest more or less complete descrip- divided in their opinion concerning the sources tion of the celestial sky in Greek astronomy is used by Aratus. In his recent edition of the that by Aratus of Soli (ca. 310–240/239 BC) in his Aratean poem Douglas Kidd adopted the opin1154-line poem, entitled Phaenomena and writ- ion popular among science historians, but ten at the turn of the third century BC.2 In it, he Manfred Erren considers it unlikely that Eudoxus describes the appearances and relative positions should have written two treatises on the same

T

1 Evans 1998, pp. 39–44; Bowen and Goldstein 1983, p. 331; Steele 2008, pp. 30–37. 2 The bibliography on both Aratus’s original Greek poem and its numerous Latin translations is extensive.The reader is directed to Martin 1956 and to annotated editions and translations of

the text: Aratus (Mair 1921), Aratus (Erren 1971), Aratus (Kidd 1997), and Aratus (Martin 1998). 3 Hipparchus (Manitius 1894), I.1.3, p. 9. 4 Neugebauer 1975, p. 577; Dicks 1985, p. 154; Evans 1998, p. 40.

Preliminaries course, have named or identified all the stars taken individually, because there are so many all over the sky, and many alike in magnitude and colour, while all have a circling movement; therefore he decided to make the stars into groups, so that different stars arranged together in order could represent figures; and thereupon the named constellations were created, and no star-rising now takes us by surprise; so the other stars that shine appear fixed in clear-cut figures, but those beneath the hunted Hare are all very hazy and nameless in their courses.’7

subject.5 He argues that one prose treatise is probably a later revision of the other. Eudoxus would then have written the treatise labelled Enoptron whereas the other treatise labelled Phaenomena would be a later copy made after Aratus had written his poem of that name. This then would explain the identical names of the poem and of one of the prose texts. A third and more controversial point of view was put forward by Jean Martin in his recent edition of Aratus’s Phaenomena.6 Although he admits that it is difficult to maintain that Eudoxus should not have written an authentic treatise on the subject, he is convinced that neither of the two prose versions mentioned by Hipparchus can be attributed to Eudoxus. Either treatise, Enoptron as well as Phaenomena, would be a prose paraphrase of Aratus’s poem.We do not find Martin’s reasoning convincing (objections to Martin’s arguments are given in the Appendix 1.2) and therefore accept here the opinion of most science historians that Hipparchus’s quotations from the treatises Enoptron and Phaenomena can be attributed to Eudoxus and that most of Aratus’s astronomical definitions and assessments go back to Eudoxus. In discussing some anonymous groups of stars Aratus explains the principle underlying the constellation figures:

Clearly, constellations were introduced as an aid to identify and to memorize individual stars in the sky in order that these could be recognized at their rising and setting.8 The fixed stars could be remembered in terms of being on the head, on the right shoulder, on the left arm or leg, and so on of a constellation figure. The locations of these stars in the sky determine in turn how the constellation figure as a whole should be drawn. This cartographic function is only one side of the significance of constellations. Probably long before Eudoxus and Aratus wrote their work, constellations were connected to stories that helped to memorize the various stellar configurations and often served to explain why the gods placed a particular figure in the sky. These stories or myths followed their own track independent of the astronomical side of the matter.The constellation myths were collected, possibly for the first time, in a now lost work attributed to Eratosthenes (ca. 276 BC–ca. 195 BC). Traces of this work are found in the Epitome Catasterismorum in which the myths are supplemented by descriptions of the locations of the individual stars

‘Other stars covering a small area, and inset with slight brilliance [ . . . ] are not cast in any resemblance to the body of a well-defined figure, like the many that pass in regular ranks along the same paths as the years complete themselves, the constellations that one of the men who are no more devised and contrived to call all by names, grouping them in compact shapes: he could not, of

5 Aratus (Kidd 1997), pp. 14–18.Aratus (Erren 1971), pp. 114–15. 6 Aratus (Martin 1998), vol. 1, pp. LXXXVI–LCXXV.

7 Aratus (Kidd 1997), pp. 98–101, ll. 365–85. 8 Carruthers 2006, pp. 25–26.

2

1.1 The Descriptive Tradition within a constellation.9 For example, of Bootes it is said:

myths nor do they explicitly list the locations of the stars within constellations. It is generally assumed that the star catalogue in the Epitome ‘This is said to be Arcas, the son of Callisto and can be attributed to Eratosthenes but this is far Zeus. Lycaon, , cut up the infant and served him at been suggested that the data were taken from a the table when he entertained Zeus.The god, , overturned the of the authorship. As discussed in more detail table, whence the city Trapezus received its name, below, a number of peculiarities of the descripthen struck the house with lightning . Arcas was created anew, that its composition is neither the result of obsermade whole by Zeus, . It is said that as a young man Arcas entered vation nor the work of a capable astronomer the sacred precinct of Zeus Lycaeus and wed his such as Eratosthenes. If the descriptions in the mother, unaware of her true identity. When the star catalogue were put together by an anonyinhabitants were about to sacrifice them both, in mous author from consultation of a globe, this keeping with the law, Zeus carried them away text could have been joined at some stage to because of his prior relationship with Callisto and Eratosthenes’s collection of constellation myths. placed them among the stars. This composite text would then have served as The figure has four stars on the right hand; these the common source from which all known stars do not set. There is one bright star on the head; one bright star on each shoulder; one star on descriptive star catalogues derive. In this comeach breast, the one on the right breast being posite text the constellations were not yet bright. Beneath this last star is one faint star.There adapted to the Aratean order. A change in order is one bright star on the right elbow; one very must have taken place when at some stage the bright star between the knees, which is called text was merged with early Greek editions of Arcturus; and one bright star on each foot. The Aratus’s Phaenomena. However that may be, the total is fourteen.’10 constellation myths and the listings of locations The Epitome appears to combine two traditions: of the stars within a constellation are believed to a literary one describing the constellation myths have been transmitted by way of a Greek astroand a cartographic one describing the positions nomical text, the so-called edition Φ, the existof the stars within a constellation. Neither tradi- ence of which was postulated by Martin.11 This tion finds its origin in the descriptions of the edition Φ must have consisted of material taken celestial sky by Eudoxus and Aratus. The works from a Greek version of Aratus’s poem with schoof these latter authors do not include many lia attributed to Theon the grammarian (first century BC) and the now lost manual of Eratosthenes. Characteristically, in this edition Φ 9 Eratosthenes (Robert 1878); Eratosthenes (Olivieri 1897); the Aratean poem is interspersed with texts in Eratosthenes (Pàmias and Geus 2007). English and French translations were published by respectively Condos 1997, and Charvet and Zucker 1998. 10 Condos 1997, pp. 55–6.

11 Martin 1956, pp. 69–72.

3

Preliminaries which mythological and positional information are given side by side. The significance of Aratus’s poem in GrecoRoman popular astronomy cannot be overestimated. Its significance in educating astronomy is expressed in Fig. 1.1 showing a mosaic from Trier. Aratus and Urania, the personification of astronomy, are shown around a celestial globe. The sphere is mounted in a legged stand and covered by a number of circles, the zodiacal band, and presumably the summer solstitial colure. A number of Latin translations of Aratus’s work made by Marcus Tullius Cicero (106–43 BC), Germanicus Julius Caesar (15 BC– AD 19), and Rufius Festus Avienus (fourth century ad), underline the importance of the poem in Roman education.12 Before the turn of the

third century the Greek collection of mythological and positional details included in the edition Φ was translated into Latin (now known as the Scholia Basileensia) and added to Germanicus’s translation of Aratus’s Phaenomena.13 Connected with, but yet different from, these medieval texts is the astronomical treatise De Astronomia by Hyginus (first century BC).14 Martin has argued that this work is a direct reworking of the lost manual of Eratosthenes.15 Hyginus refers on many occasions to Eratosthenes in the myths he describes in Book II but his collection of myths is more extensive. In his star catalogue in Book III the name of Eratosthenes is mentioned only twice.Although it cannot be denied that Hyginus’s descriptions of the stellar configurations in Book III are closely linked to the listings in the Epitome, it is also clear that they depart from it in characteristic ways. The Hyginian order of the constellations deviates from the original order used in the now lost work attributed to Eratosthenes as well as from the Aratean order. And, as discussed in Section 2.5, Hyginus’s descriptions of the locations of the stars strongly suggest that he used a globe in addition to his main source. In Antiquity the progress made in mathematics was the basis of another, mathematical, approach in celestial mapping. Before turning to this mathematical tradition, which distinguishes itself from the descriptive one by marking the place of the stars by coordinates on a sphere, we must first have a closer look at the properties of the sphere.

Fig. 1.1 Mosaic with Aratus and Urania. (Foto Th. Zühmer -Rheinisches Landesmuseum,Trier.)

12 Cicero (Buescu 1966), Cicero (Soubiran 1972), Germanicus (Le Boeuffle 1975), Germanicus (Gain 1976), and Avienus (Soubiran 1981).

13 Dell’ Era 1979c. 14 Hyginus (Le Boeuffle 1983); Hyginus (Viré 1992). 15 Martin 1956, pp. 73–126.

4

1.2 The Geometry of the Cosmos

. THE GEOMETRY OF THE COSMOS

pole to pole (colures) and the so-called oblique circles (the ecliptic and the horizon). These circles are schematically presented in Scheme 1.1. It was a complex astronomical problem to relate these circles to the real, observed phenomena of the apparent daily and annual motions of the Sun and the stars. The apparent daily motion of a star takes place along a fixed parallel. Its intersections with the horizon are its points of rising and setting. For a star located at equal distances from both poles, the daily motion runs along the Equator and it rises at the point of true east and sets at the point of true west of the local horizon.19 The closer a star is to the northern celestial pole, the further its points of rising and setting shift along the horizon to the north-east and the northwest, respectively, until they coincide in the north. At this point, the parallel circle of the daily track of a star becomes tangential to the local horizon and always remains completely above it, so that the star never sets. In Antiquity, this particular parallel was called ‘the ever-visible circle’. It separates the stars that never set from those that do. Similarly, the closer a star is to the southern celestial pole, the further its points of rising and setting along the horizon shift to the south-east and the south-west, respectively, until they coincide in the south.At this point, the parallel circle of the daily track of that star is— again—tangential to the horizon, but this time it is completely below it. For this reason, this track is called the ‘ever-invisible circle’. It is thus clear that two of the five parallel circles (the ever-visible and ever-invisible circles) depend on the local horizon, which, in turn, depends on

The concept of the sphere was key in Greek astronomy for modelling the geometry of the cosmos. It is an essential part of the cosmological theories among philosophers such as Plato (ca. 427–348 BC) and Aristotle (384–322 BC) and onwards.16 The generation of a spherical model of the Heavens and the Earth resulted in what is called the two-sphere model—‘an arrangement of two concentric spheres in which the inner sphere represents the earth, and the outer, the orb of the fixed stars’.17 This particular model is attributed to the Greek astronomer and geographer Eudoxus. Since the fourth century BC, the properties of the sphere have formed the basis of understanding the celestial phenomena visible to the naked eye. Early mathematical treatises on the properties and movements of the sphere by Autolycus (fl. 330 BC), Euclid (fl. 300 BC), and Theodosius (fl. 100 BC), demonstrate how the concept of the sphere can explain the changing patterns of the rising and the setting of the Sun and stars, the changing length of the day and night throughout the year.18 The model of the rotating sphere provided a mathematical definition for the axis of rotation of the sphere of the universe and its extremities, the northern and southern celestial poles. Connected with this polar axis are series of parallel circles perpendicular to it (the Equator, the tropics and the ever-visible and ever-invisible circles), a series of semicircles extending from 16 Evans 1998, pp. 19–20. 17 Bowen and Goldstein 1983, p. 333. 18 For editions of these treatises see Autolycos (Aujac 1979); Berggren and Thomas 1996;Theodosius (Kunitzsch and Lorch 2010) and Theodosius (Kunitzsch and Lorch 2011).

19 That the stars rise and set in a fixed point of the horizon is a property regularly reported in early treatises. See Aratus (Kidd 1997), p. 113. See also Manilius (Goold 1977), p. 43.

5

Preliminaries of rising of the Sun shifts from a northernmost point (summer sunrise) through the east (autumn) to the southernmost location (winter sunrise) and returns again to the east (spring). Similarly, the point of setting shifts from its northernmost point (summer sunset) through the west (autumn) to the southernmost location (winter sunset) and returns again to the west (spring). These points on the horizon, shown in Scheme 1.3, are dependent on local, geographic latitude.20 By observing the rising and setting of the Sun through the year, these points can in principle be determined. And, again in principle, by noting these spots on the horizon, one can observe and list which stars are on the various circles or between them. For example, a star located on the Tropic of Cancer will always rise and set at the Scheme 1.1 The celestial grid. same points on the horizon as the Sun does when it is in the summer solstice, and so on. In the geographic latitude of the observer on Earth. practice, however, making observations close to It is also clear that the stars located on the ever- the horizon is fraught with difficulties. The visible circle can be easily found by observing increase in atmospheric density at the horizon those stars that graze the horizon daily in the causes extinction, refraction, and colour distornorth. In Scheme 1.2 this is illustrated for the tions.As a result, horizon observations are always moment that the left shoulder of Bootes grazed slightly problematic and may well be the source the horizon in the north at the epoch 375 BC for of several ‘untraceable’ errors in astronomical an observer in Athens. sources.Yet, as the ancients lacked sophisticated The apparent daily motion of the Sun takes observational instruments, it may well have been also place along a parallel. The intersections of the dominant observational mode of the early this parallel with the horizon are the points of Greek astronomers.This hypothesis is supported sunrise and sunset. Unlike the fixed stars, the Sun continually moves through the heavens 20 Already Aristotle incorporated in his Meteorologica 2.6 the from one parallel to another until its parallel points of summer and winter rising in schemes for wind direccoincides either with the Tropic of Cancer in tions, see Aristotle (Lee 1978), p.193. Ptolemy placed these the north or with the Tropic of Capricorn in points in his Geography 30º from the east west line regardless the latitude, see Berggren and Jones 2000, p. 15 and p. 75, note 50. the south.This shift from one parallel to another The value of 30º is close to that for the latitude of Rhodes (36º). is caused by the Sun’s annual path through the For geographical latitudes of 32º and 40º the summer and winter points are respectively 28.7º and 32.1º from the east-west stars along an oblique circle called the ecliptic. line. For geographical purposes the approximate value of 30º In the course of a year, the azimuth of the point may well have sufficed. 6

1.2 The Geometry of the Cosmos

Scheme 1.2 The ever-visible circle drawn for the latitude of 40° at the moment that the left shoulder of Bootes is grazing the horizon in the north (epoch 375 BC).

fulfilling years. Many guide-stars lie along them all, by the attention given to the rising and setting of to mark them, all bound closely together all the the constellations in the treatises of Eudoxus and way; the circles themselves are without breadth Aratus. and fastened all to each other, but in size two are Aratus introduces the ecliptic, that is the matched with two’.21 oblique circle defined by the annual motion of the Sun on the sphere, together with the other, After first listing the constellations that mark the parallel circles, the tropics and the Equator: tropics and the Equator Aratus continues to say that the latter circles are parallel ‘but the fourth is ‘There are indeed these four circles set like wheels, for which there will be particular desire and need if you are studying the measurements if the self-

21 Aratus (Kidd 1997), pp. 106–7, I. 462.

7

Preliminaries through three circles and conceals by its downward slope the straightness of its path.’24

The points on the ecliptic, which it shares with the Equator and the tropics, are the so-called equinoxes and solstices, respectively. When the Sun is at one of the equinoxes its daily track follows the Equator. This situation happens twice a year—in spring and in autumn when the Sun rises and sets respectively in the true east and true west on the day that the length of night and day are equal.When the Sun is at one of the solstices, its daily track follows one of two parallel circles that are tangential to the ecliptic (the Tropic of Cancer and Tropic of Capricorn). Scheme 1.3 The northern- and southernmost points This situation occurs in summer when the Sun of sunset and sunrise for a latitude of 40°. rises and sets respectively in its northernmost eastern and western points, on the day of longgripped obliquely between the two tropics, est daylight; and in the winter, when the Sun which hold it on opposite sides, while the mid- rises and sets respectively in its southernmost dle one cuts it in the middle’.22 Of this oblique eastern and western points, on the day of shortcircle he says: est daylight. The equinoxes and solstices also determine ‘Men call it by the name the circle of the Zodiac. On it is the Crab, and next the Lion, and under that the colures.These are by definition the four semthe Maiden, after her the Claws and the Scorpion icircles that pass through the north and south itself, the Archer and Capricorn, and after equatorial celestial poles and through one of the Capricorn the Water-pourer; after him the two equinoxes and solstices. Geminus (first century Fishes are starred, after them the Ram, the Bull BC) wrote a treatise on elementary astronomy, after that and the Twins.’23 Introduction to the Phenomena, in which he explains The location of the ecliptic with respect to that ‘they are called colures because certain parts the tropics is also detailed by Manilius in his of them are not to be seen’, that is, since they extend below the horizon they always remain Astronomica: partially invisible.25 ‘This circle [the ecliptic] is held by the Crab at the One of the difficulties in relating the celestial top, at the bottom by Capricorn, and is twice circles to specific astronomical features is the fact crossed by the circle which balances day and night, that the circles are actually invisible in the sky. whose line it cuts in the signs of the Ram and the Balance. Thus the curve of the circle is drawn Geminus stresses that, with the exception of the 24 Manilius (Goold 1977), I.672–76, pp. 58–9. 25 Geminus (Aujac 1975),V.49, p. 29; the English translation is taken from Evans and Berggren 2006, V.49, p. 157.

22 Aratus (Kidd 1997), pp. 110–11, ll. 525–9. 23 Aratus (Kidd 1997), pp. 112–13, ll. 545–9.

8

1.2 The Geometry of the Cosmos Milky Way, these circles are purely conceptual.26 This rationale of the parallel circles being without thickness was not generally adhered to in Antiquity. In his Commentary to Aratus, Hipparchus reports that Eudoxus observed that the Sun does not always rise and set in the winter and summer solstices at the same points of the horizon, which suggests a certain width for some of these circles.27 The belief of early astronomers that the tropics and subsequently the other circles also must have a certain width seems to have been widespread. In some copies of Aratus’s poem one reads that the circles are without a width, whereas in others it says that they do have a certain width. The latter opinion is also expressed by Attalus (fl. middle of the second century BC), one of the early commentators of Aratus.28 One finds further echos of this idea in the book On the Marriage of Philology and Mercury of the Roman writer Martianus Capella (fl. Carthage, ca. AD 365–440): the Sun’s course does not depart from the ecliptic except in the sign of Libra where it is now half a degree to the north and then the south.29 Hipparchus’s criticism of this viewpoint in early astronomy is clear from his persuasive demonstrations that all celestial circles must be without a width.30 The width here alluded to does not refer to the well-known and generally accepted width of the zodiacal belt, in the middle circle of

which the Sun moves.This width is determined by the northern and southern limits of the planets that ‘circulate all the way through the twelve figures of the zodiac’.31 Unlike the Sun, the motions of the planets possess a component perpendicular to the ecliptic.Aratus does not discuss the planets because—as he says—he does not feel confident in dealing with them and no mention is made in his poem of the actual size of the zodiac. Geminus provides the earliest record of the zodiac’s width as being 12º. He explains that the zodiac consists of three circles, two of which determine its width and the third is called the circle in the middle of the signs.32 Despite this reference, however, it is not possible to set a precise value for the width of the zodiac in Antiquity. In the shortened star catalogue included in the Handy Tables of Ptolemy, the Alexandrian astronomer and geographer of the second century ad, for example, only stars within 10º of the centreline of the zodiac are listed, suggesting that some astronomers, at least, believed that the width of the zodiacal band was 20º, instead of the 12º mentioned by Geminus.33 Regardless,the important point to note is that, in Antiquity, the zodiac is envisioned as a band rather than a circle, a feature that has certainly introduced some errors in early mapping. Amongst the later, Latin authors, it is worth noting that Martianus Capella follows Geminus in his description of the zodiacal band, giving it a width of 12º. He adds that the Sun is the only body that moves along the middle of

26 Geminus (Aujac 1975),V.11, pp. 22–3; Evans and Berggren 2006,V.11, p 151. 27 Hipparchus (Manitius 1894), I.9.2, pp. 88–89.This notion may well be related to Eudoxus’s efforts to explain the irregularity in the annual motion of the Sun through a three-sphere model in which he introduces a small motion perpendicular to the ecliptic. See Dicks 1985, p. 181; Neugebauer 1975, pp. 677–80; and Evans 1998, pp. 305–12. 28 Hipparchus (Manitius 1894), I.9.1–3, pp. 88–91. 29 Martianus Capella (Dick 1925), VIII, 867, p. 457; Stahl et al. 1977, p. 337. 30 Hipparchus (Manitius 1894), I.9.6, pp. 90–1.

31 Aratus (Kidd 1997), pp. 106–7, ll. 455–6. 32 Geminus (Aujac 1975),V.51–53, p. 30; Evans and Berggren 2006,V.51–53, p. 157. Neugebauer 1975, p. 583, noticed that the width of the zodiac equals two units of 6º, which is the unit used by Geminus for the division of the circle, a coincidence that may not be accidental. 33 Neugebauer 1975, p. 1050 and note 40.

9

Preliminaries the belt.34 Elsewhere in his treatise, however, we find the already mentioned Eudoxan echo on a motion in latitude. This apparent contradiction may reflect the varied source material used by Martianus Capella in composing his chapter on astronomy. Geminus is clear in stating in his Introduction that the tropics are tangent to the circle in the middle of the zodiac, that is, the ecliptic. But, again, not all sources are consistent in this matter. For example, a different definition is given by Cleomedes (fl. AD 200):

. THE MATHEMATICAL TRADITION

The mathematical tradition in celestial cartography is based first and foremost on ‘the highly significant idea of mathematically fixing the positions of the stars’.36 An important advantage of mathematical star catalogues over the descriptive type is that errors in identification are in principle ruled out. The location of any star inside a constellation figure is in the mathematical tradition fixed by two elements: its description within a constellation and a set of coordinates. ‘The band of the zodiac is at an oblique angle Together these data guarantee a far more reliable because it is positioned between the tropical circles and equinoctial circle, touching each of the presentation of the starry sky. Precise measurement in Greek astronomy tropical circles at one point, while dividing the seems to date from the time of Timocharis (first equinoctial circle into two equal parts.’35 half of the third century BC) and Aristyllus (fl. ca. One could interpret this passage as meaning that 270 BC), as data on stellar declinations measured the upper boundary of the zodiac touches the around 280 BC show.37 By what instrument these summer tropic and the lower boundary the win- data were obtained is not known. The use of ter tropic. The analysis of the maps discussed in angular distances expressed in units of 1° as Chapter 3 shows that this erroneous interpreta- known today came relatively late in Greek scition was not exceptional. ence. An inscription of the second century BC In spite of the uncertainties of the nature of found in Keskintos, on Rhodes, mentions that a some of the circles used to delineate the heavens, circle comprises 360 degrees whereas a division the properties of the celestial grid described of the circle in 360 parts was used by Hypsicles above made it possible to map the starry sky (ca. 150 BC).38 One can therefore be fairly certain without the help of astronomical instruments that neither the concept of degrees nor the and without using mathematical stellar coordi- equipment to measure them by actual observanates. What was needed was a well-defined tion were available during the first stage of Greek horizon, a good knowledge of the Sun’s north- globe making. ernmost and southernmost points of rising and The earliest records of sets of stellar coordisetting through the years, the local meridian, nates suitable to fix the location of a star on the and the location of the equinoxes with respect to sphere are found in Hipparchus’s Commentary to the stars. 36 Toomer DSB vol. 15, p. 217. 37 Goldstein and Bowen 1991. 38 Neugebauer 1975, pp. 698–99; Jones (A) 2006, p. 13;Van Brummelen 2009, pp. 33–4.

34 Martianus Capella (Dick 1925),VIII, 834, p. 438; Stahl et al. 1977, pp. 324–5. 35 Bowen and Todd 2004, p. 41.

10

1.3 The Mathematical Tradition Aratus.39 In the first part of this critical assessment of the descriptions of the celestial sphere by Eudoxus and Aratus, Hipparchus occasionally uses numerical data to support his criticisms. In the second part he provides systematic data to show the reader how the simultaneous risings and settings occur in reality at the geographical latitude of 36°, where the longest day lasts 14½ hours.To this end he indicates for each constellation which point of the ecliptic (expressed as the number of degrees within a zodiacal sign) rises when the first and the last star of a constellation rises, and similarly, which point sets when the first and the last star of a constellation sets. He also records which point of the ecliptic and which star(s) culminate at these various moments.40 For example, the rising of Bootes is recorded as follows:

Although Hipparchus does not express the locations of the stars in the more familiar spherical coordinates as, for instance, ecliptic longitude and latitude, the positions of the stars are nevertheless very accurately fixed and it is usually not difficult to identify the stars.42 The accuracy with which Hipparchus described his phenomena suggests that he did not obtain them by direct observations. Indeed, as Duke points out, ‘stars on the horizon are almost always unobservable due to atmospheric extinction’.43 For that reason science historians either consider it likely that the data were determined with the help of a celestial globe or by (trigonometric) calculation from positions in more conventional coordinates, such as right ascensions and declinations or related quantities such as mentioned in Hipparchus’s Commentary.44 In either case Hipparchus may have had a star catalogue at his disposal. It also suggests that the Commentary was written after finishing his star catalogue which would make the Commentary the work of an experienced astronomer and not really that of a young student, as has been taken for granted by some scholars.45 Whatever the case, it seems

‘Bootes rises together with the zodiac from the beginning of the Maiden [Virgo] to the 27th degree of the Maiden.When it is rising, the section of the zodiac from the middle of the 27th degree of the Bull [Taurus] to the 27th degree of the Twins [Gemini] culminates. And the first star of Bootes to rise is the one on his head (β Boo), the last is the one in the right foot (ζ Boo). Of other stars, on the meridian when Bootes begins to rise are Orion’s left shoulder (γ Ori) and left foot (β Ori), both having gone about a halfcubit beyond the meridian.When Bootes finishes rising, the bright star in the Dog’s [Canis Major] haunches (δ CMa) culminates. All of Bootes rises in approximately 2 equinoctial hours.’41

why Hipparchus marked β Boo as the first star to rise while other stars (γ, λ, θ, ι, and κ) are above the horizon at the time that β Boo is in the horizon. At Hipparchus’s latitude four of these stars (λ, θ, ι, and κ) are ever-visible; they never rise and set.This does not hold for γ Boo which is 1.6º above the horizon and rises before β Boo. Manitius supposes that the use of β Boo might be explained by proper motion but that possibility can be dismissed, see Hipparchus (Manitius 1894), p. 299, footnote 22. 42 With a modern computer program such as Chris Marriott’s SkyMap Pro I have verified the identifications by Manitius, who himself used a precession globe for this purpose. Only in a few cases did I arrive at a notably different identification. Grasshoff 1990, has listed in his Appendix C, pp. 317–34, all events recorded by Hipparchus.This appendix cannot be used without verification though, and where his identification differs from that of Hipparchus (Manitius 1894) I in most cases agree with Manitius. 43 Duke 2002, p. 430. 44 Nadal and Brunet 1983/1984. Grasshoff 1990, pp. 190–1. Duke 2002, pp. 432–3. 45 Thiele 1898, p. 33.

39 Hipparchus (Manitius 1894), especially pp. 183–281. 40 For a discussion of the interpretation of the coordinates used by Hipparchus, see Neugebauer 1975, pp. 277–80, and Duke 2002. 41 Hipparchus (Manitius 1894), II.5.1, pp. 186–7.The English translation is from Duke 2002, pp. 429–30 where it is explained in footnote 13 that in normal Hellenistic usage, the cubit is 2° (see also Toomer 1984, p. 322, n. 5). Duke 2002, p. 431 wonders

11

Preliminaries quite likely that Hipparchus compiled a now lost star catalogue with star positions in right ascension and declination and may also have had a celestial globe based on it at his disposal. Some science historians have tried to fix the total number of so-called Hipparchan stars. One attempt was based on lists of constellations included in the texts of the Aratus latinus and the later revised version thereof.46 Rehm and, in greater detail Boll, have manipulatively argued that these lists refer to a Hipparchan register of stars which would have included about 850 stars.47 Already in 1956 Martin showed that the star lists as ‘discovered’ by Rehm and Boll are part of the Aratean corpus, however, and belong to the descriptive tradition.48 Another, more interesting list associated with Hipparchus was discovered in 1936 by W. Gundel in a fifteenth-century astrological manuscript with a treatise entitled Liber HermetisTrismegisti.49 This title recalls a silver plate in the collection of the Paul Getty Museum, shown in Fig. 1.2. Gathered around a globe are a number of figures. The person on the left, writing in a book, is Ptolemy and looking over his shoulder is Skepsis, the personification of doubt. The figure to the right, opposite to Ptolemy, is labelled Hermes by whom probably Hermes Trismegistus is meant. Behind him is a female figure pointing upwards towards the incomplete figure on top that recalls the image of Christ Pantocrater who is overseeing it all.The precise interpretation of this scene is not clear but considering the globe in the centre, the topic of the discussion between Ptolemy 46 Maass 1898, pp. 134–9. 47 Rehm 1899b; Boll 1901. See also Neugebauer 1975, p. 285 and the discussion in Grasshoff 1990, pp. 34–42. 48 Martin 1956, pp. 109–15. 49 Gundel 1936, pp. 123–34 and pp. 148–59.A recent edition is in Feraboli 1994, pp. 12–17 and Appendix II, pp. 276–83.

Fig. 1.2 Plate with relief decoration by an unknown artist, ca. 500–600; 45 × 28 cm. (The J. Paul Getty Museum,Villa Collection, Malibu, California.)

and Hermes will be on the significance of astrology.50 The treatise named after Hermes Trismegistus describes among sources relevant for astrology a list of 68 stars in which for each zodiacal sign a number of stars is mentioned, with their Latin description and a value of its location in the sign. For example, ‘In Cancro uersus orientem sunt duae quae uocantur Asini, quarum septentionalis (γ Cnc) est in octauo gradu, meridionalis uero (δ Cnc) in nono.’ 51 The positions in this list are mostly ecliptic longitude but a few appear to be mediations, that is, the degree of the point of intersection 50 Field 1996, pp. 112–13.The plate has been dated by some earlier than 700, and others to the sixteenth and even to the twentieth century. 51 Feraboli 1994, p. 12.

12

1.3 The Mathematical Tradition and in the fourth, the class to which it belongs in magnitude.’55

between the ecliptic and the meridian circle through the star concerned. On average the stellar positions are correct for the Hipparchan epoch 128 BC, and presumably derive from a Hipparchan source.52 Although the precise background of the star list is uncertain, its existence shows that Hipparchus’s data did leave definitive traces. Next in chronological order is Ptolemy’s Almagest, in which Books VII and VIII are devoted to the fixed stars.53 BooksVII.5 through VIII.1 deal with the star catalogue, the most extensive known from Antiquity. It comprises in all 917 stars divided over 48 constellations. In addition to these‘formed’stars Ptolemy described 108 so-called ‘unformed’ stars, located outside the constellation figures. Thus the Ptolemaic catalogue includes in all 1025 stars.54 How the organization of the stars in constellations is described in the catalogue is explained by Ptolemy as follows:

This shows that the Ptolemaic descriptions include information on the location of a star in ecliptic coordinates. Also the magnitudes of the stars are marked in a consistent and systematic way.The recorded star positions are valid for the epoch AD 137, the beginning of the reign of Antoninus. A typical entry, for Bootes, includes 23 stars of which one, Arcturus, is outside the constellation figure. Of these 23 stars 12 (Boo 1–6, 9, 16, 19, 21, 22, and Boo 1e) are mentioned by Hipparchus in his Commentary. As an aside I note that in the present work stars are identified in one of three ways: by the BPK numbers first employed by Baily 1843 and Peters and Knobel 1915, by the serial number of each star within each Ptolemaic constellation, and occasionally by their modern name using the convention adopted by Kunitzsch.56 Thus Regulus, the brightest star in Leo, will be denoted as BPK 469, Leo 8, or α Leo. Unformed stars described by Ptolemy as belonging to the constellation Leo are labelled as Leo 1e, 2e, and so on. In the Almagest a special chapter is devoted to the Milky Way. For example, of Perseus he tells that its right side lies in the Milky Way such that

‘For each star (taken by constellation), we give, in the first section, its description as a part of the constellation; in the second section, its position in longitude, as derived from observation, for the beginning of the reign of Antoninus ([the position is given] within a sign of the zodiac, the beginning of each quadrant of the zodiac being, as before, established at [one of] the solstitial or equinoctial points); in the third section we give its distance from the ecliptic in latitude, to the north or south as the case may be for the particular star;

‘its northern edge, which is very rarefied, is defined by the lone star outside the right knee of Perseus [Per 2e], and its southern edge, which is very dense, by the bright star on his right side [Per 7] and by

52 Neugebauer 1975, p. 286. 53 Ptolemy (Heiberg 1898–1903); Manitius 1963; Toomer 1984. 54 In the Ptolemaic star catalogue the total number of stars is not given as 1025 but as ‘1022 plus 3 faint stars in Coma’.This has been a source of great confusion, the more so because the catalogue includes three doubles and has thus 1028 entries. All three numbers—1022, 1025, and 1028—are cited in ancient and modern literature.

55 Toomer 1984, pp. 339-40. 56 Kunitzsch I 1986, Kunitzsch II 1990, Kunitzsch III 1991. In Kunitzsch III 1991, pp. 187–94, the relation between the three identifications is given. In Toomer 1984, the serial numbers within a constellation deviate from those used by Kunitzsch because the unformed stars are not counted separately.

13

Preliminaries

. SIGNS, CONVENTIONS, PRECESSION, AND EPOCHAL MODES

the two rearmost stars [Per 9, 10] of the three to the south of that [Per 8, 9, 10]. Enclosed in it also are the nebulous mass on the hilt [Per 1], the star in the head [Per 5], the star in the right shoulder [Per 3] and the star on the right elbow [Per 2].The quadrilateral in the right knee [Per 16, 17, 18, 19] and also the star on the same [right] calf [Per 20] lie in the midst of the milk, while the star in the right heel [Per 21] is also inside it, a little distance from the southern border.’57

Babylonian astronomers introduced the wellknown division of the zodiac circle into 12 equal parts, or signs because the varying sizes of the zodiacal constellations themselves are not treNote that Ptolemy mentions here that the nebu- mendously suitable to mark the positions of the lous mass [Per 1], which in the star catalogue is planets, or the wandering stars, with any great said to be in the right hand is on the hilt presum- degree of consistency.60 Historians disagree, ably of a sword of some sort. It suggests that he however, on the precise date of the introduction had a pictorial source in front of him which of this Babylonian division of the ecliptic in could be a map or a globe.58 Greece.All references in the texts of early astronThe authenticity of the Ptolemaic star cata- omers such as Eudoxus are to zodiacal constellalogue has been and still is a topic of debate.59 tions, not to signs. As Bowen and Goldstein Some science historians take it for granted noted: ‘the ultimate source of our knowledge of that the star catalogue included in Ptolemy’s Eudoxus’ Phaenomena and Enoptron, does not Almagest is nothing but the lost star catalogue by support the claim that Eudoxus divided the Hipparchus, but adapted to another epoch. The ecliptic into 12ths and each of these into 30 Ptolemaic stellar longitudes are—contrary to degrees of arc but even suggests that he did not’.61 Ptolemy's claim—not in keeping with the epoch Indeed, the Greek zodiac described by Aratus is AD 137. One explanation for this is that Ptolemy delineated by the twelve well-known constellaobtained his longitudes by adding 2º 40´ to tions Aries,Taurus, Cancer, Leo,Virgo, the Claws, Hipparchus’s longitudes.The Ptolemaic star cat- Scorpius, Sagittarius, Capricornus, Aquarius, alogue, whether in essence Hipparchan or not, and Pisces.62 The first mention of signs could formed the foundation on which all globe and have been by Autolycus who divided the ecliptic map makers of the mathematical tradition from into 12 equal arcs although he did not express the second until the sixteenth century have these arcs as units of 30º.63 based their work. I shall have ample opportunity One confusing aspect of the transmission of to return to Ptolemy’s star catalogue in later the concept of the signs is that often sources do chapters. not distinguish between ‘signs’ and ‘constellations’. The same Greek word is used to indicate both (or either) ‘sign’ and ‘constellation’. In this 57 Toomer 1984, p. 402. 58 Toomer 1984, p. 401, note 165. 59 Grasshoff 1990; Evans 1998, pp. 265–74. Some historians, notably Newton 1977 and Rawlins 1982, have accused Ptolemy of scientific fraud. Recent discussions of the controversy by Thurston 2002, Gingerich 2002, and Schaefer 2002 show that the debate continues.

60 61 62 63

14

Van der Waerden 1952–53; Steele 2008, pp. 45–7. Bowen and Goldstein 1991, p. 245. Aratus (Kidd 1997), pp. 112–13, ll. 545–9. Autolycos (Aujac 1979), p. 103.

1.4 Signs, Conventions, Precession, and Epochal Modes study, the word ‘zodiacal sign’ is used exclusively for the section of 1/12th part of a circle and the word ‘zodiacal constellation’ refers to the corresponding stellar configuration. The division of the ecliptic into twelve parts provides a convenient structure for describing positions of the stars in longitude only after the zero-point of the scale is fixed.There are in principle two ways for choosing the zero-point, both of which have been used in the past. Babylonian astronomers connected the boundaries of the signs to the fixed stars.64 The Greek astronomers tied the zero-point of the ecliptic to the vernal equinox. At first sight the two approaches seem to be equivalent but the phenomenon called precession, discussed below, causes the fixed stars and the equinoxes to move away from each other. In the Babylonian approach, connecting the scale of the ecliptic to the stars, precession causes the equinoxes to move slowly through the zodiacal circle in the course of time; in the Greek system, tying the scale of the ecliptic to the equinoxes, the reverse situation applies: precession causes the fixed stars to drift slowly along the ecliptic in time. Babylonian astronomers were not aware of precession. The places of the equinoxes with respect to the signs seem to have been chosen in close association with their various arithmetic schemes for predicting the place of the Sun and the Moon in the zodiac circle.This may be why a number of conventions were ultimately used and transmitted to Greek astronomy. Modern astronomers place the beginning of the sign of Aries (Ari 0°) at the vernal equinox. By definition the summer solstice then coincides with the first point of Cancer (Cnc 0°), the

autumnal equinox with the first point of Libra (Lib 0°), and, finally, the winter solstice with the first point of Capricorn (Cap 0°). This modern usage is known as the Ari 0°-convention. In Scheme 1.4 the scale of the zodiac based on the Ari 0°-convention is illustrated on top, for the epoch 128 BC.The intersection between the ecliptic, Equator, and the colure is placed at the beginning of the sign of Aries and the vernal equinoctial colure, which passes though the vernal equinox and is perpendicular to the Equator, passed then just west of the constellation Aries. The first astronomer to discuss and use the Ari 0°-convention explicitly was Hipparchus, who tells us that the ecliptic was also similarly divided by the ancient mathematicians, if not by all than yet by most of them.65 By using the term ‘ancient mathematicians’, Hipparchus may have been thinking of Euctemon (430 BC) or Callippus (ca. 330 BC), who are believed to have placed the cardinal points (the equinoxes and solstices) on the first days of the respective signs in their parapegma, a special type of calendar, in which the days are counted according to the motion of the Sun through the zodiac. Hard evidence for the early use of the Ari 0°-convention is not available. The parapegmas appended to the treatise of Geminus are a reworking of older documents and one cannot rely on them.66 Hipparchus’s belief that Aratus used the Ari 0°-convention is based on interpretative errors on his part.67 Eudoxus did not have a clear notion of an ecliptic consisting of 12 signs of 30º each, and one cannot expect that he or after him Aratus would have been aware of something like a convention by which the location of the vernal 65 Hipparchus (Manitius 1894), II.1.19, pp. 132–3. See also Neugebauer 1975, p. 600. 66 Evans and Berggren 2006, pp. 275–89. 67 Dekker 2008b, pp. 217–22.

64 Huber 1958; Steele 2008, p. 47.

15

Preliminaries

Scheme 1.4 The scale of the ecliptic for three conventions for the epoch 128 BC.

‘The two solstices and the two equinoxes occur, in the way of thinking of the Greek astronomers, in the first degrees of these signs; but in the way of thinking of the Chaldeans, they occur in the eighth degrees of these signs. The days on which the two solstices and the two equinoxes occur are the same days in all places, because the equinox occurs in all places at one time, and similarly the solstice. And again, the points on the circle of signs at which the two solstices and the two equinoxes occur are

equinox with respect to the signs is fixed.What is certain is that Hipparchus’s own usage of the Ari 0°-convention was taken over by Ptolemy in his Almagest and through him transmitted to the Middle East and the Western world. It is the only convention of significance in the mathematical tradition in celestial cartography. The existence of alternative conventions is explained in detail by Geminus: 16

1.4 Signs, Conventions, Precession, and Epochal Modes exactly the same points for all astronomers.There is no difference between the Greeks and the Chaldeans except in the division of the signs, since the first points of the signs are not subject to the same convention for them: among the Chaldeans, they precede by 8 degrees.Thus, the summer solstitial point, according to the practice of the Greeks, is in the first part of Cancer; but according to the practice of the Chaldeans, in the eighth degree.The case goes similarly for the remaining points.’68

the zodiac based on the Ari 8°-convention is illustrated in the middle, at the epoch 128 BC. The vernal equinox is located at a distance of 8° from the beginning of the sign of Aries. Another convention was based on the Babylonian ‘System A’.The Roman poet Marcus Manilius writing in the first century AD mentions the Ari 10°-convention in his astrological poem Astronomica alongside the Ari 8°-convention:

As is often the case, the ‘Chaldeans’ represent an often-quoted, but historically vague, authority.69 Neugebauer has suggested that the Ari 8°-convention may be related to a practice used in Babylonian astronomy for the calculation of lunar ephemerides, the so-called ‘System B’.70 Regardless of its origins, records of the Ari 8°-convention are found within the context of Roman parapegmas and calendars, and in a number of the writings of Roman authors, such as Vitruvius, Varro, Hyginus, and Pliny.71 And it was through these Roman writings that this convention penetrated and was perpetuated throughout the Middle Ages.72 In fact, then, the use of the Ari 8°-convention continued long after Hipparchus had assured the reader that the ‘modern convention’ (the Ari 0°-convention) was common practice. In Scheme 1.4 the scale of

Some ascribe these powers [to change the seasons] to the eighth degree [of each cardinal sign]; some hold that they belong to the tenth; nor was an authority lacking to give the first degree [i.e.: 0°] the decisive influence and the control of the days.73

Furthermore, Achilles (ad 250) reports that a number of values were assumed for the place of the summer solstice: Cnc 0°, Cnc 8°, Cnc 12°, or Cnc 15°. In his study of these conventions, Neugebauer was not able to find an explanation for the Ari 12°-convention. The convention of placing the equinoxes and solstices in the midpoints of their respective signs is the Ari 15°-convention. It could be related to another Babylonian scheme in which the equinoxes and solstices are placed in ‘the midpoints of the respective schematic month’. This so-called ‘mid-point convention’ appears in two Greek papyri from the 2nd and 3rd centuries BC.74 In Scheme 1.4 the scale of the zodiac based on the midpoint, or Ari 15°-convention, is illustrated at the bottom, for the epoch 128 BC. The vernal equinox is now at a distance of 15° from the beginning of the sign of Aries. Hipparchus argued that Eudoxus used the Ari

68 The translation is from Evans and Berggren 2006, I.9, p. 115. See also Geminus (Aujac 1975), I.9, p. 3. 69 Evans and Berggren 2006, pp. 13–14. 70 Neugebauer 1975, pp. 368, 594–6. 71 Neugebauer 1975, pp. 594–6. See, for example,Vitruvius (Soubiran 1969), p. 18: IX. 3: ‘Namque, cum Arietis signum iniit et partem octauam peruagatur, perficit aequinoctium uernum’. (When [the Sun], after entering the sign (or constellation) of the Ram, arrives at the eighth degree, he fixes the vernal equinox.) See also Hyginus (Le Boeuffle 1983), IV.2.3, p. 118 and Rehm 1941, esp. his chapter III. 72 The Ari 8°-convention is recorded in the medieval text Revised Aratus latinus edited in Germanicus (Breysig 1867), pp. 105–6 and it is then copied from there into the Scholia Strozziana, see Dell’ Era 1979b, p. 170.

73 Manilius (Goold 1977), III.681, pp. 218–19; Neugebauer 1975, vol. 2, p. 598. 74 Neugebauer 1975, pp. 599–600. See also Evans 1998, p. 202.

17

Preliminaries 15 convention.75 However, Hipparchus did not realize that Eudoxus placed the equinoxes in the middle of the zodiacal constellations instead of in the middle of the zodiacal signs.76 How the various conventions work out in celestial cartography depends on precession.The precise cause of precession became clear only after the Newtonian concept of gravity had been formulated in the seventeenth century. The (equatorial) plane of rotation of the Earth is inclined to its (ecliptic) orbital plane, and gravitational forces tend to pull both planes together, causing the mean polar axis of the Earth to move in a cone around an axis perpendicular to the ecliptic plane in a period of about 26,000 years. As a result of this motion of the polar axis the vernal equinox, by definition the intersection of the Equator and the ecliptic, shifts along the ecliptic in that period. The phenomenon was discovered in the second century BC by Hipparchus who noticed that the equinoxes shift their positions slowly with respect to stars at a rate of more than 1° in 100 years.77 Thus the longitudes of the stars, say, expressed in terms of the Ari 0º-convention, are valid only for a certain moment in time, which is called the epoch. From Hipparchus’s summary of the stars marking 24 hour circles, one finds that in his day (128 BC) the summer colure passed through the star at the end of the tail of Canis Maior (η CMa); the autumnal colure through the star following after the two bright ones in the thyrsus staff , in the middle of the breast of the Centaur (φ Cen) and it passed a little west of the star in the middle of those in 75 Hipparchus (Manitius 1894), I.5.11, I.6.4, and II.1.15. Neugebauer 1975, p. 599. 76 Dekker 2008b and the section on ‘Epochal modes’ below. 77 Evans 1998, pp. 259–62.

the left foot of Bootes (τ Boo); the winter colure passed a little west of the northernmost of the three bright stars in the body of Aquila (γ Aql); the vernal colure passed through the star in the tip of the Triangle (α Tri) and a little west of the most advanced star of the three on the head of Aries (γ Ari).78 The three conventions illustrated in Scheme 1.4 show that the constellation Aries is fully confined to the sign of Aries in 128 BC only when the Ari 0º-convention is used. This holds for most zodiacal constellations. Notable exceptions are Virgo, Leo, and, for example, Pisces because these constellations extend more than 30º in longitude. It seems therefore only natural that Hipparchus promoted the use of the Ari 0º-convention. Precession was unknown to astronomers before Hipparchus and it seems to have been ignored by most popular writers in Antiquity after him. Geminus does not mention precession and Roman authors on popular astronomy seem to have been fully unaware of the phenomenon. Manilius, for instance writes: ‘These circles [the colures] the seasons have fixed in a permanent abode; their paths through the signs [constellations] do not change, and their position remains the same forever’.79 Goold translates signum as ‘sign’, but considering that Manilius describes these circles with respect to constellations (see the section on epochal modes below), it could just as well mean (zodiacal) constellation. Ptolemy is the first to present a detailed account of the precession.80 He showed that only the longitudes of the stars are affected by it, and fixed the rate on 1° in 100 years. In Ptolemy’s days precession was a very novel feature, the 78 Hipparchus (Manitius 1894), III.5.1–23, pp. 271–81. 79 Manilius (Goold 1977), I.631–632, pp. 54–5. 80 Toomer 1984, pp. 327–30.

18

1.4 Signs, Conventions, Precession, and Epochal Modes understanding of which was crucial in discussing the main theme of the Almagest, the motions of the Sun and the planets. It is for this reason that a description of a relevant demonstration model, the precession globe, is included in the Almagest. This model will be discussed in more detail in Section 5.2 in connection with Cusanus’s globe. In Ptolemy’s precession globe the equatorial poles rotate around the ecliptic poles. When the positions of the equatorial poles shift, the colures and the Equator move along with them.The vernal equinox also shifts along the ecliptic. During this motion the latitude of a star remains fixed whereas the longitude, measured from the vernal equinox, appears to increase. Using this model the longitudes of a star, λ1 and λ2, at respectively the epochs E1 and E2 are related through

These descriptions are brought forward as evidence for Hipparchus’s assertion that Eudoxus had placed the equinoxes at the midpoints of the respective signs Aries and the Claws (Libra) and had placed the solstices at the midpoints of the respective signs Cancer and Capricorn (in keeping with the Ari 15°-convention discussed above). Hipparchus feels that his conclusion is further corroborated by the following statement: ‘For concerning the circles called colures that are described through the poles and through the tropic and equinoctial points, he says as follows: “Different (from the circles discussed so far) are the two (great) circles through the poles, that bisect one another at right angles. On them are these constellations: first, the ever-visible pole of the cosmos, next, the middle of Ursa Maior (taken) widthwise and the middle of Cancer.” And after a little, he says: “The tail of Piscis Australis and the middle of Capricorn.” In what comes next, he says that both the middle (parts) of Libra (taken) widthwise and the back (parts) of Aries (taken) widthwise lie with the other (constellations) with which they are counted, on the other circle through the poles’.82

λ2 − λ1 = (E2 − E1 ) / 100 where λ1 and λ2 are expressed in degrees and E1 and E2 in years.

Although precession does not play a role in the descriptive tradition, some information on the position of the equinoxes with respect to the stars is available in its corpus of texts, namely, in the form of descriptions of the constellations that were located on the colures, the great circles through the north and south poles and the equinoxes and solstices. Such descriptions, however, cannot always be related straightforwardly to specific epochs and for that reason I shall refer to them as epochal modes.The descriptions are relatively rare, only a few authors –Eudoxus, Manilius, and Martianus Capella—endeavoured to provide them. The earliest descriptions of what the colures are and how they are positioned with respect to the constellations are ascribed to Eudoxus.81

I have italicized the word ‘constellation’ here because it is evident that Eudoxus mentions Cancer, Aries, Libra, and Capricornus without discrimination from other non-zodiacal constellations. Hipparchus took it for granted that Eudoxus was referring to the zodiacal signs and not to the constellations.83 Hipparchus’s interpretive error is particularly clear from Eudoxus’s

82 Hipparchus (Manitius 1894), II.1.21–2, p. 133. The English translation is from Bowen and Goldstein 1991, pp. 243–4. A French translation appears in Aratus (Martin 1998), pp. 125–6. 83 This conclusion was reached already by Bowen and Goldstein 1991, pp. 241–5.

81 Hipparchus (Manitius 1894), I.1.15, p. 119.

19

Preliminaries description of the colures with respect to the constellations. ‘Again, Eudoxus makes a clear statement also about the stars situated on the so-called colure circles, and he says that on one of them are situated the middle of the Great Bear and the middle of the Crab and the neck of Hydra and the (part) of Argo that is between the stern and the mast, and next, after the invisible pole, the tail of the Southern Fish, and the middle of the Goat-Fish, and the middle of the Arrow; (he says further that) it is described through the neck and the right wing of the Bird and through the left hand of Cepheus and beside the tail of the Little Bear.’84 ‘He says that on the other colure are situated, first, the left hand of Arctophylax and the middle of him in length; next, the middle parts in breadth of the Claws and the right hand and the front knees of the Centaur; and after the invisible pole, the bend of the River and the head of the Whale and the back parts in breadth of the Ram and the head and the right hand of Perseus.’85

These passages were severely and at first sight convincingly criticized by Hipparchus for their inaccuracy.86 Hipparchus found that most constellations described by Eudoxus were on a colure lying too far to the east, by about 10°, with respect to the colures observed by himself in 128 BC. This consistency of error suggests a common cause. Indeed, the great circles which pass on the average through the non-zodiacal constellations on the Euduxan list are 11° ± 4° east of the true colures in 375 BC, that is, the astronomically correct ones in Eudoxus’s days. 84 Hipparchus (Manitius 1894), I.11.9–10. I am indebted to Alexander Jones for providing the English translation.A French translation is in Aratus (Martin 1998), pp. 127–8. 85 Hipparchus (Manitius 1894), I.11.17. I am indebted to Alexander Jones for providing the English translation.A French translation is in Aratus (Martin 1998), p. 127. 86 Dekker 2008b, p. 216.

Here and elsewhere these numbers are expressed in the modern convention based on Ari 0º-convention. The details of this calculation are presented in Appendix 1.3. The location of the Eudoxan colures is illustrated in two modern maps (in globe-view) of the sky north and south of the Equator for the epoch of 375 BC (Scheme 1.5).87 In these maps, I have highlighted the constellations which Eudoxus describes as being on the colures. I have also marked two straight lines that represent the astronomically correct or ‘true’ colures (full straight lines) and the Eudoxan colures, that is, the great circles through the north and south poles that are 11° east of the true colures (straight lines of dots-and-dashes).The standard deviation (± 4°) is also indicated around the latter lines. From the map, it is abundantly clear that the great circles passing through the middle of the zodiacal constellations of Aries, Cancer, Libra (the Claws), and Capricorn also pass through most of the non-zodiacal constellations that Eudoxus lists in the passages quoted above as being located on his colures. Inversely, it is also evident that the ‘true’ colures do not pass through them. The practice of Eudoxus to locate the colures in the middle of the zodiacal constellations has been the cause of controversy on the presumed origin of the Eudoxan sky because errors in the location of the colures with respect to the true colures at the Eudoxan epoch around 375 BC generate an apparently artificial shift in precession. Or, to put it differently, the Eudoxan colures through the middle of the zodiacal constellations are astronomically correct only around the year 1000 BC.

87 These maps were produced with the help of Chris Marriott’s SkyMap Pro,Version 8.

20

1.4 Signs, Conventions, Precession, and Epochal Modes

21 Scheme 1.5 Location of the Eudoxan colures with respect to the stars for the epoch 375 BC.

Preliminaries The idea that Eudoxus’s description of the sky is based on observations carried out at a much earlier epoch was discussed by Schaefer with all the apparent rigour that statistical methods can offer.88 The results of such a statistical analysis can be reliably interpreted only if it is known how the data were collected. In the absence of any knowledge thereof one cannot take statistical data at face value and accept on their basis conclusions regarding much earlier epochs.89 The question remains why Eudoxus came to place the equinoxes and solstices in the middle of the respective constellations. Neugebauer has emphasized that in certain Babylonian schemes the equinoxes and solstices are placed in ‘the midpoints of the respective schematic months’.90 From here it is only a small step towards a convention placing the equinoxes and solstices in the midpoints of their respective zodiacal signs. Midpoint schemes do not neccessarily imply— warns Neugebauer—Babylonian influence. Such devices are too simple and too natural to exclude an independent origin. The use of midpoints may well have been attractive for reasons of symmetry. In describing the main parallel circles Eudoxus lets the equator pass lengthwise through the middle of Aries and the Claws (Libra), the summer tropic through the middle of Cancer and the winter tropic through the middle of Capricorn.To have the colures passing widthwise through the middle of the same constellations creates a regularity that may have appealed to the early astronomers. Once the positions of the colures had been chosen the constellations located on them could easily be determined by observation. All one has to do is

88 Schaefer 2004. 89 Duke 2008. 90 Neugebauer 1975, p. 599.

22

to observe which non-zodiacal constellations are in the local meridian at the moment that the midpoint of the relevant zodiacal constellation is observed in it. Considering the uncertainty of interpretation of the Eudoxan colures in terms of epochs it is in our opinion better to speak of epochal modes instead of epochs, for the sole purpose of identifying certain traditions in cartography in the descriptive tradition. Indeed, for the present study, it is not as important to know what caused the errors in the Eudoxan sky as to apprehend the location of the Eudoxan colures exactly, irrespective of any post hoc interpretation. In chronological order Manilius is the next author who provided in his Astronomica a description of the colures with respect to the stars: ‘There are two circles, placed crosswise to each other, which are drawn from one pole and received by the other: they cut all the circles mentioned above and cut each other, converging at the two poles of heaven; thence they traverse the sky and are drawn straight to the pole.They mark the seasons of the year and the division of heaven along the zodiac into four portions of equal months. One line [the equinoctial colures], descending from the summit of the sky, passes through the Dragon’s tail and the Bears that shun the ocean, and the yoke of the Claws which revolves in the midmost circle. It cleaves the extremity of the Water-snake and the middle of the southern Centaur, and again converges upon the opposing circle at the pole; returning thence heavenward, it marks the scaly back of the Whale, the boundary of the Ram, the bright Triangle, the lowest folds of Andromeda’s robe, and her mother’s feet, and, the pole regained, ends with its beginning. The other circle [the solstitial colures] rests upon the middle of this one at the upper pole, whence it passes through the forefeet and neck of that Bear which with the setting of the Sun seven stars bring first to view as it offers its lights to the

1.4 Signs, Conventions, Precession, and Epochal Modes blackness of night; it parts the Crab from the Twins and grazes the Dog with the blazing face and the rudder of the Ship which conquered ocean; thence it touches the hidden pole, cutting at right angles the path of the former circle. On its way back from this line it touches Capricorn and, leaving Capricorn’s stars, marks the Eagle; it runs through the inverted Lyre and the coils of the Dragon, and passes by the stars of Cynosure’s hind feet, whose tail it cuts at right angles close to the pole. Here it meets itself again, mindful whence it came.’91

Some historians have argued that Manilius is not consistent in his use of conventions.92 In some places he seems to employ the modern convention, but in others he refers to the eighth degree. In truth, though, there is only one place in his descriptions of the path of the Sun, where Manilius seems to refer to an identifiable convention: ‘and when, moved to the south in chill winter-tide, it shines in the eighth degree of the two-formed Capricorn’.93 In all other cases, his text is either of a general nature or can equally When the great circles which pass on the aver- well describe a zodiacal constellation as a zodiaage through the non-zodiacal constellations on cal sign. Indeed, if his description of the colures Manilius’s list are compared to the true colures were based on a globe one would expect that he in 128 BC, we find that his colures deviate on would have described the constellations rather average only 0.2° ± 3.3° from the astronomically than the signs. Irrespective of whether one deals true colures at this epoch.The details of this cal- with the one convention or another, there is no doubt that the data described by Manilius refer culation are again presented in Appendix 1.3. In 128 BC, the summer solstitial colure indeed to the Hipparchan epoch of 128 BC. Another more or less complete description of separated the constellations Cancer from Gemini, touched Capricornus, and marked the boundary the constellations that mark the colures is by of the Aries, as Manilius says. However, the Martianus Capella in his On the Marriage of autumnal equinoctial colures do not pass through Philology and Mercury: the ‘yoke of the Claws’, if one understands this to ‘Let us indicate the colures more clearly.They too indicate the stars α and β Lib. In 128 BC Hipparconceal part of their circles and do not reveal chus places the stars in the feet of Virgo on the themselves entirely to our view; yet our assumptions about them are reliable, and it is possible to colure. This discrepancy in coordinates could trace their courses. The first of these [equinoctial be resolved if one assumed that the ‘yoke of colure] takes its beginning at the equinoctial point the Claws’ refers to ‘the first degree of Libra’ but (that is, the eighth degree of Aries); it touches the this reading seems implausible. In order to desfar angle of Deltoton [Triangulum];next it touches cribe the colures in such detail, Manilius may the top of the head of Perseus and his right arm; have had a globe at his disposal. If this Manilian next, cutting his hand, it crosses the arctic circle globe was based on the Ari 0º-convention for and reaches the celestial north pole; from here it fixing the signs of the zodiac, the constellation goes through the tail of Draco to the left side of Boötes, and then to the star of Boötes; next to the Aries would have been completely inside the sign of Aries, as mentioned before and illustrated 92 Manilius (Goold 1977), p. lxxxi. See also Neugebauer in Scheme 1.4 at the top. 1975, p. 596, note 28. 93 Manilius (Goold 1977), III. 257, pp. 182–3;‘et cum per gelida hiemes summotus in austros Fulget in octava Capricorni parte biformis’.

91 Manilius (Goold 1977), I. 603–30, pp. 52–5.

23

Preliminaries right, and then the left foot of Virgo; to the eighth degree of Libra; and from here it goes to the right hand of Centaurus, in which he holds Panthera; not far distant from the place where it touched the left hoof of Centaurus, it disappears from sight, in a region below the horizon; emerging again below Cetus, it passes through his body and shoulder to the head, and returns to the eighth degree of Aries. A second colure, which is called the tropical colure, originates at the eighth degree of Cancer, passes to the left front paw of Ursa Major, through his chest and neck; then it reaches the celestial north pole; from here it goes through the hind quarters of Ursa Minor, on through Draco and the left wing and neck of Cygnus, touches the tip of Sagitta and the beak of Aquila, from which point it descends to the eighth degree of Capricornus; not far from here it plunges from view and rises again below Argo; it cuts through its rudder and upright stern and returns to the eighth degree of Cancer.’94

first century BC, most notably on the lost work of Varro.95 Our result raises many issues.The discrepancy between the colures described by Martianus Capella and the true, astronomical ones at 128 BC recall the Eudoxan colures. Both sources seem to represent the starry sky at a considerably earlier epoch than their time of life. It suggests that the Capellan data might not be independent of those of Eudoxus. When the descriptions of the colures by Eudoxus and Martianus Capella are compared, one finds that some features in the descriptions of Martianus Capella—such as the head and right hand of Perseus, the neck and left wing of Cygnus, the right hand of Centaurus and the head of Cetus—go back to Eudoxus.96 Other elements of that description—such as the left side of Bootes and Arcturus—seem to be an The descriptions of Martianus Capella clearly echo of the Eudoxan colures passing through indicate that the locations of the equinoxes and the left hand and the middle of Boötes lengthsolstices are in keeping with the Ari 8º-conven- wise. Others—such as the right and left foot of tion, which one recognizes as being so popular Virgo, the far angle of the Triangle and the beak with Roman authors. However, conventions of Aquila—are absent from the description of have nothing to do with the position of the Eudoxus, however. The question that remains is how the Eudoxan colures with respect to the fixed stars.When the great circles which pass on the average through colures might have been transmitted to Martianus the non-zodiacal constellations on the Capellan Capella. Any likely explanation has to fit within list are compared to the true colures in 128 BC, the development of the Eudoxan tradition, since we find that the Capellan colures appear to pass Martianus Capella’s description of the constella7.5° ± 5° east of the astronomically true colures tions on the other main circles shares so many at that epoch (see Appendix 1.3). The choice of details with Eudoxus (see the lists in the next sec128 BC, the Hipparchan epoch, as a standard of tion). One solution would be that Martianus comparion seems valid in light of the fact that Capella used both texts and a globe with Eudoxan most scholars have argued that Martianus Capella characteristics (i.e.with the colures passing roughly seems to have relied on sources written in the through the middle of the zodiacal constellations

94 Martianus Capella (Dick 1925), VIII, 832–3, pp. 437–8. The translation is from Stahl et al. 1977, p. 324.

24

95 Stahl et al. 1977, pp. 50–3. 96 From the position it is clear that only the right wing can be meant.

1.4 Signs, Conventions, Precession, and Epochal Modes

Scheme 1.6 The configuration of the constellation Aries, the signs of the zodiac and the positions of the equinoctial colures in three epochal modes.

of Aries, Cancer, Libra, and Capricorn) to construct his colures. In the absence of a welldeveloped notion of precision, such a feature could easily have been interpreted in the context of later calendar concepts as colures passing through the

eighth degree of the respective constellations.97 This would be especially applicable if that author 97 If a globe was used some deviations from the Eudoxan colures may have been the result of a copying process.

25

Preliminaries were acquainted with the practice of the Roman calendars, such as those cited by Varro.98 In this connection, it is interesting to recall that another, first-century BC Roman author, Columella, reported that Eudoxus placed the solstices and equinoxes in the eighth degree.99 One wonders whether Columella’s reference is to constellations or signs. And although our analysis of Eudoxan colures has shown that Columella’s claim is historically incorrect, this information could well be an echo of Columella’s interpretation of Eudoxan data. The oldest of the three epochal modes discussed here goes back to Eudoxus; the more recent one connects in one way or another to Hipparchus. All three modes will be encountered in the medieval maps in the descriptive tradition, discussed in Chapter 3. For this later reference the three epochal modes are summarized in Scheme 1.6. The configuration on top shows schematically the Eudoxan epochal mode, with the vernal equinoctial colure passing through the middle of the constellation Aries. The zodiacal signs have deliberately been left out since Eudoxus seems not yet have been aware of them. The one in the middle characterizes the Capellan epochal mode, that is, with the vernal equinoctial colure passing through the eighth degree of the constellation of Aries and the sign. The Eudoxan and Capellan epochal modes represent the starry sky at a considerably earlier epoch than their time of life. The last epochal mode from Manilius is shown at the bottom of Scheme 1.6. It is astronomically correct, in the sense that it is possible to attach a reliable epoch, that of 128 BC, to it and presumes the Ari 0º-convention for fixing the signs of the zodiac. 98 Rehm 1941, esp. chap. III, pp. 44 and 115. 99 Rehm 1941, p. 18.

26

Although the last two configurations in Scheme 1.6 seem similar in locating the constellation Aries completely inside the sign of Aries, the position of the stellar configuration of Aries with respect to the colures is completely different. In the Capellan case a substantial part of the stellar configuration of the Aries is west of the vernal equinoctial colure.

. PREREQUISITES TO GLOBE MAKING In order to draw the grid on a sphere one has to know the obliquity ε of the ecliptic and the inclination φ of the polar axis of the rotating sphere with respect to the horizon. There are several problems connected with finding the values of these two parameters. Neither the concept of degrees nor the equipment to measure them by actual observation was available in Eudoxus’s time. How then was an ancient astronomer able to locate these circles on a sphere? Probably the most common way of expressing a dependence on geographical latitude in Antiquity was by the use of sundials. In Scheme 1.7, the shadow of a gnomon in two types of dials, one spherical and the other planar, is shown at four crucial times of the year when the Sun is in the local meridian. In summer, when the Sun reaches the Tropic of Cancer and its distance from the zenith of the observer is φ-ε, the shadow is seen in S. In the winter, when the Sun descends to the Tropic of Capricorn and its distance from the zenith of the observer is φ+ε, the shadow is seen in W. In the spring and autumn,when the Sun is in the Equator and its distance from the zenith of the observer is φ, the shadow is seen in E. From this diagram, it is clear that both the value of the geographical

1.5 Prerequisites to Globe Making

Scheme 1.7 Recording meridian altitudes of the Sun with sundials for a latitude of 40°.

latitude φ and that of the obliquity of the ecliptic ε can be determined as arcs of a circle, directly from a spherical sundial and, indirectly, through graphic means by plotting the shadow lengths on a plane dial. Roughly speaking it seems that as soon as dials were constructed all necessary ingredients were in principle available to draw the required celestial grid on the surface of a globe. It is not known whether this indeed was done. If Herodotus can be relied on we may assume that the gnomon was known in Greece in his days (450 BC).100 Early use of the gnomon is attested by shadow tables that are associated with the fourth or fifth century and with Philip of Opus, a contemporary of Eudoxus.101 Herodotus also mentions another instrument, the ‘polos’, which more often than not has been identified with a hemispherical dial showing unequal hours. This

interpretation has recently been questioned by Schaldach who argues that the ‘polos’ is an equinoctial dial indicating equinoctial hours.102 He reserves a special role for Eudoxus as the inventor of such a dial. Vitruvius mentions in his chapter on dials that Eudoxus was the inventor of the arachnê, or spider web which in the absence of further specifications has been interpreted either as a grid on a celestial sphere, a network on the surface of a hemispherical dial or on an astrolabe or, recently, as one on an equinoctial dial.103 This recent interpretation is strengthened by the fact that the earliest Greek dial, dating from ca. 325 BC, is of this type and seems to reflect the Eudoxan ratio of 5:3 (see p. 29). On a multi-faced sundial

102 Schaldach 2004; Schaldach 2006. 103 Schlachter 1927, p. 15, proposed the grid explanation; Bowen and Goldstein 1983, p. 336, the hemispherical dial and Schaldach 2006, the equinoctial dial.

100 Damsté 1974, II.109, p. 119. 101 Neugebauer 1975, p. 740.

27

Preliminaries on Tenos made by Andronikos of Kyrros, who around 100 BC built the Tower of Winds in Athens, the maker is compared in a poem to the famous astronomer Eudoxus who is praised for his knowledge of the art of the Aratean sphere.This underlines the close connection between globe making and dialling but it does not tell us exactly how the main parameters ε and φ were obtained for the former. Amongst the Greek sources, the earliest quantified report on the ecliptic appears in the Astronomy of Eudemus of Rhodes (325 BC), a pupil of Aristotle who attributed the discovery of the ecliptic to Oenopides of Chios (450 BC). Some studies even claim that Oenopides discovered that the obliquity of the ecliptic amounts to 24°.104 This attribution is based on a mistaken interpretation of a text of Theon of Smyrna (second century ad):

The notion that the obliquity of the ecliptic corresponds to the side of a regular pentadecagon is also attested in Vitruvius’s De Architectura (IX, 7). How this was found out is not known but the construction of sundials may well be at the bottom of it. One could in principle obtain the value of 1/15th of a circle for the obliquity of the ecliptic when one happened to live at geographical latitude of 36º.108 Then the special situation arises that in Scheme 1.7 ⦟ZOW = φ+ε = 60º and ⦟ZOE = φ = 36º. If it had been recognized that the cords ZW and ZE correspond respectively to the sides of a regular hexagon and a regular decagon inscribed in a circle with radius OZ, it would have followed that ε should be equal to 1/15th of a circle. Around 300 BC the complicated construction (by a rule and compass) of finding the side of a penta‘Eudemus recounts in his Astronomy that Oenopides decagon is described in Euclid’s Elements and was the first to discover the encircling belt of the zodiac [ ...] Others added other discoveries to these: the simpler constructions of the sides of a reguthat the fixed stars move around the axis which passes lar hexagon and decagon will have been known through the poles, but that the planets move around by the mathematicians preceding him.109 the axis which is perpendicular to the zodiac, and With the obliquity of the ecliptic known that the axis of the fixed stars and the axis of the through this construction, one can draw the tropplanets are separated from one another by the side of ics on the globe. In order to complete the celestial the pentadecagon, that is, by 24 degrees.’105 grid, one only needs to find a way to fix the everSome authors prefer to interpret the encircling visible circle and ever-invisible on the sphere, belt of the zodiac as the inclined belt.106 However which as mentioned above, depends on the geothat may be, the above text shows that, after 450 graphical latitude of a place. The simplest way to BC but before 325 BC when Eudemus discussed determine one’s latitude would have been to the matter, it became known that the obliquity measure the height of the north pole above the of the ecliptic corresponds to the side of a regu- horizon. But this particular relationship between lar polygon with fifteen angles, that is, by 1/15th the geographical latitude and the elevation of the north pole was applicable only after the part of a circle or 24°.107 measurement of arcs in terms of degrees came within reach of ancient astronomers. Beyond this,

104 Schlachter 1927, pp. 12–13. Heath 1981/1913, p. 131. A more recent assertion is in Heilen 2000, p. 61. 105 The English translation is from Evans 1998, p. 58. 106 Boeme 2001. 107 The obliquity (ε) of the ecliptic is nowadays is 23.5°, but in Antiquity was closer to 24°.

28

108 Eudoxus lived at least part of his life in Cnidos with φ = 36.4º. 109 For Euclid, Elements Book IV.16, see Heath 1981/1921, vol. 1, p. 383.

1.5 Prerequisites to Globe Making even the place of the north pole in the sky was not clearly established in Antiquity. This was due to the fact that it cannot be identified with a particular star. Hipparchus seems to have been the first astronomer to recognize this fact. He concluded that the north pole was located in one of the corners of a quadrangle defined by the stars λ and κ Dra and β UMi (Scheme 1.8B). Nevertheless, there was a strong tendency in Antiquity for associating the north pole with a particular star. Hipparchus, for example, reports that Eudoxus seems to have believed that the north pole coincided with a star that remained always in the same place.110 Another early report on the north pole is made by Euclid in his Phaenomena: ‘A certain star between the Ursae is seen not to change from place to place but to revolve in the place where it is’.111 In the description of Ursa Minor in the Epitome, one reads that ‘beneath the second of the two westernmost stars, there is another star, called Polus, around which the entire universe appears to revolve’. 112 It is impossible to say with certainty which star that could have been (see Scheme 1.8A). Hyginus tells us that Eratosthenes considered the first of the three stars in the tail of Ursa Minor as the pole and the other two the ‘Choreutae’, because of their rotation around the pole.113 Hyginus also cites another, unnamed source, which claims that the pole is represented by the star in the end of the tail of Draco.114 This same source could lie behind Vitruvius’s claim that, among the stars of Draco, there is the

star which shines near the head of Ursa Maior, called pole.115 Martianus Capella also imagined that the pole was marked by a star: (‘at the very pole of the universe I have set a brilliant star’).116 It is obvious that there was a tacit agreement among the majority of the Greek and Latin authors writing on popular astronomy that the north pole could be marked by a specific star; but not clear at all is which one that might have been. Since the position of the north pole was obviously uncertain— differences as great as 10º occur—one cannot assume that the pole was correctly plotted in any antique globe based on the descriptive tradition. Let us return to the problem of drawing the ever-visible and ever-invisible circles. In the earliest written sources on the heavens, geographical latitude was expressed indirectly as the ratio between the longest day-time and the shortest night-time—specifically, the day:night ratio that occurs at mid-summer, when the Sun revolves along the Tropic of Cancer. Aratus describes this as: ‘If the circle is measured approximately in eight parts, five revolve in the sky above the earth and the other three below the horizon’.117 This division was used also earlier by Eudoxus in his treatise, The Mirror.118 The ratio of 5:3 marks a longest day of 15 hours and a shortest night of 9 hours, and it is accurate for geographical latitudes 40.7° N.119 This value is

110 Hipparchus (Manitius 1894), I.4.1, p. 31. 111 For the citation, see Berggren and Thomas 1996, p. 44; it occurs in the introduction of Euclid’s Phaenomena, which Berggren and Thomas consider a later addition (p. 10). 112 Condos 1997, p. 201. 113 Hyginus (Le Boeuffle 1983), III.1.2, p. 87. See also Le Boeuffle 1977, p. 92. 114 Hyginus (Le Boeuffle 1983), IV.8, pp. 125–6.

115 Vitruvius (Soubiran 1969), IX.4.6, p. 22. The star is best identified with λ Dra in the end of the tail of Draco, closest to the head of UMa. 116 Martianus Capella (Dick 1925), Liber VIII, 827, p. 435. Stahl et al. 1977, p. 322. 117 Aratus (Kidd 1997), pp. 108–9, ll. 497–9. 118 Hipparchus (Manitius 1894), I.2.22, p. 23. 119 This latitude is correct for Constantinople.

29

Preliminaries

Scheme 1.8 Summary of presumed locations of the north pole.

close to the 41° used by Leontius for making his ‘Aratean globe’.120 Hipparchus severely criticizes Eudoxus and Aratus for its use since, in ‘the neighbourhood of Greece’ the longest day lasts 14 ³/5 hours, which corresponds to a latitude of 37° N. He further points out that Eudoxus, in his treatise The Phaenomena, reported another ratio of 12:7, which corresponds to the slightly higher latitude of 42° N. According to Hipparchus, the ratio of 12:7, agrees with the one used by astronomers from the school of a certain mathematician and astronomer, whom Hipparchus refers to simply as ‘Philip’.121 According to Neugebauer, the ratio of 5:3 quoted by Eudoxus and Aratus may have been obtained by calculation rather than arrived at by

observation. It can be derived theoretically from an arithmetical pattern created by a linear variation of daylight over a period of six months.122 As an aside I note that in his discussion of the lengthening of the days, Cleomedes proposes a more refined algorithm in terms of the difference between a longest day of 15 hours and a shortest night of 9 hours, amounting to ½ hour in the first month, 1 hour in the second, ³/2 hour in the third and fourth month, 1 in the fifth, and ½ hour in the sixth month such that the longest daytime exceeds the shortest by 6 hours.123 Neugebauer further suggests that the value of 12:7 could be a corruption of the ratio 11:7, which has historical associations with ‘Athens’.124 More recently, Bowen and

120 Halma 1821, pp. 69–70. 121 Hipparchus (Manitius 1894), I.3.10, pp. 28–9. The astronomer ‘Philip’ is perhaps Philip of Opus, who flourished in the 4th century BC, but this is not certain.

122 Neugebauer 1975, p. 711. 123 Bowen and Todd 2004, I.4.18, p. 51. 124 Neugebauer 1975, pp. 730 and 733, note 28 (climate IIIb of the Babylon sequence).

30

1.5 Prerequisites to Globe Making Goldstein have demonstrated that both quantities, 5:3 and 12:7, are part of a series of ratios recorded in ancient texts, which could have been derived by simple mathematical calculation from a theorem known to early Greek astronomers.125 If their explanation is correct, one cannot simply connect geographical latitudes with the ‘calculated’ values of 5:3 or 12:7. Bowen and Goldstein also suggest that it is unlikely that Eudoxus divided the day into hours (whether equinoctial or seasonal) or into degrees of time, but that the ratios of 5:3 and 12:7 quoted by him should be understood as ratios of arcs. Whatever the real answer might be, it does seem that the appearance of these ratios in the treatises by Eudoxus and Aratus may have been included in order to express the inclination of the five parallel circles with respect to the horizon, because this affects the rising and the setting of the stars and fixes the location of the ever-visible circle tangential to the horizon.126 How can one draw, in practice, the evervisible circle on a sphere if 5/8th of the Tropic of Cancer is above and 3/8th is below the horizon? In Scheme 1.9, a construction is proposed of how this could have been done. The Tropic of Cancer is indicated as ABCD and is divided into 8 parts, such that arc ADC contains 5/8th and arc ABC of 3/8th parts. For the sake of clarity the division of the Tropic of Cancer is presented

symmetrically with respect to the circle BNDS. Since the arc ADC is supposed to be above and the arc ABC below the horizon, by definition, the line AC lies in the plane of the horizon at a specific moment. Since the horizon through A and C is a Great Circle, its pole H (the zenith) is easily found by the intersection of two great circles which have A and C as their poles. These great circles—by definition 90° away from their poles A and C—can easily be drawn on the sphere. Once the zenith H is fixed one can draw (for the sake of construction only) the horizon circle on the sphere.127 By definition, the ever-visible circle is parallel to the Tropic of Cancer and tangential to this horizon. It touches the horizon in point F,where the points of intersections between the horizon circle and parallel circles conflate (Scheme 1.9). Thus, the distance of the evervisible circle from the north pole (the arc NF) can be found by direct construction. Although there is no evidence to support the hypothesis that this construction was indeed used by early Greek astronomers, it shows that one does not need a detailed knowledge of degrees or of the division of the days into hours to find the location of the ever-visible and everinvisible circles.What is needed is an understanding of a few elementary properties of the sphere and its circles, which the ancient Greeks certainly possessed. The ratio 5:3 mentioned by Eudoxus and Aratus between the parts of the Tropic of Cancer above and below the horizon continued to be quoted in Greek and Latin astronomical literature for centuries. It was adopted by Geminus in his discussion of the characteristics of the five

125 Bowen and Goldstein 1991, pp. 237–8. 126 Aratus (Martin 1998), I, Annex 3, pp. 91–6. As an aside, Martin commented that, given the relatively rudimentary state of Greek mathematics in Eudoxan times, the difference between the two ratios mentioned by Eudoxus is not as great as it seems. Indeed, the two ratios reflect a difference of about 1° in latitude.The point made by Hipparchus, however, is that the latitude for ‘Greece’ is about 37° N, which is actually 4° less than the value implied by the ratio 5:3. One might also note how Martin (p. 95) incorrectly interprets the ratio 4:3 of shadow lengths mentioned by Hipparchus as being the ratio of the longest day and shortest night.

127 As a rule, the horizon is not traced on a sphere, but is part of the mounting of a globe, see Geminus (Aujac 1975), V.62, pp. 31–2; Evans and Berggren 2006, V.62, p. 159.

31

Preliminaries this to be correct for the latitude in the place where he lived (Rome).133 In addition to the ratio of 5:3 for Greece, Geminus reports that for the horizon of Rhodes (latitude 36° N), the longest day lasts 14 ½ hours, a value quoted by Hipparchus in his Commentary.134 Therefore, for latitude of 36° N, there are 29 of 48 parts of the Tropic of Cancer above and 19 out of 48 parts below horizon at Rhodes.135 Whereas we know that Hipparchus divided his circle into 360 degrees, it is nearly impossible to uncover what methods of dividing the circle may have been used before Hipparchus since, in all his writings, he systematically converts whatever measurements there may have been into his own, preferred system. From later evidence, we do know of an alternative rule for drawing celestial circles on a sphere, based on the division of a circle

Scheme 1.9 Construction of the ever-visible circle.

parallel circles as being correct for the horizon of Greece.128 In discussing the lengths of daylight, Geminus says that the longest day lasts 15 hours in Rome.This amounts to a ratio of longest daytime to shortest nighttime of 5:3.129 Strabo linked the ratio 5:3 to the region between Naples and Rome, and Pliny to the whole of Italy.130 Finally, a later author on the construction of globes, Leontius, applied this ratio to Constantinople.131 Hyginus (in the chapter on the Tropic of Cancer in his De Astronomia) tells us that, if one adjusts a globe so that the ever-visible circle is completely above the horizon and the ever-invisible circle therefore completely below it, one finds that 5/8 of the tropic is above the horizon and 3/8 is below it.132 Hyginus considers

133 Hyginus (Le Boeuffle 1983), IV.2.3, pp. 117–18. Hyginus certainly confuses his readers by adding that the division of the day and night into the ration of 5:3 is not arrived at according to the evidence supplied by sundials (horologiis), but that it follows the geometry of the sphere (ex sphaerae ratione). He adds to this discussion a lengthy argument suggesting that all circles should be divided into 8 parts—a discussion that seems to have more to do with number mysticism than with the celestial sphere. 134 Geminus (Aujac 1975), V.23–25, pp. 24–5, and VI.7, p. 34; Evans and Berggren 2006, p. 16,V.23–25, p. 153, and VI.7, p. 162. The values for the longest day of 14 ½ hours and the shortest night of 9 ½ hours are also quoted by Manilius (Goold 1977), III. 257–61, p. 183. Manilius adds, however, that it is ‘the measurement in the latitude of the lands inundated by the Nile’. 135 In Hyginus (Le Boeuffle 1983), IV.3, p. 204, note 9, Le Boeuffle points out that 29/48 is only 1/48 less than 5/8 (= 30/58) and he suggests that Aratus (or Eudoxus?) may have conscientiously simplified the ratio and, thereby, changed the latitude from 36°N to 40.7°N. One could imagine, for practical reasons, the ratio of 29/48 being turned into 5/8, if only because it is much easier to divide a circle into 8 parts. On a globe of 30 cm in diameter, however, 1/48 of the Tropic of Cancer is 1.8 cm, and, in terms of hours, a value of 1/48 implies a difference of ½ hour in the length of daylight—neither of which is negligible.

128 Geminus (Aujac 1975), V.23, pp. 24–5; Evans and Berggren 2006, V.23, p. 153. 129 Geminus (Aujac 1975),VI.7–8, p. 34; Evans and Berggren 2006, VI.7–8, p. 162. 130 Strabo (Jones 1917/1997), Book II.5.40, p. 513. See also Pliny (Rackham 1938/1979), Book II.187, p. 319. 131 Halma 1821, pp. 65–73. 132 Hyginus (Le Boeuffle 1983), IV.2.2, p. 116.

32

1.5 Prerequisites to Globe Making into 60 segments of 6° each.136 In this system one sexagesimal part (1p) is equal to 6° or 1/60th of a full circle. Strabo credits Eratosthenes as being the first to use this system, reporting that he fixed the arc between the tropics and the equator as ‘four parts’ (4p x 6° = 24°).137 The realization that the obliquity was actually slightly less than 24° (or half the value of 11/83 part of a circle) is also attributed to Eratosthenes.138 This more accurate value has played an important role in mathematical astronomy, but since the difference between 1/15th part and half the value of 11/83 part of a circle on a globe with a diameter of 30 cm amounts to only 0.4 mm, the more accurate value is of no practical consequence when it comes to the construction of descriptive globes. The division of the circle into 60 parts is also used by Geminus, who gives the following recipe for tracing the group of five parallel circles on a sphere:

as extending 6° on both sides of the ecliptic.140 Geminus presents his rule of tracing the evervisible and ever-invisible circle at a distance of 6 sixtieths part of a circle (36°) as being correct only for the horizon of Greece.What is more, he assures his readers that, in spite of the variation in the distances of the ever-visible and ever-invisible circles from their respective poles for different places on the Earth’s surface, all globes have been configured for the horizon of Greece.141 This may explain why this model for the geographical latitude of 36 ° was popular in Antiquity and why the same plan for tracing the circles on the sphere is described by Roman authors, such as Hyginus and Manilius, who were working in Rome, a city for which the geographical latitude of 42° N would have been more appropriate.142 Anyway, the antique grid with parallels shown in Scheme 1.1 is also the basis for the zonal diagrams known from early medieval manuscripts of Macrobius’s Commentary on the Dream of Scipio.143 It is not clear which sources Macrobius used but his model was very influential throughout the early Middle Ages and his book may have been the main source to have transmitted the antique grid in the Latin West. Another recipe for tracing the group of five parallel circles on a sphere is reported by Martianus Capella, who describes ratios of the distance between the ever-visible circle and the pole and the distance between the ever-visible circle and the summer tropic as a ratio of 8:6.

‘The entire meridian circle being divided into 60 parts, the arctic [circle] is inscribed 6 sixtieths from the pole; the summer tropic is drawn 5 sixtieths from the arctic [circle]; the equator 4 sixtieths from each of the tropics; the winter tropic circle 5 sixtieths from the antarctic; and the antarctic [circle] 6 sixtieths from the pole.’139

This division is illustrated in Scheme 1.1. Of course, the arc of 4 sixtieths of a circle (4 × 6° = 24°) also allows one to mark the pole of the ecliptic and to draw the ecliptic. Finally, the unit of 1p (= 6°) can also be used for the width of the zodiacal band, which Geminus describes

140 Geminus (Aujac 1975), V.53, p. 30; Evans and Berggren 2006, V.53, p. 157. 141 Geminus (Aujac 1975), V.48, p. 29 and XVI.12, p. 78; Evans and Berggren 2006, V.48, p. 156 and XVI.12, p. 213. 142 Hyginus (Le Boeuffle 1983), I.6.1–2, p. 8. Manilius (Goold 1977), I.566–96, pp. xxxii, 49–53. 143 Stahl 1952, pp. 200–12.

136 Neugebauer 1975, p. 590, and note 2, says that this division seems to have been introduced around 250 BC, and is probably Babylonian in origin. 137 Strabo (Jones 1917/1997), Book II.5.7, p. 439. 138 Jones (A) 2002; Goldstein 1983. 139 Geminus (Aujac 1975), V.46, pp. 28–9. The translation is from Evans and Berggren 2006, V.46, p. 156.

33

Preliminaries He fixed the ratio between the distance of the summer tropic above the Equator and that of the ever-visible circle above the summer tropic as 4:6.144 If these numbers can be taken at face value, it seems as though Martianus Capella is referring to a fourth system, in which the circle is divided into 72 parts, that is, into units of 5°.145 Four of these units (20°) are believed to fit the arc between the tropics and the Equator; six of them (30°) the arc between the summer and winter tropics and the ever-visible and ever-invisible circle, respectively and eight of them (40°) fit the arc between the ever-visible and ever-invisible circle and their respective poles. In suggesting that distances of the arcs between the tropics and the Equator are 20°, Martianus Capella is off by 4°, since they should be 24°. This suggests that there is some kind of confusion underpinning the data quoted by Martianus Capella, but what precisely is difficult to determine.146 In summary, one finds that the obliquity of the ecliptic is generally consistent and equal to 24° (with the exception of Martianus Capella’s 20°). Arguments based solely on how the geographical latitudes are related to the ever-visible and invisible circles are not very reliable. When using data solely derived from antique sources, the ever-visible and ever-invisible circles can be found anywhere along a band of 36°–41° north and south of the Equator. Another reason to be careful with the use of values based on geographical latitudes and their relationship to the

ever-visible and invisible circles is Geminus’s claim that, despite the fact that the circles are not the same everywhere, the ever-visible and invisible circles are placed at 6/60th part of a circle (36°) from the poles—which he conveniently identified with the value for Greece.147

. HIPPARCHUS’S RULE The last issue raised in this chapter is about the manner in which constellations are to be drawn on a globe, a matter that already in Antiquity resulted in differences in the left and right characteristics of the constellation figures.The example par excellence is the case of Hercules of which Aratus says that the tip of his right foot is placed above the mid-point of the head of the Draco.148 Hipparchus severely criticizes this description because Hercules should have his left foot above the head of the Draco. The reason is that ‘all the stars are described in constellations from our point of view, and as if they were facing us, except for such of them as are drawn in profile. This opinion is also more than once expressed by Aratus; where he explicitly points out the right or left side of a constellation his indications agree everywhere with the assumption just mentioned. In general this assumption is also fully justified and appropriate from an artistic point of view’.149 The rule here referred to by Hipparchus for describing the stars in constellations makes good sense and is of great importance in celestial 147 Neugebauer 1975, p. 733 argues, that the choice of the value of 36° could well be based on the ease of construction instead of being a carefully determined value for the latitude. For that reason, globe makers may well have used a value of 36° for the whole of ‘Greece’, which strictly speaking, holds true only for Rhodes. 148 Aratus (Kidd 1997), pp. 76–7, ll. 68–70. 149 Hipparchus (Manitius 1894), I.4–6, p. 33. Part of the translation is taken over from Toomer 1984, p. 15.

144 Martianus Capella (Dick 1925), VIII.837, p. 439; Stahl et al. 1977, p. 325. 145 In describing the division of the ecliptic, Martianus Capella used a division of the circle in 12 times 30°. See Martianus Capella (Dick 1925), VIII.834, p. 438. 146 For example, he may have maintained the four units of 6° regularly quoted in the literature without compensating for the change in the unit from 6° to 5°.

34

1.6 Hipparchus’s Rule cartography, especially because it fixes unambiguously what is meant in this field by left and right. In the absence of mathematical data on the positions of the stars—as is the case in the descriptive tradition discussed above—Hipparchus’s rule is indispensable. How the rule works is explained for the stellar configuration of Orion shown in Scheme 1.10. On the top left (A) is Orion’s configuration as it is seen in the sky by an observer looking south, with east on his left and west on his right side. Hipparchus’s rule states that all the stars are described as if the constellation figure were facing us, thus we see Orion in front view.Then it is clear that the stars on the eastern side constitute Orion’s right and those on the western side his left side, as indicated in the top right figure (B) in Scheme 1.10 where the labels left and right have been added. For an observer the situation explained by Hipparchus is quite clear, but how should globe makers draw the constellations on their globe? One of the essential aspects of globes is their correspondence with world around them. Since in the real world Aries rises and sets before Taurus, and Taurus before Gemini, and so on these constellations should be drawn on the globe in keeping with this order of rising and setting. Because a globe is always set up in agreement with the true directions in the user’s place this implies that the order of the constellations on the globe has to be reversed from that seen in the sky.The change in order applies also to each individual stellar configuration.Thus on a globe Orion’s stellar configuration is the mirror image of that seen in the sky as shown in bottom left (C) in Scheme 1.10. All globe makers of the past have agreed on this way of ordering the stars. Differences occur in the manner of drawing constellation figures, the function of which is in

the first place to help identifying and memorizing the stars in the night sky. This requires that a star said to be in the left hand side as seen in the sky, should also to be found on a globe in the left hand side.To bring this about a globe maker has to reverse all human images as they are seen in the sky when drawing them on a globe. In other words, to conserve the left and right characteristics of the constellation figures as defined by Hipparchus’s rule on his globe a globe maker should draw, say, the human constellation figures as if they are looking into the globe, with their backs turned to the viewer. Thus the figure of Orion on a globe is drawn as shown in the bottom left (D) in Scheme 1.10, with his left shoulder on the western and his right shoulder on the eastern side.This way of presenting the constellation figures is seen on the Farnese globe (Section 2.6) and on globes and maps made in Renaissance Europe (Section 5.4). For a long time historians have considered the Farnese globe, on which all human constellations (except Andromeda) are shown from the rear, exemplary for globe making in Antiquity. However, in the last decade of the twentieth century two other antique celestial globes were discovered which demonstrate that this assumption cannot be maintained. On Kugel’s globe (Section 2.3) the majority of the constellations are the mirror image of those as seen in the sky, with the result that the right foot of the Kneeler is above the head of Draco and the right hand of Virgo is on the Equator. On the Mainz globe (Section 2.4) one finds that most human constellation figures (for example Gemini) are the reverse and a few others (for example Cepheus) the mirror images of those as seen in the sky. It is generally assumed that in star catalogues the descriptions of the left and right characteristics of the locations of stars within constellations 35

Preliminaries

Scheme 1.10 The stellar configuration of Orion, as seen in the sky and as seen on a sphere.

reflect the situation as seen in the sky. In his translation of the Almagest Toomer states that ‘on the matter of the orientation of the figures, I have satisfied myself that Ptolemy describes them as if they were drawn on the inside of a globe, as seen by an observer at the centre of that globe, and fac-

ing towards him’.150 In other words, Toomer believes that all Ptolemaic descriptions refer to sky-view and he concludes that this is in agreement with Hipparchus’s rule. I do not know 150 Toomer 1984, p. 15.

36

1.6 Hipparchus’s Rule how Toomer arrived at his conclusion but there are a few examples showing that Ptolemy did not describe all his constellations‘as if they were drawn on the inside of the globe’. Orion presents a case in point as is clear from Scheme 1.10. In pictures B and D, presenting the stars of Orion respectively in sky-view and in globe-view, the left and right characteristics of the stars within the constellation figure agree with the descriptions given in the Ptolemaic catalogue: right and left shoulder, left foot, right knee, and so on. Since the left and right characteristics of Orion have been conserved in Scheme 1.10B and D they do not allow us to distinguish between the constellation in sky-view and in globe-view. More details are needed to adjudicate between the two situations. In this respect the stars which Ptolemy described as ‘the 4 stars almost on a straight line just over the back’ (Ori 13–16) are telling. Had Toomer been right that Ptolemy describes his figures as seen from the inside of a sphere ‘the 4 stars almost on a straight line’ should have been describes as ‘just over the chest’ (compare Scheme 1.10B). Ptolemy’s reference to the back of Orion is only internally consistent with the right and left shoulder and so on of a figure as it would be seen on a globe with reversed images (compare Scheme 1.10D). This conclusion does not imply that Ptolemy’s description of Orion violates Hipparchus’s rule. Orion and the other human figures are described as being right-handed, showing that on the pictorial model used by Ptolemy the left and right characteristics of Orion are conserved. This and other examples show that Ptolemy’s descriptions sometimes refer to a picture in globe-view and sometimes to one in sky-view. In most cases however, insufficient information is available to tell which way the figure is oriented. The left and right characteristics described in star catalogues can be instructive for understand37

ing how they were fabricated. For example, Ptolemy’s description of Orion indicates that he had a globe at his disposal when he made the descriptions of his constellations in his star catalogue. Another interesting example is the star catalogue in the Epitome.The idea that this descriptive star catalogue was not obtained by direct observation but derived from pictorial sources is supported by Pàmias and Geus who note that the wording of the description reflect the use of a pictorial source.151 An example is Aquarius, who in the Epitome is described as follows: ‘This figure is thought to have been named the Water-Pourer [Aquarius] because of the action he represents.The Water-Pourer stands holding a winejar, from which he is pouring a stream of liquid. Some find in this image sufficient proof that the figure represented is Ganymede, and they call Homer to witness, because the poet says that Ganymede, adjudged worthy by the gods, was carried away on account of his beauty to be cup-bearer to Zeus.’152

The image here referred to and used for identifying Aquarius with Ganymede may come from a series of the illustrations of the individual constellations, but this is not likely because the pictorial presentations in constellation cycles do not provide cartographic information on the positions of constellations with respect to the main circles. The thesis that a globe is the source of the star catalogue in the Epitome is best demonstrated by the description of Bootes listing in all 14 stars: ‘[Bootes] has four stars on the right hand; these stars do not set.There is one bright star on the head; one bright star on each shoulder; one star on each breast, the one on the right breast being bright. Beneath 151 The first reference to a globe is by Rehm 1899b, p. 259. Eratosthenes (Pàmias and Geus 2007), p. 25, note 34 and p. 216, note 7. 152 Eratosthenes (Pàmias and Geus 2007), pp. 148–9; the English translation from Condos 1997, p. 29.

Preliminaries this last star is one faint star.There is one bright star on the right elbow; one very bright star between the knees, which is called Arcturus; and one bright star on each foot.The total is fourteen.’153

The most telling aspect of this description is the stars on the right hand and arm. Since the four stars in the right hand are described as never setting, they are easily identified because these stars are within the ever-invisible circle, that is, the parallel circle separating the stars that set from those that do not.Three of these never setting stars correspond to those that Ptolemy place in the left arm (κ, ι, and θ Boo) and have declinations around 61º.These stars are about 5º above the ever-visible circle for the geographical latitude of 36º.154 Similarly, the star described in the Epitome as on the right elbow corresponds to the one that Hipparchus and Ptolemy place in the left elbow. Thus, the depiction of Bootes that emerges from the descriptive star catalogue is clearly the mirrorimage of the constellation described by Hipparchus and Ptolemy. Such an image is not the result of meticulous observation from the night sky. Instead, it can only have been come into being through the intermediary of a globe with an image of Bootes with interchanged left and right characteristics. This justifies the conclusion that the descriptions in the Epitome derive from a globe. Not all constellations on this Epitome’s globe appear to be presented by mirror images. For some constellations the left and right characteristics have been conserved. Examples are Auriga and Virgo. In the Epitome Capella is said to be on Auriga’s left shoulder and Spica inVirgo’s left hand, in keeping with Hipparchus’s rule.The Epitome’s globe clearly had a mixture of reversed and mirror images. 153 Eratosthenes (Pàmias and Geus 2007), pp. 82–3; the English translation from Condos 1997, pp. 55–6. 154 Toomer 1984, p. 346; Grasshoff 1990, p. 278.

38

Although the left and right characteristics are well defined by Hipparchus’s rule artists working in celestial cartography have—as we shall see in the next chapters—not always appreciated their significance with the result that left and right handed hunters and warriors compete in populating the celestial world.

APPENDIX . Summary of the ancient constellations Aratus recognized in all 51 stars groups summarized in Tables A1.1 and A1.2. Of these 47 are connected with well-known classical constellations.These latter include: Twenty constellation north of the zodiac: Ursa Minor, Ursa Maior, Draco, Cepheus, Bootes, Corona Borealis, Hercules, Lyra, Cygnus, Cassiopeia, Perseus, Auriga, Ophiuchus, Serpens, Sagitta, Aquila, Delphinus, Pegasus, Andromeda,Triangulum. Twelve zodiacal constellations: Aries, Taurus, Gemini, Cancer, Leo, Virgo, the Claws of Scorpius, Scorpius, Sagittarius, Capricornus, Aquarius, Pisces. Fifteen constellations south of the zodiac: Cetus, Orion, Eridanus, Lepus, Canis Maior, Canis Minor, Navis, Hydra, Crater, Corvus, Centaurus, Lupus, Ara, Corona Australis, Piscis Austrinus. The constellation Corona Australis was not known by name to Aratus but he described it as a nameless group of stars below Sagittarius. In addition to these 47 standard constellations Aratus appears to have considered the Pleiades and the stream of water pouring from Aquarius’ right hand (Aqua) as independent stellar configurations. He also discusses two more nameless configurations which we have listed as Anonymous I and II, which are considered in detail in Section 2.3. All the 51 Aratean star groups were probably also known to Eudoxus. The author of the Epitome and Hyginus also consider the Pleiades and the stream of water (Aqua) as independent configurations. Both sources mention in addition the star group that later became known as Coma

Appendix 1.1 Summary of the Ancient Constellations Berenices.They also describe Corona Australis as a nameless group of stars below Sagittarius, but since they miss the Aratean groups Anonymous I and II they discuss a total of 50 star groups. In the Epitome these are discussed in 42 chapters. The constellations Hydra, Crater, and

Corvus are confined to one chapter (chapter 41) and so are Ophiuchus and Serpens (chapter 6), the Claws and Scorpius (chapter 7), and Centaurus and Lupus (chapter 40).The star groups representing Coma Berenices, Aqua, and Corona Australis are discussed respectively in the

Table A1.1 Summary of ancient constellations Latin name

Aratus

Epitome

Hyginus

Hipparchus

Geminus

Ptolemy

UMi UMa Dra Cep Boo CrB Her Lyr Cyg Cas Per Aur Oph Ser Sge Aql Del Peg And Tri

+ + + + + + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + +

Ari Tau Gem Cnc Leo Vir Lib Sco Sgr Cap Aqr Psc

+ + + + + + + + + + + +

+ + + + + + + + + + + +

+ + + + + + + + + + + +

+ + + + + + + + + + + +

+ + + + + + + + + + + +

+ + + + + + + + + + + +

Cet Ori

+ +

+ +

+ +

+ +

+ +

+ +

North of the zodiac Ursa Minor Ursa Maior Draco Cepheus Bootes Corona Borealis Hercules Lyra Cygnus Cassiopeia Perseus Auriga Ophiuchus Serpens Sagitta Aquila Delphinus Pegasus Andromeda Triangulum In the zodiac Aries Taurus Gemini Cancer Leo Virgo Libra/Claws Scorpius Sagittarius Capricornus Aquarius Pisces South of the zodiac Cetus Orion

(continued )

39

Preliminaries Table A1.1 (Continued ) Latin name Eridanus Lepus Canis Maior Canis Minor Navis Hydra Crater Corvus Centaurus Lupus Ara Corona Australis Piscis Austrinus

Eri Lep CMa CMi Navis Hya Crt Crv Cen Lup Ara CrA PsA

Aratus

Epitome

Hyginus

Hipparchus

Geminus

Ptolemy

+ + + + + + + + + + + [+] +

+ + + + + + + + + + + [+] +

+ + + + + + + + + + + [+] +

+ + + + + + + + + + + [+] +

+ + + + + + + + + + + + +

+ + + + + + + + + + + + +

+: present; [+]: described as a unnamed groups of stars.

Table A1.2 Summary of special groups Latin name Anonymous I Anonymous II Pleiades Hyades Aqua Coma Berenices Thyrsus-lance Equuleus Caduceus

— — — — — Com — Eql —

Aratus

Epitome

Hyginus

Hipparchus

Geminus

Ptolemy

+ + + + + — — — —

— — + + + + {+} — —

— — + + + + — — —

— — {+} {+} {+} + {+} (+) (+)

— — {+} {+} + + + + +

— — {+} {+} {+} {+} {+} + —

+: present; (+): implied by Geminus; {+}: present but not as an independent constellation.

chapters devoted to Leo (chapter 12), Aquarius (chapter 26), and Sagittarius (chapter 28). Hyginus in Book III uses only 40 chapters for describing the 50 star groups because he treats the Ursae in one chapter and the Pleiades are discussed in the chapter on Taurus. Coma Berenices is only discussed in his Book II as part of Leo and since Ursa Maior and Minor are treated separately one has 41 chapters for the 50 star groups. In the mathematical tradition exemplified by the Ptolemaic star catalogue, 2 of the 51 stellar Aratean star groups, the Pleiades and the stream of water

40

(Aqua), are not treated independently. These groups became part of the constellations Taurus and Aquarius, respectively. And of the two nameless Aratean configurations, Anonymous I and II, only one has been maintained, not as a constellation but as a group of unformed stars belonging to the constellation Canis Maior. Also the star group later known as Coma Berenices and introduced in the Epitome can be found in the Ptolemaic star catalogue as unformed belonging to Leo. Thus in the Ptolemaic star catalogue 47 constellations are used for describing 49

Appendix 1.2 On Sources the zodiacal signs. Hipparchus tells us that, in the treatises he attributes to Eudoxus, the author lists those constellations that either rise or set during the time it takes a zodiacal sign to rise. Aratus constructs his lists differently and mentions those constellations that are rising or setting when a zodiacal sign is beginning to rise. When the two versions are compared it appears that the constellations listed by ‘Eudoxus’ as rising or setting during the rise of a zodiacal sign are actually the same as the ones that are recorded by Aratus as rising or setting when the following zodiacal sign is beginning to rise. For example, in his Commentary, Hipparchus cites from the ‘Eudoxan’ prose treatise:

of the 51 stellar Aratean star groups. In addition to the 47 classical constellations already mentioned by Aratus, one finds in this mathematical tradition one more constellation: Equuleus. According to Geminus the constellation Equuleus was first introduced by Hipparchus. Geminus’s list of constellations is the most extensive.155 In addition to the 48 Ptolemaic constellations he mentions a number of star groups explicitly as a separate constellation: Coma Berenices, Aqua, the Thyrsus-lance held by Centaurus together with Lupus, and Caduceus. From the alignments recorded by Ptolemy it becomes clear that Hipparchus recognized the stars of Coma Berenices.156 Geminus seems to suggest that Hipparchus considered the Thyrsus-lance as an independent constellation.This attribute of Centaurus is mentioned in the Epitome as well as in the Ptolemaic star catalogue as belonging to the constellation Centaurus. Another, really problematic, star group also attributed to Hipparchus is the Caduceus belonging to the southern constellations. It is not known where this group is supposed to be and no sensible identification seems possible.

‘When Cancer rises, none of the northern constellations [i.e. north of the zodiac] rises. Of the southern constellations [i.e. south of the zodiac] the Hare [Lepus], the forelegs of the Greater Dog [Canis Maior], the Lesser Dog [Canis Minor], and the head of the Water snake [Hydra]. Setting is on the other hand of the northern constellations the head of Arctophylax [Bootes].’158

This paragraph has to be compared with the Aratean description for the zodiacal sign following Cancer, that is, for Leo:

APPENDIX . On sources

‘At the Lion’s coming the constellations that were setting with the Crab now go down completely,159 and so does the Eagle [Aquila].The crouching figure [Hercules] is already partly set, but his left knee and foot are not yet curving under the billowing ocean. Rising are the Hydra’s head, the glassy-eyed Hare [Lepus], Procyon [Canis Minor] and the forefeet of the blazing Dog [Canis Maior].’160

In his recent edition of Aratus’s poem Jean Martin has launched the point of view that the texts of Enoptron and the presumed ‘Eudoxan’ Phaenomena must be later, corrected versions of the original Aratean text.157 As this proposal is certainly novel, it seems worth investigating the evidence more closely. One of Martin’s arguments rests upon the ‘format’ that Eudoxus and Aratus use to describe the simultaneous risings and settings of the constellations with

158 Hipparchus (Manitius 1894), II.2.13, pp. 142–3. 159 The constellations that are described as setting with Cancer are Corona Borealis, Piscis Austrinus, Hercules, Ophiuchus, and Serpens, see Aratus (Kidd 1977), pp. 114–15, ll. 570–80. 160 Aratus (Kidd 1977), pp. 116–17, ll. 590–6. I have changed the left ‘hand’ of the crouching figure into his left ‘knee’.

155 Geminus (Aujac 1975), III, pp. 17–20; Evans and Berggren 2006, III, pp. 137–43. 156 Toomer 1984, p. 322. 157 Aratus (Martin 1998), I, p. xci.

41

Preliminaries Thus, those constellations that the prose version lists as rising or setting while Cancer is rising among those that are found rising or setting when Leo is beginning to rise. As a result, Hipparchus quite reasonably concludes that there is no substantive difference between the two formats. Indeed, after citing the Aratean list of constellations rising and setting simultaneously ‘when Leo is at the point of rising’, Hipparchus plainly concludes that this agrees with those listed by Eudoxus as rising or setting with Cancer. He then adds a telling remark, stating that ‘a similar presumption has to be made for all the other signs, as well’.161 The difference between the two versions was first discussed by Franz Boll in 1903, in relation to a text he had found in an Anthology of Vettius Valens (second century ad).162 The Valens text contains a list of constellations that rise and set simultaneously with a sign, and some of the examples from this list agree with those that Hipparchus cited as coming from the treatises he had attributed to Eudoxus. This similarity in content implies that Valens had access to a copy of an astronomical treatise closely related to those that Hipparchus attributed to Eudoxus. Boll agrees with Hipparchus that each of these formats lists the same sets of constellations and that there are no astronomically significant differences in their contents. Nevertheless, Martin seems to believe that the difference in the way that the two lists are presented means that Aratus could not have derived his information from the ‘Eudoxan’ prose treatises. He argues as follows.The Aratean list of rising and setting constellations begins with the sign of Cancer which is most appropriate since the beginning of the sign of Cancer marks the summer solstice. However, had Aratus derived his list directly from Eudoxus this would mean that the Eudoxan list had actually begun with the previous zodiacal sign, that is the sign of Gemini. Beginning such a cycle with the astronomically insignificant Gemini makes no sense and ‘ne 161 Hipparchus (Manitius 1894), II.2.32, pp. 152–3. 162 Boll 1903, pp. 59–69.

42

peut s’expliquer que si l’on admet qu’ «Eudoxe» corrigeait le tableau d’Aratos, en reportant simplement sur le signe précédent les levers et couchers des constellations qui, chez le poète, annonçaient l’apparition de chaque signe’.163 For all intents and purposes, Martin seems to have a valid point. It is a fact that Aratus begins his list of extrazodiacal risings and settings with the beginning of the sign of Cancer, which are actually those that have risen or set with Gemini. This does not necessarily imply, however, that the Eudoxan scheme started with Gemini. Indeed, Hipparchus tells us explicitly that the chapter on risings in the ‘Eudoxan’ treatises starts with Cancer:‘At the start of the chapter on risings, after he [Eudoxus] has mentioned all the constellations that are on the eastern and western horizons when Cancer starts to rise’, 164 he then further says: ‘When Cancer rises, none of the northern constellations [i.e. north of the zodiac] rises. Of the southern constellations [i.e.: south of the zodiac] the Hare [Lepus], the forelegs of the Greater Dog [Canis Maior] . . . ’.165 Surely, there is nothing astronomically insignificant in an approach which starts, first, by listing all the constellations that are in the horizon when Cancer is about to rise and, then—after setting the sphere, so to speak, in motion—to continue by listing those constellations that are rising and setting while Cancer, Leo, and so on are rising.This order is identical to the one used by Aratus, whose text actually follows from the prose treatise by replacing the phrases ‘when Cancer, Leo, etc. are rising’ with (respectively) ‘at the coming of Leo,Virgo, etc’.Thus, we have: Eudoxus starting Aratus starting with: with: when Cancer starts = when Cancer to rise starts to rise and 163 Aratus (Martin 1998), I, p. lxxxix. 164 The constellations listed by Eudoxus when Cancer starts to rise are explicitly quoted by Hipparchus (Manitius 1894), II. 2.4, pp. 138–9. 165 Hipparchus (Manitius 1894), II.2.13, pp. 142–3.

Appendix 1.2 On Sources Eudoxus continuing: Aratus continuing with: with when Cancer rises ↔ at the coming of Leo when Leo rises ↔ at the coming of Virgo when Virgo rises ↔ at the coming of the Claws etc. etc. In doing so Aratus treats all risings of the zodiacal signs on an equal footing with the one described at the start, which for a poet may be preferable. However that may be, it clearly demonstrates that whichever labels are used,the schemes employed by Eudoxus and Aratus begin with the same list of constellations that can be seen on the eastern and western horizons. To argue that the one is astronomically significant, while the is other not, and then to use that claim as the basis of a significant proposal about the relative dating of these works, gives too much credence to what is, essentially, a clever sleight of hand. In truth, the distinction in format does not justify Martin’s conclusion that the prose texts are a paraphrase of the Aratean poem. Indeed, the Aratean scheme seems to follow naturally and easily from that used in the prose treatise. Martin presents a second argument to support his thesis that the ‘Eudoxan’ treatises are copies after Aratus.This one is based on the claim that the order used in the prose Phaenomena by ‘Eudoxus’ would have been more or less identical to the one found in Vitruvius’s De Architectura. Vitruvius’s description of the universe appears in his chapter on sundials and anaphoric clocks, which opens with a description of the motion of the Sun through the zodiac, in which he describes the zodiacal constellations in some detail. The description starts with the Sun entering the constellation Aries. Then, he continues to describe the constellations north of the zodiac and, thereafter, those located to the south of it.166 Martin seems convinced that this structure of the description of the celestial sky

166 Vitruvius (Soubiran 1969), III–V, pp. 18–24.

43

‘remonte plus ou moins directement aux Phénomènes d’Eudoxe’.167 It is true that there are correspondences between the texts of Vitruvius and the ‘Eudoxan’ prose treatises, but as Soubiran has concluded:‘les rapprochements qu’il invoque sont insuffisants à fonder cette hypothèse: on a revelé des contradictions entre Eudoxe et Vitruve, et l’on a songé plutôt à rapprocher les données du De Architectura de celles que fournissent les scholiastes d’Aratos, eux-mêmes inspiré par Eudoxe’.168 Despite this, Martin maintains that the Vitruvian order in which groups of constellations are described—first those located in the zodiac, then those to the north and south of it—is the same as that used in the prose treatises by ‘Eudoxus’, which he considers to be a ‘remise’ of the Aratean order: ‘Il me semble qu’il y a là l’une des raisons les plus fortes de penser que les Phénomènes attribués à Eudoxe par Hipparque, loin d’être le modèle d’Aratos, sont dérivés de son poème’.169 This is not the place for a detailed discussion on the sources used byVitruvius. Other scholars better suited to that task have done so. From the various opinions expressed in the literature, however, we are inclined to accept Soubiran’s view that:‘ ...il n’existe à notre connaissance, dans la littérature astronomique grecque ou latine, aucun texte antérieur à Vitruve qui présente avec ce dernier suffisamment d’analogies pour qu’on puisse le considérer comme sa source unique et directe’.170 This being so, there remains no good reason to accept the point of view adhered to by Martin that the texts of Enoptron and the ‘Eudoxan’ Phaenomena must be later, corrected versions of the original Aratean text.

167 Aratus (Martin 1998), I, p. xc. Martin justifies his claim by referring to his commentary on the Aratean lines 161 (II, pp. 226–7), 182–87 (II, p. 237), and 447 (II, p. 330), but the examples he gives are not really convincing. Interestingly, his thesis has been previously proposed by Kaibel 1894, pp. 101–2, but was rejected by Thiele 1898, p. 50. 168 Vitruvius (Soubiran 1969), p. li. 169 Aratus (Martin 1998), I, p. xci. 170 Vitruvius (Soubiran 1969), pp. xlvii–xlviii.

Preliminaries

APPENDIX . Locating colures with respect to stars In this appendix I describe the method used for finding the great circles which pass on the average through the constellation features said to be on the colures by, respectively, Eudoxus, Manilius, and Martianus Capella. First each constellation feature concerned has been translated into one or more stars. For this I have predominantly used the catalogue data of Hipparchus and Ptolemy, in each of which verbal descriptions are linked to coordinates.171 As a rule I have used two stars for each constellation feature. For example, to find ‘the middle of Aries’ we have selected one star in the western part (ϒ Ari) and one in the eastern part (τ Ari) of this constellation and assumed that ‘the middle of Aries’ lies in between. In a number of cases it is difficult to decide which star represents the feature best. Hipparchus and Ptolemy do not always agree in their verbal description. For example, Hipparchus places the nebulous mass χh Per on the sickle sword in the hand of Perseus whereas Ptolemy has the nebulous mass on the right hand. In such cases I have used the Hipparchan identification rather than the Ptolemaic one. Next the right ascensions of the stars concerned were determined for a relevant epoch. Right ascensions for the year 128 BC are listed in Grasshoff .172 Those for the year 375 BC were obtained by calculation after first subtracting 3.5° from the

171 The catalogue features of Hipparchus are described in Hipparchus (Manitius 1894), II.5.1–III.5.23. For the Ptolemaic star catalogue I consulted the English translation in Toomer 1984, and its German translation in Manitius 1963. 172 Grasshoff 1990, Appendix 8.2, pp. 275–316.

longitudes for 128 BC. Then the distance in right ascension of the stars from the relevant true astronomical colure was determined. If more than one star was used, I calculated the mean value of their distances.Thus for each constellation feature I obtain its mean distance in right ascension from the true colure at a given epoch. Finally, I have for each colure separately and for all four together calculated the mean values and the corresponding standard deviations of the distances in right ascension of the respective non-zodiacal constellations features from the true colures. In Tables A1.3–A1.5 I have listed in column 1 the constellation features described by respectively Eudoxus, Manilius, and Martianus Capella. In the next two columns the stars associated with these features are indicated by respectively their BPK numbers and their modern designation (MDES).173 Next, in column 4, the right ascensions (RA in degrees) for the epoch concerned are presented.This is followed in the next column 5 by the distance in right ascension (DRA in degrees) of the stars from the astronomically correct colures. In the last column I present for each constellation feature the mean value (MDRA in degrees) of the distances in right ascension of the stars. In Table A1.6 I have summarized the mean values and the corresponding standard deviations (all expressed in degrees) of the distances in right ascension of the respective non-zodiacal constellations features from the true colures.

173 BPK numbers were first employed by Baily 1843 and then by Peters and Knobel 1915. For the relation between BPK numbers of the stars and their modern designations we follow Kunitzsch III 1991, pp. 187–94.

44

Table A1.3 Quantified data of the Eudoxan colures (epoch 375 BC) no. feature

PBK

MDES

RA

DRA

192 195 717 713 719 722 362 371

η τ ξ2 α ρ π γ τ

Per Per Cet Cet Cet Cet Ari Ari

5.7 7.0 6.4 15.3 7.8 12.8 −2.8 18.2

5.7 7.0 6.4 15.3 7.8 12.8 −2.8 18.2

17 27 895 900 850 876 457 454

υ γ δ θ ρ α β α

UMa UMa Hya Hya Pup Pyx Cnc Cnc

95.9 140.0 97.3 106.9 96.6 107.1 91.2 101.1

5.9 50.0 7.3 16.9 6.6 17.1 1.2 11.1

105 103 89 90 950 969 529 535

ρ ε ι θ η α α γ

Boo Boo Boo Boo Cen Cen Lib Lib

191.8 195.0 192.1 195.6 184.8 185.5 191.3 202.0

11.8 15.0 12.1 15.6 4.8 5.5 11.3 22.0

4 54 166 161 164 284 281 1021 601 624

ζ δ ι η δ α γ ι α δ

UMi Dra Cyg Cyg Cyg Sge Sge PsA Cap Cap

280.4 285.7 275.3 276.8 277.6 268.5 273.2 287.9 270.7 292.4

10.4 15.7 7.2 6.8 7.6 −1.5 3.2 17.9 0.7 22.4

MDRA

The vernal equinoctial colure 1. the right hand and head of Perseus 2. the head of Cetus 3. the bend in Eridanus 4. the back of Aries breadthways

6.3 10.9 10.3 10.5

The summer solstitial colure 5. the middle of Ursa Maior 6. the neck of Hydra 7. between stern and mast of Navis 8. the middle of Cancer

27.9 12.1 11.9 6.1

The autumnal equinoctial colure 9. the middle of Bootes lengthways 10. the left hand of Bootes 11. the right hand of Centaurus 12. the front knee of Centaurus 13. the middle of the Claws breadthways

13.4 13.8 4.8 5.5 16.7

The winter solstitial colure 14. 15. 16. 17.

past the tail of Ursa Minor through the bend of Draco the left (sic) hand Cepheus the neck and right wing of Cygnus

18. the middle of Sagitta 19. the tail of Piscis Austrinus 20. the middle of Capricorn

10.4 15.7 7.2 7.2 0.9 17.9 11.6

Notes to Table A1.3: 1. Hipparchus places the nebulous mass χh Per on the sickle sword whereas Ptolemy has it on the right hand. 3. Hipparchus has the quadrangular formed by ρ, σ, ε, π Cet in the bend of Eridanus and Ptolemy has it in Cetus. 11. Hipparchus places η Cen in the hand of Centaurus and Ptolemy has κ Cen in it. 16. Hipparchus presumed that Eudoxus placed ι Cep in the left hand. However, Eudoxus tells us that the right hand of Cepheus is near the right wing of Cygnus. Since the Eudoxan colure is said to also pass through the right wing of Cygnus it is clear that Eudoxus must refer here to the right hand. On the Farnese globe Cepheus has long extended arms in line with the Eudoxan description (see Chapter 2). For that reason we assume that the right hand of Cepheus can be identified with ι Cyg because of the two stars in the extreme part of the right wing (ι and κ Cyg) this star is closest to Cepheus.

45

Preliminaries Table A1.4 Quantified data of the colures described by Manilius (epoch 128 BC) no. feature

PBK

MDES

RA

DRA

183 184 349 350 358 361 362 725 726

χ ι γ φ α γ γ ζ θ

Cas Cas And Per Tri Tri Ari Cet Cet

357.0 2.4 1.2 356.3 0.2 4.9 0.4 1.6 −5.7

−3.0 2.4 1.2 −3.7 0.2 4.9 0.4 1.6 −5.7

16 20 21 457 456 425 835 893

23 ι κ β µ β η τ

UMa UMa UMa Cnc Cnc Gem CMa Pup

92.0 94.9 96.2 94.8 89.9 83.1 90.1 89.3

2.0 4.9 6.2 4.8 −0.1 −6.9 0.1 −0.7

— 529 531 918 939 940

α β π ι θ

— Lib Lib Hya Cen Cen

— 194.5 201.6 183.0 172.4 182.7

— 14.5 21.6 3.0 −7.6 2.7

UMi — Lyr Aql Aql Aql Cap

269.5 — 261.4 264.5 272.6 271.6 274.3

−0.5 — −8.6 −5.5 2.6 1.6 4.3

MDRA

The vernal equinoctial colure 1. the feet of Cassiopeia 2. the lowest folds of Andromeda’s robe 3 the bright Triangle 4. the boundary of the Ram 5. the scaly back of the Whale

−0.3 −1.2 2.6 0.4 −2.1

The summer solstitial colure 6. the neck of the Greater Bear 7. the forefeet of the Greater Bear 8. parts the Crab from the Twins

9. grazes the Dog with the blazing face 10. the rudder of the Ship

2.0 5.5

−0.8 0.1 −0.7

The autumnal equinoctial colure 11. Dragon’s tail and the Bears? 12. the yoke of the Balance 13. the extremity of the Water-snake 14. the middle of the southern Centaur

— 18.0 3.0 −2.4

The winter solstitial colure 15. 16. 17. 18.

passes by the stars of Cynosure’s hindfeet the coils of the Dragon? runs through the inverted Lyre marks the Eagle

19. touches Capricorn

η

5 — 149 297 287 288 601

α δ β α α

Note to Table A1.4: The features 11 and 16 are too vaguely described to allow a reliable identification.

46

-0.5 — −8.6

−0.4 4.3

Appendix 1.3 Locating Colures with respect to Stars Table A1.5 Quantified data of the colures described by Martianus Capella (epoch 128 BC) no. feature

PBK

MDES

RA

192 — 195 358 361 713 717 725

η τ α γ α ξ2 ζ

Per — Per Tri Tri Cet Cet Cet

16 17 20 21 893 851

23 υ ι κ τ ξ

72 73 92 110 522 521 950 969 4 54 161 164 166 281

DRA

MDRA

The vernal equinoctial colure 1. 2. 3. 4.

the right hand of Perseus touches Perseus’s right arm? touches the top of the head of Perseus touches the far angle of Deltoton

5. the head of Cetus 6. Cetus’s body and shoulder

9.0 — 10.4 0.2 4.9 18.5 9.6 1.6

9.0 — 10.4 0.2 4.9 18.5 9.6 1.6

UMa UMa UMa UMa Pup Pup

92.0 102.2 94.9 96.2 89.3 95.0

2.0 12.2 4.9 6.2 −0.7 5.0

α κ γ α µ λ η α

Dra Dra Boo Boo Vir Vir Cen Cen

197.6 155.1 196.1 189.6 193.5 187.0 188.1 189.9

17.6 −24.9 16.1 9.6 13.5 7.0 8.1 8.9

ζ δ η δ ι γ

UMi Dra Cyg Cyg Cyg Sge

274.6 286.2 279.2 279.6 278.8 273.2

4.6 16.2 9.2 9.6 8.8 3.2

9.0 — 10.4 2.6 14.0 1.6

The summer solstitial colure 7. the chest and neck of Ursa Major 8. he left front paw of Ursa Major 9. the rudder and stern of Navis

7.1 5.5 2.2

The autumnal equinoctial colure 10. the tail of Draco 11. the left side of Bootes 12. the star of Bootes (Arcturus) 13. the feet of Virgo 14. the right hand of Centaurus 15. touches the left hoof of Centaurus (?)

−3.6 16.1 9.6 10.3 8.1 8.9

The winter solstitial colure 16. 17. 18. 19.

asses the hindquarters of Ursa Minor through Draco the neck of Cygnus the left (sic) wing of Cygnus

20. touches the tip of Sagitta

Notes to Table A1.5: 1. Hipparchus places η Per in the right hand of Perseus and Ptolemy has χ Per in it. 2. The feature is too vaguely described to allow a reliable identification. 14. Hipparchus places η Cen in the hand of Centaurus and Ptolemy has κ Cen in it.

47

4.6 16.2 9.2 9.2 3.2

Preliminaries Table A1.6 Mean values and the corresponding standard deviations of the distances of the constellation features from the true colures in 375 BC for Eudoxus, and from those in 128 BC for Manilius and Martianus Capella Eudoxus

Mean

StD

Vernal equinoctial colure Summer solstitial colure Autumnal equinoctial colure Winter solstitial colure All colures All colures excepting nos. 5 and 18*

9.2 17.3 9.4 9.9 11.0 10.5

2.0 7.5 4.2 5.7 6.1 3.8

Manilius

Mean

StD

Vernal equinoctial colure Summer solstitial colure Autumnal equinoctial colure Winter solstitial colure All colures

-0.3 1.7 0.3 -3.2 -0.2

1.7 2.4 2.7 3.8 3.3

Martianus Capella

Mean

StD

Vernal equinoctial colure Summer solstitial colure Autumnal equinoctial colure Winter solstitial colure All colures

8.2 4.9 7.5 7.5 7.5

5.9 2.1 4.8 4.9 4.9

* The large standard deviation of the mean of all non-zodiacal constellations stems from the deviations of two features in Table A1.3: UMa (no. 5) and Sge (no. 18). When these two constellation features are left out the remaining non-zodiacal constellations appear to lie on average on the hour circles that are 10.5° ± 3.8° east of the true colures.

48

CHAPTER TWO

celestial cartography in antiquity

M

ost early records on globes in literary sources are more curious than reliable and do not allow us to draw conclusions on either the construction or the uranography of early globes.1 For this one has to turn to the few copies that survive today.The best known example is the statue of the Farnese Atlas carrying a celestial globe of around 65 cm in diameter. It was found in Rome in or around 1575 and is now in the collection of the Museo Archeologico in Naples. In 1898 Thiele had already published an extensive study of it.2 In the last decade of the twentieth century two other celestial globes turned up. One globe is in the collection of the Römisch-Germanisches Zentralmuseum in Mainz. It is made of messing and has a diameter of about 11 cm and appears to have formed part of a gnomon.The other is a gilt silver globe with a diameter of only 6.3 cm, first offered for sale in Paris by Galerie J. Kugel, the present owner of the globe.These three globes will be discussed in detail below together with two globe fragments that have survived. Before doing so a few words must be said about maps. Spheres have the reputation of being inconvenient in use. Unless small they are difficult to 1 Schlachter 1927; see also the discussion of Archimedes’s globe in Gee 2000, pp. 96–100. 2 Thiele 1898, pp. 19–42.

transport and when small they rarely include sufficient detail. Yet a reader of texts such as Aratus’s Phaenomena would benefit from illustrative material in some form showing the positions of the constellations with respect to each other. For other texts, such as the Epitome, drawings of the individual constellations would have been more instructive.Thus in addition to globes illustrations on flat surfaces may have been available either as maps or in the form of constellation cycles. To present the celestial sky on a flat surface requires a greater amount of abstraction than drawing the images on a sphere. As there are many ways to present a celestial grid on a plane surface there are also many ways to map the sky. These various ways of mapping are conveniently labelled projections. However, one should be cautious of applying modern concepts to earlier periods in which they might not yet have been fully developed. In the early stage of mapping the celestial sky a clear notion of projecting a point on a sphere onto a plane surface may not yet have been developed mathematically. There are many diagrams showing a grid consisting of five parallel circles and the ecliptic. Sometimes such diagrams mark wind directions and terrestrial zones, as for example the anemoscope of Eutropius, of ca. ad 200, found in Rome and

celestial cartography in antiquity

Fig. 2.1 Drawing of a fragment of an anaphoric dial. Reproduced from Benndorf, Weiss and Rehm 1903, p. 39.

now in the Oliveriano Museum at Pesaro.3 There the boundary circle seems to represent simultaneously the horizon and the meridian circle. Other diagrams in books on the celestial sphere are rough drawings in which attempts are made to express the sphericity of the world rather unsuccessfully.4 The only antique artefact that comes close to a celestial map is a fragment found in 1899 near Salzburg and now in the collec-

tion of the Salzburg Museum.5 This fragment (Fig. 2.1) dates from the second century ad. Most historians agree that it is part of an anaphoric dial such as described by Vitruvius (died after ad 27) in his De Architectura.6 The anaphoric dial is a kind of astronomical clock consisting of a flat open grid formed by a number of celestial circles among which the unequal hour lines and the 5 The discovery was published for the first time in Maass 1902. 6 Neugebauer 1975, pp. 869–70.Vitruvius (Soubiran 1969), pp. 33–6.

3 Dilke 1987, pp. 248–49, and fig. 14.8. 4 Obrist 2004, p. 123 and p. 207, and figs. 39–40.

50

celestial cartography in antiquity horizon circle are the most prominent.7 These circles are presented in stereographic projection. Behind this open grid is a disc with a map of the starry sky which rotates around the northern equatorial pole in 24 hours.The disc is presumably driven by water power and when the clock is properly adjusted for the time of the year by marking the position of the Sun in the zodiac one can find the time of the day and see at what time (in unequal hours) constellations rise and set. The Salzburg fragment is a part of the disc moving behind the flat open grid.With a radius of 40.6 cm the circular disc was quite large. Using the traces of the ecliptic, the Equator, the Tropic of Cancer, and the marking of the north pole, Rehm showed convincingly that the celestial grid engraved on the disc is based on stereographic projection.8 At the ecliptic is a series of circular holes which were used to set the position of the Sun for a given time of the year. The northern boundary of the zodiacal band is indicated by an arc (or a section of a circle). The zodiac is divided into (twelve) compartments of unequal sizes, which represent the zodiacal signs. On the back of the fragment, at the rim, are the names of the signs of the zodiac and below them the names of the months: [PI]SCES/[M]ARTIVS; ARIES/ APRILIS; TAVRVS/MAIIVS (sic); GE[MINI]/ JV[NIVS]; and so on. These markings served to set the position of the Sun from behind the disc. The presentation of the celestial sphere on the disc is in globe-view, that is, the order of the zodiacal constellations is counter-clockwise, and since the annual motion of the Sun is opposite to the daily rotation the disc would have moved clockwise. Only a few constellations are depicted on the fragment: four zodiacal constellations

(Aries, Taurus, and parts of Pisces and Gemini) and four northern ones (Perseus, Andromeda, Triangulum, and Auriga). Perseus turns his back to the viewer, Auriga is in profile, and Andromeda and the western Twin are facing the viewer. The presence of a well-defined mathematical grid might suggest that the map of the constellations would belong to the mathematical tradition. However, the few constellations are erratically placed on the disc.Triangulum should lie between Aries and Andromeda and the Fish belonging to Pisces should be more or less perpendicular to the zodiacal band instead of being drawn parallel to it. Some constellations such as Cassiopeia have not been marked at all. The example of Auriga shows that the constellation images stem from the descriptive tradition and do not fit into a mathematical projection. The charioteer wears a long dress, faces to the right and both arms are stretched in front of him (see Fig. 2.1). The star said in star catalogues to be on his left shoulder is called the Goat (α Aur) and in ad 137 its right ascension was 45º. The stars said to be on his left wrist are called the Kids (η and ζ Aur) and their right ascension was 44º in ad 137. Since Auriga is drawn in profile with his arms extended to the east the Goat is on one side of his head and the Kids are on the other side, whereas they should astronomically be on one and the same (left) side since they have the same right ascension. In other words, the Goat and the Kids fit the descriptions of their location in the constellation figure but not the coordinates. This is to be expected in the descriptive tradition in which constellations serve as the cartographic frame for locating the stars. Although the stereographic projection was known and applied in such instruments as the anaphoric dial, it is not clear when it was first

7 Turner (A) 2000, pp. 539–40. 8 Benndorf, Weiss, and Rehm 1903, pp. 41–9.

51

celestial cartography in antiquity

Fig. 2.2 Fragment of a Greek globe. Inc. No. Sk 1050 A; 11.2 × 33 cm. (Photo: Ingrid Geske—Antikensammlung, Staatliche Museen zur Berlin—Preusisscher Kulturbesitz.)

applied to plotting stars on the plane mathematically.The oldest extant treatise on stereographic projection is a work called Planispherium by Ptolemy.9 In this description the celestial sky is confined to the visible sky, the space north of the ever-invisible circle, as seen on later medieval planispheres.10 The earliest reference to this projection in connection with a plane star map is by Synesius (fl. ad 400) in a letter to Paeonius.11 Several scholars have associated this latter description with the astrolabe, but this is not yet certain. Yet it is in constructing astrolabes that stereographic projection was used most frequently in the Islamic world and later in medieval Europe. Contrary to prevailing ideas, the maps found in the medieval illustrated manu-

scripts discussed in Chapter 3 are not based on stereographic projection even though their roots lie in Antiquity. But let me now turn to the extant antique celestial globes.

. THE BERLIN FRAGMENT The marble Berlin fragment of 33 cm × 11.2 cm originates from Rome and is now in the Antikensammlung of the Staatliche Museen in Berlin. It clearly presents a segment of a sphere showing a number of constellations in relief (Fig. 2.2).12 From left to right one can see the outstretched hand (at the bottom) and the foot (at the top) of an upside-down Hercules, the figures of Lyra and Cygnus, and on the right side

9 Drecker 1927; Sidoli and Berggren 2007. 10 Neugebauer 1975, pp. 870–2. 11 Neugebauer 1975, pp. 872–7.

12 Thiele 1898, pp. 42–3.

52

2.1 The Berlin Fragment the upside-down image of Cassiopeia. Also a number of stars are marked which serve mainly to create an illusion of the starry sky since they are placed at random around the constellation figures. The upper boundary of this fragment is marked by the foot of Hercules which according to all literary sources stands on the head of Draco. In Antiquity its right ascension was around 250° and its declination around 50°. The northernmost star of Cassiopeia then had a right ascension of 358° and a declination around 54°.The lower boundary of the segment is marked by the head of Cygnus which is recorded as being on the Tropic of Cancer.Its declination would be around 24°. Together these data suggest that the segment covers a difference in declination of about 30° and in the right ascension of about 110° as illustrated in Scheme 2.1. The upper boundary seems to agree with the ever-visible circle corresponding to geographical latitude of 36° and the lower boundary with the Tropic of Cancer. These circles reflect the antique grid described by Geminus and others (see Chapter 1).

Since the lower and upper boundaries seems to agree with parallels at declinations respectively of 24° and 54°, the diameter of these circles on the original globe would have been respectively Dcos24° and Dcos54°, where D is the diameter of the sphere. Künzl reports that V. Kästner of Berlin estimated the diameters of the lower and upper boundaries to be respectively 44 cm and 25 cm.13 These values suggest that the diameter of the sphere D lies between 48 cm and 42 cm.14 Next to stars and constellations there is an oblique line crossing Cassiopeia and the northern wing of Cygnus which have been interpreted—correctly in my opinion—as a section of the Milky Way.15 Of all the circles recognized by ancient astronomers there is only one that can actually be observed. Aratus described it as follows in his Phaenomena: ‘If ever on a clear night, when all the brilliant stars are displayed to men by celestial Night, and at new moon none in its course is dimmed, but all shine sharply in the darkness – if ever at such a time a wondering has come into your mind when you observed the sky split all the way round by a broad circle, or someone else standing beside you has pointed out to you that star-emblazoned wheel (men call it the Milk), no other circle that rings the sky is like it in colour . . .’16

The presentation of the Milky Way as a great circle on the sphere is a simplification that is also seen on medieval maps discussed in Chapter 3. Aratus does not provide information on the location of the Milky Way with respect to the stars but later sources, discussed below in the section on the Mainz globe, tell that it passes through Cassiopeia and Cygnus, in agreement with the 13 14 15 16

Scheme 2.1 Globe segment.

53

Künzl 2000, p. 545 and note 290. Künzl 2000, p. 545 arrived at a diameter of 60 cm. Thiele 1898, p. 42. Aratus (Kidd 1997), pp. 106–7, ll. 469–79.

celestial cartography in antiquity situation presented on the globe segment. Künzl proposed another interpretation of this oblique line, namely that it would be a section of the evervisible circle.17 Künzl’s thesis implies that Lyra would be completely north of the ever-visible circle (see Fig. 2.2). In Antiquity the declination of Lyra’s southernmost star (λ Lyr) was around 31º. Thus the constellation Lyra can only be completely above the ever-visible circle in places with a geographical latitude of 59º or more, a condition that shows that Künzl’s thesis cannot be maintained.

latter two constellations he noticed a thigh-bone, the foot of which is said to show up under the ‘zone-line’, the meaning of which is discussed below. He also saw a hand and a very blurred image of a walking dog. The constellations recognized by Sauer raise a number of questions, especially his identification of Navis and a walking dog. Sauer may have supposed (understandably) that the pole marked on the sphere in Fig. 2.3 represented the north pole and therefore thought that he could recognize Cancer and Navis. As Künzl rightly pointed out, however, the pole visible on the sphere is really the south pole.19 Thus one has to view the sphere upside. THE LARISSA GLOBE down as shown in Fig. 2.4. Then one can idenToday only a photograph (Fig. 2.3) remains of tify the autumnal equinoctial colure [1], the the globe found in Larissa in Thessaly, Greece. winter solstitial colure [2], and three parallel cirThe globe was seen in November 1888 in the cles: the ever-invisible circle [3], the Tropic of local school by B. Sauer who put his notes at the Capricorn [4], and the Equator [5]. Also the disposal of Thiele.18 Sauer reports having seen a northern and southern boundaries of the zodiac sphere of bluish marble (of Thessaly?) with a [6 and 7] are clearly visible. Most intriguing is the diameter of 90 cm, from which a cone of 23 cm oblique circle [8] which runs from the autumnal diameter had been removed for hollowing out equinox towards a point on the winter solstitial the sphere. The rough surface is marked by a colure north of the ever-invisible circle and grid of circles and the zodiacal band. Sauer which Sauer may have called the ‘zone-line’. Its thought that he could identify the following interpretation is not straightforward but a possiconstellations: Cancer, Sagittarius presented as ble explanation is discussed below. When viewing the sphere upside-down the centaur, Piscis Austrinus, and Navis. Between the identification of the most striking figure on the sphere, that of a scorpion, with the constellation 17 Künzl 2005, p. 82 and his figure 7.5. Scorpius is evident. Scorpius is always found 18 Thiele 1898, p. 171: B. Sauer stellt mir freundlichst folgende Notizen über einen Himmelsglobus, den er im south of the Equator [5], east of the autumnal November 1888 in Larissa vor dem Schulgebäude gesehen, zur equinoctial colure [1], with its body between the Verfügung: ‘Fragmentierte Himmelskugel von bläulichem (thessalischem ?) Marmor, Dm. 0,90 m. Eine Kugelcalotte von ca. 0,23 m boundaries of the zodiac [6 and 7]. Following the Höhe ist abgearbeitet und die ganze Kugel ausgehöhlt. Oberflache constellation Scorpius one sees the image of zum Teil gerauht (unvollendet?), zum Teil mit Gradnetz und Ekliptik Sagittarius presented as a centaur and located in versehen. Die Sternbilder, die ich erkennen kann, sind: Krebs, Schütze als Kentaur, Fisch, Schiff. Zwischen Fisch und Schiff ein l. Schenkel, the Tropic of Capricorn [4] as it should. Its dessen Fuss unter der Zonenlinie noch zum Vorschein kommt; auch hindlegs are cut by the winter solstitial colure [2]. scheint oben an der Seite eine Hand zu liegen. Dann, sehr verrieben, etwas, das einem laufenden Hunde gleicht u. s. w. Alles sehr verrieben, überdies war das Ganze früher mit Kalk bedeckt.’

54

19 Künzl 2000, p. 545.

2.2 The Larissa Globe

Fig. 2.3 The sphere found in Larissa, Greece, D-DAI-ATH-Tessalien 6. (Courtesy of the Deutsches Archäologisches Institut, Athens.)

One can also discern the legs of Ophiuchus above the back of Scorpius and the figure of Ara below its tail. Aratus tells of Ophiuchus that ‘he constantly, with a good firm stance, tramples with both feet the great monster’.20 The wavy image left of Ophiuchus’s feet belongs to the constellation Serpens. East of the winter solstitial colure [2] is Piscis Austrinus, the southern fish, with the oblique circle [8] passing through its tail. In Scheme 2.2 I have drawn a map of the southern hemisphere with all circles marked on the sphere for the epoch 128 bc and with the area visible on the globe highlighted.21 It shows that the constellations mentioned by Sauer (Navis and Canis Maior) are on the invisible side of the sphere in the photograph (Fig. 2.3). It also suggests that the vague image below the foreleg

Fig. 2.4 The sphere of Larisa with a number of circles marked: the autumnal equinoctial colure [1], the winter solstitial colure; [2], the ever-invisible circle[3], the Tropic of Capricorn [4], the Equator [5], the southern and northern boundary of the zodiac [6 and 7, respectively], an oblique circle [8].

20 Aratus (Kidd 1997), pp. 78–9, ll. 83–4. 21 I used Chris Marriott’s SkyMap Pro for this.

55

celestial cartography in antiquity

Scheme 2.2 Map of the southern hemisphere. The area visible on the Larisse globe is highlighted.

of Sagittarius may be the remains of Corona Australis, the southern crown. No straightforward interpretation seems to exist of the round figure close to the intersection of the winter solstitial colure [number 2 in Fig. 2.4] and the oblique circle [number 8 in Fig. 2.4]. Anyway, the non-zodiacal images show that the globe 56

does not belong to the group of ‘zodiac’ globes but must instead have been a rather complete celestial globe of which most constellations have by now faded away.22 22 Cuvigny 2004, p. 347, says that only the zodiac is depicted on the globe.

2.3 Kugel’s Globe How should one interpret the oblique circle [8] that seems to start at the autumnal equinox [1], passes through Ara, then cuts the winter solstitial colure [2] north of the ever-invisible circle [3] and next intersects the tail of the Piscis Austrinus? This circle presumably is Sauer’s ‘zone-line’. Künzl does not comment upon it.23 Since it intersects the Tropic of Capricorn [4] and the southern boundary of the zodiac [6], it is obviously not a circle parallel to the Equator or the ecliptic. It also cannot represent the Milky Way since this circle or band was known in Antiquity to pass in the southern hemisphere through Centaurus and Sagittarius. The available information makes it hard indeed to make an educated guess. If we may assume that the section of the circle seen on the Larissa sphere is part of a great circle, it could represent an oblique horizon circle. In the map of the southern hemisphere (Scheme 2.2) I have for the sake of discussion drawn the circle (dotted line) corresponding to the horizon circle of Larissa (assuming a geographical latitude of 40°). This circle passes through the equinoxes, between the tail of Scorpius and Ara and intersects Piscis Austrinus (PsA). Thus the oblique circle could be equivalent to the horizon of Larissa. If this interpretation is correct it is nevertheless a curious conclusion because first, the oblique circle does not touch the ever-invisible circle [3] as it should, and second, as a rule the horizon is not traced on a sphere, but is part of the mounting of a globe. Why one must not trace a local horizon on a mobile sphere is explicitly explained by Geminus: the horizon circle is by nature immobile and always in the same place. If it were traced on the sphere, then—by turning the sphere—it would participate in this motion and run the risk of passing through the zenith. As Geminus notes, this is unconceivable and contrary 23 Künzl 2000, p. 545.

57

to the theory of the sphere.24 This means that, if the oblique circle is indeed the horizon for Larissa, it represents a particular moment in time, namely when the vernal and autumnal equinox are in respectively the eastern and western horizon. This unusual configuration may have been inspired by the fact that the Larissa globe is very heavy and immobile. For such a globe in a fixed position it may have been tempting to draw the horizon circle on the sphere. Another query regarding the Larissa globe that is hard to answer is why a cone was cut out around the north pole instead of at the empty region around the south pole. This had possibly to do with the decorative function of the sphere because surely the empty region around the south pole would have been a better choice for hollowing the sphere. It is of interest to see that the Farnese globe also has a hollow cone at its north pole but again it is not clear why.

. KUGEL’S GLOBE In 2002 a description was published of a small silver globe with a diameter of 6.3 cm which was believed to have been found as one of three artefacts in the area of LakeVan, the largest lake in Turkey, located in the far east of the country.25 Two of the objects have been attributed to the second century bc, the small silver celestial globe is thought to be of a later date.26 In Figs 2.5–8 four sides of the globe are shown, with the equinoctial and solstitial colures on the left side in each image. A description of the globe is presented in the catalogue appended to this chapter. On the sphere, 48 figures are depicted of which 46 belong to the canonical set of classical constel24 Geminus (Aujac 1975),V.62, pp. 31–2; Evans and Berggren 2006, V.62, p. 159. 25 Kugel 2002, pp. 22–6. 26 Cuvigny 2004, p. 373.

celestial cartography in antiquity

2.5 side east of the vernal equinoctial colure

2.6 side east of the summer solstitial colure

2.7 side east of the autumnal equinoctial colure

2.8 side east of the winter solstitial colure

Figs 2.5–2.8 Kugel’s globe (Courtesy of Galerie J. Kugel, Paris.) See also Plate I.

lations and, as I shall discuss below, two represent unnamed groups of stars (Table 2.1).The constellations have been drawn on the globe with respect to a celestial grid consisting of the Equator, the tropics, the ever-visible and ever-invisible circles, 58

the equinoctial and solstitial colures, and the ecliptic. The points of intersection between the equinoctial colures and the Equator coincide with the points of intersection between the ecliptic and the Equator. The intersection of the eclip-

2.3 Kugel’s Globe tic and the summer solstitial colure is just below the Tropic of Cancer, and the intersection of the ecliptic and the winter solstitial colure is just above the Tropic of Capricorn.The circular hole of 35 mm diameter at the south pole seems to coincide with the ever-invisible circle.

Table 2.1 Constellations on antique globes Modern

Kugel

Mainz

Farnese

UMi UMa Dra Cep Boo CrB Her Lyr Cyg Cas Per Aur Oph Ser Sge Aql Del Peg And Tri Ari Tau Gem Cnc Leo Vir Lib Sco Sgr Cap Aqr Psc Cet Ori Eri Lep CMa CMi

+ + + + + + + + + + + + + + + + + + + + + + + + + + − + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + − + + + + + + − + + + + + + + + + + +

− [+] + + + + + + + + + + + + − + + + + − + + + + + + + + [+] [+] + + + + + + + +

Navis Hya Crt Crv Cen Lup Ara CrA PsA Anon I Anon II

+ + + + + + + + + + +

Totals

48

+ + + + + + + + + + + 47

+ + + + + + + + − − − 43

A very special feature of the celestial grid on this globe is that the ecliptic is drawn as a single line instead of as a zodiacal band, and that it is not divided into 12 zodiacal signs, that is, 12 sections of 30°. The absence of zodiacal signs reminds us of the characteristics of early globe making.27 Constructing globes in the descriptive tradition required knowledge of how the constellations were located with respect to the celestial grid. Only Eudoxus provides a complete set of data which allow the construction of a proper globe, and since Eudoxus did not divide the ecliptic into 12 sections of 30°, this would not have been the case on the first generation of globes. Another striking feature of the first generation of Greek globes is that—following Eudoxus—their colures pass through the middle of the constellations Aries, Cancer, the Claws, and Capricorn (see Chapter 1). On Kugel’s globe the colures pass west of their respective zodiacal constellations, and in this respect it agrees better with the Manilian epochal mode in keeping with an epoch of 128 bc (see Chapter 1).Yet, one finds a number features on the colures on Kugel’s globe which seem to echo the early Eudoxan tradition. The globe’s summer solstitial colure passes through Ursa Maior (Fig. 2.9); its autumnal colure through the 27 Dekker 2009.

59

celestial cartography in antiquity forefeet of Ursa Maior.29 Finally, Eudoxus fixes the position of Ursa Maior with respect to the zodiacal constellations:Gemini is placed below the head, Cancer below her middle, and Leo below the hindfeet of Ursa Maior. Opposite the head of Ursa Maior and obliquely above the feet of Gemini the shoulders of Auriga are said to lie. 30 Hipparchus questions the location of Ursa Maior on the summer solstitial colure and also finds fault with Gemini, Cancer, and Leo being placed below the head, the middle, and the hindfeet of Ursa Maior, respectively. Hipparchus’s criticisms are actually based on two presumptions. He assumed that Eudoxus in his descriptions refers to zodiacal signs instead of zodiacal constellations Fig. 2.9 Kugel’s globe: region around the north (see Section 1.4) and as a result did not realize that pole. (Courtesy of Galerie J. Kugel, Paris.) See also Eudoxus placed the colures in the middle of the Plate I. respective constellations Aries, Cancer, Libra, and Capricornus. His other assumption is that most northern hand and middle of Bootes (Fig. 2.9) in old astronomers, presumably including Eudoxus the north and through the right hand and the and Aratus, fixed the outline of Ursa Maior by the front knees of Centaurus in the south (Fig. 2.6). well-known seven stars, known as the Wagon or The globe’s winter solstitial colure passes through Wain, and not by the more extended shape used the neck of Cygnus, close to its right wing (Fig. by him. Thus according to Hipparchus the stars 2.8), and intersects the middle of Sagitta.All these α and β UMa are, respectively, in the head and features agree with Eudoxus’s description of the in the forefeet of Eudoxus’s Ursa Maior.31 Since colures (see Section 1.4). Hipparchus found the stars α and β UMa on the The position of Ursa Maior with respect to its meridians through Leo 1° and Leo 4°, respectively, surrounding constellations (see Fig. 2.9) on Kugel’s at the beginning of the sign of Leo, he concluded globe is also in line with Eudoxus: between the that these two stars are more than 30° removed bears is the tail of Draco, with its most extreme star from the astronomically correct colure at the at the end of the tail above the head of Ursa Maior. beginning of the sign of Cancer.This explains why She (Draco) makes a bend near the head of Ursa Hipparchus cannot comprehend why Eudoxus Minor and stretches below its feet. After making a second bend there (below the feet of Ursa Minor) 29 Hipparchus (Manitius 1894), I.2.1, pp. 112–13.The declishe raises her head again and brings it forwards.28 nation of the southernmost star in the head of Draco (γ Dra) Eudoxus reports further that the head of Draco is was in Eudoxus’s days around 53°, that is, 37° from the north on the ever-visible circle which passes below the pole and therefore was on the ever-visible circle for locations with geographical latitude around 37°. 30 Hipparchus (Manitius 1894), I.2.8, pp. 12–13 and I.5.1, pp. 44–5. For Auriga, see I.2.10, pp. 14–15. 31 Hipparchus (Manitius 1894), I.11.11, pp. 116–17.

28 Hipparchus (Manitius 1894), I.2.3, pp. 8–11.

60

2.3 Kugel’s Globe placed the middle of Ursa Maior on the summer solstitial colure. For the same reasons he also does not understand why Eudoxus placed Gemini below the forefeet and Cancer below the middle of Ursa Maior.32 If one adds to this picture the fact that Hipparchus found the star at the end of the tail of Ursa Maior (η UMa) to lie on the meridian through Lib 4°, one can see why Hipparchus concludes that Ursa Maior lies above the signs of Leo, Virgo, and the Claws. However, the discrepancy disappears if it is assumed that Eudoxus employed a much more extended image of Ursa Maior in which the position of the head of Ursa Maior is identified with the star ο UMa, as it is today. The image of Ursa Maior on Kugel’s globe surely refers to an extended image,such thatAuriga and Gemini are opposite and below its head.And Ursa Maior is located on the summer colure,albeit on one which does not pass through the middle of Cancer but just west of it. In other respects Kugel’s globe also betrays elements which belong to an early stage in the development of globe design. On Kugel’s globe Libra is presented by the Claws of Scorpius as it was in the time of Eudoxus and Aratus, and also in the days of later mathematical astronomers Hipparchus and Ptolemy. In the Epitome Scorpius is said to ‘extend over two twelfths of the zodiac because of its size. One part comprises the claws, the other the body and tail’.33 The question of whether the conversion of the Claws into a separate constellation Libra is a Greek or Roman development is difficult to answer. The Greek name of Libra appears in a passage attributed to Hipparchus, but the authorship of these particular lines has been questioned.34 Geminus seems to have been the 32 Hipparchus (Manitius 1894), I.5.2–5, pp. 44–5 and I.11.11, pp. 116–17. 33 Condos 1997, p. 187. 34 Hipparchus (Manitius 1894), III.1.5, p. 222.

61

first Greek writer to mention in his Introduction to the Phenomena the term Ζυγός (balance) which he uses 28 times against the term Χηλαί (claws) only 6 times.35 Ptolemy records an observation saying:‘In the 75th year of the Chaldaean calendar, Dios 14, at dawn, [Mercury] was half a cubit [ca 1°] above the [star] the southern scale [of Libra]’.36 So in the third century bc the expression ‘scale’ was in use by the astronomers who constructed that calendar. Le Boeuffle argues that the constellation Libra never really took hold in the Greek imagination, and there does seem to be a self-conscious ‘latinity’ associated with this name or image. In the Georgics, for example,Virgil speaks of the appearance of Libra as a portent of the divinization and catasterization of Octavius: ‘Or whether you make a new sign in the Zodiac, where amid the slow months a gap is revealed between Virgo and Scorpio (Already the burning Scorpion retracts his claws to leave you more than your share of heaven)’.37 Manilius appears to hesitate between recognizing Libra as a separate constellation and seeing it as part of Scorpius.38 Similarly Hyginus shifts between the two presentations. In Books II and III Hyginus speaks of Libra as the ‘prior pars’ or the ‘dimidia pars’ of Scorpius; but in Book IV he refers to the Claws and Libra as two constellations.39 This may indicate that the introduction of Libra as an independent constellation was a relatively recent development. Also notable on Kugel’s globe is the presentation of the cord connecting the two Pisces and 35 Le Boeuffle 1977, p. 171. For an edition with French translation, see Geminus (Aujac 1975), pp. 98–108. For an English translation, see Evans and Berggren 2006. 36 Toomer 1984, IX.7, p. 452. 37 Virgil (Rushton Fairclough 1916), Georgics I.32–35; the translation is from Day Lewis 1983, p. 52. See also Le Boeuffle 1977, p. 172. 38 Manilius (Goold 1977), I.611; II.305; IV.203, III.413; IV.216 and IV.547. 39 Le Boeuffle 1977, p. 172.

celestial cartography in antiquity emerging from the forefoot of Aries, west of the vernal colure (Fig. 2.5). Cuvigny calls this one of the globe’s significant features. Aratus tells in his poem about the cord connecting the two Pisces:

the vernal equinox. If true, one can understand why the knot was seen as the ‘celestial knot’.The precise location of α Psc in Antiquity is easily verified. In Eudoxus’s days (375 bc) the right ascension of α Psc was around 0° and its declination 10° ‘The tail-chains,by which the extremities of the Fishes south.Therefore α Psc was then indeed located on are held, both come together as they descend from the tail-parts, and behind the Monster’s back-fin move or close to the astronomically correct equinoctial jointly as they converge and terminate in a single star colure for 375 bc but it did not coincide with the equinox which lies on the Equator. In 128 bc α that lies close to the top of the Monster’s spine’.40 Psc was 3.5° east of the then astronomically corWhat the single star here referred to may be is not rect colure and 8.5° south of the Equator. The hard to guess. It is known as the ‘knot’ and can be location of the knot on Kugel’s globe does not identified with the star α Psc. In the descriptions agree with the positions quoted above because— of the constellation Pisces in the Epitome and in although south of the Equator—the knot lies Hyginus’s De Astronomia (Book III. 29) this knot is west of the vernal equinoctial colure passing in said to be at the forefoot of Aries.41 Actually, front of Aries. This apparent erroneous position Hyginus connects this description with the could well be a remnant of an old Eudoxan globe Aratean location of the knot ‘to the top of the on which the equinoctial colure passes through Monster’s spine’ by noting that Aries’s forefeet are the middle of Aries (see Section 1.4 and Scheme almost in contact with the head of Cetus.42 1.6), with the effect that the knot lies west of the Hyginus underlines the importance of the knot Eudoxan vernal colure. This could also explain by claiming that both Aratus and Cicero emphawhy the constellation Triangulum is west of the sized that the knot is not only connecting the globe’s equinoctial colure instead of on it, as Fishes but the whole sphere.43 The reason for this expected in 128 bc. is that the vernal equinoctial colure was believed In addition to the well-known Aratean conto pass through the knot at the forefeet of the stellations, there are on Kugel’s globe a number of Aries in the very spot where the colure intersects less known nameless stellar configurations shaped the Equator. In other words, the knot would mark as rings, located below the feet of Sagittarius, Lepus, and Aquarius. One of these rings is known 40 Aratus (Kidd 1997), p. 99. 41 See Condos 1997, pp. 43–47 or those in Charvet and today as Corona Australis, reported by Aratus as an Zucker 1998, pp. 97–99 and p. 217. Hyginus (Le Boeuffle 1983), unremarkable ring of stars beneath the forefeet of pp. 106–7. Hipparchus (Manitius 1894), III.3.9, pp. 254–55, and III.4,10, pp. 266–67, placed the bright star η Psc in the forefeet Sagittarius (Fig. 2.7).44 The other two nameless of Aries. In 128 bc this star was 4° above the Equator and about groups of stars represented by rings I have for the 5° west of the colure. 42 Hyginus (Le Boeuffle 1983), Book III.19, p. 100 in his sake of reference labelled Anonymous I and II. description of Aries and Book III.30, p. 108 in that of Cetus. One of the rings on Kugel’s globe (Anonymous 43 Hyginus (Le Boeuffle 1983), III, 29:‘Qui utrique [Aratus and I) lies below Lepus, just west of the rudder of Navis Cicero] volunt significare eum nodum non solum Piscium, sed etiam totius sphaerae esse. Quo enim loco circulus ab Arietis pede mesembrinos (Fig. 2.5). Its position agrees with the group of stars dicitur, qui meridiem significat, et quo loco is circulis mesembrinos coniun- that according to Eudoxus lie between Eridanus gitur et transit aequinoctialem circulum, in ipsa coniunctione circulorum nodus Piscium significatur’. Here Hyginus means by the meridian the circle indicating the middle of the day.

44 Aratus (Kidd 1997), lines 399–400, pp. 102–3.

62

2.3 Kugel’s Globe and the rudder of Navis, below Lepus, in a not a very great space.45 The same unnamed group of stars is described by Aratus as lying between Cetus (not Eridanus!) and the rudder of Navis, and beneath Lepus.46 Aratus seems to have overlooked Eridanus which lies between Cetus and Lepus.47 Hipparchus gives the position of the star labelled ‘the bright and unnamed one below the Hare’ in his list of stars that culminate when the last of the stars of the constellation Crater rises.48 This enables its identification with the one described in the Ptolemaic star catalogue as CMa 10e. Actually, all stars belonging to the unnamed group below Lepus have been described in Ptolemy’s catalogue as unformed stars below the constellation Canis Maior, that is, stars nos CMa 2e–11e. Thus although unnamed, the identification of the configuration ‘Anonymous I’ is not difficult. The stars CMa 2e–11e were shaped into a dove in 1592 by the Dutch cartographer Petrus Plancius, and they belong now to the constellation known as Columba.49 The other ring on Kugel’s globe (Anonymous II) lies below Aquarius, between Piscis Austrinus and the water streaming from Aquarius’s hand (Fig. 2.8).The identification of the stars belonging to this configuration is more difficult. It is likely the group of stars that Aratus describes as: ‘Other stars lying scattered below the Water-pourer hang in the sky between the celestial Monster and the Fish, but they are faint and nameless’.50 Aratus is the only author to mention this group, but we may presume that it was also recognized by Eudoxus. How to identify the group in the sky is complicated by the fact that, so Aratus continues: 45 Hipparchus (Manitius 1894), I.8.6–7, pp. 76–7. 46 Aratus (Kidd 1997), pp. 98–9, ll. 367–9. 47 Hipparchus (Manitius 1894), I.8.2–7, pp. 74–7, scriticizes Aratus’s description. 48 Hipparchus (Manitius 1894), p. 221. 49 Warner 1979, pp. 202–3. 50 Aratus (Kidd 1997), p. 101.

‘Close to them, like a light spray of water being sprinkled this way and that from the right hand of the illustrious Water-pourer, some pale and feeble stars go round.Among them go two rather brighter stars, not so very far apart nor yet very close, one beautiful and bright star beneath the two feet of the Waterpourer, the other below the dark Monster’s tail’.51

In Scheme 2.3 the area cornered by Aquarius, Cetus, and Piscis Austrinus is reproduced, using a modern computer program.52 For the sake of discussion a number of areas are highlighted and a number of stars labelled. Looking at this map one has the feeling that actually a number of definitions of the stream of water are possible. One scenario is that Aqua, departing from λ Aqr, the star below the right hand of Aquarius, streams south-east and ends close to β Cet without turning in the direction of α PsA.This stream would pass east of the stars Aqr 36–41, located in the highlighted rectangle in Scheme 2.3, which then could represent indeed the stars of Anonymous II. Such a configuration is in line with that engraved on the silver globe on which Aqua streams from Aquarius’s hand, passes east of the ring and does not end in the mouth of Pisces Austrinus.This course has not been considered in the literature because most discussions have centred on the ‘two rather brighter stars’ mentioned by Aratus. Most scholars agree that ‘the beautiful and bright star beneath the two feet of the Waterpourer’ must be the bright star in the mouth of Pisces Austrinus (α PsA).53 Kidd and Martin consider the star β Cet the most likely candidate for the bright star below the tail of Cetus (see Scheme 2.3).54 Another suggestion was made by Soubiran 51 Aratus (Kidd 1997), p. 101. 52 I used Chris Marriott’s SkyMap Pro. 53 Kidd and Martin suggest that this must be α PsA, see Aratus (Kidd 1997), p. 325 and Aratus (Martin 1998), p. 313. 54 Aratus (Kidd 1997), p. 325 and Aratus (Martin 1998), p. 313.

63

celestial cartography in antiquity

Scheme 2.3 A modern map of the region around Aqua.

who proposed α Scl for the star below Cetus.55 This star is, however, not particularly bright. Both stars are more than 30° distant from the mouth of Pisces Austrinus (α PsA). If this second star is to be connected to the stream through ‘sprinkled drops of water’ β Cet seems to be preferred above α Scl. The identification of Aratus’s two stars with α PsA and β Cet (or α Scl) is not without problems. It implies that Aqua would stream first all the way to the south-east and then, after reaching β Cet, would turn west to the mouth of Pisces Austrinus (α PsA). This latter western course of Aqua would then pass through the stars Aqr 36–41, the group of stars best suited to fit the

configuration of Anonymous II. Martin suggests, however, that the stars of Anonymous II belong to what nowadays is the constellation Sculptor, but rather than being cornered by Aquarius, Piscis Austrinus, and Cetus, the stars of Sculptor lie east of Piscis Austrinus, and below the stream of Aqua (see Scheme 2.3). The uncertainty of the two bright stars mentioned by Aratus may well be the reason that the author of the Epitome dropped the requirement that one of the bright stars should be below Cetus. In the Epitome, where Aquarius is identified with Ganymede pouring liquid from a jar, Aqua is said to be swallowed by the great fish (Piscis Austrinus).56 Hyginus went 56 Condos 1997, p. 29; Eratosthenes (Pàmias and Geus 2007), pp. 148–9.

55 Aratus (Martin 1998), p. 313.

64

2.3 Kugel’s Globe one step further and identified in Book III.28 the two bright stars as being in the beginning and end of the flow of water.57 Thus, if Hyginus is correct, the other bright star would be λ Aqr. The course of Aqua, departing from λ Aqr, streaming south-east, and below Aquarius changing direction and turning south-west in the direction of α PsA, is encountered in the descriptions of Hipparchus and Ptolemy (Scheme 2.3). This possibility may represent a later development in which the course of Aqua is redirected and the nameless groups of stars below the feet of Aquarius, Aqr 36–41, is completely usurped (see Scheme 2.3). If so, the configuration on Kugel’s globe could present a hitherto unknown early version of Aqua. A proper assessment of the early shapes of constellations is not always possible. The configuration of Aqua on Kugel’s globe shows that it should not be taken for granted that Aqua followed the pattern encountered in the later star catalogues in the mathematical tradition.Another equally problematic watery constellation is Eridanus, which on Kugel’s globe is seen to depart from the western foot of Orion and meanders along the Tropic of Capricorn in the direction of Cetus. It turns southwards in front of Cetus and ends below it, close to the ever-invisible circle, just east of the vernal equinoctial colure. In Scheme 2.4 the region south of Cetus and Orion is reproduced, using again a modern computer program. For the sake of discussion a number of areas are highlighted and a number of stars labelled. Also the Tropic of Capricorn, the ever-invisible circle for a geographical latitude of 36º, and the vernal equinoctial colure are drawn. In Eudoxus’s days the spring colure passed through the brightest star in Aries (α Ari), the 57 Hyginus (Le Boeuffle 1983), p. 106.

65

Knot of Pisces (α Psc) and also through the star α Eri, not known in ancient times because it was south of the ever-invisible circle. The course of Eridanus on Kugel’s globe agrees well with the description of Eudoxus, who says that 1) it parts from the left foot of Orion (β Ori), that 2) its bend is on theTropic of Capricorn, that 3) it is below Cetus, and that 4) the extreme parts of Eridanus are on the ever-invisible circle.58 Aratus description, though less detailed, agrees with this.59 Yet, generally speaking, the descriptions of this constellation in the literature remain rather vague, in the sense that Eridanus’s course is not clear after it reaches Cetus. In the Epitome the river is also departing from the left foot of Orion (β Ori) but it is believed to have three bends between its source and its effluence. It adds that the star Canopus (α Car), which touches the steering-oars of Navis, is below the river.60 Hyginus also refers in Book III.31 to three bends. Hyginus is more specific for he says that Eridanus,after departing from the left foot of Orion (β Ori), reaches Cetus, then turns its way round towards the feet of Lepus and continues straight on to the ever-invisible circle.The image is divided by theTropic of Capricorn at the place where it almost touches Cetus, presumably in η Eri or π Cet. Canopus is not mentioned by Hyginus but his description of the stellar configuration is in the main the same as that described in the Epitome. Martin interprets Eridanus as consisting of three parts, the first from Orion to Cetus, the second from Cetus to Lepus, and the third part 58 Hipparchus (Manitius 1894) I.8.6–7, pp. 76–7 (foot of Orion and below Cetus); I.2.20, pp. 22–3 and I.10.17, pp. 106–7 (on Tropic of Capricorn); I.11.6, pp. 114–15 (ever-invisible circle). 59 Aratus (Kidd 1997), pp. 98–9, ll. 357–66. 60 Condos 1997, pp. 105–7 or Charvet and Zucker 1998, pp. 169–71 and 221; Eratosthenes (Pàmias and Geus 2007), pp. 186–7.

celestial cartography in antiquity

Scheme 2.4 A modern map of the region around Eridanus.

moving in the same direction as the second, from Lepus to the ever-invisible circle and (above) Canopus, presumably passing through the group identified here as Anonymous I and centred on α Col. Martin’s interpretation implies that stars involved in the third part of Eridanus include the Aratean group Anonymous I.This could well be correct because this group is not part of the uranography described in the Epitome and by Hyginus. However, Martin is wrong in his assessment when he says that this would also agree

with the Eudoxan uranography. The course of the Eudoxan river ends close to the Eudoxan equinoctial colure, on the ever-visible circle (compare Scheme 2.4). Since the Eudoxan vernal colure is about 10° east of the astronomically correct vernal colure drawn in Scheme 2.4, the Eudoxan Eridanus probably ended in the star θ Eri, and therefore not above Canopus as said in the Epitome. Therefore, after reaching Cetus (η Eri or π Cet) this Eudoxan river may have streamed first east and then turned west in the 66

2.3 Kugel’s Globe direction of θ Eri. If so, Eudoxus would have been the first to present Eridanus with a second turn, presumably close to υ1 and υ2 Eri, thus moving away from Canopus and towards the bright star θ Eri.61 An alternative course for the Eudoxan river is that after reaching Cetus (η Eri or π Cet) it turned more or less south in the direction of the southern stars α For and θ Eri and never came near the stars υ1 and υ2 Eri. If this latter possibility is correct, and the configuration on Kugel’s globe would suggest this, one may conclude that the Eudoxan river differed not only from that described in the Epitome and Hyginus but also by later astronomers such as Hipparchus and Ptolemy. Most (human) constellations on Kugel’s globe (Figs 2.5–8) are the mirror image of those seen in the sky, with the result that on this globe their left and right characteristics as defined by Hipparchus’s rule have been exchanged. Thus the right foot of the Kneeler is close to the head of Draco, the right hand of Bootes is north of the ever-visible circle, and Spica is on Virgo’s right side on the Equator. Exceptions are Centaurus and perhaps Sagittarius. This makes it difficult, not to say impossible, to use this globe as a teaching aid for identifying the stars in the sky. However, globes in the descriptive tradition, as the present one, served in the first place for teaching the relative positions of the constellations. For reading Aratus’s Phaenomena the globe is indeed well suited. Two figures on Kugel’s globe have a peculiar orientation. Cancer’s claws are on the west side instead of directed towards Leo, and Orion appears to be face on with a staff in his right hand and a kind of cloth extending over his left shoulder. One would expect to see Cancer and Orion in the sky in this way, never on a globe! The 61 Aratus (Martin 1998), p. 299. Martin claims that Hipparchus was the first to introduce a second bend.

67

image of Cancer as seen in the sky is also found on the majority of the hemispheres copied from antique globes and surviving in medieval manuscripts (Chapter 3). It must have been a common feature on such globes.The peculiar orientation of Orion on Kugel’s globe becomes clear if it is, for example, compared with the drawings in al-Ṣūf ī’s Book of the Constellations (Oxford, The Bodleian Library, MS Marsh 144, pp. 325–26) shown in Fig. 4.8, in which Orion as seen on the sphere is presented as the mirror image of Orion as seen in the sky.The image of Orion on Kugel’s globe with the staff in the right hand compares best with al-Ṣūfī’s drawing of Orion as seen in the sky and not with that of Orion as seen on the sphere with the staff in the left hand.The images of Cancer and Orion must have been borrowed either from a record of individual constellations showing them as seen in the sky, or from a map presenting the constellations in sky-view such as discussed in Chapter 3. Unfortunately, no copy of either is known from Antiquity. Most of the constellations are naked excepting Cepheus, Cassiopeia, Andromeda, Virgo, and Orion. Further, most of the constellations are without attributes. Andromeda is without chains, Gemini are without club or lyre, and Virgo and Pegasus have no wings. Hercules is a kneeling figure holding a ball in his right hand without a club or lion’s skin. Mythology was apparently not of great concern to the maker of this globe. Leaving aside the ball, an attribute which is completely unknown in the textual history of constellation design, one may conclude that the shape of Hercules is part of the earlier tradition one connects with Eudoxus and Aratus rather than with the Epitome and Hyginus. In the early days of Eudoxus and Aratus, and also in the time of later mathematical astronomers Hipparchus and Ptolemy, the constellation was known as the

celestial cartography in antiquity Kneeler, or Engonasin.The image of Hercules on Kugel’s globe points to an iconographic tradition preceding the transition to the more usual figure of Hercules with a club and a lion’s skin seen on the Mainz globe discussed below. A notable inaccuracy on Kugel’s globe is that the head of Hercules is east of the head of Ophiuchus, whereas it should be west of it. All Eudoxus says about this is that the head of Hercules is next to that of Ophiuchus, but he does not specify their order in an eastern or western direction.62 This may well be the reason why this error occurs often in early celestial cartography, the more so because the body of Hercules is east of that of Ophiuchus. Aratus describes Ophiuchus as standing upright and trampling Scorpius with both his feet—one placed on the beast’s eye and another on his chest.63 He deviates here from Eudoxus who says that the right foot is above the body of Scorpius.64 On Kugel’s globe Ophiuchus stands with only his western foot on Scorpius, a position agreeing with Eudoxus. However, the attitude of Ophiuchus does not in every respect concur with Eudoxus, who says that the Tropic of Cancer passes through the head of Ophiuchus and the Equator intersects his knees.65 In two cases, Perseus and Auriga, the images are influenced by mythological associations. Perseus is drawn with Medusa’s head in his southern hand and a hooked sword in his northern hand and he has small wings on his head which recall Hermes. More unique is the carriage of Auriga which, according to Cuvigny, is Greek rather than Roman.66 The same is said of the stylis in Navis. This would support the 62 Hipparchus (Manitius 1894), I.2.7, pp. 11–12. 63 Aratus (Kidd 1997), pp. 78–9, ll. 84–7. 64 Hipparchus (Manitius 1894), I.4.15, pp. 40–1. 65 Hipparchus (Manitius 1894), I.2.18, pp. 20–21; I.10.14, pp.104–5, and I.10.22, pp. 110–11. 66 Cuvigny 2004, p. 360.

68

impression gained above of an early Greek background of Kugel’s globe, a clear trend which seems to be upset by the throne of Cassiopeia. Cassiopeia is presented on Kugel’s globe as a female figure with outstretched arms, in a sitting attitude (see Fig. 2.9). She is parallel to the Tropic of Cancer such that the lower part of her body is turned towards the east and the upper part to the west, where the spring equinoctial colure grazes her feet. This orientation is unusual. More often Cassiopeia is shown with her head south and her feet north, close to or on the ever-visible circle.67 Another curious element is the ring consisting of two concentric circles north of Cassiopeia’s legs and south of the ever-visible circle. Cuvigny argued that this ring could represent Cassiopeia’s chair since such a ring-like seat is seen on certain coins of the Roman empire.68 Anyway, no straightforward alternative explanation is at hand if the ring is not meant to represent Cassiopeia’s chair.Another explanation proposed by Cuvigny is that the ring is a mistaken extra Corona Borealis. Rings on this globe often represent anonymous groups of stars and therefore the question arises whether this ring could also represents an unnamed group of faint stars. north of the feet of Cassiopeia there is indeed such a group with a ring-like appearance which includes four stars with an apparent magnitude brighter than the fifth magnitude: 50 Cas (3.94m), 48 Cas (4.63m), ω Cas (4.96m), and ψ Cas (4.73m). Given that the earliest record of these stars is from the sixteenth century by the astronomer Tycho Brahe it is very unlikely that this group of faint stars is meant here. Whatever the explanation, the presentation of Cassiopeia is unique to this globe. 67 Aratus (Kidd 1997), pp. 120–1, ll. 655–6. Hipparchus (Manitius 1894) I.11.1 and 4, pp.112–15. 68 Cuvigny 2004, p. 357.

2.4 The Mainz Globe In her study Cuvigny noted also some correspondences with descriptions in Hyginus’s De Astronomia.69 However, the globe’s uranography includes many features, such as the course of Eridanus and the presentation of nameless groups, that are not part of Hyginus’s description of the celestial sphere. Taking all the features together one cannot help feeling that here is a globe following a tradition stemming from the oldest Eudoxan branch in globe making, but adapted to corrected views on the relative location of the zodiacal constellations with respect to the colures. This means that it was made either in the first century bc or, if Cuvigny’s dating to the second or third century ad is correct, that it was made after an early Greek model. It adds greatly to the present knowledge of early globe making and shows that the making of mirror-image

globes was not the prerogative of Islamic globe makers but has its roots in Greek globe making.

. THE MAINZ GLOBE It is not known where precisely the antique brass globe with a diameter of about 11 cm in the Römisch-Germanisches Zentralmuseum in Mainz was found, but it is believed that it came from western Asia Minor.70 In Figs 2.10–13 four sides of the globes are shown, centred more or less on the equinoctial and solstitial colures. A description of the globe is presented in the catalogue appended to this chapter. Details of the construction of the globe, especially the small square opening (8 × 8 mm) at the north pole and the circular hole (39 mm in diameter) at the south pole (see Fig. 2.14), make

Fig. 2.10 a–b Mainz globe: part centred on the vernal equinoctial colure. (Courtesy of the Römisch-Germanisches Zentralmuseum, Mainz; Photo: RGZM/ E. Künzl-drawing RGZM/J. Ribbeck.)

69 Cuvigny 2004, p. 373.

70 Künzl 2000, p. 501.

69

celestial cartography in antiquity

Fig. 2.11 a–b Mainz globe: part centred on the summer solstitial colure. (Courtesy of the Römisch-Germanisches Zentralmuseum, Mainz; Photo: RGZM/E. Künzl-drawing RGZM/J. Ribbeck.)

Fig. 2.12 a–b Mainz globe: part centred on the autumnal equinoctial colure. (Courtesy of the Römisch-Germanisches Zentralmuseum, Mainz; Photo: RGZM/E. Künzl-drawing RGZM/J. Ribbeck.)

70

2.4 The Mainz Globe

Fig. 2.13 a–b Mainz globe: part centred on the winter solstitial colure. (Courtesy of the Römisch-Germanisches Zentralmuseum, Mainz; Photo: RGZM/E. Künzl-drawing RGZM/J. Ribbeck.)

it likely that the globe was once a decorative part fixed on top of an obelisk serving as a gnomon. As an example Künzl recalls the Solarium Augustus that stood on the Campo Marzio in Rome. Another well-known example is the obelisk brought to Rome by Caligula in ad 37 for the Vatican Circus and relocated by Pope SixtusV in 1586.71 The ancient metal balls on top of such obelisks, which have been preserved, show no sign of decoration.72 The Mainz globe probably served a smaller construction in a private house, so that one could see the decoration on the sphere. On the Mainz globe 47 figures are depicted of which 45 belong to the canonical set of classical constellations (Table 2.1). In addition there are two figures representing unnamed groups of stars, Anonymous I and II, which are also depicted on 71 Exhibition catalogue 1999, No. 124, p. 469 72 These balls are now in the Palazzo dei Conservatori Museum in Rome, see Künzl 2000, Plate 77, 3 and 4.

71

Kugel’s globe. The constellations have been drawn on the globe with respect to a celestial grid consisting of the Equator, the tropics, vague traces of the ever-visible circle and perhaps also of the ever-invisible circle, the equinoctial and solstitial colures, and the zodiacal band with in the middle the ecliptic.These circles are incomplete, which may be the result of wear. Generally speaking the circles have not been very accurately drawn. The summer and winter tropics should be tangential to the ecliptic in the corresponding solstices, that is, the intersections of the ecliptic and the solstitial colures, but on the Mainz globe the tropics pass just above and below the ecliptic (see Figs 2.11 and 2.13). Also the Equator, the ecliptic, and the equinoctial colures do not pass through one and the same point as they should (see Scheme 2.5). In a correctly drawn grid the points A, B, and C marked in Scheme 2.5 should coincide, and so should the points D, E, and F. On the Mainz globe the

celestial cartography in antiquity

Fig. 2.14 a–b Mainz globe: region around the north and south pole. (Courtesy of the Römisch-Germanisches Zentralmuseum, Mainz; Photo: RGZM/Iserhardt-drawing RGZM/J. Ribbeck.)

72

2.4 The Mainz Globe

Scheme 2.5 Displaced equinoxes on the Mainz globe.

intersections of the ecliptic with the Equator (labelled B and F in Scheme 2.5) are east of the corresponding intersections of the colures with the Equator (labelled A and D in Scheme 2.5). Künzl states that on the Farnese globe the points of intersection between the Equator and the ecliptic are also shifted to the east as on the Mainz globe but, as we shall discuss in the next section, on the Farnese globe the intersections of the ecliptic and the Equator are west of the intersections of the Equator and the colures, not east.73 On decorative globes such inaccuracies are not exceptional. Clearly outlined on the Mainz globe is the zodiacal band, which is bounded by two circles parallel to the ecliptic. The band has a width of about 13.5° and seems to be divided into 12 roughly equal parts, but the boundaries between

the signs of Aries and Taurus, and between Libra and Scorpius are hard to perceive. Each of the zodiacal constellations is confined to one sign in longitude, with the exception of Scorpius which extends over two signs of the zodiac. One part comprises the claws, the other the body and tail.74 In latitude the constellations extend as a rule beyond the boundaries of the band. The extension of Scorpius suggests that Libra is here depicted as the Claws of Scorpius. Künzl has argued that the two circlets at the feet of Virgo in front of the Claws (see Fig. 2.12) represent Libra.75 Although one could imagine these circlets as being part of a pair of scales, their location questions such an interpretation. One would expect them to coincide with the two stars marked in the Claws of Scorpius, roughly in the middle of the 74 Condos 1997, p. 187. 75 Künzl 2000, p. 513.

73 Künzl 2000, p. 528.

73

celestial cartography in antiquity

Fig. 2.15 Overview of the mapping of the Mainz globe. (Courtesy of the Römisch-Germanisches Zentralmuseum, Mainz; Drawing RGZM/J. Ribbeck.)

zodiacal sign east of the equinoctial colure. If the two circlets at the feet of Virgo are indeed part of a pair of scales, they may instead belong toVirgo in her role as Justitia, a mythological interpretation already mentioned by Aratus, and seen for example in the medieval hemisphere in Vat gr. 1086 (see Fig. 3.10). A constellation definitely missing on the Mainz globe is Triangulum. Although part of the Aratean uranography this tiny constellation is easily overlooked and is often missing on most of the hemispheres and planispheres described in Chapter 3. The representations of unnamed configurations of stars on the Mainz globe confirms that the stars of Corona Australis and the unnamed groups of stars Anonymous I and II were regular inhabitants of the constellation sky. On the Mainz globe and Kugel’s the image of Corona Borealis apparently provided the pictorial code for presenting unnamed groups, in the first place for those of Corona Australis, which in turn provided the model for presenting the groups 74

unnamed Anonymous I and II. Indeed, on the Mainz globe Corona Borealis and all unnamed groups consist of a series of circlets placed in a ring (see Fig. 2.15), on Kugel’s globe all configurations are presented by two concentric circles forming a ring. On the Mainz globe more attention is given to mythology than on Kugel’s globe in drawing constellation images. Pegasus is presented as half a horse with wings (see Fig. 2.10) and Virgo is a female figure with wings facing the viewer (see Fig. 2.12). She holds an ear of wheat in her raised right hand. Hercules is not the Kneeler described by Aratus, Hipparchus, and Ptolemy. He holds a skin or piece of cloth or something like it over his outstretched left lower arm and a club in his outstretched right hand behind him (see Fig. 2.13). The transition of the Kneeler into Hercules is a Greek development. The Epitome seems to be the earliest extant source describing the Kneeler as Hercules, that is a figure with a club and a lion’s skin. It is not precisely known why

2.4 The Mainz Globe the figure of the Kneeler was conflated with the hero Hercules, but from a mythological point of view the kneeling figure cannot have been really satisfactory. The fact that the tip of his foot is placed above the head of Draco may have inspired the connection between the Kneeler and the Greek Hercules. Anyway, the Mainz globe has the oldest image of the mythological Hercules in an astronomical context.Also typical for the iconography devoted to myth is that Canis Maior has a halo and that the stern of Navis is shaped as a dog’s head with a collar, the mast is at the cutoff of the ship and on deck are a small house and four shields. Another case in point is, for example, Pisces (Fig. 2.10). Its fishes are connected by their mouth to a cord, a presentation that is not dictated by the stars by which pattern the cords would be attached to the tails and connected in a knot as they are on Kugel’s globe. Yet the orientation of the fishes themselves is fairly good. Fishes connected by their mouth to a cord is the dominant view in diagrams of the zodiac and in constellation cycles in medieval manuscripts belonging to the descriptive tradition.76 Next to its emphasis of mythology, the Mainz globe has stars marked on its surface in the shape of circlets, sometimes with a dot in the centre. There are several possibilities to explain the background of these stars.

3. A third possibility is that the locations of the stars derive ultimately through a globe from the mathematical tradition.

1. The stars could have been added to the globe more or less at random as is the case with the stars on the Berlin fragment. 2. Another possibility is that the stars have been placed in keeping with a star catalogue in the descriptive tradition, as for example included in the Epitome and Hyginus’s De Astronomia.

There seems to be enough structure in the stars marked on the Mainz globe to waive the first at-random thesis aside. In Ursa Minor (see Fig. 2.14) seven stars are marked in the body, in keeping with both the descriptive and the mathematical tradition.77 These two traditions differ in their approach to mapping stars by the order in which the stars and their constellations are marked on the sphere. In the descriptive tradition, a globe maker would, say, first draw the image of Orion on the globe, and then place Orion’s stars in keeping with the positions listed in the descriptive catalogue. In contrast, in the mathematical tradition a globe maker would first mark Orion’s stars on the sphere using the mathematical coordinates, and then would draw the image of Orion such that the stars are indeed in the locations corresponding to the descriptive part of the mathematical catalogue. This latter method is of course the more reliable. A close look at the schematic picture of the Mainz globe (Fig. 2.15) shows that the positions of many constellations deviate considerably from their expected locations. For example, on the Mainz globe Canis Minor is placed below the Equator whereas its two stars (α and β CMi) lie instead above it. Canis Maior is located east of the summer solstitial colure but in the second century ad Sirius, the brightest star in Canis Maior (α CMa), was actually 10° west of this colure. Navis should be below the head and Centaurus below the tail of Hydra but since Canis Maior is shifted eastwards, Navis is now

76 See for example the image of Pisces in the zodiac in Rome, Biblioteca ApostolicaVaticana,Vat. gr. 1291, fol. 9, reproduced in Butzer and Lohrmann 1993, following p. 203.

77 Künzl 2000, p. 519, figure 12 no. 30, presents Ursa Minor with nine stars but two of these stars in the tail belong to the feet of Cepheus.

75

celestial cartography in antiquity below the tail of Hydra and Centaurus east of the autumnal equinoctial colure. On the Mainz globe Ophiuchus’s head is on the winter solstitial colure which suggests that the right ascension of the star marking the head is 270°, which is 30° in excess of the value derived from the coordinates in the Ptolemaic star catalogue. Ophiuchus’s head is west of that of Hercules, as it is on Kugel’s globe and often seen in maps of the descriptive tradition (see Chapter 3) but not in the mathematical tradition (see Chapters 4 and 5) since the star marking Hercules’s head (α Her) lies west of the one marking Ophiuchus’s head (α Oph). The winter solstitial colure should pass between Lyra and Cygnus, but it passes west of both since these two constellations are also out of place by about 30°.A last example is the fact that the vernal equinoctial colure passes through the shoulder instead of the feet of Andromeda. These inaccuracies seem to show in the first place that the Mainz globe is a copy of a copy, and so on, and that in this process the stars were copied rather casually. This makes it difficult to decide from which tradition, the descriptive or a mathematical one, the stars on the Mainz globe derive. In both the descriptive and the mathematical traditions a few stars are mentioned as being shared by two constellations. Andromeda and Pegasus shared one which may be represented on the Mainz globe by the circlet between them. There is however no trace of the star shared by Taurus and Auriga, or of the one shared by Bootes and Hercules. Künzl has drawn attention to a number of special circlets or stars. Two of them, at the feet of Virgo, have been discussed above for their possible relation to Libra. He interprets the circlet above the tail of Leo as representing Coma Berenice. In the Epitome this group of stars is described as consisting of seven faint stars being above Leo in a triangle near the 76

tail.78 This description does not seem to fit the circlet marked on the Mainz globe.As discussed in Chapter 3, Berenice’s lock of hair, introduced around 250 bc by Conon, is well attested in literary sources, but there are no images known of it before the sixteenth century. In all cases that the lock of Berenice is mentioned in connection with medieval illustrations, the image of an ivy leaf is meant.79 Therefore, if the circlet is connected with the group of stars above the tail of Leo—and it needs some imagination to think so—it would more likely represent the ivy leaf. However, the odds are that the circlet represents the star which, according to both descriptive and mathematical traditions, is located at the end of Leo’s tail. The most outstanding feature of the Mainz globe is the Milky Way, here outlined as a broad band rather than as the great circle seen on the Berlin fragment described above and on the planispheres discussed in Chapter 3. In the early literature on the Milky Way various theories were proposed to explain its physical nature.80 In the Aratean context no such explanations are discussed. Only the fact that it is a great circle in contrast to, say, the tropics, is mentioned. Early sources provide no information concerning its position with respect to the stars. Aratus offers nothing that could be used to plot the Milky Way on a map or globe. The information in Geminus’s Introduction is not a great help in this respect either. Geminus confirmed that the Milky Way is a great circle in the sky and added: ‘The Milky Way also is an oblique circle.This circle, rather great in width, is inclined to the tropic 78 Robert 1878, p. 98; Condos 1997, p 125; Charvet and Zucker 1998, p. 73; Eratosthenes (Pàmias and Geus 2007), p. 98. 79 The earliest picture of the lock of Berenice is on a celestial globe by Vopel of 1536, see Dekker 2010a, pp. 173–5. 80 Evans 1998, pp. 94–5.

2.4 The Mainz Globe circle. It is composed of a cloud-like mass of small parts and is the only [circle] in the cosmos that is visible.The width of this circle is not well defined; rather, it is wider in certain parts and narrower in others. For this reasons, the Milky Way is not inscribed on most spheres.’81

Obviously a pictorial source is behind this description, considering its details. A globe would be a likely candidate if only because, as discussed in Chapter 1, the colures described by Manilius seem to correspond to Hipparchus’s epoch, another globe-related feature of Manilius’s One can understand that the varying width of description of the celestial sphere. However it is the circle would have been a handicap in plot- not possible to tell from Manilius’s account of ting the Milky Way on maps and globes. It cer- the Milky Way whether its finite width is taken tainly does not make it easier to describe its into account. position with respect to the constellations. Yet, The most detailed ancient description of the this has not prevented a few authors describing stars marking the Milky Way is by Ptolemy in his the Milky Way circle in some detail in terms of Almagest. Ptolemy distinguished between the constellations. The earliest and most impressive main belt ‘through which the great circle drawn is that by Manilius in his Astronomica: approximately along the middle of it would pass’ and a bifurcated part consisting of two forks.83 ‘The other circle [Milky Way] is placed crosswise to it [the ecliptic]. It approaches the Bears but bends One of these forks starts from Cygnus in the back its outline a little way from the circle of the north through the bird’s head up to the right north; passing through the constellation of the shoulder of Ophiuchus and the other from Ara inverted Cassiepia it thence descends by a slanting in the south, passing through the first three segpath to reach the Swan; it cuts the summer bound- ments of the tail of Scorpius, the right foot and ary [Tropic of Cancer], the supine Eagle, the circle right hand of Ophiuchus, with a gap between of equal day and night [Equator], and the zone the two forks above the right hand of Ophiuchus. which carries the horses of the Sun [zodiacal band], These bifurcations are refinements which are passing between the blazing tail of the Scorpion and the tip of the Archer’s left hand and arrow; from not mentioned in the descriptions of prethere it winds its tortuous trail through the legs and Ptolemaic writers. Leaving the bifurcations aside hoofs of the southern Centaur, and begins once one finds that the Milky Way belt according to more to climb the sky; it cuts the ship of the Greeks Ptolemy passes through the following constellathrough the top of the stern-post, heaven’s middle tions: Cassiopeia, the right hand and foot of circle [Equator], and the Twins through the bottom Perseus, Auriga, the legs of Gemini, the staff of of their sign; then it enters the Charioteer and, mak- Orion, the ears of Canis Maior, the stern of Navis, ing for Cassiepia, whence it set out, passes over the the legs of Centaurus, Ara, the tail of Scorpius, figure of Perseus; and it completes in Cassiepia the the right front hock of Sagittarius, the hand circuit which it began with her.At two points it cuts the three middle circles and the circle which carries and the arrow of Sagittarius, Aquila, the souththe signs and is as often cleft itself. One need not ern wing of Cygnus, the tiara of Cepheus.84 search to find it: of its own accord it strikes the eyes; it tells of itself unasked, and compels attention.’82 83 Toomer 1984, pp. 400–4, esp. p. 400. 84 The account by Ptolemy has been summarized to mark only its main features in order to make a comparison with other lists possible.

81 Geminus (Aujac 1975),V.68–69, p. 33.The English translation is from Evans 1998, p. 93. 82 Manilius (Goold 1977), pp. 58–61.

77

celestial cartography in antiquity Table 2.2 Milky Way features 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Cassiopeia Perseus (right side) Auriga the legs of Gemini the Twins, through the bottom of their sign the staff of Orion the feet of Canis Minor the ears of Canis Maior grazes the first bend of Hydra the tip of the mast of Navis the stern of Navis the legs of Centaurus Ara touches Lupus the tail of Scorpio the right front hock of Sagittarius the hand and the arrow of Sagittarius Aquila Sagitta Cygnus the tiara of Cepheus

Pto Pto Pto Pto

Man Man Man

HIII HIV HIV HIV

HIII

HIV

HIII

MaC

Pli

M M M M

Man Pto

M Pli

Pto

M M M M M M M M

HIV

Totals

Pto Pto Pto

Man Man

HIV

Pto Pto Pto Pto Pto Pto Pto

Man

HIV

Man Man

HIV HIV

Man

HIV

10

10

16

HIII

MaC HIII HIII

6

2

Pli

M M M M M

3

18

Pto: Ptolemy; Man: Manilius; HIV: Hyginus Book IV; HIII: Hyginus Book III; MaC: Martianus Capella; Pli: Pliny; M: Mainz globe

When Manilius’s description is compared to that of Ptolemy (see Table 2.2), one finds that nine of the ten features mentioned by Manilius are part of Ptolemy’s description. Often Ptolemy provides more detail. In this comparison I have translated Manilius’s phrase ‘between the blazing tail of the Scorpion and the tip of the Archer’s left hand and arrow’ as touching both the tail and the arrow. Only where Manilius tells his readers that the Milky Way is passing through the bottom of the sign of Gemini, have I marked this as being distinct from other descriptions that let the Milky Way pass through the (lower) legs of Gemini. However that may be, Manilius represents a fair description of the Milky Way, which suggests that he had access to a fairly reliable pictorial source. Apparently at the begin78

ning of the first century globes with the Milky Way drawn on it already existed. It is impossible to tell whether they were then a novelty or already part of a tradition stemming from previous centuries. Descriptions of the Milky Way are also found in Book III and IV of Hyginus’s De Astronomia (see Table 2.2). Five features of Book IV are not mentioned in Book III and, in turn, one feature listed in Book III is not mentioned in Book IV. Yet these differences do not suggest that Hyginus used different sources for Books III and IV. Cassiopeia is not included in the description of Book IV but this may have been an oversight since Cassiopeia is included among the features of Book III. Instead Hyginus mentions in both books the feet of Canis Minor, a feature missing

2.4 The Mainz Globe in the descriptions of Manilius and Ptolemy. Hyginus’s Milky Way seems to pass somewhat north-east of the belt described by Manilius and Ptolemy, that is, through the knees instead of the feet of Gemini and through the tip of the mast instead of the stern of Navis. By such a slightly different orientation the Milky Way passes indeed through the feet of Canis Minor. Such deviations suggest strongly that Hyginus must have used a different source from that used by Manilius. One finds echos of Hyginus’s orientation of the Milky Way circle in Pliny’s Natural History, in which book it is said that the Milky Way cuts the tropics in respectively Sagittarius and Gemini, and the Equator on the one side in Aquila and on the other in Canis Minor.85 Pliny’s description could have been taken over from Hyginus since only there is the Milky Way said to pass through Canis Minor. How the Milky Way as drawn on the Mainz globe compares to the textual descriptions is clear from Table 2.2. To describe the outline of the Milky Way on the Mainz globe I have distinguished 18 features and added these to Table 2.2 in the last column. The identification of course depends strongly on how the constellations are drawn. For example,Ara and Lupus almost touch each other with the Milky Way passing between them instead of below Lupus. Another example is the closeness of the head (halo) of Canis Maior and the first bend of Hydra with the Milky Way passing between them (see Fig. 2.15) in the direction of the top of the stern and the tip of the mast of Navis. Anyhow, the Milky Way features thus determined show that: 1. All nine features that Manilius’s description shares with Ptolemy’s are on the Mainz globe 85 Pliny (Rackham 1938/1979), XVIII pp. 366–7, ll. 280–1.

79

2. 3. 4. 5.

(nos 1–3, 11–12, 15, 17–18, and 20). Many of these features occur also in Hyginus (except no. 11). Five features (nos 6, 8, 13, 19, and 21) occur exclusively in Ptolemy. One feature (no. 4) is shared with Ptolemy and Hyginus Book IV. One feature (no. 10) is shared with Hyginus Book IV. Two (nos 9 and 14) are not explicitly mentioned among the literary sources included in Table 2.2.

Thus the majority of the Milky Way features on the Mainz globe occur in Ptolemy’s description. Conversely one finds all but one of the Ptolemaic features represented on the Mainz globe. The only exception is that on the Mainz globe the Milky Way is not passing through the right front hock of Sagittarius. Taking into account how inaccurately the constellations are located on the Mainz globe, it is in fact surprising to find a great correspondence between Ptolemy and the Mainz globe. It suggests, in my opinion, that the Milky Way on the Mainz globe ultimately goes back to a map of the globe in the mathematical tradition. But this would not apply to the globe as a whole. Globes in the mathematical tradition would have been far more accurate. Moreover, other features on the Mainz globe, such as the nameless configurations of stars, are typical for the descriptive tradition. As far as left and right characteristics are concerned the Mainz globe is of a mixed type. Some human constellation figures are the reverse of those as seen in the sky, thus preserving left and right characteristics as defined by Hipparchus’s rule.86 Others such as Cepheus, Cassiopeia, Andromeda, and Virgo are the mirror images of those as seen in the sky. For 86 Künzl 2000, pp. 495–581 and Künzl 2005.

celestial cartography in antiquity a maker of decorative globes it would have been more attractive to present the constellation figures in a recognizable way. The copying process has completely washed out information about its date or epoch, except that the zodiacal constellations are placed in keeping with the epochal mode described by Manilius. Indeed, the model of the Mainz globe could well belong to the same branch of globe making as the one used by this Roman author.

intellegere licebit. And without a globe it would— according to Hyginus—have been impossible to teach the risings and settings of the signs throughout the year: Book IV.10.2: quid de reliquis signis sine sphaera possit intellegi, sic inuenietur.88 Le Boeuffle has suggested that confusions between right and left in some of Hyginus’s descriptions of the constellations reflect the use of globes. Virgo is a case mentioned by Le Boeuffle. According to Hyginus’s description (Book III.24)Virgo has the star Spica in her right hand in contrast to the description in the Epitome . HYGINUS’S GLOBE where it is placed in the left hand.89 As explained As an intermezzo I like to draw attention to a in Chapter 1, the star Spica (α Vir) should indeed globe which is only known through a text.It shows be Virgo’s left hand because Hipparchus’s rule how globes have left their impact on popular astro- requires that when seen in the sky the constellanomical literature. Indeed, since globes more often tion is face-on. On a globe conserving left and than not replaced the real world one can under- right characteristics Spica remains positioned in stand that an author like Hyginus used such instru- the left hand of Virgo. Hyginus’s right-handed ments in preparing his text DeAstronomia. Hyginus Spica can only have come into being through attempted to teach more than the description of the intermediary of a globe with an image of the starry sky found in Aratus’s Phaenomena. Virgo seen face-on, with interchanged left and Certainly, the mythological aspects of the constel- right characteristics, as on Kugel’s globe (Fig. 2.6). lations in Book II show a purely literary interest in The never-setting stars of Bootes discussed the sky and recall the Epitome. However, chapters I, before in Section1.6 present another example of III, and IV of De Astronomia are directed in the first left–right characteristics occurring in Hyginus’s place to explaining the structure of the world. It is book that deviate from their description in the in these chapters that the traces of the use of a Epitome. In the introduction in Book III.3 one globe as a source would be expected to be most reads that Bootes’s left hand is within the evernoticeable. visible circle, and one never sees it rising or setThe case for a globe as being the source of ting. This assertion is consistent with Hyginus’s some of the statements made in the De Astronomia claim in the same entry that the four stars which has been brought forward by Le Boeuffle who never set are in the left hand.Yet, the Epitome and even argued that Hyginus’s book was actually all the other descriptive stars catalogues place written as a manual for the use of a globe.87 The these never-setting stars in the right hand. As importance of the globe for understanding the argued in Chapter 1, the description in the phenomena of day and the night is explicitly stated in Book IV.9: Sed aliter esse ex ipsa sphaera 88 Hyginus (Le Boeuffle 1983), pp. 126–7. 89 Hyginus (Le Boeuffle 1983), pp. xi–xii; Eratosthenes (Pàmias and Geus 2007), pp. 86–7.

87 Hyginus (Le Boeuffle 1983), p. ix.

80

2.5 Hyginus’s Globe Epitome was ultimately taken from a globe on which Bootes was depicted face-on. However, on a globe presenting Bootes with his back to the viewer, as he is on the Farnese globe (Fig. 2.21), Bootes’s left hand is within the ever-visible circle. The reason for Hyginus departing from the version on the Epitome is thus easily explained by the use of a globe.This is not to say that Hyginus copied his complete star catalogue from such a globe. He did not, for example, correct the location of the star in Bootes’s right elbow, showing that he remained close to the source from which he copied his star catalogue. The descriptions of the constellations in Book III often indicate how the constellations are placed with respect to others. An example is given in Book III.18, where Hyginus says that the constellation Triangulum is above the head of Aries, not far from the right leg of Andromeda. According to Aratus Triangulum is south of Andromeda, and according to Hipparchus’s rule, the south side of Andromeda is her left side.Thus Triangulum should be close to Andromeda’s left leg. Hyginus’s deviating right leg cannot have been derived from a known textual source. The best explanation is that Hyginus used—again— a pictorial source in which first the relative positions of the constellations are shown, and second on which Andromeda is presented with interchanged left and right characteristics. A globe with an image of Andromeda seen face-on does fit these requirements. On Kugel’s globe (Fig. 2.5) one indeed finds Triangulum below the right side of Andromeda. This conclusion of a mirrored image of Andromeda is supported by Hyginus’s description of Andromeda Book III.10 where he mentions that the Tropic of Cancer cuts through Andromeda’s breast and her left hand. The same items are listed in chapter IV.2, where the reader is assured that the Tropic 81

of Cancer intersects Andromeda’s breast and left hand such that her head, breast, and right hand are between the Tropic of Cancer and the Equator. Hyginus clearly deviates here from the Aratean tradition, exemplified by Eudoxus and Aratus, which placed the right hand or arm on the Tropic of Cancer.90 Unique to Hyginus is also his detailed description of Hercules (Book III.5.1) with respect to the ever-visible circle: both feet and the right knee are on it, of the right foot it is actually the end of his great toe that is on the circle and the left foot is crushing the head of Draco.91 The left side of Hercules is further specified by the lion’s skin which he holds in his left hand. Astronomically, this sketch of the attitude of Hercules is correct. Hyginus’s very detailed assertion that the end of the great toe of Hercules is on the ever-visible circle is not found in any written source but may well originate from studying a globe. The attitude of Hercules on the Farnese globe (but not the iconography) agrees in all details with Hyginus’s description (see Fig. 2.21, p. 88). Another example of a unique feature of Hyginus’s description of Hercules is that Hercules touches the Tropic of Cancer with his extended right hand. No written source is known to mention this detail but again it is clearly seen on the Farnese globe. An ambiguous feature of Hyginus’s book is that his data in Book III are not always consistent with those mentioned in Book IV. For instance, only in Book III is the right hand of Virgo reported as being on the Equator. And Hyginus confuses his readers when in Book IV.6 he says that the right foot, the left knee, and the end of the great toe of his left foot of Hercules are on 90 Hipparchus (Manitius 1894), I.10.14, pp. 104–5; Aratus (Kidd 1997), pp. 108–9, ll. 484–5; 91 Hyginus (Le Boeuffle 1983), Book III. 5, p. 89.

celestial cartography in antiquity the ever-visible circle, which reflects the mirror image of the details of Hercules in Book III.5.1. It seems as if Hyginus has adjusted in some places in Book IV his descriptions of Book III to conform to Aratus.92 In addition to the evidence already presented one finds in Hyginus’s De Astronomia such details as (in the entry of Cygnus, III.7) that the tip of the tail of Cygnus touches the head of Cepheus. This piece of information is not sustained by the tradition of star catalogues. The line connecting the stars in the body and the tail of Cygnus (γ and α Cyg, respectively) points indeed in the direction of the brightest star in the head of Cepheus (ζ Cep) but the star in the tail of Cygnus (α Cyg) and the one in the head of Cepheus (ζ Cep) are almost 20º apart.The feature of the tip of the tail of Cygnus touching the head of Cepheus is an unrealistic detail which is seen for example on one of the maps discussed in Chapter 3 (Darmstadt Hs 1020) and which may derive from Hyginus’s text. Its inclusion in Hyginus’s description can only be explained by the use of a not very accurately constructed celestial globe or map. The description of constellations with respect to colures is not part of the descriptive texts associated with Aratus and Eratosthenes. In that sense it comes as a surprise to read in Book III.3 that Bootes’s shoulders and chest are separated from the body by the circle that passes through the poles and touches Aries and the Claws, that is the vernal equinoctial colure. The location of Bootes on the autumnal equinoctial colure is reminiscent of Eudoxus (see Section 1.4), who claims that the autumnal equinoctial colure passes length-

92 Hyginus (Le Boeuffle 1983), pp. xxiv–xxv, notes that the text in Book IV.6 is very uncertain and so it seems wise not to try to explain the differences between Book III and Book IV.

82

ways through the middle of Bootes. Although astronomically incorrect, this Eudoxan position has left several traces in Antiquity. The source employed by Martianus Capella, for instance, describes Bootes on the autumnal colure, and on Kugel’s globe Bootes is also placed on that colure instead of east of it as he should be, more or less in agreement with Hyginus’s description (apart from the matter of the left vs right hand).93 Another Eudoxan feature reported by Hyginus is that the winter solstitial colure passes through Sagitta (Book III.14). Considering that in Hipparchus’s days Sagitta was already completely east of the winter solstitial colure this too may be seen as a trace of Eudoxan astronomy. Le Boeuffle has convincingly argued that in Book IV Hyginus has made not only an attempt to present Aratus’s description in his well-known poem but has also tried to complete it.94 Thus, next to discussing which constellations are located on the circles considered by Aratus (the tropics, the Equator, and the zodiac) Hyginus also treats in Book IV which constellations are located on three more circles: the ever-visible circle, the ever-invisible circle, and the Milky Way. Hyginus could have taken this information from his globe since very few descriptions of the series of constellations located on these circles are known from other manuals. Table 2.3 summarizes the texts in which such descriptions occur. Only Eudoxus and Hyginus present lists of constellations lying on the ever-visible and ever-invisible circles.95 Although Hyginus agrees with Eudoxus in placing one of the wings of 93 Martianus Capella (Dick 1925),VIII, 832, p. 437; Stahl et al. 1977, p. 324. 94 Hyginus (Le Boeuffle 1983), pp. xxiv–xxv. 95 Hipparchus (Manitius 1894),I.11.1–8,pp.112–15;Hyginus (Le Boeuffle 1983) IV.6, pp. 123–4; the features in Book III are dispersed over the constellations described on pp. 87–113.

2.5 Hyginus’s Globe Table 2.3 Sources with descriptions of the constellations on the five parallel circles Source

Tropic of Cancer

Equator

Tropic of Capricorn

Ever-visible circle

Ever-invisible circle

Eudoxus Aratus Germanicus Hyginus Book III Hyginus Book IV Martianus Capella

+ + + + + +

+ + + + + +

+ + + + + +

+ –* –* + + +

+ – – + + –

* There is not an explicit description of the features but a few are indirectly described.

Cygnus on the ever-visible circle, his list is not a simple copy of Eudoxus because he includes on the ever-visible circle features such as the right hand of Perseus and the feet and knee of Hercules and on the ever-invisible circle the feet of Centaurus, features not listed by Eudoxus. Another Late–Antique author who discussed the constellations on the main celestial circles is Martianus Capella. Some (but not all) of the details of his list of constellations located on the ever-visible circle agree with Hyginus, but he deliberately refrains from telling his readers which constellations are on the ever-invisible circle.96 When one compares the lists of constellations located on the main circles, one has to conclude that Hyginus provides additional details. In Table 2.4 the features that occur exclusively in Hyginus’s descriptions of the constellations in Book III are summarized. The most obvious explanation is that Hyginus consulted a globe for them. As mentioned in Section 1.1, Martin believes that the myths and the star catalogue, which survive in the Epitome and have been attributed to 96 Martianus Capella (Dick 1925),VIII, 831, p. 436–37; Stahl et al. 1977, p. 331.

83

Table 2.4 List of Hyginian characteristics from Book III, not included in Book IV or known from other sources. Circle

Exclusive Hyginian characteristics

On the ever-visible circle The right hand of Perseus On the Tropic of Cancer The right foot of Bootes The hand of Hercules The head of Cassiopeia and her right hand On the Equator The feet of Canis Minor The right hand of Virgo The tip of the tail of Serpens The tip of the rounded tail of Delphinus

Eratosthenes, formed part of a more extensive treatise which has survived in Hyginus’s Astronomia. Such a hypothesis cannot be excluded. However, Hyginus’s descriptions of the constellations in Book III differ significantly in structure and contents from those in the Epitome. Yet, the text of the Epitome has in general been well preserved in other star catalogues, and it is unlikely that the explanation for the deviations seen in Hyginus’s descriptions should originate from a work closely related to the Epitome. In contrast one finds that all deviating details are well explained by the thesis that Hyginus used a

celestial cartography in antiquity celestial globe in composing his treatise in addition to the text of Aratus and the star catalogue in the Epitome. The globe consulted by Hyginus in writing his astronomy was one that would fit in a postEudoxan tradition in which equinoctial colures touch Aries and the Claws, but in which Bootes is still on the vernal equinoctial colure and Sagitta on the winter solstitial colure. Hyginus’s globe would have been of the mixed type in which some constellations (Virgo and Andromeda) were drawn face-on and others (Hercules and Bootes) as seen from behind. The globe would have been mounted to enable one to show the rising and setting of the Sun and the stars. In Book IV.2.2, in a chapter on theTropic of Cancer, Hyginus tells how to adjust a globe to the correct latitude by positioning it such that 5/8 of the Tropic is above and 3/8 is below the horizon. The above analysis shows that Hyginus learned his astronomy not only from the flat surfaces of ‘books’. It is hard to imagine that he could have written his treatise without a profound consultation of a celestial globe. In short, Hyginus’s De Astronomia exemplifies more than any other written source the corpus of Roman popular astronomy as it existed in books and globes.

. THE FARNESE GLOBE Very little is known about the background of this oldest-known globe. We do not know where it was made and opinions on the date of production differ considerably. There even exists confusion about its discovery in sixteenth-century Rome, although it is so far sure that it was found there in a deplorable state. A drawing from the Codex Coburgensis made in Rome between 1550 and 1555 shows that the 84

statue was then without face, arms, and legs (Fig. 2.16).97 The celestial sphere itself is better preserved (Figs 2.17–20). Only the regions around the north and south pole are damaged. As a result Ursa Minor and the greater part of Ursa Maior are missing in the north, and Piscis Austrinus and parts of Sagittarius and Capricornus in the south. Two constellations are absent for reasons other than damage.These are Sagitta and Triangulum (Table 2.1). Some have argued that Sagitta could be identified by a curious feature connected with Cygnus, but since the location is too northern this thesis has been rejected by most.There also is no trace of the star groups Anonymous I and II, which are so prominent on Kugel’s and the Mainz globe. The absence of Anonymous II could be due to the damage around the south pole but this does not hold for Anonymous I. Although making a marble sphere of a diameter of 65 cm should perhaps not present a problem to a sculptor, it does not mean that it was carried out with astronomical precision.Valerio has measured the distances of the parallel circles from the Equator on the sphere. In Table 2.5 these distances have been summarized and compared to their expected astronomical values.98 Deviations of a few degrees, equivalent to a few cm on the globe, are not exceptional. Drawing circles on the (uneven) surface of a huge marble globe was clearly not easy for the maker. This may well be the reason why the three great circles marked on the sphere (the ecliptic, Equator, and the equinoctial colures) do not intersect each other in the vernal and autumnal equinoxes as they should. I shall return to this inaccuracy in more detail below. 97 Pighius 1587;Wrede and Harprath 1986. 98 Valerio 1987, pp. 97–124, 105.

2.6 The Farnese Globe

Fig. 2.16 Drawing of the Farnese globe made between 1550 and 1555. (Kunstsammlungen der Veste Coburg, Germany.)

85

celestial cartography in antiquity

Fig. 2.17 part east of vernal colure

Fig. 2.18 part east of summer colure

Fig. 2.19 part west of the autumnal equinoctial colure

Fig. 2.20 part east of the winter solstitial colure

Figs 2.17-2.20 Farnese globe. (Courtesy of the Museo Archeologico, Naples; Photo Soprintendenza speciale per i beni archeologici di Napoli e Pompei.)

The best study of the provenance is that of Wrede who suggested that the Farnese globe belonged to the collection of antiques owned by the Del Bufalo family already around 1500. A record by Petrus Sabinus around 1500 states that the statue which in the sixteenth century 86

was described commonly as of Hercules, was kept ‘in domo Angeli Bubali, ubi est statua Herculis et multum deorum in ciclo’.99 The antiquarian Stephanus Pighius visited Rome in 1550 and 99 Wrede 1982, p. 14.

2.6 The Farnese Globe Table 2.5 Angular measures Circle

Standard

Valerio Schaefer distances distances

Schaefer stellar data

Mean ever-visible circle* Mean ever-invisible circle Mean Tropic of Cancer Mean Tropic of Capricorn** Equator Vernal equinoctial colure Summer solstitial colure Autumnal equinoctial colure Winter solstitial colure

δ = 54° δ = 54° δ = 24° δ = 24° δ = 0° α = 0° α = 90° α = 180° α = 270°

56.7° 55.4° 25.5° −25.1°

51.8° ± 1.3° 51.3° ± 0.8° 24.0° ± 1.1° −23.9° ± 1.1° −1.8° ± 1.3° 3.7° ± 2.7° 89.3° ± 2.2° 183.5° ± 1.8° 271.3° ± 1.6°

57.8° ± 0.5° 57.0° ± 0.5° 26.3° ± 0.2° 26.0° ± 0.4°

Standard: values of the antique grid. * According to Valerio the ever-visible circle varies from 58.4° to 55.7°. ** According to Valerio the Tropic of Capricorn varies from -25.9° to -24.6°.

records the finding of the statue with globe in the vineyard of the Del Bufalo:‘Vidisse me memini Herculis statuam Romae in vinea Stephani Bubalii repertam; qui non horographium sciotericon, sive vas horoscopium cervice, sed caelisphaeram ingentem Zodiaci, atque fixarum stellarum imagibus pulcherrime sculptis exornatam gestabat’.100 The presence of the statue in the house of Stephano del Bufalo is also mentioned before 1560 by the antiquarian Pirro Ligorio.101 Ulisse Aldrovandi indicated in 1550 its provenance as:‘in casa di M. Bernandino de Fabbii à le botteghe oscure, presso di Santa Lucio’. At first sight this statement seems to contradict the records of Sabinus and the antiquarian Stephanus Pighius, but this conflict can be resolved by the hypothesis put forward byWrede that Aldrovandi actually referred to the studio of the restorer of the statue, Guglielmo della Porta. It is well documented that restoration took place before the statue was sold in 1562 for 250 scudi to become the property of Cardinal Alessandro

Farnese the Elder.102 After being restored anew in Rome by Carlo Albacini the statue was transported in 1796 to Naples. The Farnese globe became widely known in the eighteenth century through a map (Fig. 2.21) in stereographic projection made by Martin Folkes (1690–1754), an antiquarian who became president of the Royal Society and of the Society of Antiquaries.103 The map was published in 1739 in the edition of Manilius, Astronomia, prepared by Richard Bentley. Kristen Lippincott has pointed out that this map is closely related to a manuscript copy of the Farnese globe in the collection of the British Library.104 She showed ‘that the globe in the British Library was a copy of the Farnese globe commissioned by Martin Folkes, probably from an Italian artist, sometime between 12 November 1733 and January 1735. Whether the piece was carried with Folkes on his return journey or was later shipped to 102 Wrede 1982, p. 14 and note 155. 103 A short, not very kind biography of Martin Folkes is in Rodney DSB vol. 5, pp. 53–4. 104 Lippincott 2011.

100 From Pighius 1587, pp. 360–1, cited by Wrede 1982, p. 14 and note 147. 101 Korn 1996, p. 27.

87

celestial cartography in antiquity

Fig. 2.21 Engraving of the mapping of the Farnese globe prepared by Richard Bentley and published in 1739 in the edition of Manilius, Astronomia. (Courtesy of the University Library Utrecht.)

England, we know that it was in London by July 1736, when he presented it to the Society of Antiquaries. Bentley had started work on the Astronomicon in the 1690s; his book was reportedly “ready to be printed” in 1736, but was not seen through the press until 1739’.105 Lippincott has compared Folkes’s map, his manuscript globe, and the Farnese globe in detail and showed that many small differences exist between these three sources. One of the more striking differences is that Canis Minor, which is hidden behind the hand of Atlas on the Farnese globe but nevertheless present, is neither marked on Folkes’s map nor on his manuscript globe. Of all studies of the Farnese globe Thiele’s of 1898 has been the most influential. To him we owe first the hypothesis that the model used for the Greek original would be an astronomical globe by Hipparchus rather than a decorative

piece, and second the idea that the Farnese Atlas could be a Roman copy made during the reign of Hadrian (ad 117–38).106 Thiele used astronomical arguments to link the globe to Hipparchus and art-historical ones to label it as a Roman copy.A somewhat different date was put forward by Korn, who concluded that the style and workmanship of the celestial globe indicates a date before the beginning of the classicism of the Augustan period.107 Another often quoted date is based on the appearance on the globe of a rectangular form which some recognize as the ‘Throne of Caesar’ (Fig. 2.21).When combined with the appearance of a comet at the funeral games of Julius Caesar in 44 bc, it would show that the model for the Farnese globe has to be dated at the beginning of the Roman Empire, during the reign of 106 Thiele 1898, pp. 27–42, esp. p. 40. 107 Korn 1996, pp. 33–4.

105 Lippincott 2011, p. 290.

88

2.6 The Farnese Globe August.108 Since the hypothesis for the interpretation of the rectangular form as being the ‘Throne of Caesar’ was taken on by many authors it is instructive to take a critical look at it. In dating the globe with the help of the rectangular form, it is supposed that the comet seen in 44 bc at the funeral games of Julius Caesar, known as the Sidus Julius, provided the connection between the globe’s rectangular form and the constellation described by Pliny as the Caesaris Thronus in his Natural History Book II in discussing geography and astronomy: ‘The cause of the remaining facts that surprise us is found in the shape of the earth itself, which together with the waters also the same arguments prove to resemble a globe. For this is undoubtedly the cause why for us the stars of the northern region never set and their opposites of the southern region never rise, while on the contrary these northern stars are not visible to the antipodes, as the curve of the earth’s globe bars our view of the tracts between. Cave-dweller Country and Egypt which is adjacent to it do not see the Great and Little Bear, and Italy does not see Canopus and the constellation called Berenice’s Hair, also the one that in the reign of his late Majesty Augustus received the name of Caesar’sThrone, constellations that are conspicuous there. And so clearly does the rising vault curve over that to observers at Alexandria Canopus appears to be elevated nearly a quarter of one sign above the earth, whereas from Rhodes it seems practically to graze the earth itself, and on the Black Sea, where the north Stars are at their highest, it is not visible at all. Also Canopus is hidden from Rhodes, and still more from Alexandria; in Arabia in November it is hidden during the first quarter of the night and shows itself in the second.’109

It is a pity that this text on Caesar’s Throne is so corrupted. For example, the asterism called Berenice’s hair is visible in Italy, contrary to Pliny’s statement. Pliny is not the best astronomical source for Antiquity and in order to accept his interpretation one would rather have it confirmed in another context, if only because it is not clear that Pliny’s ‘Throne of Caesar’ is a true constellation, related to the fixed stars. Unfortunately, Pliny’s text seems to be the only source reporting Caesar’s Throne.110 The comet concerned was also described in some detail by Pliny elsewhere in his Natural History (Book II, 23): ‘The only place in the whole world where a comet is the object of worship is a temple at Rome. His late Majesty Augustus had deemed this comet very propitious to himself; as it had appeared at the beginning of his rule, at some games which, not long after the decease of his father Caesar, as a member of the college founded by him he was celebrating in honour of Mother Venus. In fact he made public the joy that it gave him in these words: “On the very days of my Games a comet was visible for seven days in the northern part of the sky. It was rising about an hour before sunset, and was a bright star, visible from all lands.The common people believed that this star signified the soul of Caesar received among the spirits of the immortal gods, and on this account the emblem of a star was added to the bust of Caesar that we shortly afterwards dedicated in the forum.” This was his public utterance, but privately he rejoiced because he interpreted the comet as having been born for his own sake and as containing his own birth within it; and, to confess the truth, it did have a healthgiving influence over the world.’111

110 Emma Gee 2000, p. 160, note 19: this is likely to be a fantasy of Pliny’s. 111 Pliny (Rackham 1938/1979), Book II. 23, p. 237.

108 Boll 1899, pp. 121–4, note 3. 109 Pliny (Rackham 1938/1979), Book II.176–78, p. 311, discussing Geography and astronomy.

89

celestial cartography in antiquity This description is confirmed by many sources, mean declination of 40°. A star in this place would for instance by Suetonius who wrote: rise in the north-east, about 30° east of the northern direction. However, it does so only in mid ‘On the first day of the Games given by his succeswinter, in December. Julius Caesar died on 15 sor Augustus in honour of this apotheosis, a comet appeared about an hour for sunset and shone for March 44 bc, and the funeral games started on 20 seven days running. This was held to be Caesar’s July of the same year.117 This means that it is simsoul. Elevated to heavens; hence the star, now ply impossible that the place where the rectanguplaces above the fore head of his divine image.’112 lar form on the Farnese globe is seen represents the location in the sky where the comet was Also the temple referred to by Pliny where a observed. Surely, if there is a connection between comet is worshipped is confirmed. Ovid menthe rectangular form on the Farnese globe and tions it in his Fasti (Book 3. 704) and there is a coin the constellation described by Pliny as theThrone struck by Octavian in 36 bc where Caesar is seen of Caesar, one has to find better reasons than its in the middle of a temple with a star placed on the association with the comet seen in 44 bc. edifice of the building above his head.113 A comThiele excluded the possibility that the recplete survey of all texts related to the comet is tangular form could be a constellation and only provided by Ramsey and Licht, showing that the after great hesitation subsequently suggested comet was a real thing rather than a fancy.114 that the Farnese rectangular form could be a The two passages cited above have been the ‘Throne’.118 His doubts regarding this interpretabasis of interpretation of the rectangular form on tion appear to have been removed by a comparithe Farnese globe. Boll proposed that the conson of the rectangular form with pictures on stellation named the ‘Throne of Caesar’ is to be coins. A throne in the heavens must have been found in the sky just where the comet appeared devoted to a God, but since the rectangular form shortly after the death of Julius Caesar, and that it would represent at best an empty throne it could coincides with the rectangular form seen on the at most refer to an earthly ruler. One can Farnese globe.115 As said before, many have taken understand Thiele’s hesitation. The feature does on this hypothesis without verification.116 Yet, it not look like a throne. Recently Künzl suggested is not difficult to check whether the rectangular that a sella curulis on coins around 43 bc could form on the Farnese globe meets the requirehelp to solve this problem, but he also noted that ments of comet’s description: that it was seen in the interpretation of these coins is difficult and the northern part of the sky, and rising about an that the Farnese rectangular form does not comhour before sunset. The coordinates of the recpare very well with a sella curulis.119 So, on the tangular form on the Farnese globe correspond basis of the available evidence, none of the proto a mean right ascension of about 105° and a 117 On the games and the Sidus Julius, see Domenicucci 1996, pp. 31–3 and Ramsey and Licht 1997, pp. 19–57; Ramsey and Licht p. 89, show that if the comet was seen around 20 July, the most probable location of it was just south of Cassiopeia, which is consistent with my conclusion that the place of the comet cannot coincide with a location above Cancer. 118 Thiele 1898, p. 41. 119 Künzl 2000, p. 535.

112 Graves 1957/1977, Book 1.88 p. 48. 113 For Ovid, see Nagle 1995, p. 99. The coin is in the Bibliothèque National and depicted on the cover of Graves 1957/1977. 114 Ramsey and Licht 1997, pp. 155–68. 115 Boll 1899, pp. 121–4, note 3. 116 Künzl 2000, p. 535; Schlachter 1927, p. 43; Stückelberger 1994, p. 34, note 20; Le Boeuffle 1977, p. 151.

90

2.6 The Farnese Globe posals for explaining the strange rectangular form on the Farnese globe seem plausible. In fact, there is no good reason to presume that the rectangular form, placed in a fairly empty region of the sky, is meant as a constellation. However that may be, a date based on it is meaningless as long as its significance is obscure. But are dates determined by astronomical methods more telling? As mentioned before, when making a globe in the mathematical tradition a maker would first mark the stars on the sphere using the coordinates presented in a star catalogue and then he would draw the constellation images such that the stars are in the locations corresponding to the descriptive part of the mathematical catalogue. It is clear that this is not how the Farnese globe was made. There are, however, a number of reasons to suspect that the model used by the sculptor derives ultimately from a mathematical globe. If so, a number of the characteristics of the model globe may have survived in the Farnese copy. These properties would concern the epoch of stars and perhaps the constellation designs. Since there are only constellations indicated on the Farnese globe, the ‘stars’ referred to in the discussion below are specific locations within these constellations,which according to the description in star catalogues represent the locations of particular stars. For example, the point in the middle of the head of Ophiuchus is identified with the location of α Oph because that fits the description of this star in catalogues. A major argument used by some historians to favour a date for the globe in the late second century ad is related to the fact that the points of intersection between the ecliptic and the Equator (points A and D in Scheme 2.6) on the Farnese globe are displaced westward with respect to the points of intersection between the equinoctial colures and the ecliptic (points B and E in Scheme 2.6). As a result the intersections between the 91

Equator and the equinoctial colures (points C and F in Scheme 2.6) do not coincide with either A and D or B and E. Where one normally expects to find points, there are now triangles. This presents a problem in interpreting data from the Farnese sphere because the zero-point from where coordinates have to be counted is not clearly defined. One can in principle determine the epoch of a globe from the ecliptic longitudes of the stars since their values increase slowly by precession. For example, the longitude of the star now known as Regulus (α Leo) was 117° in Eudoxus’s day (epoch about 375 bc); it was 120.5° in Hipparchus’s day (epoch about 128 bc) and in the Ptolemaic star catalogue (ad 137) it is 122.5°.120 Conversely, once the longitude of Regulus is known, one can find the epoch. However, such a method cannot be applied without further ado if the zero-point from where the longitudes are to be counted is not clearly defined, as is the case on the Farnese globe. Should the longitudes of stars be measured from point A,the point of intersection between the ecliptic and the Equator, or from point B, the point of intersection between the equinoctial colures and the ecliptic? In his study of the Farnese globe Valerio states that ‘the precession of equinoxes is very clearly expressed in the globe and is fully described by Ptolemy after the now lost work by Hipparchus on the “Displacements of solstitial points” ’.121 120 Grasshoff 1990, pp. 275–316, provides a table with longitudes, latitudes, right ascensions, and declinations for the stars in the Ptolemaic star catalogue and for the epoch of Hipparchus (128 bc). The Ptolemaic star catalogue in Toomer 1984 gives longitudes and latitudes only. 121 Valerio 1987,p.103.Valerio confuses his readers by saying that the phenomenon of precession was never referred to in any astronomical treatise before Ptolemy as late as ad 150.Thus the precession of the equinoxes can only have been clearly expressed in a globe after the appearance of Ptolemy’s explanation of it.Somehow it did not occur to Valerio that if Hipparchus’s treatise ‘On the displacement of the solstitial and equinoctial points’ was known to Ptolemy it must also have been available to other astronomers living before Ptolemy (but of course after Hipparchus).

celestial cartography in antiquity

Scheme 2.6 Displaced equinoxes on the Farnese globe.

This is a rather confusing way of putting it. Different epochs are marked by different equatorial grids and the grid associated with a specific epoch can be obtained from that of another epoch by rotation of the solstitial colures around the ecliptic pole. But can this explain the confusing triangles at the equinoxes on the Farnese globe (∆ ABC and ∆ DEF in Scheme 2.6)? In order to answer that question the following thought experiment can be made. Suppose one wanted to adapt a globe designed for a given epoch TB to an epoch TA. The new equinoxes (A and D) and solstices (at points 90° away from A and D) for the epoch TA on the ecliptic are then determined by a shift over a distance BA, where B represents the vernal equinox for the epoch TB. The new solstitial colures for the epoch TA pass through the new solstices (at points on the ecliptic 90° away from A and D) and the fixed ecliptic poles. The new equatorial 92

poles for the epoch TA are found along the new solstitial colures at a distance of about 24° from the fixed ecliptic poles.The new Equator for the epoch TA passes through the new equinoxes (A and D) and the points along the new solstitial colure at 90° away from the newly established equatorial poles.The new equinoctial circles for the epoch TA pass through the new equinoxes (A and D) and the new equatorial poles. To adapt a globe for a new epoch in this way, the sphere would thus have been provided by two grids associated with two different epochs. Of course, if the globe was to be valid for the new epoch TA one would expect that the grid corresponding to this new epoch would be emphasized whereas the old grid corresponding to the epoch TB would have been suppressed. However, if an error was made and the artist, confused by so many circles, made the wrong choices, a mixed grid could have been the result.

2.6 The Farnese Globe Then the colures would belong to the older epoch TB and the Equator to the other more recent epoch TA. If this hypothesis is correct, the difference in time between the two epochs is fixed by the distance AB along the ecliptic which is 5.5°. If this distance is converted into an interval of time by using the value for the rate of precession of 1° in 100 years as was usual in Antiquity, the following conclusion is inescapable:

tic and the Equator (A and D in Scheme 2.6) are the correct equinoxes, and consequently the ‘colures’ depicted on the globe are not true colures but a set of hour circles. This apparently was the starting point of Francesco Bianchini who in cooperation with Gian Domenico Cassini carried out an extensive astronomical examination in 1695. The first report of this examination appeared in 1697.122 Further studies, announced by Bianchini, were published TA = TB + 550 years after his death by his cousin, Guiseppe Bianchini. This implies for instance that, were the epoch TB To establish a date Francesco Bianchini com(of the older globe) the same as that of Hipparchus pared the positions of a few stars on the globe (128 bc) as Thiele believes, the epoch TA (of the with their positions in the Ptolemaic star catanew globe) would be around ad 420. Conversely, logue.123 For instance, the right ascensions of the if one believes that the new globe was produced stars which Ptolemy describes as being in the at the epoch of Ptolemy (ad 137), as Bianchini horns of the Ram (γ and β Ari) were then 3° and believes, the older globe would have had an 3.5° and that of the star in the beck of Cygnus epoch TB equal to 410 bc. Neither result is really (β Cyg) was then 273°. And since these stars are convincing. close to or on the ‘colures’, which Bianchini Another, more probable explanation of the believed to be the hour circles for 3°, he conconfusing triangles at the equinoxes on the Farnese cluded that the epoch of the globe coincides globe is based on the hypothesis that the globe with ad 137, that of the Ptolemaic catalogue. was indeed designed for one epoch only and that Another approach has been to assume that the the triangles at the equinoxes are the result of ‘colures’ depicted on the globe are the true inaccurate workmanship. Such a conclusion is colures and that the points of intersection not farfetched. The triangles at the equinoxes between them and the Equator (C and F in would result if the sculptor first marked the equa- Scheme 2.6) represent the correct equinoxes. tor and the colures and subsequently made an This was done by Thiele in 1899.124 He comerror in locating the poles of the ecliptic. A dis- pared the positions of the stars on the globe with placement of ca. 2° is equivalent to 1.1 cm. Considering the deviations from the standard 122 Valerio 1987, pp. 97–124, esp. p. 98 and note 15. Bianchini model found elsewhere on the sphere (see 1697, chapter 28 entitled:‘Espedizioni militari in Colchide, e in Troja con vantaggi, non tanto degli stati di Grecia, quanto degli Table 2.5) this is not at all impossible. Irrespective studi piu gravi’ reprinted by Antonio Giuseppe Barbazzo of whether precession can or cannot satisfacto- (Rome 1747) with newly engraved plates by Pier Santi Bartoli rily explain the confusing triangles at the equi- (1635–1700). It may well be that this examination of the Farnese globe was the motive for Cassini’s design of a precession globe noxes on the Farnese globe, the problem of dating published in 1708, see Dekker 2003, p. 225. 123 Bianchini’s publication of 1752 is unfortunately not the Farnese globe or its model clearly remains. available to me and for that reason I have used the notes proOne way to tackle the problem is to assume vided by Valerio 1987, pp. 101–3. that the points of intersection between the eclip124 Thiele 1898, pp. 30–3. 93

celestial cartography in antiquity those used by Hipparchus to define a set of 24 hour circles in the sky, four of which coincide with the colures.125 For instance, the right ascension of the star which Hipparchus describes at the end of the tail of Canis Maior (η CMa) is 90° and that of the star in the middle of the left foot of Bootes (τ Boo) is close to 180°. Since on the Farnese globe these stars are on or close to colures, respectively, Thiele concluded that the epoch of the globe was 128 bc, the epoch of Hipparchus. Thiele’s hypothesis was challenged by Valerio who claimed:‘The Farnese globe is to be considered [. . .] an original piece of science and art, not a mere copy from an ancient original.The globe represents the state of knowledge at the time of the Almagest even if it may show [. . .] in some details a spurious and different tradition. In fact it embodies the astronomical knowledge of antiquity as the Almagest does’.126 In presenting his case Valerio added arguments to those put forward by Bianchini discussed above. He selected the star Spica in the left hand of Virgo, because in the period between Hipparchus and Ptolemy it had moved by precession from a position slightly above (+ 0° 36´) to a position slightly below the Equator (-0° 30´).127 SinceVirgo’s hand is located below the Equator,Valerio concluded that the data on the Farnese globe agreed with the Ptolemaic catalogue. The results of Bianchini, Thiele, and Valerio mainly show that one can always find a few individual stars to fit one’s preferred hypothesis, especially if one is prepared to ignore the large errors which mark on the whole the mapping of the Farnese globe. For instance, the two stars 125 Hipparchus (Manitius 1894), III.5.1–23, pp. 271–81. 126 Valerio 1987, p. 103. 127 Toomer 1984, p. 332. On the Farnese globe this difference would amount to a displacement of about 5 mm.

which Ptolemy describes as being in the horns of the Ram (γ and β Ari) lie on the Farnese globe at least 15°–18° north of the Equator, which is 5°–8° in excess of the declination of 10° predicted by the data in the Ptolemaic catalogue. The declination of the star in the end of the tail of Canis Maior (η CMa) which according to Thiele was plotted ‘painfully accurately’ on the globe, is about -43°, which is 16° in excess of the correct value of -27° in Hipparchus’s day. In turn Valerio ignored the fact that according to the Ptolemaic catalogue the right ascension of Spica is 176° whereas on the Farnese globe it is 172° when counted with respect to the point of intersection between the ecliptic and the Equator (A). Surely the error of at least 4° in right ascension makes an assessment of the globe based on a variation in the declination of one star within ½° north or south of the Equator quite doubtful. The inaccurate locations of the constellations do not permit a determination of the epoch of the Farnese globe on the basis of a few individual stars.The only hope is that a statistical approach based on many more stars, such as was published by Schaefer in 2005, may give more reliable answers. In Schaefer’s study a number of procedures were used, all based on photographic material:128 1. The declinations of the tropics and evervisible and ever-invisible circles were determined by measuring distances. 2. The positions of the main circles were also determined with individual ‘stars’ located on them by comparing the stellar data with positions generated from modern data and using a least squares technique for finding the mean angular distances of the celestial circles. 128 Schaefer 2005, pp. 182–94.

94

2.6 The Farnese Globe 3. The measured locations of individual ‘stars’ were compared with positions generated from modern data and a least square technique was used for finding an epoch. Schaefer’s results for the mean angular distances of the Equator and the parallel circles are summarized in Table 2.5 alongside the measurements of Valerio. Schaefer’s values obtained by measuring distances compare fairly well with those of Valerio. In contrast one finds that Schaefer’s results obtained by stellar data differ systematically from those measured by distances. Especially striking is the fact that the stellar data give values for the declinations of the tropics close to the expected values. Scheafer explains these systematic errors by the sculptor’s use of two standards: one for the celestial grid and one for the star positions.129 This explanation is hardly convincing. Before accepting it one has to make sure that other explanations can be ruled out, but this is not easy. Systematic errors can arise from a variety of causes: the technique used to analyse the data, the instruments used by an observer of the stellar data, the non-spherical surface of the globe, and, for example, from repeated copying. Such uncertainties prevent a straightforward interpretation of the statistical data. For this very reason Schaefer’s determination of an epoch 125 bc ± 55 bc is controversial.130 Schaefer’s stellar data are the results of a complicated and not very transparent process of trial and error, adjusting and averaging positional data fixed with reference to two points of intersection between the vernal equinoctial colure and the tropics (which is equivalent to assuming that the correct vernal 129 For a discussion of these differences the reader is referred to Schaefer 2005, pp. 190–1. 130 Schaefer 2005, p. 193. See also the discussion in Duke 2006, pp. 88–9.

95

equinox is located in point C in Scheme 2.6). Schaefer presumes that his statistical stellar data are free from systematic errors, but, as long as it is unknown how the celestial circles were marked on the Farnese globe and from what source constellations were copied and how, it is impossible to control the errors involved and interpret the results of his statistical analysis reliably.131 In other respects too Schaefer claims more than his study justifies. He believed to have shown that ‘the constellations on the Farnese Atlas are based on the now-lost star catalogue of Hipparchus. This is proved by the perfect match with the constellation symbols used by Hipparchus and only for these, by the perfect match with the date of Hipparchus (with the exclusion of all other known candidate sources), by the requirement that the source be a star catalogue such as that compiled by Hipparchus, and by the many points of consistency with what we know about ancient Greek astronomy.’132

And also that ‘The existence of this “new” source for Hipparchus’s catalogue is likely to be valuable for our understanding of Hipparchus’s astronomical methods and for investigations of the origin of the star catalogue in the Almagest.’133

Hipparchus’s star catalogue is a sensitive topic among historians of astronomy, especially in relation to the debate on the origin of the Ptolemaic star catalogue, and it is not amazing 131 This certainly applies, for example, to Schaefer’s claim— also obtained by statistical methods—that the data in Aratus really date to 1130 ± 80 bc, see Schaefer 2005, p.176. For an alternative interpretation, see Dekker 2008b, pp. 220–1. As an aside I note that Schaefer is mistaken when he claims that Aratus says that the summer solstice is at the start of Leo, see Dekker 2008b, p. 219. 132 Schaefer 2005, p. 182, conclusion no. 7. 133 Schaefer 2005, p. 182, conclusion no. 9.

celestial cartography in antiquity that Schaefer’s claims provoked a strong response, in drawing constellations is clear only when stars which was put into words by Dennis Duke who are considered more important than constellaconcluded tions. This is what could be expected from a globe in the mathematical tradition, not from a ‘that nothing in Schaefer’s paper constitutes a descriptive globe on which, as seen above, left proof that Hipparchus is the only source of the data underlying the globe, that Schaefer’s stated and right features are often confused. The presuncertainty in the date is much smaller than it ervation of the left and right characteristics of should be, that there are many discrepancies the stars within a constellation figure as defined between Hipparchus’ known data and the globe, by Hipparchus’s rule is not seen on all globes and that the possibility of sources other than the belonging to the mathematical tradition. On ones considered by Schaefer is potentially impor- Islamic globes all figures are presented consisttant to consider’.134 ently as the mirror image (see Chapter 4). Only I agree with Duke that the Farnese globe does when the mathematical tradition got off the not shed new light on Hipparchus’s astronomi- ground in Western Europe in the fifteenth cencal methods or on the now lost Hipparchan star tury did rear figures reappear in celestial mapcatalogue. However, this does not exclude the ping (see Section 5.3). Very little is known of the first generation of possibility that the Farnese globe ultimately mathematical globes, but it is very possible that derives from a Hipparchan mathematical globe, as Thiele, and after him Schaefer, postulate.135 these all derive from a globe made by Hipparchus. This hypothesis is in my opinion acceptable if Even if one admits Duke’s argument that any only because on the Farnese globe all human astronomer could have created stellar data with figures—with the exception of Andromeda— an accuracy of 2º, Hipparchus remains a serious are seen from the rear. How did this outstanding candidate as the maker of such a background feature of constellation design come about? It is mathematical globe. The very existence of a not in the nature of an artist to hide the faces of Hipparchan globe is mentioned by Ptolemy.136 his figures. More likely the maker of the model Hipparchus’s globe is hypothesized by Grasshoff globe is responsible for this. He—an astronomer and other historians for explaining the accuracy no doubt—must have applied a specific rule in of the stellar data in his Commentary to Aratus.137 drawing the constellation figures, namely that Besides, the creation of a reliable star catalogue is the left and right characteristics of the stars no easy task, and not often done. There are not within a constellation figure as defined by many astronomers who observed the starry sky Hipparchus’s rule (see Section 1.6) are preserved. completely anew from the basics. Time and again the available star catalogues By insisting that a star described in the right have attracted the attention of globe makers.The hand or in the left foot ends up on the globe in the right hand or in the left foot of the constel- star catalogues of Ptolemy, al-Ṣūfī, and Tycho lation figure all human figures should be pre- Brahe, are at the bottom of important traditions sented from the rear. The significance of this rule in making globes in the mathematical tradition 134 Duke 2006, p. 87. 135 Schaefer 2005, p. 182, conclusion no. 8.

136 Toomer 1984, p. 327. 137 Grasshoff 1990, pp. 2 and 124; Nadal and Brunet 1984.

96

2.6 The Farnese Globe and it seems only fair to assume that the now lost star catalogue of Hipparchus had the same effect. Indeed, Hipparchus’s globe, if there was such a globe, must have been too good not to have been copied again and again. Dependent on the globe’s purpose, an artist would be more or less faithful in copying, and the departures from the model would depend on the traditions known. Among these post-Hipparchan globes one would have found, for example, the globe used by Manilius for his description of the colures, which are consistent with a date of 128 bc. Using his description I have introduced in Section 1.4 the Manilian epochal mode to circumvent a meaningless discussion of the epochs of globes in the descriptive tradition. To be sure, the Farnese globe is meant to be a decorative globe belonging to the group of globes sharing the Manilian epochal mode, and as such it fits well in a copying practice stemming from Hipparchus’s globe. In such a scenario all one can conclude about the date is that the globe was made later than 128 bc. In his study of the Farnese globe, Thiele believed that it was possible to ascribe its uranography completely to Hipparchus.138 Of course, it did not escape Thiele’s attention that there were some obvious departures from what he believed to be Hipparchus’s iconography. Yet, for Thiele this reflected only a later development in the work of Hipparchus: ‘er änderte also später seine Astrothesie’.139 More surprising are Schaefer’s arguments for concluding ‘that the Farnese Atlas is virtually identical to the constellation descriptions by Hipparchus, yet is greatly different from the descriptions from all other ancient sources’.140 Artists do not always follow faithfully the sources

they are supposed to copy but create their own pictorial language and use traditions outside the astronomical context. For example, according to the descriptive tradition Serpens encircles the waist of Ophiuchus, contrary to what is seen on the Farnese globe. However, this cannot be used as an argument against the descriptive tradition since on Kugel’s globe Serpens passes in front of Ophiuchus (see Fig. 2.7). Another example is the water jar held by Aquarius, depicted on the Farnese globe, which Schaefer uses as an argument in favour of Hipparchus and against Ptolemy since a jar is mentioned by Hipparchus but not in the star catalogue in the Almagest. However, the jar is mentioned in texts in the descriptive tradition (Epitome) and seen on the Mainz globe (see Fig. 2.13). Manilius (I.272) refers to it and Germanicus says first that Aquarius pours out water from the outstretched right hand and adds that the figure pours water from a small pitcher.141 The vessel is also drawn on Islamic globes, which are all based on translations of the Almagest. As explained in Chapter 4 it belongs to certain lawa-zim, that is, attributes that were needed to complete some of the constellation figures, which are not mentioned explicitly in the Ptolemaic descriptions.142 Schaefer notes that Corona Australis is depicted on the Farnese globe before the front legs of Sagittarius but not mentioned in the Epitome.143 Yet the constellation was mentioned by Aratus as an unremarkable ring of stars beneath the forefeet of Sagittarius and, as discussed above, it is depicted on Kugel’s and the Mainz globe (Figs 2.7 and 2.13). Duke points out that the Southern Crown was known to Geminus and that it is the only southern constellation on 141 Germanicus (Gain 1976), pp. 29 and 60, ll. 284–5; Germanicus (Gain 1976), pp. 38 and 68, ll. 559–60. 142 Kunitzsch 1974, p. 78, note 199. 143 Schaefer 2005, p. 174.

138 Thiele 1898, pp. 34 and 40. 139 Thiele 1898, p. 33. 140 Schaefer 2005. p. 174.

97

celestial cartography in antiquity the globe that is not in Hipparchus’ list of rising and setting southern constellations. Although Corona Austrinus is indeed not mentioned by Hipparchus as a constellation, the alignments recorded by Ptolemy ascribed to him show that he recognized the stars. Ptolemy describes one of them as ‘the midmost of the three bright star in the Circle’, which shows that Hipparchus did know the stellar configuration but may not have called this group of stars the Southern Crown.144 Some features on the Farnese globe are beyond doubt induced by artistic choices. Examples are that Taurus’s left horn does not extend to the right foot of Auriga and that Andromeda’s head does not touch Pegasus’s cut-off. All authors in Antiquity agree that Auriga and Taurus share the star on the tip of Taurus’s left horn and that Pegasus and Andromeda have the star in Andromeda’s head in common.145 Such characteristics do not discriminate between the mathematical and the descriptive tradition, but makers of decorative globes are more inclined to ignore such details. In his critical discussion of Schaefer’s assessment of the uranography of the Farnese globe, Duke presented list of a number of discrepancies in constellation design between the globe and a presumed Hipparchan iconography. I agree with most of these examples but must make an exception for Ara of which Duke says: ‘On the globe Ara is shown right side up and tilted, instead of inverted, as Hipparchus (and also Ptolemy in the Almagest) describes it. This inversion is clearly established by Hipparchus’ language that, e.g. the 144 Toomer 1984, p. 323. See Toomer’s note (n. 20) that Ptolemy does not describe this shape as a quadrilateral. 145 For the star shared by Auriga and Taurus, see Hipparchus (Manitius 1894), I.2.10, pp. 14–15; Aratus (Kidd 1997), pp. 84–5, l. 174. For the star shared by Pegasus and Andromeda, see Hipparchus (Manitius 1894), I.2.13, pp. 16–17; Aratus (Kidd 1997), pp. 88–9, l. 205.

98

lip of the Altar is the first star to set while the last to set is the northern of those in the base’.146 However, on the Farnese globe Ara is depicted as an altar, standing on three feet, with two handles (compare Fig. 2.21). The bottom part is close to the tail of Scorpius. It is upside down with respect to the zodiacal band as Hipparchus (and also Ptolemy in the Almagest) describe it and, contrary to what Duke concludes, does not agree with Aratus. The astronomical accuracy of a globe is no issue for the sculptor of a decorative globe, the stories that can be told about the constellation figures are more to the point. It is therefore to be expected that the iconography was adapted in the copying process. Following the hypothesis that the mathematical model globe has its origins in a globe of Hipparchus it is of great interest to see what images do not agree with the Hipparchan iconography and which in the eyes of the sculptor needed more expression. In the following list only those constellation features are included that in my opinion are most telling in discussing deviations from what we think is Hipparchus’s uranography. A detailed description of each constellation is presented in the description of the globe in Appendix 2.2. Deviations from Hipparchus’s uranography: 1. Cepheus ’s outstretched hands extend over an angle of about 70° whereas in the descriptions of Hipparchus (and Ptolemy) the arms of Cepheus cover about 50° or less. Hipparchus places the star θ Cep at the end of the right hand. The right ascension of this star is around 297° which is 20° east of the stars in the tip of the right wing of Cygnus (ι and κ Cyg) with right ascensions around 146 Duke 2006, p. 90.

2.6 The Farnese Globe 277–279°.147 It is not clear which star Hipparchus placed in the left hand, but it is unlikely that it extended all the way below the seat of Cassiopeia. In contrast, Eudoxus says that the right hand of Cepheus is near the right wing of Cygnus (ι and κ Cyg), a statement severely criticized by Hipparchus.148 Eudoxus says also that Cassiopeia is in front of Cepheus.149 If anything, the wide range on the Farnese globe is reminiscent of the descriptions of Eudoxus and Aratus, even if the latter says that the belt of Cepheus is on the ever-visible circle, whereas on the Farnese globe this circle intersects Cepheus’s neck.150 And Hipparchus is certainly wrong when he claims that the star ι Cep, which he himself placed on the left shoulder, was placed by Eudoxus on the left hand. Hipparchus adds that many place the star ι Cep in the (left) shoulder. Hipparchus obviously did not realize that when Eudoxus referred to the star in the left hand near the right wing of Cygnus he actually meant the right hand. 2. Perseus has in his right hand a sword (or a stick with a handle) which is oriented parallel to and a little east of the vernal equinoctial colure. Hipparchus says that the right hand coincides with the star η Per and that the nebula χh is in the sickle sword. The orientation of these two stars is such that the sword cannot be parallel to the colure but has to be more or less perpendicular to it. The situation on the globe is closer to Ptolemy who places the star η Per in the right elbow and the nebula χh in the right hand. In Greek mythology Perseus

received the (hooked) sword, a sickle, from Mercury and decapitated Medusa with it.151 The sword is not explicitly mentioned in the Ptolemaic catalogue description but in describing the Milky Way Ptolemy refers to the hilt of a sword, suggesting that this weapon was part of the astronomical figure and would have been known among artists.152 This also may apply to the wings on Perseus’s feet. Germanicus says that Perseus is ‘winged’ and, later, that he has ‘wing-bearing’ feet.153 Neither Hipparchus nor Ptolemy mentioned wings on Perseus’s feet. 3. Pegasus has wings but Hipparchus does not mention them and speaks only of the rump.154 Ptolemy seems to have been the first to mention the wings: he placed the star (γ Peg) in the wing tip. As Kidd points out, Aratus does not mention any wings in his description of the Horse, despite the fact that he clearly identifies it with the figure of Pegasus.155 On Kugel’s globe Pegasus is without, but on the Mainz globe he is with wings. Manilius (5.24 and 5.633) speaks of a flying horse. On the Farnese globe Pegasus’s right hoof is on the Tropic of Cancer and the left one is nearly touching it. Hipparchus identified the left hoof with κ Peg, the declination of which in Hipparchus time was 17°. It is not clear which star Hipparchus placed in the right hoof but Ptolemy identified that hoof with π Peg, the declination of which in Hipparchus’ time was 24°. However that may be, the Tropic of Cancer passed at best through one hoof only whereas Eudoxus 151 Philips 1968. 152 Toomer 1984, p. 402. 153 Germanicus (Gain 1976), pp. 28 and 59, ll. 248 and 253–4. 154 Duke 2006, p. 91. 155 Aratus (Kidd 1997), pp. 258–9.

147 The positional data for the epoch of Hipparchus were taken from Grasshoff 1990, pp. 275–316. 148 Hipparchus (Manitius 1894), I.11.16, pp. 118–19. 149 Hipparchus (Manitius 1894), I.2.13 and 15, pp. 16–17. 150 Schaefer 2005, p. 173.

99

celestial cartography in antiquity had the tropics go through both feet of the Horse.156 According to both Aratus and Germanicus, the Tropic of Cancer touched the Horse’s hooves.157 For Hipparchus it was not clear at all which stars Aratus placed in the hoofs of the horse.158 Clear or not, the hoofs of the Farnese Pegasus are more in line with the descriptions of Eudoxus and Aratus than with that of Hipparchus. 4. Aries is standing on its hindlegs with forefeet as if jumping.The Equator passes through his right front hoof, his left front knee, and the hoofs of his hindlegs. The orientation of the forefeet does not correspond to the description of Hipparchus who places the star η Psc in the forefeet.As a result the forefeet are stretched in front of the Hipparchan Aries such that the forefeet are west of the equinoctial colure, and remain above the Equator, as shown in Scheme 2.7. Only the star in the hindlegs (μ Cet) is, according to Hipparchus, on the Equator.159 In Hipparchus’s day the declination of μ Cet was indeed 0°. Aries would certainly be bisected by the Equator if the forefoot of the Aratean constellation is identified with α Psc.The declinations of γ Ari (the horn) and α Psc (the forefoot) were respectively 8° north and 8.5° south of the Equator. Ptolemy does not place stars in the forelegs of Aries. 5. Gemini consists of two nude embracing figures. The right arm of the right or following twin is lowered which does not correspond to the description of Hipparchus who places the star μ Cnc in the right hand of that twin. Ptolemy places this star in the northern back

6.

7.

8.

9.

10.

11.

156 Hipparchus (Manitius 1894), I.2.18, pp. 20–1 and I.10.13, pp. 104–5. 157 Aratus (Kidd 1997), pp. 108–9, l. 486–90. 158 Hipparchus (Manitius 1894), I.10.7, pp. 100–1. 159 Hipparchus (Manitius 1894), I.10.18, pp. 106–9.

100

leg of Cancer and does not specify the orientation of the right arm of the twin. Cancer is symmetric with respect of the ecliptic, but Hipparchus does not specify the northern back leg (see Gemini). Virgo has two hands, one on the Tropic of Cancer and the other on the Equator. Although Hipparchus does specify the right and left hand, the star marking the right hand (ζ Vir) is not on the Tropic of Cancer but close to the skirt. Ptolemy places this star under the apron on Virgo’s right buttock and specifies only the left hand Spica. Libra is depicted as a pair of scales, which does not conform to Hipparchus who lists it as the Claws of the Scorpius (see the discussion of the Claws on Kugel’s globe). Manilius (1.611) speaks of ‘juga Chelarium’ which Goold interprets as Claws holding a balance.160 Sag ittarius is clearly without a cloak attachment around his neck, which is a prominent feature in the description of both Hipparchus and Ptolemy. Aquarius holds an urn from which water streams. The stream runs down and intersects the zodiacal band and subsequently flows along the Tropic of Capricorn until it touches the tail of Cetus.The path followed by the stream does not agree with the description of both Hipparchus and Ptolemy. It seems closest, but not quite enough, to a confusing description of Aratus (see the discussion of Aqua on Kugel’s globe). Pisces are not connected on the Farnese globe by a line or cord as all authors agree that they should. All authors mark the knot in the cord (α Psc), which in Hipparchus’s

160 Manilius (Goold 1977), p. 52, l. 611.

2.6 The Farnese Globe

Scheme 2.7 Schematic presentation of Aries as defined by Hipparchus.

day was a little east of the colure. Germanicus describes the knot as shining directly above the crest of the Sea Monster (Cetus).161 12. Orion kneels on his right knee and his left leg is bent, conforming to the description of Ptolemy who places the star κ Ori in the right knee. Hipparchus places this star in the right foot which would make him standing. The Equator seems to intersect Orion in the middle.Aratus says that the celestial Equator runs through the belt of Orion.162 It is ironic that this is confirmed by Hipparchus.163 Modern editors agree that this text is problematic because the stars in the belt of Orion (δ, ε, and ζ Ori) were in Hipparchus’ day respectively 4.5°, 5°, and 5.5° below the Equator. It is not like Hipparchus to make such an error.

13. Canis Maior has rays emanating from his head which have no place in the description of either Hipparchus or Ptolemy. Do all these deviations suggests that the Farnese globe cannot have its origins in a Hipparchan globe? The answer is far from clear. Artists had access to many sources.The corpus of constellation drawings in Antiquity, especially those belonging to the descriptive tradition, must have been substantial and well-known. The beautiful decoration of the ship Navis (Fig. 2.18) exemplifies this. Besides, the definition of constellation figures was changing continually as Ptolemy testifies:‘the descriptions which we have applied to the individual stars as parts of the constellation are not in every case the same as those of our predecessors (just as their descriptions differ from their predecessors)’.164 For all such reasons constellation images developed over the course

161 Germanicus (Gain 1976), pp. 32 and 63, ll. 369–71. 162 Aratus (Kidd 1997), pp. 88–9, ll. 231–2. 163 Hipparchus (Manitius 1894), I.10.19, p. 109.

164 Toomer 1984, p. 340.

101

celestial cartography in antiquity of time. Unfortunately too few artefacts survive today to trace this development with certainty. Interventions in constellation design do not mean that the sculptor suppressed all characteristics of his model globe. For example, the fact that the head of Hercules is west of that of Ophiuchus, and that the latter is not standing with both feet on Scorpius as described in the Aratean tradition, follows from the mathematically determined locations of the stars in the heads of these two figures. The absence of images for nameless configurations of stars (Anonymous I and II) marked on Kugel’s and the Mainz globe is another indication that the model globe used by the sculptor of the Farnese globe belonged to the mathematical tradition. Indeed, of all the constellations only the image of Andromeda is reversed from rear to front, but her feet show that on the model she was depicted in rear view. Against this backdrop I am inclined to accept that—although the Farnese globe contains no actual stars, the circles on the globe are drawn inexactly, the dating of the globe is uncertain, and its sources controversial—the Farnese globe is closest to what remains today of the early mathematical tradition in globe making. Unless new information is discovered, it will remain hypothetical whether that tradition started with Hipparchus or not.

Appendix . Catalogue of antique celestial globes G1. CELESTIAL GLOBE (First century bc–second century ad?) diameter : 64 mm; height 60 mm. Galerie J. Kugel, Paris.

construction: The hollow sphere is made of (possibly gilt) silver and its thickness varies from 9 to10 mm. At the south pole is a circular hole of 35 mm in diameter. The celestial map is added to the sphere by chasing. The sphere is damaged at the surface in a number of places: east of the winter solstitial colure from the tail of Sagittarius at the Tropic of Capricorn to the tail of Piscis Austrinus; from the hindfeet of Centaurus to the border of the circular hole and at the intersection of the summer solstitial colure and this southern cut-off. cartography: Coordinates: there is an equatorial grid consisting of four parallel circles which represent the Equator, the Tropics of Cancer and Capricorn, and the ever-visible circle. The tropics are located at an angular distance from the Equator of 26° (N) and 22° (S), respectively, that is, a mean value of 24°±2°. The ever-visible is at an angular distance from the north pole of 34° (N).The ever-invisible circle is not drawn but it may well coincide with the lower limit of the sphere because the cut-off lies at a distance from the Equator of 56°, which is equivalent to a value of 34° from the south pole. Perpendicular to the five parallels are two great circles which represent the colures. In addition one oblique circle has been drawn, representing the ecliptic.The obliquity of the ecliptic amounts to about 24°. The equinoctial colures, the Equator, and the ecliptic pass neatly through the equinoxes but the ecliptic, the tropics, and the solstitial colures do not meet precisely in the solstices. constellations: All Aratean constellations (see Table 2.1) are presented (Libra is presented by the Claws of Scorpius). Most of the constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Centaurus is depicted in profile and Sagittarius is seen from behind. In addition to the Aratean constellations there are two nameless groups (Anonymous I and II) in the shape of rings, located below Lepus and Aquarius. northern constellations: Ursa Minor is a small jumping animal with a long tail. The winter

102

Appendix 2.1 Catalogue of antique celestial globes solstitial colure cuts through the middle of the body. His head faces into the second elongated bend of Draco. Ursa Maior is a great bear with a long tail. His head is below the tail of Draco. The summer solstitial colure cuts through the body just behind his front shoulders. His feet rest on the ever-visible circle. Draco is a snake with two bends, of which the second is greatly elongated. The winter solstitial colure cuts through the first bend below (south of ) Ursa Minor, the autumnal equinoctial colure through the second bend in the body of Draco, and the summer solstitial colure cuts through the tail which ends in front of the head of Ursa Maior. Draco’s head is on the ever-visible circle. Cepheus is a figure in a long dress, Phrygian hat and shoes at his feet. He is oriented perpendicular to the vernal equinoctial colure and the ever-visible circle intersects his body as low as the hips, that is, his head, arms, and breast are south of it. His left arm stretches towards the right wing of Cygnus and his right hand almost touches the left hand of Cassiopeia. Bootes is a nude male figure. His right hand points to the tail of Ursa Maior. His orientation is more or less parallel with the ever-visible circle, with the result that his head is below the left foot of Hercules. The autumnal equinoctial colure passes through his hips and it intersects the right lower arm a little north of the ever-visible circle and the latter circle intersects this arm a little west of the colure. Corona Borealis is a simple ring consisting of two concentric circles. It is located behind the back of Hercules and above the left shoulder of Bootes. Hercules is a nude male figure. He is upsidedown with respect to the Equator. He is kneeling on his left knee. His right foot is located west of the head of Draco. His own head is east of the head of Ophiuchus, his one arm is stretched out in the direction of Lyra and his other arm is raised. He holds a round object in his raised hand. His whole body is north of the Tropic of Cancer and south of the ever-visible circle. Lyra is an instrument consisting of a tortoiseshell with horns; the horns are connected by a cross bar; a number of strings go from the cross bar on the south to the shell in the north. Cygnus is a bird with outstretched wings flying down in the direction of

the Equator. The neck of the bird is at the intersection of the Tropic of Cancer and the winter solstitial colure. The southern wing is intersected by the Tropic of Cancer. The other northern wing almost touches the winter solstitial colure and its tip is a little south of the ever-visible circle. Cassiopeia is a female figure with outstretched arms, in a sitting attitude. She is parallel to the Tropic of Cancer such that the lower part of her body is turned towards the east and the upper part to the west. She is dressed. The chair, if there is one, seems to be presented by a ring of two concentric circles, close to the vernal equinoctial colure. The spring equinoctial colure grazes the feet of Cassiopeia. Perseus is a nude male figure. There are wings on his head but not on his feet. His right arm is lowered and carries the Gorgon head. In his raised left hand he carries a harpe which is oriented roughly parallel to the vernal equinoctial colure. His head is below the feet of Andromeda, his left hand with harpe below the feet of Cassiopeia, his right hand (with the Gorgon head) almost touches the Tropic of Cancer and the legs point in the direction of Auriga. Auriga is a nude male figure standing in a chariot in a driving attitude. Both arms are stretched in front of him. His chariot is intersected by the Tropic of Cancer, and the wheel rests on the ecliptic and touches the back of Taurus. Ophiuchus is a nude male figure. His head is south of the raised arm of Hercules and turned east. He holds the body of the Serpent. The Equator cuts through his thighs just above his knees. He is standing upright with his right foot on Scorpius. Serpens covers a large space. His head is not far from the left hand of Bootes. His neck is cut by the Tropic of Cancer west of the raised arm of Hercules, the middle of his body passes in front of Ophiuchus, then the body turns south and rises again intersecting the Equator twice. The tail seems to end more or less in front of the head of Cygnus, not far away from the Tropic of Cancer. Sagitta is an arrow pointing east. It is located between Aquila and Cygnus. The winter solstitial colure cuts through its middle. Aquila is a bird with outstretched wings, standing upright. The winter solstitial colure cuts through the tail and its (left)

103

celestial cartography in antiquity eastern wing such that his head, body, and western wing are west of the colure.The Equator cuts through his body and the (right) western wing. Delphinus is a dolphin with a double tail. Its snout touches the Equator and its tail is more to the north below Sagitta, just east of the winter solstitial colure. Pegasus is half a horse without wings. He is upside-down with respect to the Equator. The northern point of the cut-off touches the head of Andromeda. Pegasus’s head grazes the Equator. Andromeda is a female figure in a long dress. Her head is turned in profile to her right side. She is roughly parallel to and south of the Tropic of Cancer but the latter circle passes between her lower legs. The left arm is raised such that the lower arm is grazing the Tropic of Cancer. The other right arm is stretched in the southern direction to the equator. The vernal equinoctial colure cuts through the lower part of her dress. Triangulum is depicted as a triangle located west of the vernal equinoctial colure, between the northern fish and the head of Aries. zodiacal constellations: Aries is standing on its hindlegs with forefeet as if jumping. He has a long tail and his testicles are depicted. He is looking backwards in the direction of Taurus. The vernal equinoctial colure grazes the one horn seen at the back of his turned head, and cuts through his forelegs close to the knees.The ecliptic passes between the forelegs, cuts through the body lengthwise and passes just above the tail. The Equator passes through the left foreleg and the hoofs of his hindlegs.The left foreleg of Aries touches the cord that connects the fishes south of the Equator.Taurus is half a bull with a bent head, two front legs, and two short horns. The knee of the bent right leg and the hoof of the stretched left leg both rest on the Equator. The ecliptic passes through the back of Taurus, but the short horns remain below the ecliptic. Gemini consists of two nude figures.The left arm of the left or leading twin touches the right arm of the right twin that is following. The Tropic of Cancer cuts through the middle of both twins and the ecliptic passes through the hips. There are no attributes. Cancer is a crab with two claws facing Gemini and four legs on either side. The ecliptic and the Tropic of Cancer intersect the

body lengthways.The tip of the left claw touches the point of intersection of the Tropic of Cancer and the summer solstitial colure. Leo is a lion is standing on its hindlegs with his forefeet as if jumping. He is looking forwards to Cancer. The lion’s tail makes a loop which starts below the Tropic of Cancer and ends above it. The Tropic of Cancer intersects the main body (the breast, the back, and the tail) of the lion lengthwise. The ecliptic passes through the chest and the hindlegs. Virgo is a female figure without wings, in a long dress and a shawl.The body is aligned with the ecliptic which cuts through the right shoulder and the body lengthwise. The Equator passes obliquely through the lower part of the body and the wrist of her lowered right arm, close to the tail of Hydra.The autumnal equinoctial colure cuts through the lower part of her dress. There are no attributes. Scorpius has two long claws, four legs on both sides, and a long segmented tail. The laws representing Libra are stretched out to the feet of Virgo. The ecliptic passes between the laws, cuts the body lengthwise and intersects the end of the tail.The end of the right northern law is intersected by the Equator. The Tropic of Capricorn passes through one leg and the bend in the tail of Scorpio.The tail starts just below the ecliptic, continues south below the Tropic of Capricorn, then turns north and ends above the ecliptic close to the arc of Sagittarius. On its body rests the right foot of Ophiuchus. Sagittarius is a horse with a nude figure on top. He is looking forward in the direction of Scorpius. In his left hand he carries a bow; in his unseen right hand he draws the string. The ecliptic and the Tropic of Capricorn intersect him in the middle where the human body connects to the horse’s part. His right front hoof is inside the ring presenting Corona Austrinus. The winter solstitial colure cuts through the hind part of the horse’s body, just in front of his hindlegs. Capricornus has two horns, bent forelegs, and a double tail.The ecliptic intersects him in the middle lengthwise.The Tropic of Capricorn cuts through his body just above the forelegs. There is a distinct distance between his head and the winter solstitial colure. Aquarius is a nude figure. His head is seen in profile and turned to the east. The right arm is directed

104

Appendix 2.1 Catalogue of antique celestial globes north towards the Equator.The ecliptic passes through the hips and the wrist of the lowered left arm. The Tropic of Capricorn intersects the body at its knees. From the left hand flows a stream of water.The stream first winds its way around the ecliptic and then goes south, intersects the Tropic of Capricorn and continues all the way down to the ever-invisible circle. Just before reaching the ever-invisible circle it touches a ring consisting of two concentric circles (see Anonymous II below). Pisces consists of two fishes. The southern of the two fishes is located below the Equator. The ecliptic cuts through its body. The other, northern fish is located east of the right arm of Andromeda, parallel to the vernal equinoctial colure. The Equator cuts through its tail. There is a ‘cord’ which connects the tails of the fishes. This cord touches the left foreleg of Aries. southern constellations: Cetus is presented as a dolphin, the head of which is south of Aries. The vernal equinoctial colure cuts through the middle of the body at the point of intersection with the Tropic of Capricorn. The stream of Eridanus passes in front of its head. The tail ends east of the stream of water of Aquarius. Orion is a figure dressed in a short tunic with a cloak. He has a funny head. He carries a club in his outstretched right hand and as a consequence this club is located below Taurus instead of Gemini. His left arm seems to be covered by a piece of cloth.The Equator intersects his neck above the shoulders and his feet rest on the Tropic of Capricorn. Lepus is a running hare, below the feet of Orion. Its head grazes the Tropic of Capricorn. Eridanus is a river that starts at the right foot of Orion and winds first along the Tropic of Capricorn, intersecting this circle three times, towards Cetus in the west, where it turns south. It continues below the Tropic of Capricorn to a point just east of the vernal equinoctial colure and above the ever-invisible circle. Canis Maior is but a poor dog. The Tropic of Capricorn grazes the forefeet and intersects its hindlegs. The summer solstitial colure touches the end of his tail. Canis Minor is tiny dog sitting on the Equator, below the left foot of the twin that is following and west of the summer solstitial colure

which grazes his hind part. Navis is the rear part of a ship with a stylis, a mast, and two steering oars. The Tropic of Capricorn intersects the stern at the top, the stylis at its lower end, and the mast in the middle. The summer solstitial colure grazes the stern and intersects the steering oars. Hydra is a snake which winds its way around the Equator from west to east, intersecting this circle several times. The head is located above the Equator below Cancer and its tail is below it and above the head of Centaurus. Crater is a vase without handles, located above the Equator on top of a coil in the body of Hydra. Corvus is a bird, the feet of which seem to stand on the body of Hydra. It is pecking the body of the snake and its tail points towards the right shoulder of Virgo. The Equator cuts through the body of Corvus. Centaurus is a horse with a nude figure on top. There is a cloak floating from the neck of the figure and the horse has a long tail. Centaurus’s arms are stretched in front of him and he seems to touch with his outstretched left hand the tail of Lupus. The Tropic of Capricorn runs through the middle of the human body and the upper arms. The autumnal equinoctial colure passes through his left hand and just east of his forelegs. Lupus is an animal that seems to fall backwards such that its hindfeet touch the Tropic of Capricorn from below. Ara is an altar standing on three feet. Corona Austrinus is a ring consisting of two concentric circles, located around the right front hoof of Sagittarius. Piscis Austrinus is a fish with its back north, swimming to the east, located below Capricorn. Anonymous I is presented as a ring consisting of two concentric circles, located between Eridanus and the rudder of Navis, below Lepus. Anonymous II is presented as a ring consisting of two concentric circles, located between Piscis Austrinus and the stream of water, below Aquarius. unusual features: North of the head of Leo is a structure consisting of a vertical bar extending in the north–south direction and an horizontal one perpendicular to it which starts at the middle of the vertical bar and extends to the east. It is not treated here as a new constellation figure.

105

celestial cartography in antiquity Above the tip of the tail of Ursa Maior and inside the ever-visible circle is a small circle. Another one is placed below the tip of the tail and south of the evervisible circle. On both sides of the summer solstitial colure, just below the intersection with the evervisible circle and Ursa Maior, are two small circles, or four in all. Below the head of Pegasus and just south of the Equator is a small circle. Above the back of Aries is a small circle. Below the tail of Leo and just south of the Tropic of Cancer is a small circle (or perhaps two?). comments: On a sphere with a diameter of 64 mm, 0.5° corresponds to ¼ mm. Therefore, all values in degrees given by Cuvigny 2004 have been rounded off to within 0.5°. For more details on the globe, see Section 2.3. Literature: Kugel 2002; Cuvigny 2004.

G2. CELESTIAL GLOBE (ad 150–220) diameter: 11 mm. Mainz, Römisch-Germanisches Zentralmuseum Mainz, Inventory number: O.41339. construction: The sphere is made of messing and consists of two hollow hemispheres connected at the Equator. The thickness of the sphere varies from 0.5 mm to 3 mm. At the north pole is a small square opening of 8 × 8 mm. At the south pole there is a circular hole of 39 mm in diameter.The celestial map is added to the sphere by chasing. cartog raphy: Coordinates: there is an equatorial grid consisting of three parallel circles which represent the Equator and the Tropics of Cancer and Capricorn.The Tropics are located at an averaged angular distance from the Equator of 23.5° (N) and 23.5° (S), respectively. Perpendicular to the three parallels are two great circles which represent the colures. In addition, three oblique circles have been drawn, representing the ecliptic, the northern and southern boundary of the zodiacal band. Also the Milky Way is traced by a band marked by small circles.The ecliptic intersects the summer solstitial colure just below the

intersection of this colure with the Tropic of Cancer. Its intersection with the winter solstitial colure is just above the intersection of this colure with the Tropic of Capricorn.The points of intersection between the ecliptic and the Equator are east of those between the Equator and the equinoctial colures (see Scheme 2.5). The zodiacal band has a width of about 13.5°; it is presumably divided into twelve equal parts, but the boundaries between the signs are hard to see. constellations: Of the Aratean constellations only Triangulum is missing (see Table 2.1). Libra is presented by the Claws of Scorpius. Most of the constellations are presented in rear view and conserve the left and right characteristics as defined by Hipparchus’s rule. Exceptions are Cepheus, Cassiopeia, Andromeda, and Virgo. In addition to the Aratean constellations there are two nameless groups (Anonymous I and II) in the shape of a circlets placed in a ring, located below Lepus and the tail of Cetus. In addition, the globe is adorned by small circlets which represent stars. These stars are sometimes located within and sometimes outside constellations. The descriptions below are based on photos. northern constellations: Ursa Minor is a bear with a distinct tail. The winter solstitial colure cuts through the middle of the body. His head faces into the second bend of Draco.There are four stars in the body and three in the tail, or seven stars in all. Two additional stars in the tail belong to the feet of Cepheus. Ursa Maior is a greater bear with a less distinct tail.The summer solstitial colure cuts through the body just behind his front shoulders. The tail of Draco ends above his back on the colure. There are four stars in the body and three in the tail, or seven stars in all. Around the Bear’s head are four additional stars. Draco is a snake with two bends. The winter solstitial colure cuts through the mouth and the neck below (south of ) Ursa Minor and the summer solstitial colure cuts through the tip of the tail above Ursa Maior. It has three stars in the head and six in the body, or nine stars in all. cepheus is a figure in a long dress and a Phrygian hat who faces the viewer. He is oriented in the north– south direction and upside-down with respect to the

106

Appendix 2.1 Catalogue of antique celestial globes Equator. His feet are below the tail of Ursa Minor. His left arm stretches towards the right wing of Cygnus and his right hand touches the left side of Cassiopeia. He has three stars in the hat, two in each arm, three in the waist, and one in each foot, or twelve stars in all. Bootes is a male figure with bare feet and dressed in a short ‘tunic’, standing with his back to the viewer. His left leg is stretched and his right leg bent. His head is turned to his left side. His left arm is stretched in front of him and in his right arm he raises a club.The Tropic of Cancer passes just below his feet and the autumnal equinoctial colure cuts through his left hand and left lower leg. He has four stars in his club, two below his right elbow, two in his left arm, two in front of his left hand, three in the waist, three in his dress below his waist, three in his left leg, and one between his legs, or twenty stars in all. Corona Borealis consists of seven circlets placed in a ring, located above the head of Serpens and between Bootes and Hercules. Hercules is a nude male figure. He is upside-down with respect to the Equator. His left leg is bent and his right leg stretched behind him. His head is east of that of Ophiuchus; his left arm is in the direction of the head of Cygnus.The winter solstitial colure intersects his right leg and arm. He holds a skin or piece of cloth or something like it over his outstretched left lower arm and a club in his outstretched right hand behind him. His left foot is located south of the first bend of Draco. He has one star in the head, three in the left arm, four in the upper body, two on his right hip, three in the left thigh, two in his left foot, two on his right leg, one in his right foot, or eighteen stars in all. In addition, there is one star below the right arm with the club. Lyra is an instrument located between Hercules and Cepheus. It consists of a tortoise-shell with horns; the horns are connected by a cross bar; a number of strings go from the cross bar to somewhere underneath the shell. It has seven stars in all. Cygnus is a bird with outstretched wings, in a position as if flying southwards. The beak of the bird is between the left hand of Hercules and the eastern end of Sagitta. Its neck and left wing are intersected by the Tropic of Cancer and the wing’s tip is close to the left leg of Pegasus just south of the tropic. It has four stars in its body, three below

the tip of the left wing, and two below the right wing, or nine stars in all. Cassiopeia is a female figure with outstretched arms, sitting obliquely on a square seat. She is upside-down with respect to the Equator. She is dressed in a long robe but her breasts are shown. Her head is above that of Andromeda and touches the Tropic of Cancer. The vernal equinoctial colure intersects her chair and body length wise. She has three stars in her left arm, four in the right arm, four in her upper body, and three in the left leg, or fourteen stars in all. Perseus is a nude male figure with Phrygian hat showing his back to the viewer. His body is above and parallel to the Tropic of Cancer with his head on the western side. His head is turned south. He carries the Gorgon head in his lowered left hand. In his lowered right hand he holds a stick. His left foot is below Auriga and his right foot touches the right arm of Auriga. He has one star in each shoulder, two on his right arm, one on his left arm, two in his back, three in the left leg, and four in the right leg, or fourteen stars in all.Auriga is a male figure wearing a long dress and a spiky hat. He is kneeling to the east and faces the viewer. His head is turned east. In his left hand he carries a whip. He has one star in each shoulder, one on his left elbow, two in the left leg, and one in the right foot, or six stars in all. Ophiuchus is a nude male figure showing his back to the viewer. His head is turned west. His left arm is stretched out and holds the upper part of the body the Serpent. His right arm is lowered and holds the tail of the Serpent. He has very long legs which rest on the back on Scorpius. The Tropic of Cancer passes through his shoulders, the Equator cuts through his legs, and the winter solstitial colure intersects his head and back. He has one star in the head, one in each shoulder, two on his right arm, three on his left arm, one in his left hip, one in the left leg, and four in the right leg, or fourteen stars in all.There are two stars in front of the face of Ophiuchus. Serpens covers a large space. His head is below Corona Borealis. His neck is cut by the Tropic of Cancer and the middle of his body passes behind the visible back of Ophiuchus. His tail seems to end more or less east of Ophiuchus and west of Sagitta.The winter solstitial colure passes through its body at the middle of Ophiuchus.There are nine stars

107

celestial cartography in antiquity in the body and two in the head, or eleven stars in all. There is one star in front of the head of Serpens. Sagitta is a stick extending from the feet of Aquila to the head of Cygnus. There are no stars. Aquila is a bird with folded wings lying on his back on the equator, below the tail of Serpens. He faces north and has six stars in the body. Delphinus is a dolphin with a double tail. It is located above the Equator, between Aquila and Pegasus. It has two stars in the head, two in the ventral fin, and four in the body, or eight stars in all. Pegasus is half a horse with wings and a decorated band around its body. In front of his nose is a circlet. He is upside down with respect to the Equator, which almost grazes his head and the wing. The tip of the wing is close to the Equator. The knees and hoofs of the front legs are on the Tropic of Cancer.The head of Andromeda almost touches the cut-off of its body in the east.There is one star close to his back, close to the cut-off of the body. Andromeda is a female figure in a long dress girded around the waist but her breasts and legs are shown. She is facing the viewer. Her head almost touches the cut-off of Pegasus’s body and her feet are south of Perseus. Her arms are stretched to either side.The Tropic of Cancer cuts through her left lower arm and her left hand touches the head of Cassiopeia. Her right hand grazes the Equator.The vernal equinox intersects her breast and touches her right hand. She has one star above her head (the one in common with Pegasus), one in her southern arm, and three in her waist, or five stars in all. zodiacal constellations: Aries is lying down east of the vernal equinox and looks backwards to Taurus. The upper boundary of the zodiac grazes his horns and the ecliptic intersects its neck. The right foreleg, the lower part of his body, and the tip of his tail are on the southern boundary of the zodiacal band. The Equator passes through the body lengthways. He has two stars in the horns, one in the head, two in the chest, two below the front legs, and one on the back, or eight stars in all. Taurus is half a bull with a bent head, two front legs, and two short horns. His right horn is on the Tropic of Cancer, just below the left lower leg of Perseus.The hoof of the right leg rests on the Equator, and his left leg touches the piece of cloth carried by Orion. The short horns do not

extend to the feet of Auriga. He is confined to the zodiacal band except his front legs.There is one star in each horn, one in the head, and seven in the neck, or ten stars in all. Gemini consists of two nude male figures with curly hair. They are seen from behind by the viewer and orientated parallel to the nearby summer solstitial colure. Their heads are turned in profile towards each other. The left arm of the right or following twin rests on the back of the left or leading twin, and vice versa, the right arm of the left or leading twin on the back of the one following. The Tropic of Cancer cuts through the backs of both twins and their feet are resting on the Equator. The left or leading twin has one star in the head, one in the shoulder, one in the right hand, one on the right hip, and one in each foot, or six stars in all.The right or following twin has one star in the head, one in the shoulder, one on the left hip, one in each knee, and one in the right foot, or six stars in all. In addition, there is one star east of the head of the following twin and also east of the colure. Cancer is a crab with two claws on the side of Leo and eight legs. The ecliptic intersects the body lengthways. The main body is confined within the boundaries of the zodiacal band. It has six stars in the body and four in each of the set of legs, or fourteen stars in all. Leo is a lion standing firmly on all four feet. He is looking forward to Cancer. The lion’s tail is raised. The upper boundary of the zodiacal band intersects the upper legs of the lion. His hindpaws are just above and his forepaws just below ecliptic. He has two stars in front of his head, one in the chest, three on the back, two in the place where the tail parts from the body, one above the tip of the tail, three in each foreleg, one below the belly, and two in his left back leg, or eighteen stars in all. Virgo is a female figure with wings facing the viewer and wearing a long dress. Her body aligns with the zodiacal band and is confined to it. Her head is below Leo’s tail and her feet are touching the autumnal equinoctial colure. She holds an ear of wheat in her raised right hand. Her left hand is lowered.The Equator passes through her right foot.There are three stars on the north side of her head. At the feet of Virgo are two small circles around a dot which may be two more stars. Scorpius is a scorpion with extremely long claws representing

108

Appendix 2.1 Catalogue of antique celestial globes Libra.The claws, the main body and a part of the segmented tail are within the zodiacal band.The end of the northern claw is on the Equator.The tail is north of Ara; it starts and ends on the ecliptic but the middle part is on the southern boundary of the zodiac. It has one star in each claw, two in the body, and seven in the tail, or eleven stars in all. Sagittarius is a horse with a male figure on top and with the right leg raised.The male figure is bearded and has long hair. His human back is turned towards the viewer; his head is in profile, looking forward in the direction of Scorpius. In his left hand he carries a bow; with his unseen right hand he seems to pull the string. The ecliptic and Tropic of Capricorn intersect him in the chest. The winter solstitial colure passes through the horse’s hind part and left hindleg. He has one star in the left shoulder, one in the right elbow, two in his chest, two in the bow, onw in each foreleg, two in the left hind thigh, and one in the left hindfoot, or eleven stars in all. Capricornus has two large horns and a corkscrew tail. The tail and the horns are intersected by the northern boundary of the zodiacal band but the remainder of the body is confined to the zodiacal band. It has one star between its horns, two in the left horn, two on the nose, six in the body, and two in the tail, or thirteen stars in all. Aquarius is a nude male figure with a Phrygian hat and a scarf which emerges from the hat. His back is turned to the viewer and his body is in the north–south direction. His head is seen in profile and turned to the east to face the head of Pegasus. His feet are above Piscis Austrinus.The ecliptic intersects the body at his hips. His left arm is bent and his right arm is stretched and holds an urn from which water streams. The stream runs south and intersects the zodiacal band and subsequently ends in the mouth of Piscis Austrinus. The Tropic of Capricorn passes below the knees of Aquarius and through the middle of the stream Aqua. He has one star in the head, one in the shoulder, one above and two below his right arm, one at the tip of his shawl, one on each buttock, and one on each foot, or ten stars in all. In addition, there are seven stars in the stream of water. Pisces consists of two fishes.The southern of the two fishes is located below the Equator, and more or less parallel to it, just below the wing of Pegasus.The other,

northern fish is parallel to and west of the vernal equinoctial colure.The Equator passes through its tail.The two fishes are connected at their mouths by a cord. There are three stars in the southern fish, one in the cord, and two on the other fish, or six stars in all. southern constellations: Cetus is a monster with along corkscrew body, swimming to the east but turning its head backwards. Its head is south of Taurus and its tail is south of Pisces. Its body is almost completely confined between the Equator and the Tropic of Capricorn. Only its tail is bent southwards and intersects the Tropic of Capricorn. The hind part of its body is on the vernal equinoctial colure. It has two stars in the head and nineteen in the body, or twentyone stars in all. In addition, there are two stars above its head and two above its back. Orion is a male figure striving to the west, with his back turned to the viewer. He is dressed in a short tunic and has a cape around his shoulders which covers his left arm. His head is turned as he looks towards Taurus. He carries a stick in his raised right hand.The Equator intersects his body in the waist. On the left side below the waist a train of five small circles, presumably stars, suggest the presence of a sword. His left leg rests on the Tropic of Capricorn. He has three stars in his waist, two in the right elbow, one at the tip of his stick, five stars arranged as a sword, and two in the right leg, or thirteen stars in all. Eridanus is a river that starts at the Tropic of Capricorn, at the left foot of Orion, and streams first to the west, then turns below Cetus to the east and continues below the Tropic of Capricorn making two bends until it is south of the head of Lepus where it ends. It has one star in each claw, two in the body, and seven in the tail, or eleven stars in all. Lepus is a hare with long ears running westwards. It is intersected by the Tropic of Capricorn. It has 13 stars distributed over its body. Canis Maior is a dog jumping to the west. There are rays emanating from his head.The Tropic of Capricorn intersects its body just above the hindlegs. The summer solstitial colure touches the outstretched front paws. It has one star below its mouth, one in the head, five in the body, and two in the left foreleg, or nine stars in all. Canis Minor is a dog running to the west. It is located

109

celestial cartography in antiquity below the Equator and the feet of Gemini.The summer solstitial colure passes through the middle of its body. It has two stars in the body. Navis is the rear part of a ship with a mast at the cut-off.The stern is shaped as a dog’s head with a collar.The Tropic of Capricorn passes through the stern and the top of the mast.There are two steering oars and four normal oars. On deck are a small house and four shields. The autumnal equinoctial colure passes just east of the mast at the cut-off of the ship. It has two stars at the tip of the mast, three in the dog’s head, seven in the body of the ship, three in each steering oar, and one in each of the four oars, or twenty-two stars in all. Hydra is a snake, the head of which is located between Cancer and Canis Maior. The Equator passes through its neck. The autumnal equinoctial colure cuts through the end of the tail. It has one star in the head and three distributed over the body, or four stars in all. Crater is a vase or cup with handles, standing on the body of Hydra.The Equator intersects the middle of the vase. It has two stars on the rim, two in each handle, and two in the body, or eight stars in all. Corvus is a bird, the feet of which stand on the body of Hydra. It is picking the snake. It is below Virgo and its tail is on the autumnal equinoctial colure. It has six stars in the body. Centaurus is a horse with a nude male figure on top.The male figure is bearded and has a decorative band on his middle where the horse part joins his body.The claws of Scorpio are over his head.The Tropic of Capricorn runs through his neck. The autumnal equinoctial colure passes through his hindlegs.There is a piece of cloth over his left arm and in his right hand he holds a stick. His right hand touches the hindfeet of Lupus who is in front of him. It has two stars in the head, three in the human back, two in the waist, two in the right arm, one in the belly, one in the right forefoot, and five in the horse’s back, or sixteen stars in all. In addition, there are two stars west of his head and one above the stick in his right hand. Lupus is an animal that seems to fall backwards such that it is upside down with respect to the surrounding constellations. His head is close to Ara. There is one star below the body.Ara is an altar standing on a square base, with flames on top in the north. It has three stars. Corona Austrinus consists of seven

circular dots (representing stars) placed in a circle, located in front of the front legs of Sagittarius. Piscis Austrinus is a fish with its back south, swimming to the east, located below Capricornus and Aquarius. Its mouth is connected to the end of the stream of water poured from the urn of Aquarius. It has two stars in the head, three in the ventral fin, two in the body, two in the belly, and three in the tail, or twelve stars in all. In addition, there is perhaps a star in the eye. Anonymous I consists of seven circular dots (representing stars) placed in a circle around one dot in the middle, located below Lepus and between Eridanus and the rudder of Navis. It represents an unnamed group of stars. Anonymous II consists of seven circular dots (representing stars) placed in a circle, located below the tail of Cetus and between Piscis Austrinus and the stream of Eridanus. It represents an unnamed group of stars. the milky way is indicated by a broad band, the boundaries of which are marked by small circles.This band passes at the winter solstitial colure along the Equator until it reaches the neck of Aquila, where it continues north through Aquila and Sagitta to the head of Cygnus. It then runs south of the southern wing of Cygnus, then turns north and intersects the Tropic of Capricorn. At Cepheus’s head it turns east again, then passes southwards through the left (western) shoulder and body of Cassiopeia after which turn it goes east through the right hand and right leg of Perseus. It continues through the legs of Auriga where it turns south and passes just east of the right arm, grazes the club of Orion and continues west of the leading twin until it reached the Equator where it continues in a more eastern direction north of the Equator through the lower legs of Gemini. It crosses the Equator in front the Hydra, grazes its bend and the halo of Canis Maior. It passes below the whole length of Hydra and touches the stern and mast of Navis. At the tip of the tail of Hydra it turns south and continues along the autumnal equinoctial colure and intersects the legs of Centaurus. There the northern boundary ends. The southern boundary continues east and passes between Lupus and Ara (and grazes both), then through the left hand and bow of Sagit-

110

Appendix 2.1 Catalogue of antique celestial globes tarius until it reaches the Equator again at the winter solstitial colure.The northern boundary restarts at the end of the body of Scorpio so that its tail is between the northern and southern boundary. comments: For more details on the globe, see Section 2.4. Literature: Künzl 2000; Künzl 2005.

G3. CELESTIAL GLOBE (First century bc) diameter: ca. 65 cm. Naples, Museo Archeologico, Inventory number: 6374. construction: The sphere has a diameter of about 65 cm; it is made of marble and supported by a male figure presumably representing Atlas. The celestial map is added to the sphere in relief, such that circles appear to be behind or in front of figures.The constellations have been coloured originally, as many traces seem to indicate. On top of the sphere is a hole with a diameter of about 28.8 cm and a conical shape, the purpose of which is not clear.This hole starts in right ascension a little west of the summer solstitial colure and ends east of the autumnal equinoctial colure. In declination it extends about 50° from the north pole (which itself is clearly visible) to its southernmost point above Leo.The region above Sagittarius and that between Navis and Centaurus are damaged. There is also some damage in front of the right hand of Centaurus. cartography: Coordinates: there is an equatorial grid consisting of five parallel circles which represent the Equator, the Tropics of Cancer and Capricorn, and the ever-visible and ever-invisible circle. The tropics are located at an averaged angular distance from the Equator of 25.5° (N) and 25° (S), respectively; the ever-visible and the ever-invisible circle are at an averaged angular distance from the Equator of 56.7° (N) and 55.5° (S). Perpendicular to the five parallels are two great circles which represent the colures. In addition three oblique circles have been drawn, representing the ecliptic and the northern and southern boundary of the zodiacal band. The obliquity of the ecliptic amounts to about 25.3°. The points of intersection between the ecliptic and the Equator are

west of those between the Equator and the equinoctial colures (see Scheme 2.6).The zodiacal band has a width of about 13.5°; it is presumably divided into 12 equal parts, but there are no boundaries drawn between the signs of Aries and Taurus, Cancer and Leo, Libra and Scorpius, Capricornus and Aquarius, and between the latter and Piscis. constellations: Of the Aratean constellations the following are missing: Ursa Minor, the greater part of Ursa Maior, Sagitta,Triangulum, and Piscis Austrinus (see Table 2.1). The constellations Aquarius, Capricornus, Draco, and Sagittarius are incomplete. Canis Minor is hard to see because it is hidden behind the hand. Most of the constellations are presented in rear view and conserve the left and right characteristics as defined by Hipparchus’s rule, with the result that the heads of many figures seem rather twisted.An exception is the constellation Andromeda, but her twisted feet are still seen from behind. unusual feature: Close to the border of the hole around the north pole there is a rectangular form with an inner grid dividing it. There are two crossbeams at 1/3 from the outer edges and one through the middle of these two crossbeams.The configuration is located east of the summer solstitial colure, north of Cancer and the Tropic of Cancer but below the evervisible circle.This configuration has been interpreted by some as a new constellation figure but here it is not treated here as such. northern constellations: Ursa Maior is incomplete: only a part of his front legs is present which one finds just west of the summer solstitial colure and above the ever-visible circles. Draco is incomplete: only the head and one turn of the body located at the winter solstitial colure is presented. Cepheus is a male figure with a beard. He wears a long dress tied together at his girdle, a Phrygian hat, and shoes at his feet. He is upside-down with respect to the Equator. His head and his feet are turned east. His arms are stretched and the backs of his hands are shown. The left hand is below the feet of Cassiopeia and touches the ever-visible circle; his right hand remains north of that circle and is north of the tip of Cygnus’s right wing. The ever-visible circle touches his shoulders.

111

celestial cartography in antiquity Bootes is a male figure with bare feet, curled hair, and beard. He is dressed in an exomis which leaves his right shoulder bare. His head is turned west and touches the ever-visible circle. His left arm is raised and the ever-visible circle intersects it at his elbow. His right arm is lowered and in his right hand is a staff curved at one end (shepherd’s crook?). His left leg is stretched and his right leg bent. Both feet rest on the Tropic of Cancer and the autumnal equinoctial colure cuts through the toe of his left foot. Corona Borealis is a wreath with a bow and ribbons.The bow is on the northern side and the ribbons on the inside of the wreath. Hercules is a nude male figure and has curled hair. He is upside-down with respect to the Equator. His head is turned east to the head of Ophiuchus, his left arm is stretched out in the direction of Lyra, and his right arm is raised.The Tropic of Cancer intersects his head and his raised right arm at the wrist. He is kneeling on his right knee. His right toe, his right knee, and his left foot rest on the ever-visible circle. His left foot is located south of the head of Draco which is slightly north of the ever-visible circle. Lyra is an instrument consisting of a tortoise-shell with horns.The twisted horns are connected by a cross bar and a number of strings go from the cross bar to somewhere underneath the shell. The shell touches the winter solstitial colure. Cygnus is a bird with outstretched wings, flying south. The beak of the bird points towards the intersection of the Tropic of Cancer and the winter solstitial colure and almost but not quite touches it. Its left wing is intersected by the Tropic of Cancer and the tip touches the left foot of Pegasus just south of the tropic. The tip of the right wing touches the ever-visible circle. One foot is visible beneath the body. From under the left wing emerges a stick which is parallel to the neck of Cygnus and above the Tropic of Cancer. Cassiopeia is a female figure with outstretched arms, sitting in a chair. She is upside-down with respect to the Equator.The lower part of her body is turned towards the east.The upper part of the body is twisted in order to show the back, the hands, and the head from behind. She is dressed from the waist. Her left outstretched arm ends south of the head of Cepheus and her raises

right arm touches the dress of Andromeda. The base of the chair and her feet in front of it touch the evervisible circle.The back of the seat extends to the middle of the woman. Perseus is a male figure with bare feet, curled hair, dressed with a cape (chlamys) around his shoulders which covers his left arm. There are wings on both feet. His head is turned as if he is looking over his left shoulder. His left arm is lowered and carried the Gorgon head in his left hand. His right arm is raised and his lower right arm is close to and parallel to the ever-visible circle. In his right hand is a sword (or a stick with a handle) which is oriented parallel to and a little east of the vernal equinoctial colure. The tip of the weapon ends in the foot of Andromeda. His left leg is bent such that his left foot touches the Tropic of Cancer just above Taurus. His right leg is also bent and touches the left arm of Auriga below the elbow. Auriga is a male figure with bare feet and curled hair. He wears a long dress and his head is turned east and touches the ever-visible circle. Both arms are lowered. In his right hand he carries a whip. The Tropic of Cancer cuts through his right foot, the heel of which is on the boundary between Taurus and Gemini. Ophiuchus is a nude male figure with short curled hair. His head is turned west to face the nearby head of Hercules and touches the Tropic of Cancer. His left arm is stretched out and holds the upper part of the body Serpens. His right arm is lowered and holds the tail of Serpens.The partly invisible middle part of the body of Serpens is in front of the thighs of Ophiuchus, who is standing with both legs stretched. The Equator cuts through his hips. His right foot seems to rest on the ecliptic and his left foot is hidden by the left hand of ‘Atlas’. Serpens is a snake and covers a large space. His head is below Corona Borealis. His neck is cut by the Tropic of Cancer and the middle of his body by the Equator. He passes in front of the legs of Ophiuchus. His forked tail seems to end more or less to the right of Ophiuchus on the Equator. Aquila is a bird with outstretched wings, standing upside down with his feet on the Tropic of Cancer; both feet are clearly visible.The winter solstitial colure cuts through the body of the bird such that his feet and right wing are west of the colure and his

112

Appendix 2.1 Catalogue of antique celestial globes head and left wing east of it.The colure passes under the body and over the left wing. Delphinus is a dolphin with a beard and a double tail which shows his teeth. It is moving from the Equator to the Tropic of Cancer. Pegasus is half a horse with wings. He is upside-down with respect to the Equator, which grazes his head and the wing. His right hoof is on the Tropic of Cancer and his left hoof is close to the tip of the left wing of Cygnus. Andromeda is a female figure with bare feet, hair bound together, and a long dress with a girded top. She is upside down with respect to the Equator. She has turned her breasts to the viewer and she shows the palm of her right hand. Her head is in profile and turned to the vernal equinoctial colure and the back of her head is close to the belly of Pegasus but it does not touch the body of the horse. Her right (southern) arm is raised. The other left arm is stretched and seem to be connected to a small block (representing a rock?), south of Cassiopeia. Her right foot is on the vernal equinoctial colure, and touches the end of the weapon of Perseus. Her left foot is twisted and shows her heel. Her toe touches the vernal equinoctial colure close to the hand of Perseus. The Tropic of Cancer cuts through her left upper arm and obliquely through her breast. zodiacal constellations: Aries is standing on its hindlegs with forefeet as if jumping. He is looking backwards to Taurus. The vernal equinoctial colure passes through his curled horns at the back of his turned-round head, and cuts through his right leg close to the knee such that his right foreleg is just west of this colure. The hoof of his left foreleg is on the southern boundary of the zodiacal band just east of the colure.The Equator passes through his right front hoof, his left front knee, and the hoofs of his hind legs. The northern boundary of the zodiac cuts through his neck and the end of his tail, the southern boundary touches his left front hoof and intersects both hindlegs. Taurus is a half bull with a bent head, two front legs, two short horns, and curls on his forehead. His neck is almost touching the Tropic of Cancer. The ecliptic passes through the middle of his body and his head. The hoof of the left leg rests on the Equator, almost touching the piece of cloth carried by Orion,

and the lower part of the bent right leg is intersected by it. The short horns do not extend to the feet of Auriga. Gemini consists of two nude male figures, with curly hair and beards.Their heads are turned in profile to the north.The left arm of the northern twin is stretched and touches the whip of Auriga.The left arm of the southern twin rests on the shoulder of the northern twin, and vice versa, the right arm of the northern twin on the shoulder of the southern one. The right arm of the southern twin is lowered and his head almost touches the summer solstitial colure.The Tropic of Cancer cuts through the lower legs of the northern twin and the left hip, shoulder, and head of the southern one. Cancer is a crab with two claws facing Leo and four legs on either side. The ecliptic intersects the body lengthways and passes between his eyes. The Tropic of Cancer passes also through the body but slightly asymmetrically. The main body is confined within the boundaries of the zodiacal band. His claws and legs are symmetrical below and above these boundaries. Leo is a lion is standing on its hindlegs with his forefeet as if jumping. He has his mouth open and is looking forward to Cancer. The lion’s tail makes a loop which starts and ends at the Tropic of Cancer.This circle intersects the main body of the lion from breast to hindlegs.The ecliptic passes through the chest and in front of the right and behind the left hindleg. Virgo is a female figure with wings, bare feet, hair bound together, in a long dress with a girded top. Her feet are turned south.The body aligns more or less with the ecliptic. The ecliptic passes through her left wing and the toe of her left foot.The right hand is on the Tropic of Cancer and her lowered left hand with an ear of wheat is on the Equator.The ear of wheat is aligned to the ecliptic and intersects the Equator such that most of the ear of wheat is above it.The Equator passes through her left foot and touches the toe of her right foot.The line separating the signs of Leo and Virgo passes through the head and the top of the left wing.The autumnal equinoctial colure cuts through tip of the right wing and the dress below the knees. Libra is a balance held in the middle, just above the ecliptic, by the left claw of Scorpius.The left scale is below the southern bound-

113

celestial cartography in antiquity ary of the zodiacal band, close to the tail of Hydra. The right scale is below the hand of Atlas and is not visible.The Equator touches the northern end (of the beam) of the balance. Scorpius is only half visible. The left claw is seen to hold the balance. The main body with four legs visible on the south side is intersected by the Tropic of Capricorn. The segmented tail, of which six parts are visible, seems to start and end on the southern boundary of the zodiac; in between is south of this circle and north of the base of Ara. Sagittarius is only partly visible. He is a horse with a nude male figure on top. The male figure is bearded with curly hair. His head is in profile and turned west, looking forward in the direction of Scorpius. In his left hand he carries a bow; in his unseen right hand he presumably holds the arrow which is visible.The ecliptic and the Tropic of Capricorn intersect him in the neck, just below his head. The northernmost point of the bow is on the Tropic of Capricorn, the southernmost point touches Corona Austrinus in front of his right leg. Capricornus is only partly visible. He has two beautiful horns which are intersected by the northern boundary of the zodiacal band, where they depart from the head. The ecliptic intersects him just below the nose and through the neck. aquarius is a nude male figure with curled hair, but no beard. His head is seen in profile and turned to the east to face the head of Pegasus. The Equator passes just above the head. His left arm is bent.The ecliptic intersects the body at its knees and the right foot rests on the southern boundary of the zodiacal band. His right arm is stretched and holds an urn from which water streams. The stream runs down and intersects the zodiacal band and subsequently flows along the Tropic of Capricorn until it touches the tail of Cetus. Pisces consists of two fishes. The southern of the two fishes is located below the Equator, and more or less parallel to it, and below Pegasus.The other, northern fish is located north of the zodiacal band, between the raised arm of Andromeda and the vernal equinoctial colure, and parallel to the latter circle.There is a ‘cord’ which connects the tail of the southern fish with the head of Cetus.This cord intersects first the northern boundary of the zodiacal band, then cuts

the Equator twice; it subsequently crosses the ecliptic, the southern boundary of the zodiacal band, and the vernal equinoctial colure before it touches the head of Cetus.There is no connection between the northern fish and this cord. southern constellations: Cetus is a monster, the head of which is south of Aries and is connected to the cord emanating from the southern fish of Pisces. The mouth of the monster is wide open and his tongue is visible. Its body has many curls. The main one is touching the vernal equinoctial colure on the rear, left side and is intersected by the Tropic of Capricorn at the bottom. The vernal equinoctial colure cuts through the middle of its tail and the Tropic of Capricorn through the lower end of it. The end of the tail connects to the stream of water of Aquarius. The stream of Eridanus passes through its flossy forepaws. Orion is a male figure with bare feet and curled hair. He is dressed in an exomis which leaves his right shoulder bare. His head is turned east away from Taurus. He holds a skin or piece of cloth in his raised left arm. He carries a club in his raised right hand. He kneels on his right knee and his left leg is bent. The Equator intersects the piece of cloth and his body in the middle where on the left side a sword in a scabbard is attached. Eridanus is a river that starts at the left lower leg of Orion, below the knee, and streams first west to Cetus where it ends between his frontlegs. It continues at the Tropic of Capricorn, streaming now south and in the opposite, eastern direction until it makes another turn and continues its path in front of the steering oars of Navis until it disappears behind the shoulder of Atlas just above or at the ever-invisible circle. Lepus is a running hare with long ears. It is south of the left foot of Orion and intersected by the Tropic of Capricorn, such that the circle passes through and between the legs and below the main body. Canis Maior is a jumping dog. There are rays emanating from his head. The Tropic of Capricorn intersects its body directly below the front legs, such that the end of his left front leg is resting on it. The summer solstitial colure touches the tip of his tail, far below the Tropic of Cancer at the point where it intersects the northern steering oar. Canis Minor is

114

Appendix 2.1 Catalogue of antique celestial globes a sitting dog with a curled tail. Only the head and the two front legs are directly visible, the remainder is hidden behind the hand of Atlas. It is located above the Equator, west of the summer solstitial colure, and below the body of the following twin. Navis is the rear part of a sailing ship with mast, ropes, and a flagpole. It is nicely decorated with geometrical patterns. In the middle of the ship, east of the steering oars, is a picture of a winged figure in a long dress with a girded top and a Phrygian(?) hat, holding a round object in its raised right hand and a branch in its right lowered hand.To the right of this figure is a snake-like animal slithering to the east.The top of the mast touches the Equator.The Tropic of Capricorn intersects the stern a little east of the summer solstitial colure and cuts through the mast of Navis. There are two steering oars, the northern one of which emerges from behind the ship. The summer solstitial colure passes a little east of the stern and in between the steering oars: it passes in front of the northern steering oar and behind the southern one.The southern steering oar in front of the ship touches the ever-invisible circle. Near the southern steering oar in the front of the ship hangs a rope overboard. On the square foot of the mast are shields and on deck there is an attribute that could be a kind of hook. Hydra is a snake with a crest on his head. The head is located above the top of mast of Navis. The Equator passes through its neck. The Tropic of Capricorn grazes the second bend in the middle and the autumnal equinoctial colure cuts through the end of the tail just above the head of Centaurus. Crater is a vase or cup with handles, located above the body of Hydra. It stands upright on a support which is on the body of Hydra.The Equator intersects the left handle of the vase. Corvus is a bird, the feet of which stand on the body of Hydra. It is picking the snake and its tail point towards the left hand of Virgo. Centaurus is a horse with a nude

male figure on top.The male figure is bearded and has curly hair. The tail of Hydra is over his head. The Tropic of Capricorn runs behind his neck just above his shoulders.The autumnal equinoctial colure passes through his head, his right shoulder, his back, the front part of the horse body, and east of his left front leg.The hoofs of his hindlegs and the hoof of his left front leg all rest on the ever-invisible circle. His left arm is bent and in his invisible left hand he holds a spear. His right arm is outstretched and his right hand touches the hindfeet of Lupus (there is some damage in front of the right hand). Lupus is an animal that seems to fall backwards such that it is upside-down with respect to the surrounding constellations. His head touches the southern feet of Scorpio and his forelegs touch the Tropic of Capricorn. He seems to have some sort of rope around his neck (there is some damage in front of him which makes it difficult to specify more details).Ara is an altar, standing on three feet, with two handles.The bottom part is close to the tail of Scorpius. It is upside-down with respect to the zodiacal band. Corona Austrinus is a wreath located before the front legs of Sagittarius. The two ribbons are located outside the wreath, in front of Sagittarius. comments: The sizes given in the present description have been taken from Valerio 1987, who says that all his measures are to be taken by ‘a grain of salt’.We have therefore used only rounded off values. It is said that all the colours covering the sphere were removed during the visit of Francesco Bianchini and Gian Domenico Cassini who carried out an extensive astronomical examination in 1695, see Korn 1996, p. 31. For a review of copies of the Farnese globe, see Lippincott 2011. For a discussion of the globe, see Section 2.6. Literature: Pighius 1587; Bianchini 1697; Thiele 1898; Valerio 1987; Wrede 1982; Wrede and Harprath 1986; Wrede 1996; Korn 1996; Schaeffer 2005; Duke 2006.

115

Chapter Three

The descriptive tradition in the Middle Ages

I

n Carolingian times a student interested in the secrets of the starry sky could satisfy his curiosity by studying a variety of books. Most Latin translations of works and scholia belonging to the descriptive tradition, discussed in Chapter 1, by antique authors were directly or indirectly available. Other translations known in the Latin West are supposed to derive directly or indirectly from the so-called edition Φ, the Greek scholia of which had before the turn of the third century been translated into Latin and added to Germanicus’s translation of Aratus’s Phaenomena. The oldest surviving manuscript with these Latin Scholia Basileensia is Basle MS AN. IV. 18, apparently written in Fulda around 820–35.1 In the eighth century another version of the edition Φ—poem and scholia—was translated into Latin in the north of France. This translation is known as the Aratus Latinus.2 Other texts developed from these two Latin versions. For example, the descriptive star catalogue De ordine ac positione (early ninth century) derives directly from the catalogue included in the Scholia Basileensia.3 In contrast, the text known as De signis caeli is a concise version closely related to

1 Haffner 1997; Dell’ Era 1979c, pp. 301–79. 2 Maass 1898, pp. 175–271. Le Bourdellès 1985. 3 Dell’ Era 1974.

the star catalogue incorporated in the Aratus Latinus.4 For other texts the lines of transmission are less direct. For instance, the Revised Aratus Latinus is an improved text based among other sources on the scholia of the Aratus Latinus. Its star catalogue was adapted to enhance its readability by using data from other catalogues available at the time.5 Similarly, the Scholia Strozziana appears to be a compilation in which its author added information taken from a number of existing texts to his main source: the Scholia Basileensia.6 Books on the rudiments of astronomy were also available to the medieval reader. Copies of Hyginus’s De Astronomia were around in the ninth century, and their number increased in later centuries.7 The Commentary on the Dream of Scipio by Macrobius (ad 395–423) is in the first place a book about cosmology.8 It explains how the universe is organized and outlines its main structure. The other book a student could consult is the didactic astronomical allegory On the Marriage of Philology by Martianus Capella.9 It

4 Dell’ Era 1979a, pp. 268–301. 5 Maass 1898, pp. 175–271. See also Le Bourdellès 1985, pp. 71–81. 6 Dell’ Era 1979b, pp. 147–267. 7 Viré 1981. 8 Stahl 1952, chapters v–vii, (pp. 200–12). 9 Martianus Capella (Dick 1925); Stahl et al. 1977.

The descriptive tradition in the Middle Ages discusses in detail the celestial sphere and the properties of the wandering planets. Many texts have survived in illustrated manuscripts which have pictures of the constellations and sometimes also maps. Some constellation cycles have survived in beautifully illustrated manuscripts. Among the latter is the Leiden Aratea (Leiden, Universiteitsbibliotheek MS Voss. lat. 4° 79), produced at the court of Louis the Pious (814–40).10 The Leiden codex stands out for its contents and the size and artistic quality of its constellation images. It is a picture book in which the accompanying text lines taken from the Latin translations of Aratus’s poem by Germanicus and Avienus seem to be secondary to the images. The Leiden cycle of constellations consists of 36 full-page illustrations, comprising 42 constellations and the Pleiades. The constellations are adorned with stars represented by small squares of gold leaf. In most illustrated star catalogues the stars are placed in agreement with the catalogue descriptions they are illustrating, but the locations of the Leiden stars appear to be a rather odd mixture of a descriptive star catalogue related to the Epitome and the descriptive part of the Ptolemaic star catalogue.11 The discussion of the Leiden and other such cycles of individual constellations is outside the scope of the present study devoted to maps and globes.12 The Leiden manuscript may have had a celestial map since the tenth-century copy in

10 For a facsimile edition, see Leiden Aratea 1989. For the date, see Dekker 2008a, where I discuss previous studies on the date of the manuscript. 11 Dekker 2010b. 12 For studies of such constellation cycles, see for example Thiele 1898; Haffner 1997; Duits 2005; Blume et al., in preparation, and the Saxl project on www.kristenlippingcott.com [accessed 21 March 2012].

Boulogne-sur-Mer, Bibliothèque municipale MS 188 includes a planisphere (see Section 3.2 below).

How do all these texts relate to maps and globes? To answer this question we have examined all known medieval maps in the descriptive tradition.About 33 celestial maps survive in medieval illustrated manuscripts, the earliest extant example dates from the early ninth and the latest one from the fifteenth century, all belonging to the descriptive tradition.Among these ‘artefacts’ one can distinguish three types of medieval map.The first group of maps consists of eleven examples of pairs of summer and winter hemispheres, each of which presents a view of half of the heavens as depicted on a celestial globe, one hemisphere being centred on the summer and the other on the winter solstitial colure. Another group comprise ten planispheres, each presenting a view of the whole sky with the north pole in the centre and the ever-invisible circle as its outer boundary. Five copies are in sky-view and five present the celestial sky in globe-view. In addition to these ten medieval planispheres, there are ten more preserved in a number of closely-related codices produced in Naples and Florence during the second half of the fifteenth century. These humanist planispheres form a rather homogeneous group of maps, all of which present the celestial sky in globe-view. Finally, there are two sets of hemispheres, each of which presents again a view of half of the heavens as depicted on a celestial globe, but these hemispheres show the heavens north and south of the Equator. Contrary to the winter and summer hemispheres no antique example of this type of map is known. Since these maps might be relevant for medieval globe making we close this chapter with a discussion of

117

The descriptive tradition in the Middle Ages

Fig. 3.1 a–b The pair of summer and winter hemispheres in Aberystwyth, MS 735C, ff. 3v–4r. (Courtesy of Llyfrgell Genedlaethol Cymru/The National Library of Wales, Aberystwyth.)

the astronomical models invented by Gerbert of Aurillac at the turn of the tenth century as part of his teaching of the liberal arts. The maps described here have not been studied collectively. Central to our approach are questions of how these maps were constructed, whether one can establish the date or epoch of the archetype(s) of the maps, and to what extent the message conveyed by their astronomical contents could serve the interests and understandings of the medieval student in astronomy.

. SUMMER AND WINTER HEMISPHERES Among the maps found in medieval illustrated manuscripts are eleven so-called summer and winter hemispheres (Figs 3.1–3.11). For easy reference these maps, described in detail in Appendix 3.1, are numbered H1–H11. Six of these maps appear in the same context, namely in manuscripts containing the text of the Revised Aratus latinus.13 In all these manuscripts the maps are accompanied by the text entitled Descriptio 13 Le Bourdellès 1985, pp. 71–81.

118

Fig. 3.2 The pair of summer and winter hemispheres in Aberystwyth, MS 735C, f. 5r. (Courtesy of Llyfrgell Genedlaethol Cymru/The National Library of Wales, Aberystwyth.)

The descriptive tradition in the Middle Ages

Fig. 3.3 The pair of summer and winter hemispheres in Dresden, MS Dc. 183, f. 8v. (Courtesy of The Warburg Institute, Photographic Collection, London.)

duorum semispheriorum.14 As Martin has demonstrated the title of this text does indeed fit the maps but the text itself appears to be a Latin translation of a comment on Aratus’s poem (lines 22–23) in which he speaks of the axis of the world, a discussion which is not really appropriate for the hemispheres.15 Somehow this text came to be attached erroneously to the title Descriptio duorum semispheriorum of the maps. The background of the other five maps varies considerably. One set of hemispheres, in Vatican

City, Biblioteca ApostolicaVaticana, MS gr. 1291, is part of a Byzantine manuscript that includes Ptolemy’s Handy Tables.16 This work belongs to the mathematical tradition whereas its hemispheres belong to the descriptive tradition. Another set of hemispheres in Vatican City, Biblioteca Apostolica Vaticana, MS gr. 1087, is part of a Greek text belonging to the descriptive tradition and known as the Fragmenta Vaticana Catasterismorum.17 Its texts are closely related to the descriptions of the constellations in the scholia and in star catalogues occurring in many medieval illustrated manuscripts of the Aratean corpus.18 The two sets of hemispheres in Aberystwyth, the National Library of Wales, MS 735C, appear among a miscellaneous collection of texts (ff . 1r–9v) with verses, excerpts of Cicero and of Macrobius.This is followed by the text of Germanicus’s Aratea (ff . 11v–24v).19 Since no other known manuscript with Germanicus’s Aratea is known to include a pair of celestial hemispheres, we may assume that the maps do not belong to the Germanicus text.And no specific tradition for hemispheres accompanies Boethius’s texts, such as that in Monza, Biblioteca capitolare, MS B 24/163 (228).20 It is noteworthy that among these various manuscripts Vatican City MS gr. 1087 and the Aberystwyth MS 735 C stand out for their collection of maps, including not only hemispheres but also a planisphere. In spite of the differences in background there exists good agreement on the essential format of the celestial hemispheres. Every map depicts a view of half of the heavens in globe-view, that is,

14 Maass 1898, p. 145. 15 Martin 1956, pp. 140–1.

120

16 17 18 19 20

Boll 1899, pp. 110–38. Rehm 1899a; Eratosthenes (Pàmias and Geus 2007). Martin 1956. McGurk 1973, pp. 205–6. McGurk 1966, p. 52.

Fig. 3.4 The winter hemisphere in Monza MS B 24/163 (228), f. 67r. (Courtesy of the Museo e Tesoro del Duomo, Monza.)

The descriptive tradition in the Middle Ages

Fig. 3.5 a–b The pair of summer and winter hemispheres in Paris, MS lat. 12957, f. 61r, f. 60v. (Courtesy of the Bibliothèque nationale de France, Paris.)

as presented on a celestial globe. Moreover, the hemispheres consistently have either the summer or the winter solstitial colures as their central vertical line, and the combined spring and autumnal equinoctial colure form their circular, outer boundaries.

3.1.1 Cartography In most hemispheres the constellations are marked against the background of a grid consisting of a circle that frames the map and represents the equinoctial colures, a vertical line that runs through the middle of the map that represents the solstitial colure, and five straight lines per-

pendicular to the latter colure which represent respectively the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle. In addition there are two arcs (or sections of circles), which represent the northern and southern boundaries of the zodiacal band. The grids on our hemispheres recall the orthographic projection in which a point on a sphere is projected from an infinite distance on a plane tangent to that sphere. In this projection parallel circles appear as straight lines and meridians as semi-ellipses. If the plane of the projection is passing through the equinoctial colures

122

Fig. 3.6 The pair of summer and winter hemispheres in Paris, MS lat. n.a. 1614, f. 81v. (Courtesy of the Bibliothèque nationale de France, Paris.)

The descriptive tradition in the Middle Ages

Fig. 3.8 The pair of summer and winter hemispheres in St Gall, MS 902, p. 76. (Courtesy of the Stiftsbibliothek, St Gall.)

Fig. 3.7 The pair of summer and winter hemispheres in St Gall, MS 250, p. 462. (Courtesy of the Stiftsbibliothek, St Gall.)

the ecliptic is also presented as a semi-ellipse (Scheme 3.1), thus deviating in shape from the circular arcs used as the basic shape for drawing the zodiacal band on our hemispheres. All this suggests that the grids of the hemispheres were constructed according to a model that includes some features of the modern orthographic projection as well as elements that do not fit into that projection. Hence we propose a set of rules labelled here as the ‘hemispheric model’ for drawing the grid in the present hemispheres. Using only a ruler and a compass, the most likely sequence in which the various parts of the hemisphere would have been drawn is as follows:

1. First the circle framing the map, representing the vernal and autumnal equinoctial colures, is drawn. 2. Next a line vertically bisecting the circle, thus marking the north and south poles is added. This central line represents the solstitial colure. 3. Next the five parallel circles—all to be devised as straight parallel lines perpendicular to the solstitial colure—with their points of intersection with the boundary circle, that is the equinoctial colures, are marked. The five straight lines connecting opposite points of intersection would then represent the five parallel circles. The points of intersection of

124

3.1 SUMMER AND WINTER HEMISPHERES

Fig. 3.9 The pair of summer and winter hemispheres in Vatican City, MS Reg. lat. 1324, f. 23v. (Courtesy of the Biblioteca Apostolica Vaticana, Vatican City.)

the equinoctial colures with the Equator, that is, the equinoxes, are by definition at a distance of 90° from the north pole.The Tropics of Cancer and Capricorn cut the equinoctial colures at an angular distance of 66° from respectively the north and south pole since in Antiquity the obliquity of the ecliptic was set at 24°.The ever-visible and ever-invisible cir-

cles intersect the equinoctial colures at an angular distance from either pole equal to the geographical latitude. In the descriptive tradition a clear notion of geographical latitude did not exist but we may assume that a map maker somehow knew how to find this angular distance. For example, he might have taken it from the globe he used as the model for constructing the map. 4. The northern and southern boundaries of the zodiacal band in our model are assumed to be circular arcs through the respective points of intersection of the boundaries with the equinoctial and solstitial colures. In Scheme 3.2 these points are presented by ABC and DEF. As the value commonly used in Antiquity for the width of the zodiacal band is 12°, with the northern boundary of the zodiacal band being 6° above the ecliptic and the southern boundary 6° below it, one may assume that the zodiac boundaries intersect the equinoctial colures at points 6° above and below the equinoxes. In Scheme 3.2 the points A and C are above, D and F below the Equator. The straight lines representing parallel circles 6° above and below the Tropic of Cancer intersect the solstitial colure in the summer hemisphere in the points B and E. Using these various points, the circular arcs representing the zodiac boundaries can be easily drawn by construction.The zodiacal band on the winter hemisphere is simply the mirror image of that on the summer hemisphere. The present model for the construction of the hemisphere grids predicts certain ratios for the points at which the solstitial colure intersects the main celestial circles. When expressed as a fraction of the diameter of the circle that frames the map one has:

125

The descriptive tradition in the Middle Ages

Fig. 3.10 a–b The pair of summer and winter hemispheres in Vatican City, MS gr. 1087, f. 310r, f. 309v. (Courtesy of the Biblioteca Apostolica Vaticana,Vatican City.)

1. The solstitial colure intersects the equator southern edge at a distance of 0.25 from halfway between the north and south poles, the south pole. that is, at a distance of 0.5 from the north 4. The solstitial colure intersects the ever-visible pole. and ever-invisible circles at a distance from 2. The solstitial colure intersects the Tropic of the north pole depending on geographi cal Cancer at a distance of 0.30 and the Tropic latitude φ. In mathematical terms, these of Capricorn at a distance of 0.70 from the intersections lie respectively at a distance of north pole. ½(1-cos φ) and ½(1+cos φ) from the north 3. In the summer hemisphere, the solstitial pole.The value most quoted in Antiquity for colure intersects the northern boundary of φ is 36°. In this case the solstitial colure interthe zodiacal band at a distance of 0.25 and the sects the ever-visible circle and the eversouthern boundary at a distance of 0.35 from invisible circle at a distance of respectively the north pole. In the winter hemisphere, the 0.10 and 0.90 from the north pole. For an northern edge is at a distance of 0.35 and the ‘Eudoxan’ value of φ = 42°, the solstitial colure 126

3.1 SUMMER AND WINTER HEMISPHERES

Fig. 3.11 a–b The pair of summer and winter hemispheres in Vatican City, MS gr. 1291, f. 2v, f. 4v. (Courtesy of the Biblioteca Apostolica Vaticana,Vatican City.) See also Plate II.

intersects the ever-visible circle and the everinvisible circle at respectively 0.13 and 0.87 from the north pole.

respectively the north and south pole and the points of intersection of the various circles with the solstitial colures, expressed as fractions of the Data for comparing the grids of the hemispheres total length of the solstitial colure. The two sets with the model grid described above are pre- of hemispheres (H1 and H2) in Aberystwyth sented in Table 3.1. In the first column, the MS 735C are not pertinent to the present analynames of the celestial circles are given. In the sis because a fully-drawn grid is lacking on these second, the abbreviations S and W refer to the maps. summer and winter hemisphere, respectively. A comparison between the data shows that The third column lists the values predicted by the simplest of all requirements, namely that the the model.The remaining columns show, for all Equator passes through the middle of the maps, nine relevant hemispheres indicated by their is fulfilled only in four cases: the Monza map catalogue numbers H3–H11, the distances in (H4), the Byzantine hemispheres (H10 and H11), the summer and winter hemisphere between and one of the Paris hemispheres (H6). In all 127

The descriptive tradition in the Middle Ages

Scheme 3.1 Orthographic projection of the grid of a summer hemisphere.

Scheme 3.2 Construction of the zodiacal band in a summer hemisphere.

other five hemispheres listed in Table 3.1 the grid is deteriorated to such an extent that the Equator passes north and south of the centre of respectively the summer and the winter hemisphere. The trend indicated by the numerical data of the Equator is confirmed by those of the tropics. On the hemispheres H4, H10, H11, and H6 the tropics intersect the solstitial colure at distances from north pole in the summer hemisphere and from south pole in the winter hemisphere that lie within 0.03 units of the values (0.30 and 0.70) predicted by the model. Moreover, one finds that the tropics lie fairly symmetrically relative to the Equator on both the summer and winter hemispheres.The closeness of the data for the Equator and the tropics to the values predicted by the model supports the hypothesis that this model may indeed have been used for the construction of the map. An examination of the maps associated with the Revised Aratus latinus group other than H6

reveals that the grids on these five maps (H3, H5, H7, H8, and H9) are very corrupt. In addition to errors in the location of the Equator one finds that the tropics deviate considerably, and these errors appear to occur symmetrically with respect to the summer and winter hemispheres. Such symmetry arises from copying by foldingover the page and using the inverted summer hemisphere as a template, the one is then simply the mirror image of the other. Surely, of all the grids occurring in hemispheres of the Revised Aratus latinus group those in H6 are closest to the model. Double lines on the hemispheres in this manuscript are also present in H10. The status of the other circles is less straightforward. For example, in analysing the data relevant to the placement of the zodiacal band, the winter hemisphere in H4 is distinct from all others. The zodiac boundaries intersect the winter solstitial colure at distances from the south pole that are very close to the values (0.25

128

3.1 SUMMER AND WINTER HEMISPHERES Table 3.1 Quantitative data on the grids in the summer and winter hemispheres Circle

S/W

Modelb

H4

H10

H11

H6

H5

H7

H8

H3

H9

Equator Equatora Tropic of Cancer Tropic of Cancer Tropic of Capricorn Tropic of Capricorn Northern boundary Southern boundarya Southern boundary Northern boundarya Ever-visible circle Ever-invisible circlea Ever-invisible circle Ever-visible circlea

S W S W S W S W S W S W S W

0.50 0.50 0.30 0.30 0.70 0.70 0.25 0.25 0.35 0.35 0.13 0.13 0.87 0.87

— 0.50 — 0.31 — 0.71 — 0.26 — 0.35 — 0.13 — 0.87

0.50 0.50 0.32 0.32 0.68 0.67 0.23 0.23 0.40 0.40 0.14 0.15 0.88 0.85

0.50 0.51 0.32 0.30 0.69 0.67 0.25 0.27 0.39 0.41 0.13 0.15 0.87 0.89

0.51 0.49 — 0.33 0.68 — 0.26 0.26 0.44 0.44 0.13 — 0.85 0.83

0.45 0.39 0.22 0.39 0.61 0.81 0.22 0.19 0.40 0.35 0.09 — 0.81 0.83

0.45 0.34 0.18 0.42 0.69 — 0.18 0.11 0.40 0.28 0.06 — 0.90 0.80

0.43 0.44 0.19 0.41 0.65 — 0.19 0.16 0.39 0.38 0.06 — 0.92 0.83

0.45 0.38 0.18 0.41 0.58 — 0.18 0.13 0.39 0.34 0.08 — 0.80 0.80

0.41 0.40 0.20 0.40 0.61 0.80 0.17 0.17 0.37 0.37 — — 0.80 0.80

S: summer hemisphere; W: winter hemisphere a Measured from the south pole. b Based on the Eudoxan value of 42º.

and 0.35) predicted by the model. If one were searching for a verification of the assumptions underlying the construction of the hemispheric model, the Monza winter hemisphere fully justifies them. This moreover suggests that this hemisphere marks a relatively reliable line of transmission from the antique to the medieval tradition, not completely undermined by errors incurred during the (manifold) copying process in between. All the other zodiacal bands show increasing traces of corruption. For the maps H10, H11, and H6 I find from Table 3.1 that on the summer hemisphere the northern zodiac boundary intersects the summer solstitial at a distance within 0.02 units of the value (0.25) predicted by the model. The same accuracy is seen on the winter hemisphere for the southern zodiac boundary. The accuracy of the southern zodiac boundary on the summer hemisphere and that of the equivalent northern boundary on the winter

hemisphere are less satisfactorily. Distances deviate more than 0.04 units from the value (0.35) predicted by the model. In Scheme 3.3 the locations of the zodiacal bands in the summer hemispheres of eight maps are summarized. The first horizontal row in the chart depicts all those hemispheres on which the end-points of the southern boundary have been dropped so that they touch the Tropic of Capricorn at the equinoctial colures!21 On the hemispheres placed in the second horizontal row, the Byzantine map H11 and the two St Gall hemispheres H7 and H8, the endpoints of the southern zodiac boundary are even placed below the Tropic of Capricorn. In addition to errors in the southern zodiac boundary, there is another notable corruption in some of the hemispheres belonging to the Revised Aratus latinus group. In the summer

21 For the winter hemispheres, the equivalent is that the northern boundary of the zodiac connects to the Tropic of Cancer at the equinoctial colures.

129

The descriptive tradition in the Middle Ages

Scheme 3.3 The zodiacal band in a number of summer hemispheres.

hemispheres of H3, H5, H7, and H8 the Tropic of Cancer is set tangentially to the northern boundary of the zodiac (see Scheme 3.3). The Tropic of Capricorn is missing from most winter hemispheres of the Revised Aratus latinus group. In H5 this circle is placed tangentially to the southern boundary of the zodiac. Whether this represents a pictorial corruption or a basic misunderstanding of the placement of the tropics in relation to the zodiacal band is not clear, but it is interesting to note that this mistake is a relatively common feature on medieval celestial planispheres.The concomitant repercussions on the structure of the grid itself, in combination with the misplaced Equators on these maps, can be seen in the data presented in Table 3.1. The last set of circles that concern us are the ever-visible and ever-invisible circles, which as mentioned before depend on geographical lati-

tude and, therefore, cannot be predicted by the model. Knowing more about the construction of the maps, it is tempting to determine the latitudes represented on them from the locations of the ever-visible and ever-invisible circles. To minimize error, it would be wisest to use only those maps that are closest to the archetype, the Monza winter hemisphere being the preferred test case. In this most reliable map the solstitial colure intersects the ever-visible and the everinvisible circle at points at a distance of 0.13 and 0.87 from the north pole, consistent with the geographical latitude of 42°. Looking at the other data in Table 3.1, it appears that on the Byzantine hemispheres H10 and H11 and the Paris hemispheres H6, the solstitial colure cuts the ever-visible and everinvisible circles within only 0.02 units of the corresponding positions in the Monza map H4.

130

3.1 SUMMER AND WINTER HEMISPHERES So, even the maps that are less close to the archetype appear to have preserved the latitude of 42°. From this, it seems justifiable to consider the values of 0.13 and 0.87 as representing standard distances of the ever-visible and ever-invisible circles from the north and south pole on the summer and winter hemispheres, respectively. In addition, one might be inclined to argue that this standard feature was inherited directly from an assumed archetype of these maps. The high level of agreement between some of the maps and the hemispheric model shows that, in most, though not all, respects, an assumed archetype map might well have been constructed using the simple set of drawing instructions we presented at the beginning of this section. This would not imply that the maker of the archetype had any inkling of the concept of projection in which every point of a sphere is directly related to a point on the plane of the map according to certain mathematical rules. On the contrary, in order to construct a map similar to the hemispheric model, only straight lines and (parts of) circles had to be drawn on the plane. From this point onwards, the grid simply served as the frame for filling-in the constellations—a process leaving ample room for artistic invention and fantasy.

constellations. In the third mode described by Manilius, the colures pass in front (or west) of Aries, Cancer, the Claws (Libra), and Capricornus. In this latter Manilian mode a close correspondence exists between signs and constellations. In 128 bc the constellation Aries was located just to the east of the vernal equinoctial colure, and through the use of the convention to locate the equinoxes and solstices at the beginning of their respective signs (Ari 0°-convention) the constellation Aries coincided well with the sign Aries, the constellation Taurus with the sign of Taurus, and so on. This close correspondence between signs and constellations was maintained for centuries. In ad 300 the tail of Aries started to move into the sign of Taurus and the head of the easternmost twin started to move into the sign of Cancer. Thus for a long time, from 128 bc to ad 300, the signs of the zodiac have corresponded fairly well to the constellations carrying the same name. With this in mind it is clear that the zodiacal images placed within compartments of 30° can mean one of two things. Either the images represent zodiacal constellations, which then would mean that the archetype of the hemispheres stems from 128 bc to at least ad 300. Or the images represent zodiacal signs, in which case one cannot find an epoch from them at all 3.1.2 Astronomical considerations because they would then reflect a convention. In Chapter 1 we argued that Antiquity maps in In most pairs of summer and winter hemithe descriptive tradition follow one of three spheres the zodiacal band is divided into 12 parts epochal modes. Each mode is characterized by of 30° each.22 The zodiacal images in the hemithe position of the colures with respect to the spheres are neatly placed within their respective respective constellations Aries, Cancer, the compartments in a way comparable to that of Claws (Libra), and Capricornus. In the oldest, single zodiacs, as for instance the one depicted in Eudoxan mode the colures pass through the MS Vat. gr. 1291, f. 9 where it serves to illustrate middle and in the closely related Capellan mode described by Martianus Capella they pass 22 Exceptions in this respect are the Aberystwyth maps H1, through the eighth degrees of the respective H2, and the Monza map H4. 131

The descriptive tradition in the Middle Ages the path of the Sun throughout the year.23 Single zodiacs have a separate history and the images depicted in them are best interpreted as symbols of the zodiacal signs. Such presentations are insensitive to precession since they express simply that the zodiac is divided into 12 parts named after the respective constellations, Aries, Taurus, and so on. Therefore, the best way to find the epochal mode of the maps would be to use constellations outside the zodiac. Unfortunately, the scope to do so is relatively poor. First of all, constellation images are not always drawn in proportion to their appearance in the sky. Second, the constellations themselves are corrupt. As mentioned below, many constellations are missing on the hemispheres belonging to the Revised Aratus latinus group and there are great distortions in the celestial grid. Considering such abnormalities, we have to limit the present discussion to the two Byzantine maps (H10 and H11) and the one set of hemispheres in Aberystwyth (H1) even though the positions of some constellations on these three maps also appear corrupt. In the winter hemisphere H10 (Vatican City MS gr. 1087) Lyra is to the east of the winter colure and Aquila to the west of it. In 128 bc the bright star α Lyr was in reality about 10° to the west of the winter colure and the bright star α Aql was then roughly on that colure as is seen on the Aberystwyth winter hemisphere H1.24 The displacements of both Lyra and Aquila in the winter hemisphere of H10 seem to have an artistic origin. Lyra seems to have been pushed too far to the east because Bootes, Corona Borealis, 23 Tihon 1993, pp. 181–203, especially the figure following p. 203. 24 By precession α Lyr arrived at the winter colure in the tenth century by which time α Aql had shifted 15° to the east of the winter solstitial colure.

and Hercules barely left enough space for it to the west of the colure.Aquila, on the other hand, seems to have been displaced too much to the west because Pegasus and Delphinus did not leave enough room for it on the colure. In a like manner one can understand that in the summer hemisphere of H1 (Aberystwyth MS 735C) Canis Maior was displaced to the east of the summer solstitial colure and Navis all the way to the autumnal equinoctial colure because of the expanded figure of Orion. Such artistic adaptations may also explain, for instance, why the blazing head of Canis Maior (Sirius) in the Byzantine maps (H10 and H11) is placed prominently on the summer solstitial colure. In a discussion of the summer hemisphere H11 (Vatican City MS gr. 1291) Stückelberger concludes that Sirius is ‘richtig genau’ on the (summer) colure.25 It is not clear what exactly he meant by ‘richtig genau’. Astronomically one would expect Sirius in Antiquity to lie 10° to the west of the summer solstitial colure and only around the year ad 1000 would it be on it. Since a date of ad 1000 postpones the dates of production of most manuscripts (Vatican City MS gr. 1291 is, for example, dated to ca. 825) an astronomical explanation for the prominent position of Sirius is unlikely.We may add here that on the antique Mainz globe discussed in Section 2.4, dated to the second or third century ad, the blazing head of Canis Maior (Sirius) is placed east of the summer solstitial colure, indicating that a corrupted position of Sirius already existed in Antiquity. The prominent place of Sirius on the summer solstitial colure may have become canonized by a conceptual error which prevailed in 25 Stückelberger 1990, pp. 75–6: ‘der Sirius [. . .] steht hier richtig genau auf dem grossen Kolurkreis’.

132

3.1 SUMMER AND WINTER HEMISPHERES Antiquity, as one can conclude from a discussion by Geminus. Sirius—Geminus tells us—is often supposed to be the cause of the high summer temperatures experienced in the period following its heliacal rise.26 However, he explains why this notion is not correct: it is the Sun that produces the summer heat because in its path through the summer solstice it remains for about 40 days close to the Tropic of Cancer and in that period builds up the summer heat. By the time of Sirius’s helical rise—in Rhodes about 30 days after the Sun passed the summer solstice—it becomes really hot.The helical rise of Sirius is only a convenient marking and not the cause of the summer heat. And so, continues Geminus: ‘If, then, someone takes the rising of the Dog as a sign of the season, he takes it rightly [. . .]’.27 In an earlier chapter on the equinoxes, solstices, and seasons Geminus explains: ‘Summer solstice occurs around the intensification of the heat, in the first degree of Cancer’.28 Hence it is not hard to imagine that in popular astronomy Sirius was linked to the summer solstitial colure and this found its expression in the maps in the descriptive tradition. Surely it would be very haphazard to use the position of Sirius on the summer solstitial colure for dating purposes. With so many uncertainties regarding the positions of the constellations only one reasonably reliable dating criterion remains. Since on the maps the celestial sphere is always divided into two halves bound by the equinoctial colures, one might expect that during the complicated process of copying, the selection of constella26 The risings and settings of stars that occur just before sunrise, or just after sunset, are called helical risings and settings, see Evans 1998, p. 190. 27 Geminus (Aujac 1975), XVII 26–27;The English translations is from Evans and Berggren 2006, p. 223. 28 Geminus (Aujac 1975), I 9; The English translations is from Evans and Berggren 2006, pp. 114–15.

Table 3.2 Locations the vernal and autumnal equinoctial colure with respect to a few constellations on the two Byzantine hemispheres H10 and H11 and the Aberystwyth map H1 Relative positions with respect to the colures

Indicative date

The vernal equinoctial is east of Cassiopeia and Andromeda is west of Triangulum and Perseus intersects Cetus

around and before 128 bc around and after 128 bc around 128 bc

The autumnal equinoctial colure is west of Bootes intersects the tip of tail of Hydra intersects the horse’s back of Centaurus

after 128 bc around 128 bc after 500 bc

tions located in the summer and winter hemispheres, respectively, will have remained the same because it seems unlikely that an artist would transfer constellations from one hemisphere to another. Since this selection depends on the location of the equinoctial colures with respect to the stars, it tells us something of the epoch of the archetype of the maps. In Table 3.2 above we summarize the positions of a few constellations around the vernal and autumnal equinoctial colure for the two Byzantine hemispheres H10 and H11 (see Figs 3.10–3.11) and the Aberystwyth map H1 (see Fig. 3.1). Considering that all but one feature in the list appear to focus around 128 bc, the intersection of the back of the horse of Centaurus seems at fault. In 128 bc the border of the winter hemisphere cut through the head and shoulders of Centaurus. In ad 500 the westernmost shoulder of the centaur (ι Cen) was on the colure. The shift in the

133

The descriptive tradition in the Middle Ages location of the head and shoulders of Centaurus might have been brought about by the artist trying to represent Centaurus more convincingly. In the area in the summer hemisphere no space is left for a full picture of Centaurus, a problem that already at an early stage seems to have been solved by placing the main body in the more spacious area in the winter hemisphere. Despite all sorts of doubtful elements we think it justified to conclude that the division of the celestial sky as it is presented on the medieval hemispheres H1, H10, and H11 agrees with the configuration of the celestial sky as it was in the epochal mode described by Manilius. One can say, albeit with some hesitation, that the archetype(s) of this group of hemispheres emerged in the centuries after 128 bc, but not much later than ad 300. The Manilian epochal mode does not apply to the Aberystwyth set of hemispheres H2 and the Monza winter hemisphere H4. There the head and the front legs of Aries are west of the vernal colure of the Aberystwyth winter hemisphere (Fig. 3.2) whereas the remainder of its body is east of that colure of the summer hemisphere. The upper part of Bootes is east of the autumnal colure of the winter hemisphere and the lower part is west of that colure on the summer hemisphere. In the Monza winter hemisphere (Fig. 3.4), the vernal and autumnal equinoctial colures also pass through respectively the middle of Aries and Bootes. In addition, the vernal colure intersects Perseus, leaving one arm holding a stick inside that border.The autumnal colure passes through a hand of Centaurus. Neither the arm of Perseus nor the hand of Centaurus are drawn on the Aberystwyth winter hemisphere, but the missing hands in the pictures of these two constellations in the summer hemisphere suggest that they should have been part of the winter hemisphere.

Although the reliability of the maps (H2 and H4) may be questioned because of their lack of precision, we believe that the border features sketched here are fairly trustworthy because borders are least likely to become corrupted by copying processes.Thus we conclude that the Aberystwyth and Monza maps (H2 and H4) are based on the Eudoxan epochal mode. The fact that on these maps the zodiac is not divided into twelve compartments, is also in line with the early Eudoxan way of mapping the celestial sphere described in Chapter 1.

3.1.3 What can be learned from the constellations depicted on the maps? In Tables 3.3A and 3.3B the constellations depicted in, respectively, the summer and winter hemispheres, labelled by their catalogue numbers H1–H11, are summarized. These constellations are denoted by their modern abbreviations, to which two labels, one for the ivy leaf and one for an anomalous feature (Anomalous), have been added.These latter two features will be discussed below.The presence of a constellation on a map is marked by a plus sign (+), its absence by a minus sign (–). Most constellations appear in either the summer or the winter hemisphere but some appear to be divided over both hemispheres and this has been expressed by the fractions ¼, ½, and ¾. Looking at the constellation data it becomes clear that the sets of hemispheres appearing in manuscripts with the text of the Revised Aratus latinus (H3, H5–H9) agree among themselves well (see Figs 3.3, 3.5–3.9). On all these six maps the constellations Triangulum, Eridanus, and Lepus are lacking in the summer hemisphere (Table 3.3A). On all winter hemispheres one misses Lyra, Cygnus, Corona Borealis, and Sagitta (see Table 3.3B).Their absence shows that all six

134

3.1 SUMMER AND WINTER HEMISPHERES Table 3.3A Constellations depicted on the summer hemisphere Name

H4

H2

H1

H10

H11

H5

H6

H7

H8

H3

H9

UMa Dra Per Aur Ari Tau Gem Cnc Leo Vir Ori CMa CMi Navis Hya Crt Crv Cet Cen Ivy Leaf Anomalous Eri Lep Tri Boo

– – – – – – – – – – – – – – – – – – – – – – – – –

+ ½ + + ½ + + + + + + + + + + + + ½ ¾ – – + + + ½

+ ½ + + + + + + + + + + + + + + + ¾ ¼ – – + + + –

+ ½ + + + + + + + + + + + + + + + ¾ ½ + – + + – –

+ ½ + + + + + + + + + + + + + + + ¾ ¼ + – + + – –

+ + + + + + + + + + + + + + + + + + ½ + + – – – –

+ + + + + + + + + + + + + + + + + + ½ + + – – – –

+ + + + + + + + + + + + + + + + + + ¼ + + – – – –

+ + + + + + + + + + + + + + + + + + – + + – – – –

+ + – + + + + + + + + + + + + + + + ½ + + – – – –

+ + – + + + + + + + + + + + + + + + ½ + + – – – –

+: present; –: absent; fraction: part of the constellation is drawn.

maps derive from one and the same original that itself was already very corrupt. Other deterioration is seen within this Revised Aratus latinus group. For example, in all six maps Ophiuchus and Serpens are located inside the segment representing the sign of Scorpius instead of above it, but in the two Paris copies (H5 and H6) the artists overlooked the scorpion.Yet these two sets of hemispheres are among the most reliable that have survived.Two other sets of hemispheres (H3 and H9) are tied together by both missing Ursa Minor and Perseus. The relations between the six hemispheres of the Revised Aratus latinus group as these follow from the occurrences of their constellations are

illustrated in Scheme 3.4. These relations are reinforced by iconographic features. For example, Auriga is presented in all six maps as a warrior with a sword instead of a charioteer with the Goat (Capella or Capra) and/or Kids (Haedi) on his shoulder or arm. More striking is the appearance in all six maps of an anomalous creature to the east of Cetus and to the west of the summer solstitial colure that looks like the constellation Capricornus in the winter hemisphere. This mysterious creature is most likely the result of corruptive copying. On the two Paris copies (H5 and H6) the ivy leaf is presented by a recognizable leaf-like feature instead of the corrupted vase-like shape of the feature on all the other

135

The descriptive tradition in the Middle Ages Table 3.3B Constellations depicted on the winter hemisphere name

H4

H2

UMi Dra Cep Boo Her Cas Oph Ser Aql Del Peg And Sgr Cap Aqr Psc Cen Lup Lib Sco PsA Cet Ara Lyr Cyg CrB Sge CrA Ari Per

+ ½ + ½ + + + + + + + + + + + ½ ¼ + – + + ½ + + + + – + ½ ¼

+ ½ + ½ + + + + + + + + + + + ½ – – – + + ½ – + + + – – ½ –

H1 + ½ + + + + + + + + + + + + + + ¾ + – + + ¼ + + + + + [+] – –

H10 + ½ + + + + + + + + + + + + + + ½ + + + + ¼ + + + + – [–] – –

H11 + ½ + + + + ? ? ? ? + + + + + + ? ? [–] + + ? ? + + + – [+] – –

H5

H6

H7

H8

H3

H9

+ ½ + + + + + + + + + + + + + + ¾ + + – + ¼ + – – – – – – –

+ ½ + + + + + + + + + + + + + + + + + – + ½ – – – – – – – –

+ ½ + + + + + + + + + + + + + + + + + + + ½ – – – – – – – –

+ ½ + + + + + + + + + + + + + + – – + + – ½ – – – – – – – –

– ½ + + + + + + + + + + + + + + + + + + + – – – – – – – – –

– ½ + + + + + + + + + + + + + + + + + + + – – – – – – – – –

+: present; –: absent; fraction: part of the constellation is drawn. [. . .]: indicates that the constellation may or may not be presented on the map.

hemispheres.The two other sets of hemispheres (H3 and H9) are connected by fishes swimming in the same instead of in the opposite direction as on the other hemispheres. The data listed in Table 3.3A show that the Revised Aratus latinus maps share with the two Byzantine sets of hemispheres (H10 and H11, Figs 3.10–3.11) the image of the ivy leaf but that these latter maps have the usual images of Eridanus and Lepus in place of the anomalous creature.

The ivy leaf is missing from the Aberystwyth summer hemisphere (H1, Fig. 3.1a). Its winter hemisphere (Fig. 3.1b) has a confusing image, consisting of a ring made of two concentric circles south of the tail of Piscis Austrinus. It could either be Corona Australis or the star group we have named Anonymous II.As mentioned in Chapter 2, Corona Australis is reported by Aratus as an unremarkable ring of stars beneath the forefeet of Sagittarius and he describes the star group

136

3.1 SUMMER AND WINTER HEMISPHERES

Scheme 3.4 Relations between the hemispheres of the Revised Aratus latinus group.

Anonymous II as the group of unnamed faint stars beneath the feet of Aquarius, between Cetus and the southern fish.29 On Kugel’s and the Mainz globe (Chapter 2) both stellar configurations are presented in a similar manner, respectively as two concentric rings and a ring of dots.30 On the Byzantine winter hemisphere H11 (Fig. 3.11b) the southern ring is below the hindfeet of Sagittarius. Although Corona Australis should lie below the forefeet of Sagittarius it seems fair to conclude that in this hemisphere this image represents nevertheless Corona Australis. On the Byzantine winter hemisphere H10 shown in Fig. 3.10b a more prob29 Aratus (Kidd 1997), pp. 100–1, ll.389–90; pp.102–3, ll.399–400. 30 Compare Figs 2.5, 2.8 and 2.15.

lematic situation occurs. The ring here is also depicted as two concentric circles but it is located south of the club of Hercules and east of the back of Ophiuchus and it does not look like the nearby image of Corona Borealis between Bootes and Hercules. Note that ring-like images representing the Northern and Southern Crown, are absent in all maps belonging to the Revised Aratus latinus group. The constellation data collected in Tables 3.3A and 3.3B show that some constellations are divided over both hemispheres. This happens when the constellation is located on one of the equinoctial colures forming the boundary of the hemispheres.The occurrence of the same parts of

137

The descriptive tradition in the Middle Ages a constellation in both hemispheres is due to copying errors. For example, in all maps of the Revised Aratus latinus group Draco is drawn in the summer hemisphere as a complete animal and in the winter hemisphere as an additional tail. On other, less corrupted hemispheres one half of Draco is drawn in the summer and the other half in the winter hemisphere. The images of Cetus and Centaurus are also split. On the Aberystwyth and Byzantine hemispheres (H1 and H11) the larger part of Cetus’s body is drawn below Aries in the summer and its tail below Pisces in the winter hemisphere. This division deteriorated on the Revised Aratus latinus maps to a complete image of Cetus in the summer and a seemingly unconnected snake-like part in the winter hemisphere. In the Byzantine summer hemisphere H10 the image of Cetus has been reworked into a complete image (see Fig. 3.10a).A similar confusion is seen for Centaurus. In the Aberystwyth hemispheres H1 the larger part of Centaurus is below Scorpius in the winter and his hind part below Corvus in the summer hemisphere (Fig. 3.1a and b).This division is again deteriorated on some of the Revised Aratus latinus maps to an increasingly larger part of Centaurus in the summer and an equally increasing hind part in the winter hemisphere below Navis and the ever-invisible circle! On the Byzantine summer hemispheres H10 and H11, this is also the case (Figs 3.10 and 3.11). In the Revised Aratus latinus maps H3 and H9 the hind part of Centaurus is even turned upside-down. Two more constellations, Aries and Bootes, appear to be divided over the hemispheres, but only in the Aberystwyth set of hemispheres H2 and the Monza winter hemisphere H4. One half of the constellation Aries is in the summer and one half in the winter hemisphere whereas in all other hemispheres Aries is completely in the summer hemisphere (see Figs 3.2 and 3.4). A similar situa-

tion applies to Bootes. Above (section 3.1.2) it is shown that this split characteristic of Aries and Bootes is not the result of corruption but instead goes back to the earliest Eudoxan phase of mapping the celestial sky, which was characterized by colures that pass through the middle of their respective zodiacal constellations. The two maps share the peculiar feature that as a result of the oblique splitting of Bootes he appears upsidedown in the winter hemisphere. His presentation in the Aberystwyth summer hemispheres H2 shows that this comes about from a continuation of the figure from the one hemisphere into the other through the peculiar arrangement of the two hemispheres (see Fig. 3.2). It shows that the lost summer hemisphere of the pair in Monza MS B 24/163 (228) was arranged in the same way as H2 in Aberystwyth MS 735C. This arrangement sets these hemispheres apart from all others. The constellations depicted in the various hemispheres show that the maps belonging to the Revised Aratus latinus group are closely related and far removed from their prototype, in contrast to the Byzantine hemispheres (H10 and H11) which must have been much closer to it—although we will show that even in these hemispheres the locations of constellations leave much to be desired. This is also the case for the Aberystwyth hemispheres (H1) as is clear from the dominating wideangle view of Orion in the summer hemisphere (see Fig. 3.1a), filling almost all the space south of Gemini and the tip of his sword extending beyond the summer solstitial colure to the hindfeet of Leo. More importantly, the two Aberystwyth hemispheres (H1 and H2) are the only ones that have an image of Triangulum and one of these (H1) also includes an image of Sagitta which is absent from all other hemispheres. The constellation data indicate that the maps had widely different lines of transmission, and

138

3.1 SUMMER AND WINTER HEMISPHERES might not even stem from one and the same archetype. Our analysis shows that one can distinguish three groups.

3.1.4 Group I: the Eudoxan tradition The first group consists of the pairs of hemispheres H2 and H4. On both maps Libra is represented by the claws of Scorpius and the constellations Aries and Bootes are split by the equinoctial colures.The absence of a grid in the set of hemispheres H2 may be explained by its corrupted state. The Monza grid appears closest to a presumed archetype of the hemispheric model. The reliability of the Monza hemisphere is further underlined by the absence of constellations south of the ever-invisible circle as it should (Fig. 3.4). The Monza and Aberystwyth hemispheres H2 and H4 are representative for the earliest Eudoxan tradition in celestial cartography.

3.1.5 Group II: the Aberystwyth set of hemispheres H1 The set of hemispheres Aberystwyth H1 stands out for a number of reasons. The set H1 misses the defining characteristics of the Eudoxan tradition (group I) and those of the ivy leaf tradition (group III) described below. Instead it includes an image of Sagitta which is absent in all other hemispheres.The Aberystwyth set H1 shares an image of Triangulum with the other Aberystwyth set H2. The Aberystwyth and Monza winter hemispheres (H1, H2, and H4) coincide in presenting Libra by the claws of Scorpius instead of by ‘the figure carrying a pair of scales’ which occurs in the hemispheres of the ivy leaf tradition (group III). The absence of a division of the zodiacal band is another point of agreement between these three maps. So it seems that H1 is in tradition closer to the Eudoxan tradition (group I) than to the ivy leaf tradition (group III).

A feature unique to the Aberystwyth hemispheres H1 is the depiction of the Asses in the centre of Cancer, in the middle of its shell surrounding the Manger (Praesepe). The Manger and the Asses were used in Antiquity as weather signs.The myth associated with them is described by Eratosthenes: ‘Some of the stars in this constellation are called the Asses. These were placed among the stars by Dionysus.Their distinguishing sign is the Manger and their story is the following. When the gods were attacking the Giants, it is said that Dionysus, Hephaestus, and the Satyrs rode [to battle] on asses. As they approached the Giants, who were not yet visible, the asses brayed, and the Giants, hearing the noise, fled. For this reason the asses were honoured, being placed on the western side of the crab.’ 31

The images of the Asses are also added to that of Cancer on two other mappings in Aberystwyth MS 735C, namely on the planetary configuration (f. 4v) and on the planisphere (f. 10v) discussed below.The iconography of these two other maps is very like that of the hemispheres. As McGurk concludes, this iconography ‘must have been taken from the same model’.32 The author of the Aberystwyth manuscript, or an artist working for him, may have added the images of the Asses to the maps. If this is correct, the Asses may not have been a feature of the archetype of the map(s). It is further noteworthy that the only structure put into the Aberystwyth hemispheres H1 is through the zodiacal band which itself is not divided into segments.The grid consisting of the solstitial colure and the five parallel circles is also not drawn on the other Aberystwyth set H2.The absence of the grid in H2, which also misses the arcs representing the boundaries of the zodiacal 31 Condos 1997, p. 61; Eratosthenes (Pàmias and Geus 2007), p. 94. 32 McGurk 1973, p. 203.

139

The descriptive tradition in the Middle Ages band, could be the result of corruption but its omission on H1 may have been a deliberate choice by the artist.The grid restricts the available space for locating the constellations. For example, the region below the ever-invisible circle should be empty. Had this circle been marked on the summer hemisphere of H1, one would have found Eridanus, Lepus, and Canis Maior to the south of it. The artist of the Aberystwyth manuscript may have decided to avoid such inconsistencies by leaving the grid out. In sum, the Aberystwyth hemispheres H1 includes many features that set it apart from the other hemispheres studied here. Its constellation features, especially the presentation of Libra by the claws of the Scorpius, point to an archetype that was more inclined to a Greek than Roman taste. The Aberystwyth hemispheres H1 could well exemplify the tradition that followed after the transition around 128 bc from the one epochal mode in which the colures pass through the middle of the respective constellations to the other one in which the colures pass to the west of them.

3.1.6 Group III: the ivy leaf tradition The largest group that can be distinguished is what we shall call the ivy leaf group. It includes the hemispheres H3, H5–H9, that is, all maps belonging to the Revised Aratus latinus group, and the two Byzantine copies H10 and H11.Although there is a great amount of corruption seen in the hemispheres in this group, they all share an image of the ivy leaf. The ivy leaf is an enigmatic asterism, the roots of which are not at all clear. It is often identified with the hair of Berenice but this does not solve the problem of its origin.The only written testimony is a description in the Ptolemaic catalogue where the ivy leaf is mentioned in connection with stars belonging to the nebulous mass called

Πλόκαµος (lock of hair) between the edges of Ursa Maior and Leo.The same group is referred to in the descriptive star catalogue of Eratosthenes: There can be seen above it [Leo] in a triangle near the tail seven faint [amauros] stars which are called the locks of Berenice Euergetes.33 Ptolemy describes only three of the seven stars, namely those forming the angular points of the triangle and he labels all three stars faint (amauros). The northernmost star of the plokamos is labelled Leo 6e in the Ptolemaic catalogue, the preceding one Leo 7e, and the following one at the southern edge of the plokamos Leo 8e. In the description of the last star (Leo 8e) belonging to the lock of hair in the Ptolemaic star catalogue, is added ‘in an ivy-leaf ’.34 The precise interpretation of the text is not clear: either it says that only Leo 8e is associated with an ivy leaf or all three stars of the triangle. Locher tried to solve the problem by making an attempt to identify the ivy leaf by looking at the real sky overhead. He selected a group of stars in the sky of which only two (Leo 7e–8e) are described by Ptolemy.35 His interpretation is not very convincing because it includes many weak non-Ptolemaic stars and the shape outlined by it does not have the characteristics of an ivy leaf. A more interesting explanation was suggested by Knorr.36 He argues that the text describing the last star (Leo 8e) should apply to all three stars of the triangle, meaning that the stars Leo 6e–8e together form the shape of an ivy leaf. Thus the ivy leaf should be understood as an alternative description of the three stars in the lock of hair. 33 Eratosthenes (Robert 1878), p. 98; Condos 1997, p 125; Charvet and Zucker 1998, p. 73; Eratosthenes (Pàmias and Geus 2007), p. 98. 34 Toomer 1984, p. 368; Kunitzsch 1974, p. 284, no. 355. 35 Locher 1984. 36 Knorr 1991.

140

3.1 SUMMER AND WINTER HEMISPHERES Although the lock of hair, introduced around 250 bc by Conon in honour of Queen Berenice II Euergetes (273–221 bc), is well attested in literary sources, there are no images known of it before the sixteenth century.37 In addition to the hemispheres of the present group III, the figure of an ivy leaf is also seen on the cupola of Quṣayr c Amra and on one of the early Islamic globes discussed in Chapter 4. It seems therefore that the image of the ivy leaf was well established in the pictorial tradition in Antiquity but its literary tradition is as yet completely unknown. The apparent contradiction between the written sources describing the lock of hair and the pictorial tradition depicting an ivy leaf in its place seems to suggest a link between the two asterisms.The connection surviving in the Ptolemaic catalogue may be an echo of an as yet unexplained relation between the two asterisms.38 Perhaps the nebulous mass (the plokamos) was known as the ivy leaf before Conon called it the lock of hair. However that may be, the ivy leaf hemispheres exemplify a tradition that is attested by the Ptolemaic star catalogue. Another shared characteristic of the hemispheres in group III is the image of Cancer with claws oriented to the west towards Gemini instead of the astronomically correct direction towards Leo. Since it is seen on Kugel’s globe (Section 2.3) it may represent an old error which is not present on the hemispheres of the other two groups discussed above. Also the image of a figure carrying a pair of scales is seen exclusively on hemispheres belonging to the ivy leaf tradition.As mentioned already

in Chapter 2, Latin writers adopted the Balance as an invention of their own. Hyginus refers to the constellation as ‘nostri libram dixerunt’ and Martianus Capella as ‘quam Libram dicimus’.39 The figure carrying a pair of scales was not rare in the Roman world of Antiquity. It is seen in early pictures of the zodiac on astrologer’s boards such as the second-century ivory tablets found in Grand (a village in Lorraine) and the Tabula Bianchini, a marble astrologer’s board of the third century preserved in the Louvre.40 One also finds a figure carrying a pair of scales in the fourth-century synagogue at Hammath Tiberias and the sixth-century synagogue Bet Alfa.41 Despite being the most recent example, the set of hemispheres H10 in the fifteenth-century MS Vat. gr. 1087 is the best representative of the ivy leaf group (Fig. 3.10). The other Byzantine set of hemispheres H11 (MS gr. 1291) is in many respects inferior to H10. The northern and southern boundary of the zodiacal band on H11 intersects the equinoctial colures respectively below the Equator and below the Tropic of Capricorn. Another unreliable feature is the exchange between the constellations Aquila and Delphinus in the middle of the winter hemisphere which is not caused by its deteriorated state. The Byzantine hemispheres H11 seem to differ in the presentation of Libra which on all other hemispheres of the ivy leaf group is presented by a figure carrying a pair of scales. In Boll’s early description of 1899 Libra is said to be a pair of scales placed in the claws of Scorpius, but this cannot be confirmed.42 All one can say now is that the head and the claws of Scorpius

37 In all cases that the lock of Berenice is mentioned in connection with medieval illustrations, the ivy leaf is meant. 38 In Virgil (Rushton Fairclough 1916), Eclogue III.38–43, Conon himself is linked to ivy, but it is not clear what story this text refers to.

39 Le Boeuffle 1977, p. 171, citing Hyginus and Martianus Capella. 40 Evans 2004, p. 6, figure 1 and p. 8, figure 2. 41 Dunbabin 1999, pp. 191–2. 42 Boll 1899, p. 120.

141

The descriptive tradition in the Middle Ages extend into the segment for Libra. The condition of the map does not allow one to say what may have been present originally. The absence of Ophiuchus and Serpens in the region above the Equator would suggest that the map was not finished. The map H11 also stands out through the presentation of Sagittarius as a Centaur. The presentation of Sagittarius as a centaur is shared with the two maps H1 and H2 in theAberystwyth manuscript. In all other maps Sagittarius is drawn as an archer or a satyr. The matter of centaur vs archer was discussed in the Epitome attributed to Eratosthenes, where it is explained that ‘the Archer does not appear to have four legs, but to be standing and shooting a bow—and no centaur used a bow’.43 The image of Sagittarius as an archer is certainly part of the Greek corpus of images.44 On the planisphere in Vatican City MS gr. 1087 Sagittarius is drawn as a centaur and on that in Aberystwyth MS 375C as a satyr. Apparently these two forms for Sagittarius were considered interchangeable. In sum, the appearance of the ivy leaf on the summer hemispheres in group III suggests that the archetype of these maps was created when the ivy leaf was still a regular feature in celestial cartography, which appears to have been the case around ad 137, the epoch of the Ptolemaic star catalogue. In the literature belonging to the descriptive tradition no record of the ivy leaf is known, which seems to point to an origin for these hemispheres connected to globe making. Surely, the image of Libra as a figure carrying a pair of scales—as encountered in this group— seems to reflect a development postdating the 43 Eratosthenes (Robert 1878), p. 150; The English translation is from Condos 1997, p 183; Charvet and Zucker 1998, p. 133. 44 In certain traditions of illustrated manuscripts Sagittarius is drawn as a satyr, not as an archer.

image of Libra as the claws of Scorpius, extending over two signs, as on the Aberystwyth and Monza winter hemispheres belonging to groups I and II.

. PLANISPHERES The series of the medieval maps known as planispheres studied here are described in detail in Appendix 3.2, and for easy reference are numbered P1–P10. These maps, shown in Figs 3.12–3.21, do not seem to be linked to a particular text, if the general impression expressed in the literature can be relied on.45 There is certainly a lot of variation about the context in which the planispheres appear but some sort of common denominator is not totally absent. Four of the ten known medieval planispheres (P1, P2, P4, and P5) appear to be connected with Germanicus’s translation of Aratus’s poem The Phaenomena.46 The Germanicus manuscripts are divided into two branches, the so-called O and Z families, which division is still accepted today.47 The O-family is further divided into two subgroups: the so-called ν and μ branches, the oldest illustrated members of which are respectively Basle, Universitätsbibliothek MS AN. IV. 18 and Madrid, Biblioteca Nacional MS 19 (16).48 Two planispheres, one in Basle MS AN. IV. 18 of the ninth (P2) and another in Aberystwyth MS 735C of the early eleventh century (P1), 45 Thiele 1898, p. 163; McGurk 1973, p. 201. 46 Germanicus (Le Boeuffle 1975); Germanicus (Gain 1976); Reeve 1980, pp. 511–18; Reeve 1983, pp. 18–24. 47 Baehrens 1879, pp. 142–200, esp. pp. 142–6.The parent of the O-family is distinguished by the omission of lines 583–725 and by the absence of a number of excerpts which follow at the end of the poem in texts of the Z family (known as fragments III and II) Germanicus (Le Boeuffle 1975), pp. xxv–xxvii and pp. 45–8. 48 See for a description of these two manuscripts Haffner 1997, Anhang I: pp. 121–9.

142

Fig. 3.12 Planisphere in Aberystwyth, MS 735C, f. 10v. (Courtesy of Llyfrgell Genedlaethol Cymru/The National Library of Wales, Aberystwyth.)

The descriptive tradition in the Middle Ages

Fig. 3.13 Planisphere in Basle, MS AN. IV. 18, f. 1v. (Courtesy of the Universitätsbibliothek, Basle.)

144

3.2 PLANISPHERES Considering the close relation between the three manuscripts it has been suggested that the Leiden Aratea originally included a planisphere which then would have been the model for those in Boulogne-sur-Mer MS 188 (P5) and Bern MS 88 (P4).51 If the Leiden manuscript did not originally include a planisphere, the map must have been newly added to the Leiden Aratea corpus, when Boulogne-sur-Mer MS 188 was produced. One more planisphere, P7, in London, British Library, MS Harley 647, appears to be connected, although indirectly, with a translation of Aratus’s Fig. 3.13a Detail of the Basle map showing the poem The Phaenomena. The map is a later addiintersections of the equator with respectively the tion to an illustrated text based on Cicero’s transautumnal colure and the ecliptic. lation of Aratus with scholia from Hyginus’s serve as illustrations for the text of Germanicus’s myths.52 For a long time MS Harley 647 was Aratea belonging to the ν branch of the O-family. assumed to have been produced in the north of No medieval planispheres are known to occur in France but now it is believed to be one of the texts belonging to the μ branch of the O-family four Carolingian luxury codices produced at the although it is worth noting that of the ten Aachen court in the first half of the ninth cenRenaissance codices belonging to this branch tury.53 The underlying concept of the constellanine have a celestial planisphere. These humanist tion cycle in London MS Harley 647 is similar to the Leiden Aratea in the sense that both manuversions are discussed separately below. The planispheres in Boulogne-sur-Mer, scripts are designed as a picture book in which Bibliothèque municipale, MS 188 (P5) and drawings are accompanied by texts taken from Bern, Burgerbibliothek, MS 88 (P4) belong to a Latin translation of Aratus’s poem. The later texts of the Z-branch.The texts and illustrations addition of a planisphere to the Cicero codex in these two manuscripts are closely related to shows that it was considered helpful to have a the Leiden Aratea manuscript MS Voss. Q. 79.49 means to explain how the individual constellaThe Leiden codex appears to have been in the tions described in the codex are connected visumonastery Saint-Bertin during the abbacy of ally.When this addition happened is not certain. Odbert of Saint Omer (986–1008) where it was copied in Boulogne-sur-Mer MS 188.50 This 51 Mütherich 1989, p 58. 52 Saxl and Meier 1953, pp. 149–51. Reeve 1980, pp. 508–11; latter manuscript served in turn as the model for Reeve 1983, pp. 22–3. Cicero (Buescu 1966). Cicero (Soubiran the text and illustrations in Bern MS 88, also 1972). 53 The other three codices are the Vatican Terence (Vatican written in Saint-Bertin during Odbert’s abbacy. 49 Leiden Aratea 1989. 50 Obbema 1989, pp. 12–14. On Odbert, see Wilmart 1924, pp. 166–86 and Lesne 1938, IV, pp. 236–41.

City, Biblioteca Apostolica Vaticana MS Vat. lat. 3868), the Agrimensores (Vatican City, Biblioteca Apostolica Vaticana MS Pal. lat. 1564), and the Leiden Aratea (Leiden, Universiteitsbibliotheek MSVoss lat. 4° 79), see Mütherich 1990, p. 597.

145

The descriptive tradition in the Middle Ages

Fig. 3.14 Planisphere in Berlin, MS lat. 129 (Phill. 1830), ff . 11v and 12r. (Courtesy of the Staatsbiblothek zu Berlin-Preussischer Kulturbesitz, Berlin.)

Bischoff dates the map to the ninth or tenth century while Saxl and Meier suggest that the map is of the early eleventh century.54 Where this addition stems from is not known.The whereabouts of London MS Harley 647 in the second half of the ninth and tenth century is obscure. Some scholars assume that the codex was in Fleury at the turn of the tenth century and there served as the model for the Cicero text in London, British Library, MS Harley 2506, a manuscript with English drawings and a mixture

of English and French hands.55 Others believe that the Cicero text and illustrations in MS Harley 2506 derive from a now lost copy of MS Harley 647. If correct, it must have been this copy that at the turn of the tenth century was in Fleury, rather than MS Harley 647 itself. MS Harley 647 (or its presumed copy) was also used for another illustrated text of Cicero’s Aratea, namely that in London, British Library, MS Cotton Tib B.V, pars 1.56 Since this is believed to have been produced in England in the first half of the eleventh

54 Bischoff 2004, pp. 111–12. Saxl and Meier 1953, p. 149. McGurk 1973, p. 200 mentions the second half of the ninth century which is closer to Bischoff ’s date than that of Saxl and Meier. I thank Dr P. McGurk for his comments on this date (private communication).

55 For MS Harley 2506, see Saxl and Meier 1953, pp. 157–60, esp. p. 157 with a note about the replacement of the name Abbo (of Fleury) by Berno (pupil of Abbo and later of abbot of Reichenau). See also Blume 2007, p. 82. 56 Saxl and Meier 1953, pp. 119–28. McGurk et al. 1983.

146

3.2 PLANISPHERES

Fig. 3.14a Drawing of the planisphere in Berlin, MS lat. 129, reproduced from Thiele 1898, p. 163.

147

The descriptive tradition in the Middle Ages

Fig. 3.16 Planisphere in Boulogne-sur-Mer, MS 188, f. 20r. (Courtesy of the Bibliothèque Municipale, Boulogne-sur-Mer.) See also Plate III.

Fig. 3.15 Planisphere in Bern, MS 88, f. 11v. (Courtesy of the Burgerbibliothek, Bern.) See also Plate III.

tibus repraesentantur’.60 This suggests that the planisphere P7 (or a copy thereof) was available century, MS Harley 647 (or its presumed copy) when MS Cotton Tib B.V, pars 1 was produced. must by that time have been transferred to It is therefore likely that the planisphere was England.57 Reeve believes that MS Harley 647 already part of MS Harley 647 (and of its prewas at St. Augustine’s in Canterbury in the tenth sumed copy) before arriving in England. It century.58 shows that at least two more (and perhaps three) However confusing this story of transmission map versions existed at the time: the planisphere may be, for the present discussion it is notewor- in MS Harley 647 and its exemplar, the planithy that MS Cotton Tib B.V, pars 1, originally sphere in the presumed copy of MS Harley 647 included a map.59 Witness to this is a note of and the one in MS Cotton Tib B.V, pars 1. Humfrey Wanley (b. 1672, d. 1726), palaeograNext to maps associated with direct translapher and librarian of Robert and Edward Harley: tions of the Aratean poem three planispheres are ‘Planisphaerium, in quo Signa et Constellationes connected with an overall description of the coelestes delineationibus antiquis et non inelegan- celestial sky after Aratus. The best example of such a map is the ninth-century planisphere 57 Ker 1957, pp. 255–6. in Munich, Bayerische Staatsbibliothek, Clm 58 Reeve 1980, p. 508; Reeve 1983, p. 22. 59 Saxl and Meier 1953, p. 119: the map must have been located after f. 29 where two pages have been cut out.

148

60 Wanley 1705, pp. 215–17, esp. p. 216.

3.2 PLANISPHERES

Fig. 3.17 Planisphere in El Burgo de Osma, MS 7, f. 92v. (Courtesy of the Cabildo Catedral, El Burgo de Osma.)

149

The descriptive tradition in the Middle Ages

Fig. 3.18 Planisphere in London, MS Harley 647, f. 21v. (Copyright:The British Library Board.)

150

3.2 PLANISPHERES

Fig. 3.19 Planisphere in Munich, Clm 210, f. 113v. (Courtesy of the Bayerische Staatsbiliothek, München.)

210 (P8) included in the Liber calculationis, written under the guidance of Abbot Arno of Salzburg (785–821) during the years 810–18.This Salzburg compilation was written after another compilation was produced in Aachen in 809, when Charlemagne commissioned a number of scholars—possibly headed by Abbot Adalhard of Corbie—to compile a treatise on the computus, the Libri computi.61 The Salzburg compilation is a more extended work divided into three blocks. The map P8 is placed between the first (ff . 4r–112v) and second block (ff. 114r–129r).62 The 61 Dell’ Era 1974, pp. 5–13. See Borst 1995, pp. 156–65 and Borst 1998, pp. 312–22.

first two chapters of the second block are chapters V1. Excerptum de astrologia (ff . 114r–115r) and V2. De ordine ac positione stellarum in signis (ff. 115r–121r) which star catalogue is illustrated by coloured drawings.63 Both chapters stem from the Aachen compilation. The text Excerptum de astrologia provides a short review of the celestial sky after Aratus.64 De Bourdellès has argued that the Excerptum text 62 Rück 1888, pp. 5–10. 63 An edition of the text Excerptum de astrologia Arati is published by Maass 1898, pp. 309–12. This text is also edited in Dell’ Era 1974 with the text De ordine ac positione stellarum in signis. 64 Dell’ Era 1974. See also Neuss 1941, pp. 113–40.

151

The descriptive tradition in the Middle Ages

Fig. 3.20 Planisphere in Vatican City, MS Reg. lat. 123, f. 205r. (Courtesy of the Biblioteca Apostolica Vaticana, Vatican City.)

152

3.2 PLANISPHERES

Fig. 3.21 Planisphere in Vatican City, MS gr. 1087, f. 310v. (Courtesy of the Biblioteca Apostolica Vaticana, Vatican City.)

was composed with the help of a map, a hypothesis presumably supported by the fact that the two Aselli in the constellation Cancer are explicitly described as being placed on the back of Cancer (‘Cancer [. . .] habens in dorso Asellos albicante inter eos nubecula, quae Praesepium appellatur’).65 Pictures of the Aselli placed on the back of Cancer are rare but Asses do occur on the Aberystwyth summer hemispheres shown in Fig. 3.9, its planisphere in Fig. 3.16, and in the Aberystwyth planetary configuration as well.66 65 See Le Bourdellès 1985, pp. 85–9 (concerning the Excerptum de astrologia) and pp. 99–107. He believes that this particular text on Cancer has been taken from Pliny. Like many other sources Pliny does mention the Aselli. However he does not say explicitly that the Aselli are on the back of Cancer. 66 For the Aberystwyth planetary configuration, see McGurk 1973, Plate IV(A).

The references to the MilkyWay in the Excerptum text provide another argument to support Le Bourdellès’s thesis.67 Particularly the description of the position of Cassiopeia with respect to the neighbouring constellations and the Milky Way (‘Cassiepia contra volumen maximum septentrionalis Serpentis inter Agitatorem Perseum Andromedam Cepheumque consistit in lacteo circulo’) is quite easily 67 Le Bourdellès 1985, p. 86. The Milky Way is also said to intersect the zodiac in Gemini and Sagittarius (‘in commissura zodiaci atque lactei circulorum Gemini sunt locati; Sagittarium in commissura circulorum zodiaci atque lactei’). Le Bourdellès believes that this particular text on the Milky Way has been taken from Pliny, but Pliny says that the Milky Way cuts the Tropic of Cancer and Capricorn at respectively Sagittarius and Gemini, not the zodiac. And its two points of intersection with the Equator are on the one side in Aquila and on the other in Canis Minor. Pliny does not mention Cassiopeia whereas the references in the Excerptum de astrologia do not mention Aquila and Canis Minor.

153

The descriptive tradition in the Middle Ages suggested by a map.68 But a map is certainly not the only source for this text since the Pleiades at the tail of Taurus (iuxta caudamTauri Pliades videntur constitutae) are mentioned, a stellar configuration not seen on any of the maps studied here. Maps are not a standard feature of the text tradition connected with the Aachen and Salzburg compilations on the computus. Next to the ninthcentury planisphere in Munich Clm 210 (P8) two other maps may be connected with the text Excerptum de astrologia. The map in Vatican City, Biblioteca Apostolica Vaticana, MS Reg. lat. 123 (P9) may be one of them. It is entitled MACROBII AMBROSII. DE CIRCULIS SIGNIFERIS. CXX, and is part of an astronomical compendium, consisting of four books on respectively the Sun (ff. 1r–74r), the Moon (ff. 74v–110v), Nature (ff. 128r–150v), and Astronomy (ff. 153r–233v). The manuscript, and presumably the map, was composed in Ripoll—according to Gislaine Viré—by or under the redaction of Oliva, abbot of Santa Maria de Ripoll (c. 971–1046) sometime before 1056.69 The fourth book contains extracts from Hyginus’s De Astronomia, set within sections of astronomical commentaries by Isidore, Bede the Venerable, Aratus, and others. The chapters preceding the map consist of two parts: 1) the text ‘EXCERPTUM DE ASTROLOGIA MACROBII AMBROSII. LXXXV ’ (ff. 182r– 183r) and 2) a star catalogue based on excerpts from Hyginus (184v–2044r). It seems therefore that the authors of this compendium copied the overall review of the celestial sky (Excerptum de astrologia) but replaced the star catalogue (De ordine ac positione stellarum in signis) usually associated with it in the Aachen and Salzburg compilations by one based on Hyginus. And rather than place the map before these two sections it was added after them.That the 68 Le Bourdellès 1985, p. 86. 69 Viré 1981, p. 174; Hyginus (Viré 1992), p. xviii.

planisphere was indeed meant to illustrate the text Excerptum de astrologia is suggested by the fact that both texts in their titles are coupled to Macrobius, unjustly so.70 The other map possibly related to the text Excerptum de astrologia is P3, in Berlin, Staatsbiblothek zu Berlin-Preussischer Kulturbesitz, MS lat. 129 (formerly Phill. 1830).This manuscript with the planisphere P3 on ff . 11v–12r, was originally the first section of another codex, the other part of which is now in MS lat. 130 (Phill. 1832).The computistical texts in MS lat. 129 preceding the planisphere conceptually reunite with the texts of Bede the Venerable (De natura rerum, De temporibus, and De Temporum Ratione with glosses and a few computistical notes) on the first 80 pages of MS lat. 130 (formerly Phill. 1832). The appearance of an early planisphere within this computus context makes little sense. The map may have belonged to the text Excerptum de astrologia of the Salzburg Compilation of 810–818, Liber calculationis included on ff . 81r–85v in MS lat. 130. Finally there are two planispheres connected with texts of the Aratean corpus but not with an overall description of the celestial sky such as provided by direct translations of the Aratean poem or its summary in the text Excerptum de astrologia. Rather than serving as an illustration to the text the purpose of these maps seem to have been to provide additional information. For example, the planisphere in El Burgo de Osma, Archivo de la Catedral, MS 7 (P6) precedes a late twelfth century 70 As an aside I note that the text ‘EXCERPTUM DE ASTROLOGIA MACROBII’ is followed on f. 183r by the poem De sideribus by Priscianus ‘Ad boreae partes arcti vertuntur et anguis’, edited by Riese 1869, vol. 1, no 679. This astronomical poem occurs also in Aberystwyth NLW 735C, f. 7v, where it precedes an excerpt from Macrobius Commentary (ff. 7v–9v) and has four extra lines on the planets, and in Darmstadt Hs. 1020, f. 61v.

154

3.2 PLANISPHERES copy of the descriptive star catalogue De signis coeli, often referred to as ‘pseudo-Bede’.71 A similar function is fulfilled by the planisphere in the already mention fifteenth-century Byzantine manuscript Vatican City MS gr. 1087 (P10). This latter map is part of a series of illustrations which consists of figures of individual constellations, a planisphere, and a pair of summer and winter hemispheres.72 Presumably the need was felt to explain how the individual constellations described in the texts are connected visually. From this summary it is clear that eight planispheres (P1–P5, P7–P9) accompany an Aratean description of the celestial sky. Such a context seems only natural for, rather than describing individual constellations, Aratus presents an overall view of the constellations and emphasizes how they are placed in the sky with respect to each other. This interrelationship is exactly what the planispheres illustrate. The appearance of planispheres alongside descriptive star catalogues also makes sense.The catalogue entries that accompany the maps P6 and P10 do not explain how the constellations are related to each other in space.Thus the planispheres add here information that cannot be found in the catalogues.The presence of a planisphere shows that the catalogues themselves did not suffice to answer the curiosity of the medieval readers.

represent the ever-visible circle, the Tropic of Cancer, the celestial Equator, the Tropic of Capricorn, and lastly the ever-invisible circle as the outer boundary. In addition one finds in most planispheres two circles centred on the ecliptic north pole that mark the boundaries of the zodiacal band. In a few planispheres only one circle is drawn, presumably representing the ecliptic. In some maps two straight lines are also drawn through the celestial north pole, one passing through the ecliptic north pole representing the solstitial colures and another perpendicular to the latter representing the equinoctial colures. A last circle drawn on some of the planispheres depicts the Milky Way. Together these circles form the basic structure or ‘celestial grid’ upon which the constellations themselves are placed. Whereas the hemispheres discussed in the previous section present the celestial sky only in globe-view, the ways of presenting the sky used for celestial planispheres are twofold: in sky-view (in which mode the order of the zodiacal constellations is clockwise) and in globe-view (in which mode the order of the zodiacal constellations is anti-clockwise). These two modes of mapping appear to mark two different traditions in making planispheres.73 For example, all planispheres in sky-view include a circle representing the Milky Way which is not seen in any of the planispheres in globe-view. We shall return to 3.2.1 Cartography these distinct traditions in more detail later but Planispheres share certain cartographic elements, first discuss the cartographic characteristics of illustrated in Scheme 3.5. All maps have a number these maps. of concentric circles centred on the celestial In the few studies devoted to medieval celesnorth pole in the centre of the map.These circles tial maps it is again and again suggested that stereographic projection was used for drawing 71 Avilés 2001, p. 59. For De signis coeli, see Dell’ Era 1979a, pp. 268–301. 72 The constellation cycle is reproduced in Roscher 1884– 1937, vol. VI, Nachträge, columns 867–1071.

73 McGurk 1973, p. 201, follows Thiele 1898, p. 168, in assuming that ultimately all planispheres derive from one archetype or globe.

155

The descriptive tradition in the Middle Ages

Scheme 3.5 Overall structure of a medieval planisphere.

planispheres. As mentioned in Chapter 2, the description of an anaphoric clock byVitruvius in his De Architectura and the Salzburg dial (Fig. 2.1) appear to be based on it. North considered the planispheres included in medieval manuscripts the continuation of the Vitruvian anaphoric clock from Antiquity to the Middle Ages. He mentions in particular the example in Munich Clm 210, f. 113v (P8), of which he wrote: ‘At first sight this is merely a planisphere, showing the constellations pictorially, with one very clearly marked circle.This proves to represent not

156

the ecliptic, but the galaxy, the Milky Way. On closer examination, however, no fewer than eight circles are revealed within the outer pair bounding the planisphere, all in approximate - and not accidental - stereographic projection. Whoever painted this diagram seems to have known the principles of astrolabe projection well. He was certainly not merely painting an ordinary astrolabe rete, since the Milky Way is never - at least to my knowledge - found on an astrolabe, while there is also on the painting an uncharacteristic circle with north polar distance of about 37°.This could be a zenith-track for geographical latitude 53° N, although it is more probably an arctic circle

3.2 PLANISPHERES set to a conventional 36° (the height of the pole at Rhodes)’.74

The relation between planispheres and dial plates of an anaphoric clock are further emphasized as follows: ‘I have no wish to suggest that these diagrams were copied from an anaphoric clock plate, but they show that at least from the time of the ninth century the necessary skills for making such a plate were once again available in Europe, and that Pacificus, Archdeacon of Verona, could well have had on the clock mentioned in his epitaph a “song of the heavens” in the form of an astrolabe dial of one sort or another. It is quite possible, of course, that the medieval illustrations were copied from ancient exemplars which were themselves taken from anaphoric dials, or were even done by craftsmen skilled at both arts.’75

North’s thesis has left many traces in the literature. Eastwood uses it to support his claim that the Plinian ‘circular latitude diagrams’ are based on stereographic projection.76 In discussing medieval maps Stückelberger and Künzl both presume that the planispheres in medieval manuscripts were drawn in stereographic projection, following the description in Ptolemy’s Planisphaerium.77 North’s idea that medieval planispheres are based on stereographic projection was shared by Savage-Smith.78 Considering the apparent automatism to connect medieval planispheres with stereographic projection it may be worthwhile discussing here briefly sim74 North 1975, p. 389. 75 North 1975, p. 391. 76 Eastwood 2007, pp. 122–4. Note that his remark in footnote 45 on Munich Clm 210 as being an ‘eleven-constellation zodiac’ is not correct. There is an image of Libra as a pair of scales although it is difficult to see. 77 Stückelberger 1990, p. 75; Künzl 2000, p. 547; Stückelberger 1994, pp. 38–44. 78 Savage-Smith 1992, pp. 12–70, esp. p. 16.

ple measures that can be used for deciding which projection is really underlying a map. In Scheme 3.6 two ways of making a map of the celestial sky are shown by way of its main celestial circles (the five parallel circles and the ecliptic): stereographic projection (left) and equidistant projection (right). In stereographic projection the radius of a parallel circle centred on the celestial north pole of declination δ is Rδ = Reqtan(90º – δ ) / 2

(3.1)

where Req is the radius of the Equator. In the equidistant projection the radius of a parallel circle is proportional to its angular distance from that pole Rδ = Req(90º – δ ) / 90º

(3.2)

These two relations help to elucidate a number of typical differences between the two projections. Assuming the ecliptic pole to be 24° from the celestial north pole, it is clear that its location (E in Scheme 3.6) in the stereographic projection is at a distance of RE = 0.21Req whereas the centre of the circle representing the ecliptic (C in Scheme 3.6) is at a distance of RC = 0.45Req from the celestial north pole. Thus in stereographic projection the centre of the ecliptic (C) does not coincide with the ecliptic pole (E). In equidistant projection, on the other hand, the two centres coincide and are both at a distance RE = RC = 0.27Req from the celestial north pole. Another difference between the two modes of projection is the average value of the radii of the tropics. In stereographic projection the distance between the southern tropic and the Equator exceeds that between the northern tropic and the Equator.Assuming that the tropics are at a distance of 24° from the Equator,one finds for stereographic projection that the predicted

157

The descriptive tradition in the Middle Ages

Scheme 3.6 Overall structure of a map drawn in stereographic (left) and equidistant projection (right).

average value of the radius of the Tropic of Cancer and the radius of the Tropic of Capricorn, expressed as a fraction of the radius of the Equator, is equal to 1.09. In the equidistant projection the tropics are at equal distances from the Equator. Thus the average value of the radius of the Tropic of Cancer and the radius of the Tropic of Capricorn, expressed as a fraction of the radius of the equator, is 1.00. A similar difference occurs for the radii of the evervisible and invisible circles. In equidistant projection the average value of their radius is 1.00. In stereographic projection the average value depends on the geographical latitude: it is 1.57 for a geographical latitude of 42°. For lower values of geographical latitude the mean value of the evervisible and invisible circles increases and for 36° it

is equal to 1.70.The differences discussed here can help to decide which of the two modes of projection is relevant for the medieval planispheres. In Table 3.4 the necessary information for this has been collected. In the first column the planispheres included are listed and in the second column the radius of the Equator (Req) is given (which by definition is set equal to 1.00). In a few planispheres a few anomalous circles are drawn. It appears that in two planispheres, P8 and P9, the circle representing the Equator is displaced which is indicated in the Table as Rdc. In the next two columns the values of the ‘distance of the centre of the ecliptic’ (DC) and the ‘radius of the ecliptic’ (Recl) have been listed. If only the zodiacal band is drawn the radius of the ecliptic (Recl) was found by the aver-

158

3.2 PLANISPHERES Table 3.4 Quantitative data on the grids in planispheres Req P1. Aberystwyth MS 735C P2. Basle MS A.N. IV. 18 P3. Berlin MSLat 129 P4. Bern MS 88 P5. Boulogne-sur-Mer MS 188 P6. Burgo de Osma MS 7 P7. London MS Harley 647 P8. Munich Clm 210 P9. Vatican City MS Reg. lat. 123 P10. Vatican City MS gr. 1087 Mean values Standard deviations Predictions Equidistant projection Stereographic projection a

Rdc

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.00 1.00

DC

Recl

Rtropics

Rever

Rmean

0.26 0.28 0.21 0.23 0.25 0.30 0.20 0.27 0.27 —

0.96 1.00 1.04 1.02 1.03 0.97 0.99 1.03 1.00 —

0.99 1.00 1.00 1.05 1.08 0.98 0.98 1.03 1.00 1.00

0.95 — 1.00 1.07 1.11 0.97 0.98 0.99 1.02 1.01

0.98 1.00 1.01 1.03 1.06 0.98 0.99 1.01 1.00 1.00

0.25 0.03

1.00 0.03

1.01 0.03

1.01 00.5

0.27 0.45

1.00 1.09

1.00 1.09

1.00 1.57

†

† † † † †

All distances defined below are expressed as a fraction of the radius of the Equator. Req: the radius of the Equator, set by definition equal to 1.00. Rdc: the radius of the misplaced circle on maps P8 and P10. DC: the distance of the centre of the ecliptic from the north pole. Recl: the radius of the ecliptic. If only the zodiacal band is drawn the radius of the ecliptic (Recl) was found by the average value of the radii of its northern and southern boundaries. This is marked by a dagger (†). Rtropics: the average of the radii of the tropics. Rever: the average of the radii of the ever-visible and ever-invisible circles. Rmean: the mean value of Req/ Rdc, Recl, Rtropics and Rever a Assuming a geographical latitude of 42º. For lower values of geographical latitude the mean value of the ever-visible and invisible circles increases. For 36º it is equal to 1.70.

age value of the radii of its northern and southern boundaries.This is marked by a dagger (†). In the last two columns we have added for each planisphere the average value of the radius of the Tropic of Cancer and that of the Tropic of Capricorn (Rtropics) and the average value of the radius of the ever-visible and that of the everinvisible circle (Rever), both as a fraction of the radius of the Equator.79 In the last but two rows of Table 3.4 we have added some statistics by calculating the mean value and standard deviation 79 These average values are simple arithmetic means but in order to avoid confusion with other ‘mean values’ we have labelled them here as average values.

of the figures for all planispheres. In the last two rows the predicted values in the two models considered here have been added. In all planispheres the measured distances of the centre of the ecliptic from the celestial north pole are close to the mean value 0.25 ± 0.03 which agrees well with the prediction of equidistant projection (0.27) and not at all with that of stereographic projection (0.45). Also the mean value 1.00 ± 0.03 of Recl, that is, the measured radius of the ecliptic or the average of the measured values of the radii of the boundaries of the zodiacal band expressed as a fraction of the radius of the Equator (Table 3.4, column 4), is close to the prediction of

159

The descriptive tradition in the Middle Ages equidistant projection (1.00) and not to that of stereographic projection (1.09). The average of the measured values of the radii of the tropics (Rtropics), the zodiacal boundaries (Recl), and the ever-visible and invisible circles (Rever) in Table 3.4, columns 5–7, are all close to 1.00. The mean values of these parameters are again much closer to the predictions of equidistant projection than to those of stereographic projection. Two maps,P4 (Bern MS 88) and P5 (Boulognesur-Mer MS 188), have values of Rtropics and Rever lying slightly outside the range indicated by the standard deviations of the mean values. Closer inspection shows that these deviating values are the result of an error in the radius of the Equator, which is used as the standard for the data in Table 3.4, rather than a shift in projection.To correct for such errors we have calculated a new standard, Rmean, as the mean value of all radii listed in Table 3.4, and used this as the standard size to express all other sizes presented below. The values of Rmean are included in the last column in Table 3.4. In sum, the information presented in Table 3.4 demonstrates beyond all doubt that there is no support for North’s proposition that the planispheres in medieval manuscripts are drawn according to stereographic projection.The whole discussion of a possible relation between these planispheres, astrolabes, and the dial plates of anaphoric clocks is superfluous.80 There is no link with Ptolemy’s Planisphaerium nor is there any evidence that stereographic projection was known in the Latin West before the turn of the tenth century. Although the planispheres appear to have characteristics belonging to equidistant projection, these maps do not in every respect conform to 80 Not long ago Wiesenbach demonstrated convincingly that North’s suggestion of a possible relation of the anaphoric clock with ‘song of the heavens’ of Pacificus, Archdeacon of Verona, can be set aside, see Wiesenbach 1993, pp. 239–50.

this projection. In medieval planispheres oblique circles such as the ecliptic and the boundaries of the zodiacal band are drawn as circles centred on the ecliptic pole placed at a distance from the celestial north pole proportional to its angular distance from it. In equidistant projection proper, oblique circles are transferred into ovals, not into circles.81 For this reason, the term ‘equidistant projection’ should not be used for medieval planispheres. Instead we shall denote the maps as being made after the equidistant model because leaving oblique circles aside, medieval planispheres share with equidistant projection the proportional series of circles centred on the north pole. How the planispheres were constructed in practice is not difficult to see. First the five parallel circles are drawn with the celestial north pole as their centre, with radii proportional to their angular distances from the north pole.The radius of the celestial Equator is proportional to an angular distance of 90° and the radii of the Tropic of Cancer and the Tropic of Capricorn, at distances from the north pole proportional to angular distances of respectively 66° and 114° for an obliquity of the ecliptic of 24°.The tropics are then equal to respectively 66/90 (= 0.73) and 114/90 (= 1.27) parts of the Equator. And the radii of the ever-visible and ever-invisible circles, at distances from the north pole proportional to angular distances of respectively φ and 180° - φ (where φ is the geographical latitude), are equal to respectively φ/90 and (180° - φ)/90 parts of the Equator. The ecliptic and/or the boundaries of the zodiacal band are drawn with the ecliptic north 81 The earliest use of equidistant projection is for constructing the melon-shaped astrolabe attributed to Habash al-Hāsib (fl. 850), see Kennedy et al. 1999. No copy of such an astrolabe has survived. In western celestial cartography the earliest printed example of a planisphere using equidistant projection is by Peter Apian (1533). This celestial map—peculiar for its constellations—is discussed in Kunitzsch 1986c.

160

3.2 PLANISPHERES

Scheme 3.7 Points of intersection of the Equator and the ecliptic.

pole as their centre and with the radius of the ecliptic proportional to an angular distance of 90° (and equal to that of the Equator). The ecliptic north pole is located at a distance from the equatorial north pole proportional to angular distance of 24°, that is 24/90 (= 0.27). For drawing the northern and southern boundaries of the zodiacal band one has to fix the width of the zodiac. The value commonly used in Antiquity is 12°, with the northern boundary of the zodiacal band at 6° above the ecliptic and southern boundary of the zodiacal band 6° below it.These boundaries are of course drawn with the ecliptic north pole as their centre. If the radius of the ecliptic is equivalent to 90°, the radii of the outer boundaries are proportional to the angular distances from the ecliptic pole of respectively 84° and 96°. In other words, these radii are respectively 84/90 (= 0.93) and 96/90 (=1.07) parts of the radius of the ecliptic. Sometimes the colures are encountered on planispheres. The solstitial colures are obtained

by drawing a straight line through the equatorial and the ecliptic north pole, the equatorial colures by drawing a straight line through the equatorial north pole perpendicular to the solstitial colures. The result of constructing planispheres in this way is that the positions of the equinoxes become uncertain, as is illustrated in Scheme 3.7. In the equidistant projection the points of intersection of the Equator and the (oval) ecliptic coincide with the points of intersections of the equinoctial colures and the Equator (points marked a and b in Scheme 3.7). However, when the ecliptic is drawn as a circle following the equidistant model, the points of intersection of the Equator and the (circular) ecliptic are shifted to points a* and b* in Scheme 3.7, and do not coincide with the points of intersections of the equinoctial colures and the Equator. On the Basle map (P2) the divergence between the points of intersection b and b* is clearly observed as shown in Fig. 3.13a (see p. 145).

161

The descriptive tradition in the Middle Ages

Scheme 3.8 Left: Milky Way circle on the celestial sphere and right: Milky Way circle in the equidistant model.

This shortcoming of planispheres may well be the reason why 1) only in two cases (P2 and P10) the colures were drawn on planispheres, 2) in the Greek map (P10) the ecliptic is not drawn at all so that the problem does not show, and 3) zodiacal bands in planispheres are not divided into zodiacal signs as is done on most of the hemispheres. A last circle found on planispheres is the Milky Way. The thesis of the Milky Way being an oblique great circle implies that its construction in the equidistance model follows closely that of drawing the ecliptic. The line connecting the northernmost and the southernmost points D and E of the Milky Way (see Scheme 3.8) passes through the centre of planisphere. Since these points are by definition on the same meridian plane (the great circle through E, A, and D in Scheme 3.8), its projection passes through the north pole.The pole A of the Milky Way circle is half way between the northernmost and the southernmost points D and E. Once the pole of

the Milky Way circle is determined, the Milky Way circle can be drawn with a radius equal to that of a great circle, as for example, the Equator. Most ancient descriptions, such as the one by Manilius cited in Chapter 2, mention that the Milky Way passes through Cassiopeia at its northernmost point and through Centaurus at its southernmost point. In 128 bc the star α Cas was at RA 344°, Dec 45° and the star γ Cru at the hindfeet of Centaurus at RA 161°, Dec −45°. Therefore, the meridian plane through these two constellations was about 15° west of the plane through the equinoctial colures.82 The centre of the Milky Way circle is then to be expected at a right ascension of about 165° and a declination of about 45° (see Scheme 3.8).

82 Nowadays (epoch 1950) the Galactic pole is located in a relatively empty region in the sky, east of Coma Berenices and south of α CVn, at right ascension 192.3° and declination 27.1°.

162

3.2 PLANISPHERES For a comparison of the data of the medieval planispheres with the predicted values of the model map outlined above we have divided the maps into two groups. One group consists of the planispheres showing the constellations as they are seen on the globe. Maps of this kind are included in the following manuscripts:

equidistant model. Since the averaged values of such circles as the tropics and the ever-visible and ever-invisible circles of the maps fit into the equidistant model (Table 3.4), the deviations can be interpreted as corruptions or misunderstandings of an original archetype. Surely, none of the planispheres studied here was constructed by directly following the recipe described above. All were copied from an older map. In this copy• P1. Aberystwyth MS 735C (Fig. 3.12) ing process elements were introduced which • P2. Basle, MS AN. IV. 18 (Fig. 3.13) were presumably not present in the original • P3. Berlin MS lat. 129 (Fig. 3.14) drawing. For their interpretation an understand• P6. El Burgo de Osma MS 7 (Fig. 3.17) ing of the various effects is essential. • P10.Vatican City MS gr. 1087 (Fig. 3.21) All maps have a zodiac with a width twice or The other five medieval planispheres show the more than that predicted by the model. The constellations as they are seen in the sky. width of the zodiac of 12° assumed in the equiPlanispheres in sky-view are included in the fol- distant model is cited in many ancient sources. It is based on the latitudinal motions of the planets lowing manuscripts: and not on the latitudinal size of the zodiacal • P4. Bern MS 88 (Fig. 3.15) constellations. The broadening of the zodiac in • P5. Boulogne-sur-Mer MS 188 (Fig. 3.17) the planispheres shows that artists liked to have • P7. London MS Harley 647 (Fig. 3.18) the zodiacal constellations nicely fitted within • P8. Munich Clm 210 (Fig. 3.19) the boundaries of the zodiac. The widths of all • P9.Vatican City MS Reg. lat. 123 (Fig. 3.20) zodiacs are between 0.24 and 0.33 (see Tables In Tables 3.5A and 3.5B the measured radii of the 3.5A and 3.5B), corresponding to angular widths main circles in terms of the mean radius (Table 3.4 of 22° and 30°, respectively. Closely connected last column) for the two groups are presented. to the increased width of the zodiac are the deviTable 3.5A includes the data of planispheres in ating values for the zodiacal boundaries. Another common feature in medieval maps is globe-view, none of which include a circle reprethat the Tropic of Cancer is set tangentially to the senting the Milky Way. Table 3.5B includes the planispheres in sky-view, all of which do have a northern boundary of the zodiac instead of to circle for the Milky Way. In the first column of the ecliptic in the middle of the zodiacal band. each Table (3.5A and 3.5B) the names of the celes- Similarly one finds that the Tropic of Capricorn tial circles are given. In the second the values pre- is tangential to the southern boundary of the dicted by the equidistant model are added. The zodiac in the winter hemispheres, not to the remaining columns show the relevant data of the ecliptic itself. This same error occurs in most hemispheres, as discussed above. manuscripts of Group A and B, respectively. In practice this error is reflected by deviations of The data show that the characteristic sizes of the various circles of most maps deviate in one the radii of the tropics from the equidistant model. or more respects from those predicted by the In order to make the tropics tangential to the 163

The descriptive tradition in the Middle Ages Table 3.5A Quantitative data of the radii of the circles of the planispheres in group A: globe-view (expressed as fractions of the mean radius of a great circle calculated in Table 3.4, last column)

Radius of the Equator Radius of the Tropic of Cancer Radius of the Tropic of Capricorn Distance of the ecliptic pole from the NP Radius of the ecliptic Radius of the northern boundary Radius of the southern boundary Width of the zodiac Radius of the ever-visible circle Radius of the ever-invisible circle

Modela

P1

P2

P3b

P6

P10

1.00 0.73 1.27 0.27 1.00 0.93 1.07 0.13 0.40 1.60

1.02 0.75 1.27 0.26 — 0.85 1.11 0.25 0.36 1.58

1.00 0.75 1.25 0.28 0.99 0.87 1.13 0.26 — —

0.99 0.70 1.28 0.20 — 0.88 1.19 0.32 0.42 1.56

1.02 0.68 1.31 0.31 0.99 — — — 0.37 1.61

1.00 0.63 1.38 — — — — — 0.30 1.72

a The radii of the ever-visible and ever-invisible circles are based on a geographical latitude 36º. b The value of the radius of the northern boundary of the ecliptic is set equal to the radius of the displaced circle in this map.

Table 3.5B Quantitative data of the radii of the circles of the planispheres of group B: sky-view (expressed as fractions of the mean radius of a great circle calculated in Table 3.4, last column)

The radius of the Equator The radius of the Tropic of Cancer The radius of the Tropic of Capricorn Distance of the ecliptic pole from the NP The radius of the northern boundary The radius of the southern boundary Width of the zodiac The radius of the ever-visible circle The radius of the ever-invisible circle The radius of the Milky Way

Modela

P4

P5

P7

P8b

P9

1.00 0.73 1.27 0.27 0.93 1.07 0.13 0.40 1.60 1.00

0.97 0.68 1.36 0.22 0.84 1.14 0.30 0.30 1.77 1.06

0.94 0.67 1.37 0.24 0.83 1.11 0.28 0.31 1.78 1.10

1.01 0.66 1.32 0.20 0.87 1.14 0.27 0.32 1.65 1.05

0.98 0.64 1.40 0.27 0.89 1.14 0.24 0.34 1.60 0.98

1.00 0.55 1.46 0.27 0.83 1.16 0.33 0.32 1.72 1.00

a The data of the ever-visible and ever-invisible circles are based on a geographical latitude 36º. b The value of the Equator is set equal to the displace circle in the map. c The value of the radius of the Equator is set equal to the radius of the displaced circle in this map.

boundaries of the zodiac one has to diminish the radius of the Tropic of Cancer and to increase that of the Tropic of Capricorn. For a regular width of the zodiac of 12° the tropics are displaced to distances from the Equator of 30° instead of 24° and the corresponding radii of the tangential tropics become 0.67 and 1.33 instead of 0.73 and 1.27 predicted by the equidistant model. In this process the

average value of the radii of the tropics remains the same.Also the distance of the centre of the ecliptic from the north pole is not affected. If the width of the zodiac is at the same time enlarged to more than 12° the radii of the tropics vary accordingly. For example, for an increased width of the zodiac of 24°, the tropics are displaced in this process to distances from the Equator of 36° instead of 24°,

164

3.2 PLANISPHERES and the corresponding radii of the (tangential) tropics become 0.6 and 1.4. By increasing the width of the zodiac so far that its northern and southern boundary touches the Equator in respectively the north and in the south, the width of the zodiac becomes 0.53, corresponding to an angular width of 48°.The radii of the (tangential) tropics become then 0.47 and 1.53. Looking at the maps in globe-view (Table 3.5A), one sees that there are two planispheres with a widened zodiac without further errors such as adaptation of the tropics. These are the planispheres in Aberystwyth (P1) and Basle (P2). The Aberystwyth map is very neatly drawn and its parameters deviate just a little from the positions predicted by the equidistant model. But these minor deviations reflect errors in drawing circles correctly and do not reflect changes in astronomical concepts. The planisphere in Basle (P2) is crudely drawn, not all circles drawn in the map are perfectly circular, and only parts of the boundaries of the zodiacal band are visible. Yet, by fitting circles through the small sections available one can determine the data presented in Table 3.5A, which surprisingly are not bad at all. An interesting case of an echo of adapted tropics is seen in the planisphere in El Burgo de Osma (P6) in which only the ecliptic is drawn. The radii of 0.68 and 1.33 (see Table 3.5A) of respectively the Tropic of Cancer and the Tropic of Capricorn indicate that the artist apparently had a planisphere at his disposal in which the tropics were drawn tangentially to the boundaries of a 12°-wide zodiacal band. The copyist must have been aware of this error because he ‘corrected’ it by removing the zodiacal band and by drawing only the ecliptic, placing it tangentially to both tropics as it should. However, he did not correct the radii

of the two displaced tropics. As a result, the centre of the ecliptic in this planisphere is artificially shifted away from the north pole. This process explains the deviation from the model of the distance of the centre of the ecliptic from the north pole (0.31) in Table 3.5A in combination with the deviations of the radii of the tropics (0.68 and 1.33). The trend to adapt the tropics to the boundaries of a broadened zodiac is also clear from the data in the Byzantine map (P10) in which neither the ecliptic nor the zodiacal band have been drawn. The radii of theTropic of Cancer and of Capricorn of 0.63 and 1.38 respectively (see Table 3.5A) imply that on its model these tropics were drawn tangentially to a zodiac with a width of 20°. In the absence of additional information this is all that can be said. This leaves only one planisphere in group A (drawn in globe-view) to be discussed, the Berlin map P3.This map is a bit messy and moreover in a very bad state (see Fig. 3.14).The numerical data listed in Table 3.5A were determined from the drawing published by Thiele reproduced in Fig. 3.14a, and verified by using only one half of the map.83 Some parameters, such as the radii of the tropics, are fairly close to those predicted by the equidistant model. However, the presentation of the zodiac is troublesome, even assuming that the circle corresponding to the northern boundary of the zodiac is displaced.The size of the displaced circle in the map support such an hypothesis. However, in order to find the centre of the ecliptic only the southern boundary can be used.This circle is drawn very badly too. It is displaced from its proper place and its size is exceptionally large. The artist has drawn the southern boundary such that it crosses the winter colure about 6° south of the solstice on theTropic of Capricorn whereas its

165

83 Thiele 1898, p. 164.

The descriptive tradition in the Middle Ages intersection with the summer colure almost touches the Equator! In the absence of additional information it is too speculative to explain such deviations in terms of the errors discussed here. All maps in sky-view (Table 3.5B) show clearly the impact of the error of adapting the tropics to the widened zodiacal boundaries.Two maps, P8 and P9, have in common that they miss the Equator and possess instead a displaced circle with a diameter one would expect for the Equator. It seems therefore fair to assume that the displaced circle is the Equator gone astray and that this somehow was already part of the model from which both maps derive. The two maps differ in the sense that the width of their zodiacs differ. The size of the zodiac in the Munich map P8 (see Table 3.5B) corresponds to an angular width of about 24°. For tropics drawn tangentially to the widened zodiacal boundaries, this width predicts that the radii of the tropics should be respectively 0.60 and 1.40 which values agree fairly well with the radii of the measured tropics. The width of the zodiac in P9 (Vatican City, Reg. lat 123) has the maximum value of 0.33 (see Table 3.5B) corresponding to an angular width of about 30°. For tropics drawn tangentially to the widened zodiacal boundaries, this width predicts that the radii of the tropics should be respectively 0.57 and 1.43 which values also agree fairly well with the radii of the measured tropics. The increased width in P9 is most likely a further corruption of an original model. The effects of adapting tropics to the boundaries of widened zodiacs are also clearly displayed in the three remaining planispheres in sky-view: the London map P7, the Boulogne-sur-Mer planisphere P5, and the Bern copy P4. All three maps show similar deviations with respect to the equidistant model (see Table 3.5B): the widths of

the zodiac vary between 0.27 and 0.30, the radii of the tropics are around 0.67 and 1.33, and the distance of the ecliptic pole from the north pole varies between 0.20 and 0.24. The radii of the tropics in these planispheres at around 0.67 and 1.33 suggest an adaptation of the tropics to the boundaries of a 12°-wide zodiac, but the width of the zodiac in these planispheres is around 24°. This discrepancy is explained by taking into account yet another deviation from the equidistant model, a shift of the centre of the zodiac towards the north pole. The characteristics of the planisphere P7 are closest to the set of data generated by this process. In the planispheres P5 and P4 the adjustment of the ecliptic pole towards the north pole has not been completely carried through, as is seen by the distances of the centre the zodiac from the north pole of 0.24 and 0.22, respectively. The result is that the Tropic of Cancer in these planispheres is not tangential to the inner boundary of the zodiac. Also the data of the boundaries of the zodiac in these two maps deviate more from those indicated by the equidistant model than those of planisphere P7, indicating that the copyists of the planispheres P5 and P4 did not work as accurately as their colleague of the London map. The Milky Way is drawn only on the planispheres in sky-view. To compare its location on the various planispheres with each other and with the data predicted by the model, the right ascensions of the northern- and southernmost point of the Milky Way circle are summarized in Table 3.6. In the first column the maps are given. The remaining columns 2–5 show respectively the right ascensions of the northernmost point of the Milky Way circle (RAd ), of Cassiopeia (RACas), the southernmost point of the Milky Way circle (RAE), and of Centaurus (RACen). In

166

3.2 PLANISPHERES Table 3.6 Quantitative data on the Milky Way circle Planisphere

RAD

RACas

RAE

RACen

MODEL P7 London MS Harley 647 P4. Bern MS 88 P5. Boulogne-sur-Mer MS 188 P8. Munich Clm 210 P9. Vatican City MS Reg. lat. 123

345° 20° 5° 0° 5° 10°

345° 340° 340° 340° 340° 340°

165° 200° 185° 180° 185° 200°

165° 210° 200° 210° 195° 195°

RAD: right ascension of the northernmost point of the Milky Way circle. RAE: right ascension of the southernmost point of Milky Way circle. RACas: right ascension of Cassiopeia. RACen: right ascension of Centaurus.

the first row the values predicted by the equidistant model are added. These data show that the position of Cassiopeia is fairly constant over the planispheres and deviates not more than 5° from the model value. In contrast the position of Centaurus deviates by 30° on P8 and P9 and by about 35°–45° on the maps P4, P5, and P7. It is also clear that in all these maps Cassiopeia and Centaurus do not lie on a straight line through the centre of the map.These deviations are most likely the result of inaccurate copying. The lines connecting the northernand southernmost point of the Milky Way in all planispheres are off by about 15° (P5) to 35° (P7) in right ascension from the predicted value. Until now we have left aside the sizes of the ever-visible and ever-invisible circles. Their dependence on geographical latitude makes it hard to predict specific values. If one assumes that the latitudes concerned lie between 32° (Alexandria) and 42° (Rome) one would expect the radii of the ever-visible circles of the planispheres to be in between 0.36 and 0.47; those of the ever-invisible circles to be between 1.64 and 1.53. All five planispheres drawn in sky-view have radii of the ever-visible circles less than 0.36, pointing to latitudes below 32°, which seems

unlikely. In two of the planispheres, those in P7 and P8, the radii of the ever-invisible circles are equal to or less than 1.65, but the planispheres in the other three manuscripts, P4, P5, and P9, have radii in excess of 1.65, again pointing to unlikely latitudes below 32°.We may well label the deviating sizes in these maps as corruptions. A different situation applies to the five planispheres drawn in globe-view: four of them have radii within the ranges predicted above. Only the radii of the ever-visible and ever-invisible circles of the Byzantine planisphere P10 lie outside this range. However, it would be too speculative to derive a specific geographical latitude from any of the four maps within the allowed range. The general impression only confirms that the planispheres in globe-view seem somehow closer to their original archetype than those in sky-view.

3.2.2 Astronomical considerations I recall here again that in the descriptive cartographic tradition maps follow one of three epochal modes: one after Eudoxus, another following Martianus Capella, and a third in keeping with the description of Manilius. The question is: can we find out what the relevant mode for our planispheres is?

167

The descriptive tradition in the Middle Ages The absence of boundaries in the east–west orientation of the maps, such as the straight lines marking the colures, is an important source of errors in planispheres. Most artists appear to have been unaware that the zodiacal constellations in the smaller northern branch of the zodiac, extending 90° to both sides of the summer solstice, should possess as many images as those in the larger southern branch, extending 90° to both sides of the winter solstice.They are rather inclined to distribute the zodiacal images evenly around the zodiac. In this way systematic errors may have been produced that easily vary by half a sign, or 15°. Keeping such uncertainties in mind we have summarized in Table 3.7 the positions of the solstitial colures with respect to the nearest zodiacal constellations. The solstitial colures were selected for this purpose because in the equidistant model the positions of the equinoxes are not well defined, as we discussed above. On only two maps (P2 and P10) could we use the line drawn for representing the solstitial colures. On the other planispheres the solstitial colures were identified as the straight line through the equatorial pole in the centre of the five parallel circles and the ecliptic pole in the centre of the zodiacal belt.

In Table 3.7 the planispheres are listed in the first column. In the second and third column the positions of respectively the summer and winter colure are described.The maps are ordered after the position of the summer colure. The information in Table 3.7 shows that on six planispheres (P1, P2, P4, P5, P7, and P8) the summer colure passes between the constellations Gemini and Cancer. On four of these maps (P2, P4, P5, and P7) the winter colure passes roughly west of Capricorn. These planispheres agree fairly well with the epochal mode of Manilius in which the summer colure is predicted to pass between the constellations Gemini and Cancer, and the winter solstitial colure between Sagittarius and Capricorn. The data for these planispheres are not all internally consistent. For example, on the Aberystwyth planisphere P1 the summer colure passes between Gemini and Cancer (Manilian mode), and the winter solstitial colure through the middle of Capricornus (Eudoxan mode). The locations of the nonzodiacal constellations are too erratic to be used for solving this contradiction. Looking at the extremes in Table 3.7 one sees that on P3 (Berlin) the summer and winter colures pass respectively through the fore part of

Table 3.7 Location of constellations with respect to the solstitial colure in planispheres Maps

Summer solstitial colure

Winter solstitial colure

P9.Vatican City MS Reg. lat.123 P10.Vatican City MS gr. 1087 P2. Basle MS AN. IV. 18 P7. London MS Harley 647 P5. Boulogne-sur-Mer MS 188 P4. Bern MS 88 P8. Munich Clm 210 P1. Aberystwyth MS 735C P6. El Burgo de Osma MS 7 P3. Berlin MS lat. 129

through the middle of Gemini through the middle of Gemini between Gemini and Cancer between Gemini and Cancer between Gemini and Cancer between Gemini and Cancer between Gemini and Cancer between Gemini and Cancer through the fore part of Cancer through the fore part of Cancer

through the left shoulder of Sagittarius through the human body of Sagittarius through the rear part of Sagittarius through the rear part of Sagittarius through the tail of Sagittarius through the head and forefeet of Capricornus through the coil in the tail of Capricornus through the middle of Capricornus through the middle of Capricornus between Capricorn and Aquarius

168

3.2 PLANISPHERES Cancer and between Capricorn and Aquarius, on P9 (Vatican City) these colures pass respectively through the middle of Gemini and through the left shoulder of Sagittarius.The data on these maps disagree with all epochal modes known in Antiquity. Compared to the Manilian mode the locations of the zodiacal constellations with respect to the solstitial colures are shifted over at least one to two zodiacal signs. If one were to explain such variations astronomically in terms of precession one would arrive at epochs varying from 1500 bc (for the planisphere P3 in Berlin) to ad 1200 (for the planisphere P9 in Vatican City).This tells us that the deviations in the positions of the colures with respect to the zodiacal constellations in these maps are the result of severe copying errors. Corruption through copying may not be the whole story for the Byzantine planisphere P10. This fourteenth or fifteenth-century planisphere gives us a fair idea of how the sky looked around the year ad 1000, hence not as it was seen in Antiquity. In 1000 the summer solstitial colure passed through the middle of Gemini and through Sirius, the brightest stars in Canis Maior. The winter solstitial colure passed through Aquila and the head of Sagittarius. Considering the internal consistency of these data one wonders whether the deviations observed in this map might have been the result of the deliberate adaptation for the year 1000 of an existing antique map, or the deliberate introduction of a systematic error of 15° in reallocating the solstitial colures of an existing antique map. To update a map an astronomer would have to be aware of precession and would have to be directly or indirectly familiar with Ptolemy’s astronomical works. But such an astronomer would also be aware of a description of the celestial sky far more accurate than any map in

the descriptive tradition. It seems therefore unlikely that an astronomer would be inclined to update an old map. Thus we arrive at the other possibility, namely that a deliberate systematic error of 15° was introduced in re-locating the solstitial colures of an already existing antique map. One can understand why a relocation was made, considering that the same artist was responsible for the pair of summer and winter hemispheres in Vat. gr. 1087 discussed above. The most striking characteristic of that summer hemisphere is that Sirius is on the summer solstitial colure like we see it in the planisphere. However, on the hemisphere this summer solstitial colure passes between Gemini and Cancer. For the artist, Sirius, the flaming head of Canis Maior, seems to have assumed importance above other constellations, for reasons explained before in the discussion on the Byzantine summer hemisphere H10. One can well imagine that an artist adapted the planisphere such that in that map Sirius is located on the summer solstitial colure too. This then would explain the apparent shift of 15° of the right ascensions of the constellations in a map that in all other respects looks ancient. Although the analysis of the grids and the epochal modes has provided some insights on the quality of the maps, it does not answer such questions as whether they all stem from one archetype, especially because there is great variation in the iconography of the maps. Yet, a number of groups can be identified. In Table 3.8 the constellations occurring on the planispheres are summarized. The maps are labelled by their catalogue numbers P1–P10. The constellations are denoted by their modern abbreviations.The presence of a constellation on a map is marked by a plus sign (+), its absence by a minus sign (–). The order of the maps is determined by a number

169

The descriptive tradition in the Middle Ages Table 3.8 Constellations on the planispheres in globe-view and sky-view Globe-view

Sky-view

Name

P1

P6

P10

P2

P3

P7

P5

P4

P8

P9

UMi UMa Dra Cep Boo CrB Her Cyg Cas Per Aur Oph Ser Aql Peg And Ari Tau Gem Cnc Leo Vir Lib Sco Sgr Cap Psc Cet Ori CMa CMi Navis Hya Cen Lup Ara PsA Aqr Crt Crv Del Eri Lep Lyr

+ + + + + + + + + + + + + + + + + + + + + + – + + + + + + + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + + + + – + + + + + + + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + + + + – + + + + + + + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + + + + – + + + + + + + + + + + + + + – + + + + + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + – – + + + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + –

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + –

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + – +

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + – – + + continued

170

3.2 PLANISPHERES Table 3.8 continued Globe-view

Sky-view

Name

P1

P6

P10

P2

P3

P7

P5

P4

P8

P9

Sge Tri CrA Missing

+ + + 0

+ + – 1

– – + 2

– – + 3

– + – 4

+ – – 2

+ – – 3

– – – 4

– – – 4

– – – 5

Notes: P2. Basle MS AN. IV 18: Anomalous image for Aquarius and an Anonymous Constellation below Orion. P3. Berlin MS lat. 129: Anomalous animal above Gemini (remainder of the Goat) and an extra image of Eridanus in the shape of a bust below Hydra. P8. Munich Clm 210: Tiny obscure object between Cancer and the heads of Gemini. P9. Vatican City MS Reg. lat. 123: Anomalous bird-like image for Delphinus below Hercules.

of missing constellations and the order of the constellations is fixed by their occurrence on one or more maps.

Group I: Libra presented by the Claws of Scorpius From Table 3.8 it is clear that four planispheres do not have an image of Libra. The absence of this zodiacal constellation is not really a lacuna because, as discussed in Section 2.3, in the early days of the history of constellation design Libra was not an independent constellation but represented by the Claws of Scorpius. In this early tradition there are only 11 zodiacal constellations and Scorpius occupies a rather large part of the zodiac. The four planispheres are:

• • • •

P1. Aberystwyth MS 735C P2. Basle MS A.N. IV 18 P6. El Burgo de Osma MS 7 P10.Vatican City MS gr. 1087

Although all four maps differ considerably in style, the presentation of Libra as the claws of Scorpius show that they must belong to one of the earlier branches that can be distinguished as

far as traditions in map making are concerned. This is confirmed, for example, by another fact, namely that on all four planispheres the tip of Draco’s tail ends level with the head of the Bear Helice, in keeping with Aratus’s description.84 Its significance is underlined by that fact that on the other six planispheres (P3–P5, P7–P9) studied here the tip of the tail of Draco curls around Ursa Maior, ending below or past its hindfeet. This latter representation is an obvious deformation of the astronomically correct description by Aratus but most common in medieval illustrations of Draco and the Bears. All four maps belonging to group I are in globe-view and all miss very few constellations. The early eleventh century map P1 (Fig. 3.12) is complete in the sense that it presents all known constellations. As an aside I note that another illustration in Aberystwyth MS 735C, f. 25r, shows a planisphere scheme executed in brown ink (Fig. 3.22) following Germanicus’s Aratea on ff. 11v– 24v. This scheme has the same celestial circles as the planisphere P1 but there are no pictures of the constellations. Instead the artist has indicated

171

84 Aratus (Kidd 1997), pp. 76–7, l.51.

The descriptive tradition in the Middle Ages

Fig. 3.22 Planisphere scheme in Aberystwyth, MS 735C, f. 25r. (Courtesy of Llyfrgell Genedlaethol Cymru/The National Library of Wales, Aberystwyth.)

the names of the constellations.The names of the asterisms that in the Aratean tradition are part of another constellation, such as Corvus and Crater (part of Hydra) and Lupus (part of Centaurus) are not indicated. Also the name of Corona Australis is missing. Leaving these special cases aside one finds that all but two constellation names have been marked. The artist seems to have overlooked the names of Orion and Piscis Austrinus. One constellation is marked by two names in two distinct places. South of Scorpius the name Ara is written and in the opposite direction, south of Eridanus,Turibulum. It could be that the author was confused by the odd end of Eridanus on the planisphere P1 (Fig. 3.12). It may therefore be

related to that map. If correct, one has to conclude that the locations of some constellation names do not in all cases compare well with those of the constellations on P1. But looking at the arrangements of the constellations on P1 it is clear that the artist tried to maintain the order. However that may be, it seems that the author may–perhaps as an afterthought—have wanted to identify and name the constellations on his planisphere P1. Let me now turn again to the planispheres in group I. The planisphere P6 (Fig. 3.17) misses only Corona Australis.Two other constellations, Sagitta and Triangulum, are missing on the planispheres P2 (Fig. 3.13) and P10 (Fig. 3.21). The Basle planisphere P2 also misses Aquarius because the copyist made an error here. He drew an anomalous image shaped as a bear instead of Aquarius, which occurs on this map only and is not characteristic for the tradition to which the map belongs.Sagitta, Triangulum, and Corona Australis are all proper Aratean constellations but they are rather small and may have been overlooked in copying processes. Sagitta occurs on four maps, and the other two, Triangulum and Corona Australis, on only three planispheres (compare Table 3.8). Looking for other features in group I, one finds that two planispheres, P1 and P6, are more closely connected than others despite the completely different style used in drawing the constellation images. For instance, on both maps the image of Sagittarius is closer to that of a satyr than to that of a centaur. Aratus tells that ‘the Archer actually draws his great bow near the sting [of the Scorpion]’.85 This could well explain the curious positioning of the arrow of Sagittarius on map P6 but it does not tell us how the Archer is supposed to have been shaped. In

172

85 Aratus (Kidd 1997), pp. 94–5, l.305.

3.2 PLANISPHERES the summer and winter hemispheres discussed above Sagittarius is often drawn as a satyr,whereas the reverse holds for planispheres. Returning again to the similarities between the two planispheres P1 and P6 it is noteworthy that on both one finds, for instance, that the head of Hercules is west of that of Ophiuchus, an astronomical characteristic that appears rather spuriously on medieval maps. Both planispheres have an image of the often missing constellation Triangulum.The two planispheres have further in common that Cepheus has his arms along his side, that Bootes is without a staff, thatVirgo is without wings, and that the river Eridanus seems to come from a source or well located at the border of the map. All this underlines that these two planispheres are fairly close to an ancient model. On the other two maps in group I, P2 and P10, Cepheus has outstretched arms (as Aratus tells us he should) and Bootes carries a staff.86 These two maps have in common that Virgo is drawn with wings.The copyist of the Basle map (P2) has drawn Virgo’s wing as a floating image. On the Byzantine map (P10) the wings of Virgo are well defined. On the latter map Virgo is clearly presented as Justitia holding a pair of scales, a myth told already by Aratus.87 On the Greek hemispheres, for example, Virgo is also shown as Justitia next to a figure with a pair of scales for Libra (Figs 3.10 and 3.11).88 The iconography of the constellations depicted on the Byzantine map P10 recalls the mythology connected with them. To the image of Virgo already mentioned one could add a winged Pegasus, the halo around Canis Maior, and the bonds around Andromeda’s wrist. 86 Aratus (Kidd 1997), pp. 86–7, ll. 182–3. 87 Aratus (Kidd 1997), p. 215, and ll. 96–136. 88 Duits 2005, p. 153, confuses Virgo’s scales with those presenting Libra.

Against this background the image of Hercules is a bit disappointing since one can hardly regard him as in a kneeling position with his right foot on the head of Draco. In this connection it should be said that the Aberystwyth planisphere (P1) is in no way inferior to the Greek map regarding mythological features: it has a fitting image of Hercules, Andromeda has bonds, and it is the only map with rare images of the Asses on the back of Cancer. On the astronomical side the image of Pisces on P10 is conspicuous as being the only correct presentation astronomically when compared to that on other planispheres. The image of Pisces on map P6 (El Burgo de Osma MS 7) is close to this astronomically correct presentation but the cord connecting the two fishes is lacking here. In short, the planispheres of group I, dating from the early ninth to the fifteenth century, clearly represent a tradition in map making that has remained fairly constant for centuries. This may or may not explain the widely different artistic input in these maps.

Group II: Libra is presented by a figure holding a pair of scales Three planispheres, all in sky-view, show Libra in a very characteristic way as a figure holding a pair of scales horizontally such that it is placed in the zodiacal band in front of Scorpius (see Figs 3.15, 3.16, 3.18).These maps are:

• P4. Bern MS 88. • P5. Boulogne-sur-Mer MS 188. • P7. London MS Harley 647. The tradition represented by this group is characterized further by the presence of an image of the river god Eridanus. It is also telling that they share so-called reversed images of Navis and Corvus and that they have Perseus with the Gorgon head

173

The descriptive tradition in the Middle Ages north of him instead of south. Other peculiarities are that Delphinus is south of Hercules and west of Cygnus instead of south of Cygnus and east of Aquila. Missing on all three maps are the small constellations Corona Australis and Triangulum. The planispheres P4 and P5 both miss an image of Lyra and the Bern planisphere P4 misses in addition Sagitta (compare Table 3.8). Taking a closer look at the planispheres in group II we note that P4 and P5 share the same style, delineation and positioning of the constellation figures. Generally speaking one can say that the artist of P4 was less inclined to detail: Pegasus is without decoration, Corona is not a wreath but a simple ring, and Spica in the hand of Virgo is less detailed. All this is in line with the thesis that the Bern map P4 is a copy of P5, the map in Boulogne-sur-Mer MS 188.There is one exception to this. On the Bern map Andromeda has strings around her wrists which are missing in the Boulogne-sur-Merplanisphere. Andromeda’s strings must have been part of the exemplar since they are also drawn on the London map P7.This could mean that the exemplar of the planispheres in Boulogne-sur-Mer Ms 188 and Bern MS 88 was still around in St Bertin when the Bern map was copied. The agreements between the two maps P4 and P5 do not necessarily help to define the model from which all maps in group II derive. For example, the complete bull drawn on P4 and P5 is likely to have been introduced by the maker of the Boulogne map P5 because the artist of the Boulogne-sur-Mer manuscript also introduced a complete bull on the Boulogne copy of the zodiac in the Leiden planetary diagram, where Taurus appears as half a bull. The artist of the Boulogne manuscript must have considered a whole Taurus more appropriate than a cut-off one. The image of a complete bull was appar-

ently taken over by the Bern copyist. Their exemplar may have had the image of half a bull as one finds on the London map P7. Indeed, it would seem that P7 (London MS Harvey 647) is closest to the model, a suggestion borne out by the other differences between it and the two maps P4 and P5. On P7 in addition to Taurus’s cut-off body, one sees that Perseus carries a hooked sword, Aries has a ring around its body, Virgo has wings, and Pisces are connected by their tails. These features are missing on the maps P4 and P5 and they suggest strongly that P7 is the most authentic of the three maps in group II. Of special interest of P7 is also that it carries an inscription: ‘ISTA PROPRIO SUDORE NOMINA UNOQUOQUE/PROPRIA EGO INDIGNUS SACERDOS ET MONA/CHUS NOMINE GERVVIGUS REPPERI AC/SCRIPSI: PAX LEGENTIBUS’. (The proper names for each [of them] have I, the humble cleric and monk named Gervvigus, traced and written down with my own sweat. Peace [be] with the readers.)89

Does this message mean that Gervvigus was the maker of the map? He obviously did his best to identify and name the constellations on his model planisphere, but this was not a wholly successful undertaking. The constellation Triangulum is missing, yet the name Deltoton is set above the head of Andromeda, while the name for Andromeda herself is missing. The label Corona for Corona appears next to Lyra,that is,east of Hercules instead of west.A label appropriate for Lyra appears along the bottom edge of Cancer’s shell: lira Orpheus, and Cancer’s own label appears in a text around Eridanus: Cancer qui et Eridanus. Ursa maior is labelled arctophylax and Ursa minor Helix (written 89 Saxl and Meier 1953, p. 151. The English translation is by Paul Kunitzsch (private communication, 12 April 2002).

174

3.2 PLANISPHERES correctly with regard to the orientation of the page) and close to this is the label arcturus, (written upside-down with regard to the orientation of the page).90 These errors suggest that the names were not part of the model from which the London map P7 was copied. It could mean that the names were a later addition to the map. The question that forces itself upon us is whether the planisphere P7 was the model of the maps P4 and P5. It is difficult to answer. Some of the iconographic features on P7 missing on the other two planispheres P4 and P5, such as the ring around Aries, could have been left out during copying. However, P7 differs from P4 and P5 also by the reversed images of Cancer, Scorpius, Ursa Maior, and Ursa Minor.Were these reversed images corrected in copying P5, the map in Boulogne-sur-Mer Ms 188? It may be telling that Bischoff recognizes a Saint-Bertin hand among the addition of London MS Harley 647, but this can mean many things.91 Unless more information is found, it is hard to decide this matter.

Group III: Libra is presented by a pair of scales without a figure holding them Two other maps drawn in sky-view appear to be mutually related, again despite great differences in iconography and style:

• P8. Munich Clm. 210. • P9.Vatican City, MS Reg. lat. 123.

claws of Scorpius. In addition, the two manuscripts share some rather notable peculiarities. Both have a displaced Equator and on both maps Aquarius holds an urn in front of him, but has a stream that connects the middle of his back with the mouth of Piscis Austrinus. Cetus is looking backwards to the west and Ophiuchus does not stand on the back of Scorpius. Comparing the constellations drawn on the maps (see Table 3.8), it is clear that both maps miss Sagitta, Triangulum, and Corona Australis. The planisphere P8 misses in addition Lepus, whereas P9 does not have an image of Eridanus. On this latter planisphere there is in the location where one expects Delphinus the image of a bird.There are a number of differences between P8 and P9, the most notable of which are Corona Borealis, depicted as a wreath on P8 and as a ring of circlets on P9. Cancer is drawn as a crab on P8 and as a crayfish on P9, and Centaurus holds one animal on P8, but two on P9. Last but not least, the eleventh-century planisphere P9 is the only medieval planisphere known so far with stars marked on it. Unfortunately the artist did not complete his task and this makes it hard to identify the descriptive star catalogue he used. Together these various elements show that the two planispheres in group III must represent completely different stages of transmission.

Group IV: P3 Berlin MS lat. 129

The two planispheres are tied together by the representation of Libra as a pair of scales without a figure holding them. In both maps the pans are placed towards the feet of Virgo and not in the 90 Helix is the name of Ursa Maior, arctophylax that of Bootes, and arcturus usually the name of the brightest star in Bootes. However in some sources (in the star catalogue De signis caeli, Dell’ Era 1979a, p. 283), Ursa Minor is called Arcturus minor. 91 Bischoff 2004, p. 112.

The one planisphere not discussed so far is P3. It shares with group I that it is in globe-view and that the Gemini are standing in a north–south direction as on all the other planispheres in globe-view, in contrast to the pair lying in the east–west direction seen on all planispheres in sky-view. However, it shares with group II that the tail of Draco ends at the hindfeet of Ursa Maior, that Libra is drawn as a pair of scales, and that there is a bust representing

175

The descriptive tradition in the Middle Ages the river god Eridanus. The agreements with group II are not strict since the pair of scales is held by the side of a figure confined to the zodiac, and the river-god bust is in the wrong place, east of Navis instead of west. Thus it seems more likely that it conceptually should be counted with group I planispheres. Indeed, there are a few curious similarities in some of the details that seem to echo some distant, shared relative. For example, P3 has an image of Triangulum (also in P1 and P6, compareTable 3.8), Canis Maior has a halo (also in P10), Hercules is kneeling (also in P1). Even so it is hard to imagine which of the other maps in globe-view (all of which are part of group I) could have served as the model for the Berlin map. The depictions of figures dressed in togas in two of the corners of the Berlin planisphere with the citations of Virgil may suggest an antique appearance, but this does not mean that the map is a reliable presentation of the celestial sphere. Actually, the map is very corrupt.92 Aries is placed ‘upside-down’, with his back to the south, the locations of Perseus and Cassiopeia have been exchanged, and it is impossible to decide which of the two birds, one in front of Pegasus and the other behind Pegasus, would represent a displaced Aquila or a displaced Cygnus.The planisphere suffers further from the intrusion of a number of anomalous constellations, such as the already mentioned bust for a second Eridanus, a third Bear, and a curiously conflated image of Corona Borealis/Lyra.The locations of Lyra and Corona Borealis with respect to Hercules are confused. One expects Lyra west of the knee of Hercules and Corona at his back.The confusion is underlined by the attempt to label the constellations. The image of Cassiopeia is labelled Cepheus, while the name Cassiopeia is in the 92 Thiele 1898, p. 163, says that the dresses are drawn in a Carolingian style.

right spot near the displaced image of Perseus. One can understand why the attempt to identify the constellations was given up! The characteristics of the maps in group I show that the planispheres in globe-view are in general closer to a presumed archetype than those in skyview. Among the better maps in globe-view, the planispheres P1 and P2 are the least influenced by conceptual errors such as the widening of the zodiac or drawing tropics tangentially to the zodiacal boundaries. Following closely behind in our assessment of the presentation of the main celestial circles is the planisphere P6. All planispheres in sky-view depict the twins as being aligned to and confined within the zodiacal band in a manner often seen in illustrations of the zodiacal bands. Astronomically speaking this is a very mannered way of presenting the zodiacal constellations and presumably postdates the more natural presentation of the zodiacal constellations extending above and below the zodiacal band in the planispheres in group I.The phenomena of reversed images, seen most strongly in P7, may suggest that the ultimate model for the planispheres in sky-view was a planisphere in globe-view. If so, that model must have represented an independent tradition from those exemplified by the maps in group I. A clever map maker could have mirrored a planisphere in globe-view and added a great circle for the Milky Way. However, to add the Milky Way he must have had some understanding of the celestial sphere and this makes it more probable that the conversion was carried out in Antiquity.

3.2.3 Planispheres in the manuscripts of the Italian humanists In addition to the ten medieval planispheres discussed above, there are ten more preserved in a number of closely-related codices produced

176

3.2 PLANISPHERES in Naples and Florence during the mid-1460s to mid-1470s: a decade of intense and sophisticated scribal activity.93 The manuscripts in which these planispheres occur appear to derive from a copy of Germanicus’s Aratea made for the Florence humanist Agnolo Manetti during his stay at Naples in 1466–68. This now lost Manetti copy is in turn based on an example connected to the oldest illustrated member of the so-called μ branch of the Z family of Germanicus manuscripts: Madrid, Biblioteca Nacional MS 19 (16).94 The planispheres in these humanist manuscripts are fairly similar.They are all presented in globe-view, and all show the front sides of the figures.They are constructed according to a grid of five concentric circles centred on the celestial pole as illustrated by the planisphere in Cologny, Biblioteca Bodmeriana, MS lat. 7, shown in Fig. 3.23.95 However, there are sets of minor differences within these maps. These can be used to distil them into a series of distinct subgroups summarized below. Group I consists of two Neapolitan manuscripts, MS Cologny lat. 7 and New York, Pierpont Morgan Library, MS M. 389. Haffner has suggested that the Cologny manuscript may have been made for Giovanni Brancati, the librarian of King Ferrante of Naples, sometime before 1469.The New York manuscript was certainly commissioned by Antonello Petrucci, secretary and prime minister to King Ferrante of Naples between 1458 and 1486 and a close friend of Brancati’s.96 The New York planisphere was, according to Haffner, copied directly from the Cologny map in 1469.The Cologny planisphere 93 94 95 96

does seem to set the norm by which all the other manuscripts can be judged. Group II includes the Florentine manuscripts, Madrid, Bibioteca Nacional, MS 8282, and Vatican City, Biblioteca ApostolicaVaticana, MS Barb. lat. 77.97 Their planispheres are closely related to the Neapolitan maps of group I.The maps deviate in two respects from those in group I: Eridanus does not hold an urn from which water flows and the head of Medusa is drawn differently. Group III comprises also two Florentine manuscripts: London, British Library, MS Add. 15819, and Naples, Biblioteca Nazionale, MS XIV.D 37.98 Compared to the norm set by the Cologny planisphere the maps in this group distinguish themselves by the following deviations. The Bears have been rotated 180°, so that their heads face towards Perseus instead of Hercules. Triangulum lies further south, beneath the feet of Andromeda and south of the feet of Aries. Eridanus is missing from the maps altogether. Andromeda is depicted with chains to her wrists, and she, Cepheus, and Cassiopeia have darker faces than the rest of the constellations, perhaps indicating their mythical Ethiopian origins. Of the remaining planispheres only one can be linked with certainty to any of the three groups above. This is the planisphere in Vatican City, Biblioteca Apostolica Vaticana, MS Barb. lat. 77, the third Neapolitan manuscript that Haffner posits predates the other two Neapolitan manuscripts, Cologny MS lat. 7 and New York MS M. 389, saying that it was a royal commission, dating to sometime around 1467. She bases her argument on the stylistic closeness between the miniatures inVatican City, Barb lat. 76 and other manuscripts

McGurk 1973, pp. 200–1, no. viii. Haffner 1997, pp. 110–12. Pellegrin 1982, pp. 17–21. Haffner 1997, pp. 110–12.

97 Haffner 1997, p. 113. 98 Haffner 1997, p. 113.

177

The descriptive tradition in the Middle Ages

Fig. 3.23 Planisphere in Cologny, MS lat. 7, f. 2v (Courtesy of the Fondation Martin Bodmer, Cologny (Genève).)

178

3.2 PLANISPHERES executed for King Ferrante of Naples.99 However that may be, the Vatican planisphere in MS Barb. lat. 76 is a rather defective copy. It deviates from the standard defined by group I by the displacements of Triangulum to the north of Taurus, above his head, and of Cygnus (that is, the bird between Lyra and Hercules on the Cologny map) between Capricornus and Cepheus. The illuminator of MS Barb. lat. 76 has also added some rather unusual stylistic details. He presented Aries as a leaping bull and Cancer as a crawfish. The male figures Bootes, Perseus, Sagittarius, and Centaurus have beards and the head of Medusa is drawn as that of a bearded male. Two other planispheres in Florence, Biblioteca Laurenziana, MS Plut 89, sup 43, and Vatican City, Biblioteca Apostolica Vaticana, MS Urb. lat. 1358, seem to float between the groups defined above.100 For example, these planispheres present Eridanus with a low profile urn without a stream of water, and both have similar images of Corona and of Medusa’s head.The two planispheres differ, however, in two respects. On the planisphere in MS Laur 89 sup 43 the location of Triangulum agrees with its position in the maps in groups I and II, but the halo around Canis Maior’s head is missing. On that in MS Urb. lat. 1358 the halo is present but Triangulum is misplaced and appears above the head of Cassiopeia. This suggests that the planisphere in MS Urb. lat. 1358 is not a direct copy from that in MS Laur 89 sup 43, but that both maps derived from the same exemplar. The last planisphere related to the set of maps found accompanying the fifteenth-century texts of the Germanicus’s Aratea appears in a copy of 99 Haffner 1997, pp. 106–8,112. A description of Vat. Barb. lat. 76 is given in Haffner 1997, pp. 130–1. Saxl 1915, pp. 4–5; for a picture, see Saxl 1927, p. 21, figure 5; Pellegrin I 1975, pp. 123–5. 100 Saxl 1915, pp. 103–6, esp. p. 104; Pellegrin II.2 1982, pp. 675–7; see also Haffner 1997, p. 113.

Matteo Palmieri’s Italian poem, La Città da Vita.101 The manuscript, Florence, Biblioteca Laurenziana, MS Plut 40. 53, includes a commentary by Leonardo Dati, which is dated in an explicit manner (f. 301v) to 2 June 1473.102 At first glance the planisphere seems to follow the format of the other planispheres listed above, but closer inspection reveals a number of substantial differences.Two constellations figures have been added. One is Libra, represented by a pair of scales set to the south of the tail of Scorpio, the other is Sagitta, set to the south of Aquila. Triangulum is set around the neck of Aries, depicted as lying down. Ursa Minor and Ursa Maior walk in opposite directions. They are placed back-to-back and both are enclosed by the bends of Draco’s body. Corona Borealis is depicted as a ring of nine stars. Lyra is shaped like a lira di braccio.Aquila is configured like a heraldic eagle. Centaurus is depicted as a young male centaur with long hair and the decapitated head he holds is bearded. Ara is shaped like a triptych, set upon an altar. Last but not least there are two depictions of Bootes in this map.The first Bootes is very similar to the norm of a male figure that stands parallel to the circles, directly north of Virgo, with his head towards Ophiuchus. The second Bootes is placed between the first Bootes and the figure of Hercules. He is dressed in a short tunic and stands towards the south with his right arm holding a teardrop-shaped shield horizontally in front of his body. His left hand is raised behind his head and holds a spear or arrow. All these deviations suggest that the author of the text and the illuminator of the planisphere had access to another text. This second source 101 McGurk 1966, p. 25. 102 McGurk 1966, p. 25, mentions the date 2 June 1473 referring to the completion of the commentary; a picture is shown in plate VIIId.

179

The descriptive tradition in the Middle Ages turns out to be a very particular branch of fifteenth-century, illustrated Hyginus manuscripts, which all contain the idiosyncratic feature of the head of Aries set within the triangle.103 Other details from this source include the second figure of Bootes and the depiction of Centaurus. The series of planispheres in the manuscripts of the Italian humanists has also fostered the first printed celestial map. It appears in the printed edition of Rufius Festus Avienus, Arati Phenomena published by Antonius de Strata in Venice, 1488.104 Essentially, this printed map is a muchsimplified, mirror-image version of the planispheres found in the humanist manuscripts.The fact that it is presented as a mirror-image to the rest of the planispheres probably reflects its conversion from a manuscript drawing to a wood block image. By any standard, this planisphere is a pretty poor product, when judged by the number of errors that seems to have crept in during the copying process. For example, the constellations Andromeda, Triangulum, and Piscis Austrinus are missing and other constellations or their attributes are deformed. From a cartographical point of view the humanist maps are not remarkable considering that already in the first decades of the fifteenth century the first steps towards a mathematic approach in celestial mapping had been taken. Within the context of the present study the more interesting question is how the supposed twelfthcentury exemplar compares with the medieval planispheres discussed above. Can one assume that the Cologny planisphere is representative for the supposed twelfth-century exemplar and, if so, how does it relate to the older

medieval planispheres? The number of constellations depicted on the Coligny map, especially the representation of Libra by the claws of Scorpius and the presence of Triangulum, suggests that the model planisphere would have been part of the group I planispheres defined above. Next to lacking a separate image for Libra, all four medieval planispheres belonging to this group are in globe-view and all lack the Milky Way, as does the Coligny map. However, the iconography of the planispheres in group I and Coligny Ms 7 could hardly be more distinct.All planispheres in group I represent Eridanus by a river-like image, a representation that does not occur on the Coligny map. On the other hand one finds the image of Eridanus as a river god on the three medieval planispheres belonging to group II. These three planispheres are however in skyview, and show Libra in a very characteristic way as a figure holding a pair of scales in the zodiacal band. All medieval planispheres in groups I and II present Hercules with a lion’s skin and a club, attributes that do not occur on the Coligny map. This especially makes one wonder to what extent the Coligny map can be taken as a reliable presentation of the twelfth century model planisphere. However that may be, within the context of humanist learning and book production during the second half of the fifteenth century, this group of manuscripts provides fascinating insights into the workings of Renaissance scriptoria.

103 For additional information on this family of manuscripts, see Lippincott 2006, p. 22. 104 Printed map, woodcut, in the mirror image!, in Warner 1979, p. 270.

The maps discussed in the previous chapters are part of the legacy from Antiquity that was transmitted along with texts which in one way or

. NORTHERN AND SOUTHERN HEMISPHERES

180

3.3 NORTHERN AND SOUTHERN HEMISPHERES

Fig. 3.24 a–b The pair of northern and southern hemispheres in Bernkastel, MS 212, ff. 24r–24v. (Courtesy of St Nicolas-Hospital/Cusanusstift, Bernkastel.)

another derive from Aratus’s poem Phaenomena. Such a background is not immediately clear for the two pairs of hemispheres discussed now.105 These maps differ from the summer and winter hemispheres in showing the northern and southern half of the celestial sphere. The most recent of the two pairs of hemispheres, shown in Figs 3.24a–b, is included in an astronomical compendium (Bernkastel-Kues, Cusanus Stift, MS 212, f. 24r/v).The two hemispheres are in the first part of the codex (ff . 1–117), which appears also to be the oldest part, 105 The details of these maps are described in Appendix 3.3. Catalogue of Northern and Southern Hemispheres.

with tables for 1320 and 1365. In a later hand the years 1408 and 1419 have been added. From the several entries intended for use in Paris, one may assume that this part of the manuscript was once in Paris or written there. The pair of hemispheres is in the middle of a copy of the Alfonsine Tables which constitutes a canon of medieval mathematical astronomy. It is questionable, to say the least, that the maps would have served as an illustration for this text. Indeed, there is nothing in the northern and southern hemispheres that reminds one of the Ptolemaic star catalogue which formed the backbone of the mathematical tradition in celestial cartography. How the maps came to be

181

The descriptive tradition in the Middle Ages inserted in material relevant for medieval mathematical astronomy is hard to say.The codex was composed from several independent treatises by Stephan Schönes, the rector of St Nicolas Hospital in Bernkastel-Kues (1754–83).106 Yet, the maps do not seem to have been a later addition because, as Krchňák remarks, all 117 pages of the first part of the codex are written on paper. Apparently some scholar was intrigued by the maps and decided that it was worth his while copying them.

The oldest of the two pairs of hemispheres, shown in Fig. 3.25, is in Darmstadt, Landesbibliothek, MS 1020, f. 60v. The main (first) part of this codex includes texts on the computus (ff. 1r–58v).107 This is followed by a collection of astronomical texts (ff. 59r–66v) which contain the maps. All 66 parchment folii seem to have been written in a hand of the first half of the twelfth century.A note added in the early fifteenth century (‘Liber Monasterii Sti. Jacobi Leodiensis, cuius titulus est helpericus abbas de compoto. Quaere XVIII’)

Fig. 3.25 The pair of northern and southern hemispheres in Darmstadt, MS 1020, fol. 61r. (Courtesy of the Universitäts-und Landesbibliothek, Darmstadt.)

106 Krchňák 1964, pp. 168–71.

107 Excerpts from De temporum ratione of Bede the Venerable, Computus of Helperich of Auxerre, and excerpts from Compotus abbreviatus of Hermannus Contractus, and a series of minor texts.

182

3.3 NORTHERN AND SOUTHERN HEMISPHERES

Scheme 3.9 Hemisphere in stereographic projection and after the equidistant model.

suggests that this happened in St Jacob abbey in Liege. The map itself is in the middle of a poem ‘Summa meae cartae brevis est divisio sperae’ of which more below.

hemisphere two arcs (or sections of circles), which represent the northern and southern boundaries of the zodiacal band. The grid also includes two straight lines perpendicular to each other through the middle of the map, represent3.3.1 Cartography ing the colures. Both sets of hemispheres depict a view of the The hemispheres recall the discussion on steheavens as presented on a celestial globe and all reographic versus equidistant projection prehemispheres have the Equator as their circular, sented above for the planisphere. In Scheme 3.9 outer boundaries. Each hemisphere has a grid the two possible modes are shown for the consisting of three concentric circles, represent- northern hemisphere, which has been highing in the northern hemisphere the Equator (the lighted in grey.The differences between the two circle that frames the map), the Tropic of Cancer, modes are not spectacular since only the part and the ever-visible circle and in the southern north of the Equator is shown.The most striking hemisphere the Equator (the circle that frames characteristic of the stereographic projection is the map), the Tropic of Capricorn, and the ever- that the centre of the ecliptic (C in Scheme 3.9) invisible circle. In addition there are on each does not coincide with the location of the v pole 183

The descriptive tradition in the Middle Ages Table 3.9 Quantitative data of the grids in the northern and southern hemispheres in Darmstadt MS 1020 (D1020) and Bernkastel MS 212 (B212) D1020

Req Rtropics D1 D2 D W R36

MS

NH

SH

1.00 0.67 0.54 0.81 0.68 0.27 0.38

1.00 0.63 0.55 0.82 0.69 0.27 0.33

1.00 0.65 0.51 0.81 0.66 0.30 0.33

ME

1.00 0.73 0.60 0.87 0.74 0.27 0.40

B212 NH

SH

1.00 0.74 0.60 0.88 0.74 0.28 0.36

1.00 0.73 0.63 0.88 0.76 0.25 0.36

NH: northern hemisphere; SH: southern hemisphere; MS: stereographic model; ME: equidistant model. All distances presented below are expressed as fractions of the radius of the Equator. Req: radius of the Equator which by definition is set equal to 1.00. Rtropics: radius of the tropics. D1: distance of the northern/southern boundary of the zodiac from the north/south pole in the northern/southern hemisphere. D2: distance of the southern/northern boundary of the zodiac from the north/south pole in the northern/southern hemisphere. D: the arithmetic mean value of the distances D1 and D2. W: width zodiacal band; the model values are based on a width of the zodiacal band of 24°. R36: radius of the ever-visible circle/ever-invisible circle in the northern/southern hemisphere. The model values are based on a geographical latitude 36º.

(E in Scheme 3.9) whereas the two points coincide in the equidistant model. In Table 3.9 the necessary data for a comparison between the two sets of hemispheres and the models have been collected. In the first column a number of distances, such as the radii of the tropics, are listed. In the next two columns the values of these parameters on the Darmstadt map are given, in columns 4 and 5 the values as predicted by stereographic projection (MS) and the equidistant model (ME) are given, and in the last two columns are the data on the Bernkastel-Kues map. The picture that arises from the data in Table 3.9 is somewhat confusing.The data of the tropics and the zodiacal boundaries on the northern and southern hemispheres in Bernkastel-Kues

MS 212 (columns 6 and 7) are internally consistent and fully agree with the values predicted by the equidistant model ME in column 5. Indeed, on the maps in Bernkastel-Kues MS 212 the boundaries of the zodiacal band are drawn with the ecliptic pole as their centre in keeping with an equidistant model. The analysis of the Darmstadt map is not without problems because there is no complete symmetry between the northern and the southern hemispheres.The radii of the tropics and the ever-visible and ever-invisible circles on respectively the northern and southern hemispheres differ by a significant amount of about 0.05. One cannot help thinking that the map maker made an error in confusing, say, the radius of the

184

3.3 NORTHERN AND SOUTHERN HEMISPHERES ever-visible circle on the southern map (0.33) with the complement of the radius of the tropic on the northern map (1–0.67 = 0.33) and vice versa. This explanation is supported by the fact that the mean values of the zodiacal boundaries in the two maps are more or less equal. Regardless of this problem, it is clear that the values of the parameters on the Darmstadt maps are on average much closer to the values predicted by the stereographic projection MS in column 4. In the Darmstadt maps the boundaries of the zodiacal band respond to different centres, which is also in keeping with stereographic projection. Another conspicuous feature of the Darmstadt maps is that on both its hemispheres the zodiac runs anti-clockwise. On the northern map this corresponds to globe-view (as on a planisphere) and on the southern map to sky-view. The Bernkastel-Kues maps, on the other hand, follow the more usual convention applied to the later maps of the mathematical tradition discussed in Chapter 5, by which for maps in globeview the zodiac is anti-clockwise on the northern and clockwise on the southern hemisphere.108 Further noteworthy differences are that only on the Darmstadt map has the Milky Way circle been drawn and the zodiacal band is divided into compartments, presumably representing the signs of the zodiac. Although the sizes of the compartments on the Darmstadt maps vary, the division is not really in keeping with stereographic projection because then the signs should increase in width when we go from the summer solstitial colure via the equinoctial colures to the winter colure. Taking all the evidence together it seems therefore that, although the basic format is the same, the two sets of northern and southern hemispheres 108 It is perhaps ahistorical to speak of conventions here.

follow different models.The grid of the BernkastelKues pair of hemispheres was constructed according to an equidistant model, in which distances on the sphere are assumed to be proportional to distances on the plane, and the grid of the Darmstadt set appears to follow the stereographic regime. More differences between the Darmstadt and Bernkastel-Kues maps are seen when the astronomical content is considered.

3.3.2 Astronomical considerations We start here again with the problem of finding out which of the three antique epochal modes is relevant for the north and south hemispheres. We recall that in the Eudoxan mode the colures pass through the middle, and in the closely related mode described by Martianus Capella they pass through the eight degrees of the respective constellations. In the third Manilian mode the colures pass in front (or west) of Aries, Cancer, the Claws (Libra), and Capricornus. Looking now to the positions of the colures on the two sets of northern and southern hemispheres it is immediately clear that the Bernkastel-Kues maps fit in the older, Eudoxan mode. On the northern hemisphere the vernal and autumnal equinoctial colure passes through respectively the hind part of Aries and the end of the northern claw of Scorpius (Libra) whereas the summer solstitial colure passes through the middle of Cancer. On the southern hemisphere the vernal and autumnal equinoctial colure are passing through respectively Aries and the southern claw of Scorpius (Libra) while the winter solstitial colure passes through the body of Capricorn. On the northern Darmstadt hemisphere the vernal and autumnal equinoctial colure pass through the head of Aries and the ends of the Claws, respectively, whereas the summer solstitial colure passes through the tail of Cancer. On

185

The descriptive tradition in the Middle Ages the southern Darmstadt hemisphere the vernal and autumnal equinoctial colure are again passing through respectively Aries and the Claws of Scorpius (Libra) while winter solstitial colure passes through the neck of Capricorn. In other words, the equinoxes and solstices clearly lie at points roughly 8° from the beginning of the respective constellations. These features recall the colures described by Martianus Capella as passing through the eighth degree of Aries, Cancer, Claws, and Capricornus. The question arises whether in this context Aries and so on represent constellations or signs. The zodiacal band on the northern Darmstadt hemisphere is divided into six and that on the southern hemisphere into five compartments, such that the zodiacal constellations fit nicely into each compartment, leaving a fairly large section for Sagittarius and a small one for the two signs Libra and Scorpius.The divisions suggest strongly that the images drawn in the zodiacal band represent constellations, not signs. The irregular boundaries of the signs may be a later addition. The exemplar of the Darmstadt maps may have lacked the boundaries of the signs because the zodiacal band on the BernkastelKues maps is also not divided into signs. The medieval astronomer may not have realized that by adding boundaries around the zodiacal constellations he unconsciously introduced the Ari 8°-convention on the map, that is fixing the positions of the equinoxes and solstices with respect to the signs, since by his action the vernal equinox came to also be located roughly in the eighth degree of the sign of Aries. The Ari 8°-convention, discussed in Chapter 1, occurs especially within the context of Roman parapegmas and calendars where it is directly connected with the place of the Sun in the zodiac at the beginning of the seasons.Through

the work of Pliny the Ari 8°-convention became known in the Middle Ages and was one of the major concerns of the computus.109 The confusion between zodiacal signs and constellations is increased by the use in Antiquity of two conventions: the Ari 0°- and the Ari 8°-convention. The equinoxes and solstices lie in these conventions at respectively 0° and 8° from the beginning of the signs (see Scheme 1.4).The two conventions should of course give identical cartographic results. The distinction between constellations and signs on the one hand and the use of two conventions on the other could well explain why at the end of the Darmstadt poem the author sighed: ‘Latet et latuit loca solstitialia que sint/Namque fit in puncto dubium sapientibus in quo’ (There is, and has been, hidden which are the solstitial places/Because it is in a point (or degree) dubious for scholar in which).110 However that may be, the locations of the colures on the Darmstadt maps in about the eighth degree of the respective constellations provide an argument in favour of an antique predecessor, even though no antique example of this type of map is known. As discussed in Chapter 1, the description of Martianus Capella must have developed from the Eudoxan tradition, seen on the Bernkastel-Kues maps. The antique roots seem to be confirmed by the fact that on both maps Libra is presented by the claws of Scorpius as it is on the planispheres belonging to group I discussed above. The constellations depicted on the two sets of northern and southern hemispheres are summarized in Table 3.10. As in Table 3.9, the maps are denoted by D1020 and B212 and the constellations 109 Stevens 1997. 110 The English translation is made by Paul Kunitzsch (private communication, 25 June 2009).

186

3.3 NORTHERN AND SOUTHERN HEMISPHERES Table 3.10 Constellations on the northern Eri and southern hemispheres in Darmstadt MS Lib CrA 1020 (D1020) and Bernkastel MS 212 (B212)

Missing

D1020

– – – 0

+ – – 2

– – – 4

+ – – 2

B212

Name

NH

SH

NH

SH

UMa Dra Cep Boo CrB Her Lyr Cyg Cas Per Aur Ser Sge Del And Tri Gem Cnc Leo CMi Tau Aql Peg Oph Ari Vir Psc Ori Sco Hya Crv Crt Sgr Cap Aqr Cet Lep CMa Navis Cen Lup Ara PsA

+ + + + + + + + + + + + + + + + + + + + [+] ⅞ ⅞ ⅝ ½ ½ ½ ½ ⅛ – – – – – – – – – – – – – –

– – – – – – – – – – – – – – – – – – – – [–] ⅛ ⅛ ⅜ ½ ½ ½ ½ ⅞ + + + + + + + + + + + + + +

+ + + + + + + + – + – + – – + + + + + ¼ + + ⅞ ⅞ ⅔ ½ ½ ½ ⅛ ⅛ + – – – – – – – – – – – –

– – – – – – – – – – – – – – – – – – – ¾ – – ⅛ ⅛ ⅓ ½ ½ ½ ⅞ ⅞ – + + + + + + + + + + + +

by their modern abbreviations.The presence of a constellation on a map is marked by a plus sign (+), its absence by a minus sign (–). Most constellations appear either on the northern or on the southern hemisphere but some are divided over both hemispheres and this has been expressed by fractions such as the labels ⅛, ¼, ⅓, ½, and so on. In one case a constellation was almost completely on the northern map with a very small part in the southern hemisphere which is indicated in the table by respectively [+] and [–]. The constellation data show that on both pairs of hemispheres Libra is not drawn as a separate constellation but is instead presented by the claws of Scorpius. On both pairs an image of Corona Australis is lacking. The absence of Corona Australis is a lacuna that occurs often in maps and as such is not very significant. More important is to conclude that all other constellations to be expected are present on the Darmstadt pair but that the Bernkastel-Kues pair on the other hand misses four more constellations: Cassiopeia, Auriga, Sagitta, and Delphinus. There are a few differences among the constellations divided over the northern and southern hemispheres. For example, on Darmstadt MS 1020 Canis Minor is completely on the northern hemisphere—as it should be—whereas it is divided over the pair in Bernkastel-Kues MS 212. Hydra with Crater and Corvus is drawn completely on the southern Darmstadt hemisphere whereas it should be divided over the northern and southern hemispheres, as seen on the pair in Bernkastel-Kues MS 212. 187

The descriptive tradition in the Middle Ages The two pairs of hemispheres differ considerably in the style and iconography of the constellations. A number of the constellation drawings on the Bernkastel-Kues set of hemispheres appear to have been borrowed from a constellation cycle associated with the descriptive star catalogue De ordine ac positione stellarum in signis. The manuscripts of interest here are Madrid MS 3307, Monza MS F.9/176, and Vatican City MS lat. 645.111 The most significant iconographic characteristics in these codices, which are shared with the BernkastelKues pair of maps, are the following:

of hemispheres show beyond doubt that these maps belong to the descriptive tradition and are not in any way connected with the Alfonsine Tables. It may well be that the maps were constructed in France where the three above listed manuscripts were written. According to De Bourdellès Madrid MS 3307 was produced in Metz, Vatican City MS lat. 645 in St Quentin, and according to McGurk Monza MS F.9/176 comes from Lobbes at the border with France.112 All three manuscripts date from the ninth century. The popularity of this particular Carolingian star catalogue seems to have come to an end in the twelfth century, suggesting a date of produc1. Bootes is leaning on a staff with the curved end tion of the present maps before 1200. at the bottom, and he raises his right hand above Not all constellations on the Bernkastel-Kues his head. The more usual image of Bootes is pair of hemispheres can be connected to those in that of a figure with a club in his raised hand. the three above mentioned manuscripts. For 2. Cepheus stands with his arms outstretched example, Sagittarius is presented as a centaur on and empty scabbard on his (left) side.As a rule the southern hemisphere whereas in the above Cepheus does not carry a weapon. mentioned manuscripts he is drawn as a satyr. 3. Taurus is drawn as a whole animal.The more However, in other constellation cycles associcommon image of Taurus is that of a cut-off ated with the star catalogue De ordine ac positione bull. stellarum in signis Sagittarius is depicted as a cen4. Centaurus holds an animal by its heels in his taur.This is so inVatican City, MS Reg. lat. 309 (St outstretched left hand and the spear he carries Denis, 859) and the closely connected Paris MS in his right hand has foliate decorations at lat. 12117 (St Germain du Prés, 1060). Both manboth ends. If in other constellation cycles uscripts have a Parisian provenance. Centaurus carries a spear at all, it does not Especially striking is also the configuration of have foliate decorations at both ends. Draco and the Bears in the northern hemisphere 5. Corvus is looking towards the tail of Hydra. in Bernkastel-Kues MS 212.The astronomically The usual direction is to the head of Hydra. correct way for Draco to mingle with the Bears 6. Navis is a ship with two oars and a tri-prong is such that the Bears are seen walking into the bow. More often Navis is a cut-off ship. bends of Draco and not, as on the BernkastelThese characteristics are uniquely tied to the star Kues map, walking out of them. Actually, the catalogue De ordine ac positione stellarum in signis. orientation of the Bears is correct, but Draco is Their appearance on the Bernkastel-Kues pair drawn as the mirror image of the more usual presentation in globe-view. In the above three

111 The cycle in Madrid MS 3307 is described by Neuss 1941.

112 Le Bourdellès 1985, p. 100. For Monza MS F.9/176, see McGurk 1966, p. 52.

188

3.3 NORTHERN AND SOUTHERN HEMISPHERES Stat post delfin equus, delton tenet arietis armus

manuscripts Madrid, MS 3307, Monza MS F.9/176, and Vatican City MS lat. 645 Draco and the Bears are presented individually. In Vatican City Reg. lat. 309 and Paris MS lat. 12117 a configuration is seen like that on the BernkastelKues hemisphere although in these manuscripts the Bears are not back to back. The style and iconography of the constellation drawings on the Darmstadt maps are not connected to a particular medieval constellation cycle, nor to any of the other maps discussed in this chapter. Of greater significance for the pair of hemispheres in Darmstadt MS 1020 is that the maps are placed in the middle of a poem on ff. 60v–61v:113 f. 60v. ‘Summa meae cartae brevis est divisio sperae Pone polos primis numerum findendo curulis114 Inter utrosque nota spatiorum signa xxx Ex his vi sumptis fit circulus ille nivalis Quinque superponas protenditur altera zona Iam medium sperae statuetur. quatuor adde. Sic ab utrisque polis has zonas v notabis Sunt ursae geminae simul anguis uertice sperae Ast auriga ruit pede tangens cornua tauri Hinc cum falce uolat perseus gorgone perempta Accubat andromeda, casepheia subsidet infra Cepheus extendit palmas metuens caput anguis Post olor at lira, pugnax engonosis astat Atque genu flexo premit anguem cum pede leuo Inde corona manet, resupinus et inde bootes Sub quibus in calido reliquorum pingitur ordo Succinctus colubro, calcatur scorpius illo Alta petens aquila, superest directa sagitta

113 This poem has not been edited before. I am grateful to Paul Kunitzsch for his help in this. 114 The word ‘curulis’ (official chair of Roman consuls) does not make sense here. It is possibly a miswriting for ‘coluris’ (colures). The sentence then translates as: ‘put the poles by splitting the number for the first colures’, which may be a primitive way of stating that the poles are dividing a great circle into two parts, which parts as explained in the next line consists each of 30 units, each unit being 6°.

Omnibus his positis succedit signifer orbis Vnde calor calidae quam maxima non minor ipse115 Culmen habet cancer, leo virgo libraque post est Scorpius arcitenens capricornus tropicus idem Vrceus et pisces aries taurus quoque fratres Inferiora tenent padus et lepus et canis ardens’ f. 61r: pair of hemispheres f. 61v. ‘Orion prochion tunc hidros maxima chiron Post aram piscis pistrix procul argo biremis Latet et latuit loca solstitialia que sint Namque fit in puncto dubium sapientibus in quo Hec ita Gerbertus cui testis et auctor Higinus’

The first seven lines of this poem, here referred to as the Darmstadt poem to distinguish it from others mentioned below, describe the division of the sphere into five zones based on a grid consisting of parallel circles separated by 6, 5, and 4 units of 6° when counted from the poles. The poem continues with describing the constellations north of the zodiacal band (lines 8–19). It says, for example, that the foot of Auriga touches the horn of Taurus (‘Ast auriga ruit pede tangens cornua tauri’), that Cepheus stretches out his hand, being in fear of the head of Draco (‘Cepheus extendit palmas metuens caput anguis’), and that the belligerent Hercules tramples on Draco with his uplifted foot (‘pugnax engonosis astat atque genu flexo premit anguem cum pede leuo’). All three features are clearly marked on the northern hemisphere. In lines 20–24 follows a listing of the zodiacal constellations (or signs) in which Libra is explicitly mentioned, although it is not marked as a separate constellation on the map. This difference would 115 The word ‘quam’ is here inserted for ‘q’. Even so, as Paul Kunitzsch assures me, this sentence does not seem to make sense.

189

The descriptive tradition in the Middle Ages arise if the text refers to zodiacal signs while the map shows zodiacal constellations. The southern constellations are summed up in only three lines (25–27) with very little detail, although the fiery Dog (canis ardens) and the two steering oars of Navis (argo biremes) are mentioned.The poem is conspicuous in a number of expressions popular among poets: ursae geminae for the Bears, coluber (for the serpent encircling Ophiuchus), and fratres (for Gemini). The description of the celestial sphere does not specify how the constellations are located with respect the equator, the dividing circle of the two hemispheres. It is therefore not a priori clear to the reader that the greater part of Hydra should be in the southern hemisphere. In that sense the poem is not really fitted to the maps but seems to stand in a tradition of astronomical poems exemplified by that Priscianus Grammaticus, ‘Ad boreae partes arcti vertuntur et anguis’, a very popular poem in medieval manuscripts of the liberal arts which is also included in Darmstadt MS 1020, on f. 61v.116 Its organization is the same as in the Darmstadt poem. First the constellations north of the zodiac are listed, then those in the zodiac, and next those south of the zodiac.Thus in both poems the zodiacal constel-

116 Edited by Riese 1869, vol. II, p. 139, no. 679. This astronomical poem occurs also in Aberystwyth NLW 735C (early eleventh century), f. 7v where it precedes an excerpt from Macrobius’s Commentary on the Dream of Scipio (ff . 7v–9v) and has four extra lines on the planets. In Vatican City MS Reg. lat. 123 (early eleventh century), f. 183r, it is part of the chapter ‘INCIPIT EPITOME PHENOMENON VERSIBUS XII. LXXXVI’.The poem follows Hyginus’s excerpts of the zodiacal constellations (ff. 154v–182v) and precedes those dealing with the non-zodiacal ones (ff. 184v–204v) and a planisphere (f. 205r).The poem is also in Paris MS lat. 12957 (early 9th century), f. 74v following after the Revised Aratus latinus (ff. 57r–74v); Paris MS lat. 12117 (ca. 1060), f. 172v; Riese mentions also Paris MS lat. 5371 (13th century), f. 240v; Valentianus 393 (ninth century), f. 138v;Valentianus 330 (tenth century), f. 1r.

lations are listed as a separate group and not mixed with the other constellations as is more common in the Aratean literature.117 Another poem, by a late antique author, may be of interest here since it shares with the Darmstadt poem a reference to a map and to Hyginus: ‘Haec pictura docet quicquid recitauit Hyginus’.118 This poem occurs in Leiden Voss. Lat 8° 15 (ca. 1025), f. 61, after the text of Psychomachia (ff. 37–60v).This Leiden manuscript also includes Hyginus’s De Astronomia (ff. 155– 188) and the Fables of Romulus (ff. 195–204). All three texts are illustrated and have been attributed to Ademar de Chabannes.119 The poem ‘Haec pictura’ is also in Paris, MS 12117 (ca. 1060), f. 138r where it follows directly after the star catalogue De ordine ac positione stellarum in signis (ff. 131r–137v), an earlier version of which text is related through its iconography to the BernkastelKues pair of hemispheres.120 After six lines on the structure of the universe, a description of the celestial sphere follows (lines 7–20), again describing first the northern constellations, then the zodiacal ones and next those south of the zodiac.The remainder of the poem (lines 21–76) 117 Compare, for example, the text Involutio Sphaerae (incipit: Hic est stellarum ordo utrorumque circulorum. (Maass 1898, pp. 155–61) and the text Excerpum de Astrologia (incipit Duo sunt extremi vertices mundi (Maass 1898, pp. 309–12 and Dell’ Era 1974, pp. 41–6). 118 Riese 1869, vol.II, pp. 221–3, no. 761. Baehrens 1883, vol. V, pp. 380–2. Another astronomical poem, in the thirteenth century codex London BL. Add. 23892, is entitled Descriptio mundi secumdum Yginum. (Haye 2007, see also Hübner 2009). It is a very long poem, consisting of 518 lines. After a long introduction on the structure of the universe (lines 1–200), there follows in lines 201–216 a description of the celestial sky listing first the northern constellations, then the zodiacal ones, and next those south of the zodiac. The remainder of the poem (lines 216–515) describes other astronomical aspects, such as the planets. 119 Gaborit-Chopin 1967. De Meyier 1977, pp. 31–42. 120 The poem in MS 12117 is reproduced by Riese 1869, vol. II, pp. 221–3, no. 761. The star catalogue De ordine ac positione stellarum in signis (ff. 131r–137v) is discussed in VieillardTroiekouroff 1967.

190

3.3 NORTHERN AND SOUTHERN HEMISPHERES describes the position of the constellations with respect to the parallel circles. The Darmstadt poem differs from ‘Haec pictura docet quicquid recitauit Hyginus’and that by Priscianus by the fact that it begins the sequence of the zodiacal constellations with Cancer whereas the other poems start it with Aries. In discussing in Book IV.5 the zodiacal constellations, Hyginus explains that, although Aratus starts the sequence with Cancer, he and all other astronomers begin it with Aries.121 Clearly, the Darmstadt poem did not follow Hyginus in this respect. In the last line the author of the Darmstadt poem clearly links the description of the celestial sphere in the poem with two authors,‘Hec ita Gerbertus cui testis et auctor Higinus’. Before we discuss what the relation might be between these two authors and the maps, there is another problem that we have to consider, namely that of the date of design (or epoch) of the sets of hemispheres. What do we make of all this? The picture that emerges from the study of the two northern and southern hemispheres is far from consistent and it raises more questions than can be answered. One question that can be answered is whether the one set of hemispheres could have been derived from the other? The answer is a clear no. Although the same basic format is used, the two sets of hemispheres have a different structure in the sense that the Bernkastel-Kues pair of hemispheres are consistent with an equidistant model (ME). The Darmstadt maps on the other hand seem to be more closely linked to a stereographic model (MS). Which of the two models (MS or ME) involved came first, is a question that is hard to answer but if the exemplars of the hemispheres belong indeed to the Eudoxan tradition in map 121 Hyginus (Le Boeuffle 1983), IV.4, p. 122.

making it seems that the equidistant model (ME) is the older one since it was known from Antiquity onwards and is the basis of all the other maps discussed in this chapter. Then we have to accept that the Darmstadt hemispheres were adapted to another, stereographic way of drawing the parallel circles. This cannot be much older than the eleventh century since from that time on the principles of the stereographic projection may be assumed to have been known in the Latin West. This is supported by the reference to Gerbert of Aurillac in the last line of the poem. However, does this mean that the Darmstadt and the Bernkastel-Kues hemispheres developed from the same exemplar? Not necessarily. One argument contradicting such a thesis is that on both hemispheres in Bernkastel-Kues MS 212 the order of the constellations is in globe-view,whereas this holds only for the northern hemisphere of the Darmstadt MS 1020. But perhaps the most convincing objection to such a thesis is that the two sets of hemispheres differ in the way the Equator intersects some constellations. On the Darmstadt pair Canis Minor is completely in the northern and Hydra with Crater and Corvus completely in the southern hemisphere whereas on the Bernkastel pair they are divided over the two hemispheres. Such a difference betrays the fact that the maps were copied from a pictorial source in which the northern and southern hemispheres formed a continuity.This seems to answer another question: Could the set of northern and southern hemispheres have been copied ultimately from an existing globe? Perhaps more interesting is that especially in the case of the Darmstadt hemispheres the maps may have served to make a medieval globe. The poem associated with the maps is preceded on f. 60r by a copy of the well-known letter of Gerbert of Reims to Constantine of Fleury on

191

The descriptive tradition in the Middle Ages the construction of a sphere.122 On f. 61v, directly following the poem, is a short text (f.61v) on the construction of a globe, ‘Speram celi facturus ducas circulum per medium globum’. But more of that in the next section.

. GLOBE MAKING IN THE MIDDLE AGES In the Aratean literature available to a medieval student one finds two kinds of illustrations of globes. One drawing (see Fig. 3.26) shows Aratus and Urania gathered around a celestial globe mounted on a stand.The picture is part of a series of illustrations commonly found in Germanicus’s Latin translation of Aratus’s poem.123 The theme

Fig. 3.26 Aratus and Urania. (From Maass 1898. p. 172, after the picture in Madrid, MS 19, f. 55r.)

122 Sphaera, mi frater, de qua quaeris ... edited with French translation in Gerbert d’Aurillac (Riché and Callu 1993),Vol. II, pp. 680–6. 123 Haffner 1997, pp. 31–3. McGurk 1973, pp. 197–216, esp. p. 198, Plate II (A).

of this drawing is not in the first place to show what the starry sky looks like but to underline the globe’s educational use. Its concept goes back to Antiquity (see Chapter 1). Other, more detailed, images of celestial globes appear with the Revised Aratus latinus.These pictures usually follow after a text, labelled Involutio sphaerae, a Latin translation of a Greek poem on the Sphere describing the Aratean sky and the astrological influences of the zodiac.124 The globe drawings are followed by the main text consisting of the Scholia Sangermanensia, a revised version of the scholia of the Aratus latinus.125 Six examples of the globe drawing are known, of which two are reproduced in Figs 3.27 and 3.28.126 The globe in these drawings consists of a sphere that is fixed in a meridian ring which in turn is mounted on a stand consisting of six decorated columns supporting a horizon ‘ring’. In the centre of the stand is a support for the meridian ring. In Fig. 3.27, the meridian ring passes behind the straight fore part of the horizon ring. In all the other globe drawings (see for example Fig. 3.28), it is drawn in front of the horizon ring, showing that most medieval copyists did not fully understand the construction.The globe drawing in Fig. 3.27 represents the least corrupted copy of all. In it the north pole is indicated by a clamping screw at the meridian ring. On three of the globe drawings (described in the Appendix 3.4 as G1–G3) ten constellations are drawn on the sphere, on the remaining three (G4–G6) only nine. The three constellations in the zodiacal band are easily 124 Maass 1898, pp. 155–61; Martin 1956, pp. 219–23. 125 Germanicus (Breysig 1867), pp. 111–202 (as scholia Sangermanensia); Maass 1898, pp. 180–297 (as Recensio interpolata); Le Bourdellès 1985, p. 72. 126 The details of these pictures are described in the Appendix 3.4. Pictures of globes, numbers G1–G6.

192

3.4 GLOBE MAKING IN THE MIDDLE AGES

Fig. 3.28 Drawing of a globe in St Gall, MS 250, f. 472. (Courtesy of the Stiftsbibliothek, St Gall.)

Fig. 3.27 Drawing of a globe in Paris, MS 12957, f. 63v. (Courtesy of the Bibliothèque nationale de France, Paris.)

recognized as Aries, Taurus, and Gemini. The two constellations south of the horizon can be identified as Navis and the hind part of Canis Maior. The snaky figure south of the zodiac but above the horizon is harder to identify. The location suggests that it is Eridanus but the image is not really that of a river. However, the image of Eridanus as a snaky figure is not unusual. One of the human figures north of the zodiacal band certainly represents Auriga since in three of the drawings the Kids are drawn on his right arm. The figure preceding him ought then to be Perseus, but instead of carrying the Gorgon’s head it holds a piece of cloth, an iconography that seems closer to

either that of Orion or Bootes.The identification of the animal east of Auriga is also problematic.The beast could be Ursa Maior but on a globe one would then expect it to face westwards, in the direction of Auriga. Yet no other animal is known in that region.The last image that presents a problem of identification is that of an animal cut into two parts by the horizon east of Gemini. If it represents Leo, the image of Cancer has been suppressed. It could be Canis Minor but that identification is not very convincing either. The stand of the globes in the drawings is more telling. The central column supporting the meridian ring and the other columns are drawn in perspective as seen by the manner of

193

The descriptive tradition in the Middle Ages decoration. In the most reliable drawing (G1 in Fig. 3.27) the orders/capitals on top of the pillars are in the Corinthian style.127 The instrument could be related to the ‘Aratean globe’ described by the Byzantine mechanic Leontius of the seventh century in a treatise in which he mentions a horizon on supports.128 The globes in the drawings represent real instruments and they demonstrate that the idea of a ‘modern’ globe consisting of a sphere fixed in a meridian ring which is mounted on a stand that consists of a number of columns supporting a horizon ring was a familiar model in the Middle Ages.129

(Aliae sperae compositio signis cognoscendis).131 The semicircle with sighting tubes appears to be a simplified version of another instrument, described by Gerbert in greater detail in a letter to Constantine of Fleury and later abbot of St.Mesmin-de-Micy.132

3.4.2 Gerbert’s semisphere with sighting tubes133

Gerbert’s instruction starts with making a solid sphere of wood and drawing the five parallel celestial circles on it such that these circles (the ‘arctic’ and ‘antarctic’ circles, the tropics and the Equator) are respectively 6, 11, and 15 sexagesimal parts (1p = 6°, being 1/60th of a full circle) 3.4.1 Gerbert’s spheres from two opposite poles representing the north The question that concerns us here in the first and south pole (Scheme 3.10, left upper corplace is to what extent real solid globes were ner).134 The distances between the circles are available in the Middle Ages. Whenever globe respectively 6, 5, and 4 sexagesimal parts of a full making is discussed it is invariably focused on circle.This sphere is subsequently cut into halves the spheres of Gerbert of Aurillac (946–1003), and one half is hollowed out. Next, holes are who is well-known for his teaching activities.130 made in the middle of the five celestial circles As reported by one of his pupils, Richer of and through the points N and S, seven in all. Each Saint-Remy, he made several models in order hole serves to hold a sighting tube of half a foot, to promote the understanding of astronomy. extending from the (empty) middle of the semiThe instruments reported by Richer are 1) a sphere (Scheme 3.10, left lower corner).135 The celestial globe (Sperae solidae compositio), 2) a configuration of the two tubes through the end semicircle with sighting tubes (Intellectilium circulorum comprehensio), 3) a sphere for explaining the (orbital) properties of the planets (Sperae 131 Richer (Latouche 1937),Tome II 954–995, nos 50–53, pp. compositio planetis cognoscendis aptissima), and 4) 58–63. The instruments have been discussed several times in another sphere for teaching the constellations the literature: Lindgren 1976, pp. 28 and 30; Zinner 1967/1979, 127 The Corinthian style was adopted by the Romans in the first century bc, see Vitruvius (Soubiran 1969), book IV.1. 128 The edition of Leontius’s text is by E. Maass 1898, pp. 561–7. An edition with a French translation is by Halma 1821, pp. 65–74, esp. p. 69. 129 Obrist 2004, p. 209, believes that the globes in the drawings were highly valued, especially in eastern Byzantium. 130 Riché 1987/2006. Lindgren 1976. For a review of the manuscript traditions of Gerbert’s work, see Mostert 1997.

p. 168; Poulle 1985, pp. 597–617, esp. pp. 602–6. 132 Text edited in Bubnov 1899, pp. 25–8. Gerbert d’Aurillac (Riché and Callu 1993),Vol. II, pp. 680–7 (letter dated between 972 and 982). English translation of the letter in Lattin 1961, pp. 36–9 (letter no. 2, undated, Rheims 978?). 133 I have reserved the term hemisphere for maps and shall use the term semisphere for Gerbert’s device. 134 Gerbert d’Aurillac (Riché and Callu 1993), Vol. II, p. 680. 135 The size of the sphere must have been at least one foot in order to accommodate two sighting tubes of half a foot.

194

3.4 GLOBE MAKING IN THE MIDDLE AGES

Scheme 3.10 Construction of the semisphere with sighting tubes of Gerbert of Aurillac.

points N and S ‘will be opposite to each other so that you may see through both as if through one’.136 In order to prevent the tubes wobbling an iron semicircle is recommended to fix the tubes at their upper ends. This semicircle is two inches wide, divided into 30 sexagesimal parts of a full circle, and perforated in the same way as the semisphere. How the seven sighting tubes were actually arranged in the centre of the sphere is not technically clear. To use the semisphere, its curved part is placed upwards (Scheme 3.10, right) and the two tubes along its diameter are aligned with the polar axis.137 Then the two sighting tubes along the diameter of the sphere will point to the north 136 Lattin 1961, pp. 36–9 (letter no. 2, undated, Rheims 978?). p. 37. 137 Gerbert d’Aurillac (Riché and Callu 1993),Vol. II, p. 685: ‘Notato itaque nostro boreo polo, descriptum hemisphaerium taliter pone sub divo, ut per utrasque fistulas, quas diximus extremas, ipsum boreum polum libero intuitu cernas’.

and south pole and the other five tubes to the corresponding intersections between the local meridian and the five imaginary parallel celestial circles.138 The simplified version described by Gerbert’s pupil, Richer of Saint-Remy, consists of a semicircle provided with sighting tubes.139 The semicircle is to be divided in the same way as Gerbert’s semisphere. In fact, it may well represent a strengthened version of the iron semicircle recommended for fixing the tubes at their upper ends of the semisphere mentioned above. Perhaps it was found in due course that with this

138 Gerbert d’Aurillac (Riché and Callu 1993), Vol. II, pp. 685–6: ‘Igitur praedicto modo locato hemisphaerio, ut non moveatur ullo modo, prius per inferiorem et superiorem primam fistulam boreum polum, per secundam arcticum circulum, per tertiam aestivum, per quartam aequinoctialem, per quintam hienalem, per sextam antarcticum circulos metiri poteris’. 139 Richer (Latouche 1937), esp.Tome II, p. 60, no. 51.

195

The descriptive tradition in the Middle Ages semicircle the same results, if not a better performance, could be realized. A few drawings of Gerbert’s semisphere or semicircle survive. The image shown in Fig. 3.29 is from a collection of astronomical texts and drawings in the eleventh century manuscript Paris BnF MS lat. 7412, f. 15r.140 A similar drawing in London BM MS Old royal 15.B.IX, f. 77r is reproduced and discussed in detail by Wiesenbach.141 Both drawings have the same title (HEMISPERIUM) and both have the same text written between the tubes (SEPTEM FISTULAE SEMI PEDALES),showing that indeed Gerbert’s semisphere with sighting tubes is meant here.The text below the sphere (‘Componitur etiam aliud hemisperium similiter cum septem fistulis ad cognoscendos V paralellos cum polo’) confirms its use, of which more below. At the inner end of the tubes is the word verax (true) in both drawings. Above the semisphere in Fig. 3.29, between the sighting tubes is another series of—unexplained—letters (S E X S I G) which letters do not occur in the drawing in MS Old royal 15.B.IX.They may refer to a now lost explanatory text. In the semisphere shown in Fig. 3.29 the tubes are indicated at regular intervals of 30° of each other and do not therefore agree with the relative distances (6, 5, 4 sexagesimal parts of a full circle) mentioned in Gerbert’s letter. The distances between the tubes in the drawing in MS Old royal 15.B.IX are closer to Gerbert’s prescribed values. In both drawings (that shown in Fig. 3.29 and in MS Old royal 15.B.IX) the semisphere is apparently mounted on another semi-

circle. In Fig. 3.29 the supporting semisphere is fixed to a sort of stand, in MS Old royal 15.B.IX it ends in a kind of handle. How one is to direct the whole construction with the—in the drawing—horizontally oriented sighting tubes to the north and south poles is mechanically not clear. The drawing in the right corner of Fig. 3.29 is intended to show, in a rather complicated way, how to find the time at night with the help of a star clock invented by Pacificus of Verona.142 According to the chronicle of Thietmar of Merseburg, Gerbert built also a star clock for the emperor Otto III in 997 during his stay in Magdeburg. Gerbert’s star clock was very likely a copy of Pacificus’s instrument.143 He could have acquired the necessary know-how for building such an instrument during his many travels in Italy or during his abbacy in Bobbio, in the years 981/82–983.The star clock is designed for finding out what time it is at night, and as such is not directly related to Gerbert’s semisphere, but both instruments have in common that they have to be directed one way or another to the north pole before they can be put to use. This connects the drawing in the right corner of Fig. 3.29 with its main figure. How to direct the sighting tubes of these instruments actually towards the north pole is unfortunately not clear. Gerbert claims that there was a star located at the north pole. He explains that, if one were not sure which of the northern stars would be the ‘pole star’, that is the star at the north pole, one is advised to take a sighting tube, centre it on the star concerned, and fix the tube’s position. If the star concerned is indeed the ‘pole star’, it will remain there all night. If it is another

140 The contents of the codex is described in Borrelli 2008, p. 242. 141 Wiesenbach 1991, p. 140. Borrelli 2008, p. 192, mentions similar drawings in Vat. Reg. lat.1661 (A.44) f. 60 and f. 77v.

196

142 Wiesenbach 1993, p. 246. See also Wiesenbach 1994. 143 Wiesenbach 1993, pp. 229–36.

3.4 GLOBE MAKING IN THE MIDDLE AGES

Fig. 3.29 Drawing of a semisphere with sighting tubes, Paris, MS lat. 7412, f. 15r. (Courtesy of the Bibliothèque nationale de France, Paris.)

197

The descriptive tradition in the Middle Ages one, the star concerned will move after a short while and disappear from the range of the tube.144 A number of scholars have proposed that the star known as 32H Camelopardalis, then located near the north pole, represents Gerbert’s pole star.145 Poulle has dismissed this thesis because he claims that the stars of Camelopardalis are not visible to the naked eye.146 The star 32H Camelopardalis does not occur in the Ptolemaic star catalogue—for good reasons as Poulle asserts— but it was nevertheless observed with the naked eye by the Polish astronomer Johannes Hevelius (1611–87). He estimated its brightness as the 5th magnitude.147 Therefore, the question of visibility is not so easily dismissed. A person with sharp eyesight would be able to see 32H Camelopardalis, especially when using a sighting tube, but for an average inexperienced observer the star would be hard to see. As a method suitable for students, Gerbert’s way to direct the spheres to the north pole would not suffice. One cannot exclude the possibility that Gerbert’s pole star represents only a theoretical concept.As discussed in Chapter 1, many classical authors (Euxodus, Euclid, Eratosthenes, Hyginus, Martianus Capella) claimed that there was a star at the north pole. Gerbert could have followed in their footsteps in this respect. If he did, it 144 Gerbert d’Aurillac (Riché and Callu 1993),Vol. II, p. 684: ‘Si autem de polo dubitas, unam fistulam tali loco constitue, ut non moveatur tota nocte, et per eam stellam suspice, quam credis esse polum, et si polus est, eam tota nocte poteris suspicere, sin alia, mutando loco non occurrit visui paulo post per fistulam’. 145 Michel 1954, p. 177.Wiesenbach 1994, p. 381. 146 Poulle 1985, p. 610. Poulle 2009, p. 242. 147 Hevelius 1690, p. 170. The star is described as: ‘in cervice, seu dextra aure’.The faint star is now known to be a binary star consisting of Σ1694A (HD112028) and Σ1694B (HD112014) with magnitudes of respectively 5.28 and 5.85, see DibonSmith 1992, pp. 38–9.The same values are listed in Norton’s Star Atlas, 17th edition, Cambridge Mass, 1978, p. 118.

implies that the whole idea of his semisphere with sighting tubes was a theoretical idea, to be discussed rather than to be used. Gerbert’s model recalls the scheme of parallel circles as this was described in Antiquity by such authors as Geminus, Manilius, and Hyginus.148 The same scheme is also the basis of the‘zone’structure of the universe described by Macrobius.149 Gerbert may or may not have known Manilius and there is no evidence that he knew Geminus or Hyginus.150 However, the books of Hyginus and Macrobius were widely available in Gerbert’s days and their treatises can hardly have escaped his attention. However that may be, the grid from Antiquity cannot be applied without adaptation to higher European latitudes. The ‘arctic’ or evervisible circle, separating the always visible stars from those that rise and set, depends on the geographical latitude. For example, at a geographical latitude of 48° the ever-visible circle is not at a distance of 6 parts (=36°) but at a distance of 8 parts (=48°) from the north pole. In Scheme 3.11 the ever-visible and ever-invisible circles for the latitude of 48° are drawn. Note that these circles emerge from the northern and southern points of horizon.Was Gerbert aware of this property of the ‘arctic’ and ‘antarctic’ circles? Hyginus and Isidore of Seville define the arctic circle solely from the fact that it encloses the Bears.151 The antarctic circle is subsequently defined by these authors as the one opposite the 148 See section 1.2. 149 Stahl 1952, chapter vii, pp. 208–12. See also Obrist 2004, pp. 171–94. 150 Gerbert ordered a manuscript De astrologia by Manlius from Bobbio, see Riché 1987/2006, p. 81. Some scholars interpret ‘Manlius’ as Manilius and others as Anicius Manlius Severinus Boethius. Lindgren 1976, p. 36, footnote 180. 151 Hyginus (Le Boeuffle 1983), I.6.2, p. 8. Hyginus (Viré 1992), I.7, p.7, ll. 45–7. Barney et al. 2006, III.xliv: ‘Quorum primus circulus ideo ἀρκτικὸς appellatur, eo quod intra eum Arctorum signa inclusa prospiciuntur’.

198

3.4 GLOBE MAKING IN THE MIDDLE AGES [822] The fifth and the last parallel is called the australis, or the antarctic circle. This is plunged beneath the surface and its upper edge barely touches the southern horizon.’ 153

Martianus Capella’s treatise was available in Gerbert’s library.154 Thus Gerbert could have known that the circles at 36° from the poles do not coincide with the ever-visible and everinvisible circles of his own latitude. Poulle seems to think that Gerbert’s ‘arctic’ and ‘antarctic’ circles at 36° from their respective poles should be understood as modern polar circles which are at 24° from the poles. He dismissed Gerbert’s circles at 36° from the north pole as a grave error.155 But were the circles at 36° from the pole indeed meant to be at 24°? Scheme 3.11 The ever-visible and ever-invisible circles Poulle asserts, and I believe correctly, that for the latitude of 48°. Gerbert’s spheres belong to the Latin astronomical arctic circle.152 Indirectly Hyginus refers to the vis- tradition.156 He seems not to have realized that ibility of constellations lying on, above, or below modern polar circles at 24° are not part of the the arctic and ‘antarctic’ circles, which demon- tradition represented by the Latin treatises of strates beyond doubt that these circles correspond Aratus, Hyginus, and Martianus Capella. It is therefore more likely that the circles at 36° from to the ever-visible and ever-invisible circles. Martianus Capella in his De nuptiis Philologiae the poles are meant to represent what they et Mercurii introduces the arctic and ‘antarctic’ are: the antique version of the ever-visible and circles as proper ever-visible and ever-invisible ever-invisible circles at a latitude of 36°, and therecircles, that is to say, that these circles graze the fore are not an error but part of Gerbert’s design. edge of the northern and southern horizon as This same conclusion holds for the ‘arctic’ circle and the ‘antarctic’ circle marked in the drawing in shown in Scheme 3.11. the twelfth-century codex Munich Clm 14689, f. ‘[818] The first of the parallels is the one which is 1r, which I have reconstructed in Scheme 3.12.157 always visible and looms above, never plunging below the horizon, and just grazing the edge of the northern horizon. This is called the arctic circle, from the fact that it encompasses, along with other constellations which will be mentioned later, the constellations of the twin Septentriones. 152 Hyginus (Le Boeuffle 1983), I.6.3, p. 9. Hyginus (Viré 1992), I.7, p. 8, ll. 60–3. Barney et al. 2006, III.xliv:‘Quartus autem circulus ἀνταρκτικὸς vocatus eo quod contrarius sit circulo, quem ἀρκτικὸν nominamus’.

153 Martianus Capella (Dick 1925), VIII.18 and 822. The translation is from Stahl et al. 1977, pp. 320–1. 154 Riché 1987/2006, p. 256, Annexe. 155 Poulle 1985, p. 604. 156 Poulle 1985, p. 613. 157 A picture of the manuscript page is in Wiesenbach 1991, p. 132.The codex is available in the Digitale Sammlungen of the Bayerische Staatsbibliothek (http://www.digitale-sammlungen.de/ [accessed 13 March 2012]).

199

The descriptive tradition in the Middle Ages

Scheme 3.12 Scheme of a sphere in Munich, Clm 14689, f. 1r.

The grid closely follows Gerbert’s description. The outer rim is divided into sexagesimal parts of a full circle (that is, in parts of 6°) and the five parallel circles are at distances of respectively 6, 11, and 15 parts from the poles. The circles numbered 2–5 in Scheme 3.12 are labelled in the manuscript drawing: 2: ARTICVS; 3:TROPICVS AESTIVVS; 4: TROPICVS HIEMALIS; 5 ANTARTICVS. The circles at a distance of 36° from the respective poles agree with Gerbert’s ‘arctic’ and the ‘antarctic’ circles.158 The special interest of this drawing is that it depicts the horizon and the polar axis for a geographical latitude of 48°, that is the north and south poles are drawn 48° above and below the horizon which is the circle in Scheme 3.12 numbered 1 and labelled in the manuscript drawing: ORI. As a result the ‘arctic’ and ‘antarctic’ circles at a distance of 36° from the poles 158 In a different hand the other circles have been labelled: Aequinoctialis, Axis, and Zodiacus. And a letter K is added to the label ANTARTICVS.

(nos 2 and 5 in Scheme 3.12) do not emerge from the north and south points along the horizon. It shows that here the concept of the ‘arctic’ and ‘antarctic’ circles as being respectively the ever-visible and ever-invisible circles does not apply. Wiesenbach has shown that an earlier version of this drawing served as the model for the ‘spera’ of William of Hirsau (c. 1030–91), a Benedictine monk from St Emmeran who later became abbot of Hirsau.William’s sphere survives today. The instrument is shaped as a circular disc made of stone and provided with locks that serve for holding sighting tubes.William’s spera is in many ways reminiscent of Gerbert’s semicircle with sighting tubes and may well have developed from it. Compared with Gerbert’s construction William’s sphere is, however, a great improvement, especially because its mounting does not depend on sighting the ‘pole star’. William of Hirsau clearly knew that the height of the north pole above the horizon equals the geographical latitude of a place (see Scheme 3.12).This property became generally known in the Latin West with the introduction of the astrolabe. The ‘spera’ demonstrates well William’s capabilities in astronomy. The question remains however why he, and Gerbert before him, did not adapt the circles at a distance of 36° from the poles to the astronomically more meaningful ever-visible and ever-invisible circles of their own latitude. The main purpose for Gerbert’s design of the semisphere with sighting tubes was to show the Greek five parallel celestial circles and their constellations (ad coelestes circulos vel signa).The precise meaning of this is clear once it is realized that the celestial circles themselves are invisible and can only be observed in the sky by way of the constellations located on them as Geminus explains:

200

3.4 GLOBE MAKING IN THE MIDDLE AGES ‘One must think of these circles as without thickness, perceivable [only] by reasons, and delineated by the positions of the stars, by observations made with the dioptra, and by our power of thought.’159

Tracing the celestial circles by the stars is a very antique notion which came into being at a time when mathematical coordinates were still unknown. Eudoxus listed the constellations located on seven circles: the (Greek) ever-visible and ever-invisible circles, the tropics, the Equator, and the colures. In the Aratean corpus of texts only the constellations on three parallel circles, the tropics, and the Equator, are described. Hyginus’s De Astronomia, on the other hand, adds in Book IV which constellations are on the evervisible and ever-invisible circles, an addition which he considered a great improvement over Aratus’s texts.160 Thus the idea of observing the five parallel celestial circles and their constellations fits well in the descriptive tradition. Also the idea of observing the parallel circles with the dioptre, which in its simplest form is just a sighting tube, is clearly not a new idea. Evans and Berggren believe that, in order to sweep out the parallel circles, the dioptre had to be rotatable, but Gerbert’s design of his semisphere with sighting tube shows that this is not really necessary. Through the daily rotation of the starry sky, Gerbert’s instrument enables one in principle to see in the meridian plane, in the course of a night and through the seasons, the constellations that lie on or near four of the five celestial circles: the Greek ever-visible circle, the tropics, and the Equator. By it one can, again in principle, verify the descriptions provided in, say, Hyginus’s De Astronomia. 159 Geminus (Aujac 1975),V.11, pp. 22–3.The English translation is from Evans and Berggren 2006, V.11, p. 151. 160 Hyginus (Le Boeuffle 1983), IV.6, pp.123–4. Hyginus (Viré 1992), IV.6, pp. 133–4.

For the identification of the constellations described in the classical literature as being on the antique ever-visible circle, the sighting tube must be directed to a distance of 36° from the north pole, the value mentioned by Hyginus and others. It would not have made sense to point the sighting tube to a polar distance of 24° or 48°, the polar distance of the ever-visible circles for the latitude of 48°. Finally, we note that at a latitude of 36° one can see the constellations that lie on the ever-invisible circle for a very short time at the south point of the local horizon, but in northern latitudes this circle is well below the horizon. As Gerbert explains in his letter to Constantine of Fleury, by looking through a tube directed to the ‘antarctic’ circle one would only see the Earth, not the sky!161 The main purpose of Gerbert’s instrument was to trace the constellations located on the parallel circles, a useful project considering that the classical authors did not agree among themselves which constellations were or were not located on the parallel circles. However, the weaknesses in his design makes one wonder to what extent the whole idea would have remained just a ‘Gedankenexperiment’.

3.4.3 Gerbert’s celestial globes Construction details for Gerbert’s celestial globes are scarce. The descriptions by Richer of SaintRemy are very superficial.A few more construction details are given in the correspondence of 989 between Gerbert and Remi, a monk of Trier.162 The latter had asked for a globe and Gerbert wrote to him that the globe would be 161 Gerbert d’Aurillac (Riché and Callu 1993),Vol. II, p. 686: ‘Pro polo vero antarctico, quia sub terra est, nihil coeli, sed terra tantum per utrasque fistulas intuenti occurrit’. 162 Lattin 1961, no. 142, pp. 172–3; no. 156, pp. 184–5; no. 160, pp. 188–9; no. 170, pp. 199–200.

201

The descriptive tradition in the Middle Ages made of wood and the sphere covered with leather on which the constellations would be drawn.This description seems to apply to the first globe mentioned by Richer.163 That globe (sperae solidae compositio) is said to consist of a solid wooden sphere with the northern and the southern constellations drawn around the north and south pole respectively. The sphere was placed with its poles obliquely to the horizon to show which constellations are visible and which not. Another instrument mentioned (aliae sperae compositio signis cognoscendis) could well have been an armillary sphere like the one designed for showing the properties of the planets, but without inner rings.164 The parallel circles in this armillary instrument are said to lie at intervals of 6, 5, and 4 sexagesimal parts of a full circle from the respective poles, that is, the same intervals as used in the semisphere. It was provided with a tube for marking the poles. The constellations are said to have been attached with pieces of wire and the stars of the constellations were marked too, although it is far from clear how this was done. Poulle believes that this latter celestial sphere was not really made of rings but was solid like the first globe described by Richer of Saint-Remy, and presumes that the stars themselves were fixed on the sphere and the wires used to group them into constellations.165 How Gerbert actually marked the stars Poulle does not say. As an aside I note that the assumption of a solid sphere may be superfluous. The constellations could have been cut out of brass which then could have been attached to the rings. This is illustrated in Fig. 3.30, where a number of the constellations surrounding Cygnus are shown with two sections of circles to which they are 163 Richer (Latouche 1937), esp.Tome II, pp. 58–61, no. 50. 164 Richer (Latouche 1937), esp. Tome II, pp. 60–3, nos 52 and 53. 165 Poulle 1985, pp. 602–3.

attached.The detail is part of a Copernican sphere made in 1657 by Andreas Bösch.166 Whatever the technique used, the question of how to place the stars and their constellations on a sphere is certainly of interest. As discussed in Chapter 1, one can mark the constellations either by using descriptions of the constellations with respect to the main celestial circles and with respect to each other as described in the descriptive tradition, or by using stellar coordinates available in the mathematical tradition. Stellar data, as provided in the Ptolemaic star catalogue, were not available in the Latin West in the ninth to eleventh centuries, whereas locations of constellations with respect to the main circles were not uncommon and formed, as we have seen, the subject of Gerbert’s semisphere with sighting tubes. How could such a globe, based on the descriptive tradition, have been made? A first step in making the globe would have been, as usual, to draw the main celestial circles on a sphere. The following description by an anonymous author, in a Latin text in Darmstadt Hs 1020, f. 61v, of the construction of a celestial sphere (Speram celi facturus ducas circulum per medium globum) illustrates how Gerbert may have done this. ‘Speram celi facturus ducas circulum per medium globum quem in lx punctos distribues et quemcumque ex ipsis uolueris pro polo accepto. A littera signabis et in opposito idem in xxxi167 ab A predicta pone F. Tunc vi punctum ab A signabis per B. xi punctum ab A signabis per C. Similiter retro ab F uersus C in xi pones D, et in vi ab F uersus D pones E.Tunc posito 166 Museum of National History at Frederiksborg Castle, Hillerød. 167 This should be xxx.

202

3.4 GLOBE MAKING IN THE MIDDLE AGES

Fig. 3.30 Detail of the Sphaera Copernicana by Andreas Bösch, 1657. (Photo: Søren Andersen.)

circino in A circumduces B et C. Ita cum F circumducas E et D quod sunt v zonae. In A polo boreali considerato in F polo austra li. Ad inueniendum ergo zodiacum pone circinum in iiii puncto ab A et circumduces punctum xvii simili modo posito circino in quarto puncto post F xvii ab eo qui est xiiius ante A cir cumduces cuius latitudinem et longitudinem in xii partes di uides q168 xii longitudinum partes per xii signabis figuras et nomina xii habebunt signorum. Adhuc duces circulum per utrum 168 Could stand for quas?

que polum crucem faciens in utroque polo unusque illorum per can crum et capricornum transiens solstitialis alter per arietem et li bram equinoctialis erit. Cetera necessaria sperae docet higinus’

Following this instruction first a division of a great circle into 60 parts is made (see Scheme 3.13). Next the opposite points A and F are marked. Then the points B and C are found at respectively vi and xi points from A (at distances of respectively 36° and 66°).The opposite points E and D follow by repeating the procedure from F. Thus the five zones are constructed. Next the

203

The descriptive tradition in the Middle Ages Hyginus. What additional information could a maker have found in Hyginus? He certainly could have used the lists describing which constellations are located on which of the parallel circles, which appear to have been taken directly from a celestial globe.169 Hyginus does not recount in a systematic way which constellations are on the colures although in discussing the constellation Bootes in Book III, he tells his readers that the equinoctial colures touch the constellations Aries and the Claws, reflecting the epochal mode described by Manilius. To mark the constellations on a sphere a globe maker had to know first of all the positions of the colures with respect to the constellations. This information could be found in the astronomical Scheme 3.13 Construction of a globe. treatise by Martianus Capella which was well known in the Latin West at the turn of the tenth zodiac is drawn by marking its northern and century. A map or globe maker could use this southern boundaries. First the ecliptic pole is Capellan description to fit the constellations to found at a distance of iiii points from A (and F). the colures and from there continue to mark the Then a circle is drawn at xvii points from A and other constellations with respect to the five parthe same from F. This latter circle is xiii from A. allel circles. The globe would have the Capellan Finally the zodiac is to be divided into xii parts characteristics that the colures pass ‘through the representing the 12 zodiacal signs. The last cir- 8th degree of the constellations Aries, of Cancer, cles to be presented are the colures passing of Libra and of Capricorn’. Once the constellathrough A and B. The solstitial colure passes tions were drawn on the sphere, the stars could through Cancer and Capricorn, the equinoctial be added as described in the descriptive tradition colure through Aries and Libra. The description with respect to the various parts (head, arm, leg. ends with the assurance that other details can be etc.) of the constellation figure, as in cycles of found in Hyginus (‘Cetera necessaria sperae docet constellations in illustrated manuscripts. higinus’). Alternatively, and more probably, the globe This construction utilizes the same grid as maker might have used a celestial map for markGerbert and William of Hirsau used for their ing the constellations on the sphere. Of the instruments with sighting tubes. It adds to it a medieval maps known today and discussed in zodiacal band which extends 12° north and south detail in this chapter, especially the northern and of the ecliptic, that is, twice the value quoted in Antiquity. And it also specifies the colures, which 169 Hyginus (Le Boeuffle 1983), IV.2–7, pp. 115–12. Hyginus are essential for making a celestial globe. Interesting (Viré 1992), 4.2–7, pp. 126–35. For Hyginus’s globe see the distoo is the saying that other details can be found in cussion in Chapter I. 204

3.4 GLOBE MAKING IN THE MIDDLE AGES southern hemispheres in Darmstadt Hs 1020, f. 61v, could have served this purpose. These Darmstadt maps follow in the manuscript MS 1020 after the letter of Gerbert on his semisphere with sighting tubes and precede it by the above instruction on globe making. Surely, one can hardly think of a better a clue of what Gerbert’s celestial globe may have looked like. There is no evidence for a direct relation between Gerbert and the maps in Darmstadt MS 1020. The author of the codex is unknown but there was certainly an interest in the sphere in Liege, witness of which are the activities of Franco of Liege (c. 1015/1020–83), who was probably a student of Adelman (1000–61), from 1031 the head of the cathedral school in Liege and later bishop of Brescia.170 Franco became head of the cathedral school in 1066 and next to books on squaring the circle he wrote a treatise about the sphere.171 In a recent study of Gerbert’s celestial globe Zuccato concluded that ‘Gerbert of Aurillac assimilated some elements of Arabic astronomy related to the use and construction of a solid sphere equipped with a horizon ring’ during his stay in Catalonia (967–70).172 Gerbert’s sphaera solida described by Richer of Saint-Remy is, so Zuccato believes,‘particularly remarkable in that it displays a technical element that had no precedent in the Latin tradition’.173 The technical element concerned is the horizon ring, which separates the constellations that are visible from those that are not.174 The use of a horizon ring 170 Adelman (c. 1000–1061), was a pupil of Fulbert de Chartres, see Lehmann 1953, p. 60. 171 Halleux 1998, p. 36. Renardy 1979. 172 Zuccato 2005, p. 763. 173 Zuccato 2005, p. 58. 174 Richer (Latouche 1937), vol. 2, p. 58,‘Quam cum duobus polis in orizonte obliquaret, signa septemtrionalia polo erectiori dedit, australia vero dejectiori adhibuit; cujus positionem eo circulo rexit, qui a Graecis orizon, a Latinis limitans sive determinans appellatur, eo quod in eo signa quae videntur ab his quae non videntur distinguat ac limitet’.

on Gerbert’s sphere was, according to Zuccato, borrowed from Arabic sources. The horizon ring, so he claims, is not described in any Latin text nor was it ever employed on Latin demonstrational spheres before Gerbert, ergo Gerbert must have borrowed the idea from somewhere, presumably during his stay in Catalonia.175 Zuccato was able to identify a treatise on globe making by Dunas ibn Tamīn al-Qarawī (fl. 2nd and 3rd quarter of the tenth century), a Jewish astronomer working at the Fatimid court in Tunisia, and argues that this was very likely to be Gerbert’s source.176 Through Gerbert’s educational efforts this knowledge would then have been spread in the Latin West. There are several arguments diminishing the strength of Zuccato’s thesis. First of all, we have seen above that illustrations of globes with horizon rings are part of the Aratean literature available in the Latin West from the ninth century on (see Figs 3.27 and 3.28). The idea of a material horizon was therefore known long before Gerbert turned his attention to globe making. Second, the horizon is discussed in the classical literature in such a way that it would not have been very difficult for Gerbert himself to make the step from a theoretical circle to a material ring. Last, and most important, the concepts underlying Gerbert’s sphere do not fit into the Arabic ideas on the function of the horizon ring. As Zuccato himself explains, with the introduction of a horizon ring ‘the Aratean arctic circles become redundant and useless’ because the globe can be adjusted for different terrestrial latitudes and, when properly done, the constellations that 175 Zuccato 2005, p. 760. 176 Zuccato 2005, pp. 755–8. Zuccato also claims that Dunash’s astronomical treatise is the Arabic source of the text included in the Astronomica vetera with the incipit De horologio secundum alkoram id est speram rotundam.

205

The descriptive tradition in the Middle Ages are always visible are easily demonstrated. This is certainly correct but, as shown above, Gerbert did not dispose of the concept of Aratean arctic circles. On the contrary, he maintained the classical circles at 36° from the poles and, for reasons discussed above, he did not adjust them. The ‘classical’ grid employed and transmitted by Gerbert is not part of the mathematical tradition which characterizes Islamic globe making from the ninth century on.Another point to consider is that the Arabic ideas on the function of the horizon ring presume the knowledge that the height of the north pole above the horizon equals the geographical latitude of a place.As his instructions for directing his instruments with sighting tubes towards the ‘pole star’ bear out, Gerbert did not know this. For all such reasons the thesis forwarded by Zuccato cannot be maintained. All texts related to Gerbert fit well into the knowledge belonging to the Greco-Roman traditions in popular astronomy exemplified by Geminus and Hyginus. However tempting it is to identify Gerbert as the key figure in the transmission of Arabic science from Spain to the Latin West, this new thesis should be dismissed, in the same way as the many attempts to identify Gerbert as the author of early Latin texts on the astrolabe.177 The transition from the descriptive Aratean to mathematical Islamic astronomy in Europe was not immediate. Interested students combined elements from both sides.We have seen that the Darmstadt hemispheres of the descriptive tradition were adapted to stereographic projection, albeit clumsily, perhaps because the principles of stereographic projection were not fully under control. Another example is the treatise De circulis sphaerae et polo by anonymous author, dated eleventh century, of unknown origin.178 It was 177 Kunitzsch 1997. 178 Wiesenbach 1991, pp. 135, 141.

Scheme 3.14 Construction of lines of constant altitudes (almucantarats) on a sphere.

published by Migne and attributed earlier to Bede, the Venerable.179 Jones counted it among the Didascalica Dubia and suggested that it is ‘primarily an expansion of Isidore, Etym, 3 32–59’.180 A closer look shows that the treatise can be divided into two parts, the first of which can be identified with text from Hyginus, De Astronomia.181 The other part is more interesting since it is connected to, among other things, the construction of a globe and explains how ‘almucantarats’ are to be drawn on a sphere. [0940D] Item. ‘Inventis in sphaera rotunda coluris, et ipsa sphaera in sexaginta divisa, ad inveniendum nostri almucantarat, haec est ratio. Ab arctici centro in meridiano coluro assu-

179 Migne PL 90, 937–942B.The treatise is in Zurich Zentralbibliothek MS Car C. 176 of the tenth or eleventh century, pp. 221–4. 180 Jones (C) 1939, p. 86. 181 Migne PL 90, 937D–940C:‘Sphaera est species quaedam in rotundo conformata . . . Itaque ostenditur non per tres ipsos circulos currere, sed zodiacum transiens ad eos pervenire’. Hyginus (Viré 1992), pp. 5–10, ll. 3–117.

206

Appendix 3.1 Catalogue of medieval hemispheres mas septem sexagesimas, et ibi nostri summum habeas. In quo quidem summo uno circini pede posito, XV sexagesimas assumas ante te pede cum altero, et primum almucantarat, id est, stabilem nostri horizontem circumvolvas. Deinde interius ad XIV ponas, et iterum circumvolvas. Deinde XIII, et ita ad singulas interiores sexagimas ponas et circumducas dum ad cacumen venias. Ad erigendam sphaeram rotundam sic facias. Ad Arcticum subtus duas sexagesimas, in nostram habitabilem sumas, [941A] et id loci ad summum vasis, terrae vicem obtinentis sustentaculo erigas. Hoc uni facias, alioquin eveniet, ut signa plurima orta non videas, et contra plurima sublapsa videas. Hanc quidem positionem edocet status in aequinoctio inventus’.182

The construction is shown in Scheme 3.14. The now familiar scheme based on units of 6° is applied.The author must have lived at a latitude of 48° because he says that in this place the north pole is 48° above the horizon. This could fit St Gall (47° 25´) since the text is in Zurich Zentralbibliothek MS Car C. 176, which comes from St Gall. But a number of other places would also meet this requirement 183 We can only guess what purpose this construction served. It could perhaps have something to do with the spherical astrolabe but more likely is meant as an explanation of the concept of the almucantarat usually drawn on the astrolabe. This particular text, combining a classical source such as Hyginus with elements from the then new Islamic science, shows that in the centuries following the year 1000 not all interest was focused on Islamic texts. Hyginus’s De Astronomia in particular still had a lot to offer to the medieval student. The discussions above have shown that conceptually Gerbert’s spheres belong to the descriptive

182 Migne PL 90, 940D–941A. 183 Auxerre (47° 48´), Chartres (48° 27´), Reims (49° 15´), Reichenau (47° 42´), St Emmeram (49° 01´).

tradition as outlined by the Latin literature available in his day.This may explain why his ideas were so easily taken over by his contemporaries.The sphere of William of Hirsau, and perhaps also the globe referred to by Notker Labeo as having been made in St Gall during the abbacy of Burkart II (1001– 22), were inspired by Gerbert’s venture in globe making.184 Gerbert’s spheres seem to have been the first and the last demonstrational instruments based on the Aratean literature made in the LatinWest for teaching the structure of the universe.

APPENDIX . Catalogue of medieval hemispheres H1. ABERYSTWYTH, NATIONAL LIBRARY OF WALES, MS 735 C, ff . 3v and 4r (Fig. 3.1a–b) France (Limoges?), early eleventh century. The hemispheres appear among a miscellaneous collection of texts (ff. 1r–9v) with verses and excerpts from Cicero and Macrobius. The hemispheres are arranged on two pages (f. 3v: summer hemisphere, f. 4r: winter hemisphere) with north at the top and south at the bottom of both hemispheres. Below the summer hemisphere (f. 3v) are traces of two sets of concentric circles. One set consists of seven circles, probably an unfinished diagram showing the planetary order, the other consists of a pair of circles, the significance of which is as yet not clear. Below the winter hemisphere (f. 4r) is a picture of a seated man with a beard, who seems to be holding the edge of a sphere supported by a stand with both his hands. A female figure stands behind him holding a crown. On the top west outside the map is a figure clinging to it. cartog raphy: Each hemisphere is framed by a pair of concentric circles that represent the equinoctial colures. There are two arcs (or sections of circles) that represent the northern and southern boundaries of 184 Wiesenbach 1991, p. 141.

207

The descriptive tradition in the Middle Ages the zodiac. The zodiacal band is not divided into segments. The upper and lower boundaries of the zodiac in the summer hemisphere intersect the summer solstitial colure (not drawn) at distances of 0.30 and 0.52 from the north pole, respectively (distances expressed as fractions of the diameter of the map). The upper and lower boundaries of the zodiac in the winter hemisphere intersect the winter solstitial colure (not drawn) at distances of 0.25 and 0.49 from the south pole respectively (distances expressed as fractions of the diameter of the map). constellations: The presentation is in globeview. Of the 47 Aratean constellations, 45 are presented in the pair of maps: Libra is presented by the claws of Scorpius and Corona Australis is missing. In the winter hemisphere is an unidentified image of two concentric rings south of the tail of Piscis.There is the additional illustration of the Aselli depicted on the shell of Cancer. Most constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Exceptions are Hercules, Ophiuchus, and Aquarius. descriptions (summer hemisphere):Argo Navis is drawn as a partly visible ship with two steering oars and sails attached to a mast. Aries has curly horns, a long tail, and a ring around his body. He is leaping to the west while looking back over his shoulder to the east.Auriga is nude to the waist and wears a long skirt. His knees are bent and he holds a flail with three thongs behind him in his western hand and has two small goats on his outstretched eastern arm. Cancer has two claws and six legs, and faces to the east (towards Leo). There are two animal heads on his shell, representing the Asses. Canis Maior is a running dog; his tail touches Navis. Canis Minor is a dog racing to the west. Centaurus is intersected by the autumnal equinoctial colure. Only his back haunches, leg and tail are presented. Cetus has been drawn as a sea monster with claws on his front legs, a beard, wings, and long furry ears. Corvus stands near the tail of Hydra, pecking at its body. Crater is drawn as a vase with handles on a raised foot, placed in the middle of Hydra. Draco passes between Auriga and Ursa Maior. It ends close to the eastern front leg of Ursa Maior. Eridanus starts

below the western foot of Orion and continues as a kind of a curl that is covered with patterns (waves?). Gemini are nude and stand facing each other, embracing with both arms. Hydra is drawn like a snake. Leo is a lion with a high upward tail. Lepus is a hare running to the west. Orion faces the west and wears a knee-length tunic. He has a cloak that is draped so that it completely covers his western arm and shoulder. He holds a long sword behind him, horizontally, in his eastern hand.There is a scabbard at his waist. Perseus is nude and striding to the west with his western leg forward. From the position of his hands, it seems that his body is twisted so that his upper torso faces away from the viewer. He holds the Gorgon’s head in his western hand in front of his body and a hooked sword in the eastern hand behind him. Taurus faces to the east and is depicted as the front half of a bull, with both of his front legs bent.Triangulum is a triangle placed above the head of Aries. Ursa Maior is above Cancer. He walks to the west and is drawn as a bear with a short tail. Virgo faces the viewer, wears a long dress, and is without wings. She holds a plant (an ear of corn?) in her hand. de scriptions (winter hemisphere): Andromeda is drawn upside-down. She is nude and her eastern arm is tied with some rope. Aquarius is nude apart from a conical hat. He holds with both hands an upturned urn that pours water into a stream flowing to the mouth of Piscis Austrinus. Aquila is standing upside down, facing to the east. Ara is drawn as a three-story structure with flames on top. Bootes is standing facing frontally, nude to the waist and wearing a short skirt, with a piece of cloth over his extended eastern arm. He holds a curved staff in his raised eastern hand. Capricornus faces to the west. It has two short horns and a corkscrew tail. His front legs are bent. Cassiopeia is upside-down and sits on a square seat with a low back. She is dressed in a long robe and wears no head covering and her arms are outstretched to either side. The bottom edge of her throne is cut off by the edge of the hemisphere. Centaurus is intersected by the autumnal equinoctial colure such that only his front half is presented. He is nude to the waist and bearded. He leaps to the east holding

208

Appendix 3.1 Catalogue of medieval hemispheres a dog-like animal by its heels in his outstretched western hand and a piece of cloth is draped over his eastern arm. Cepheus stands upside down with his arms outstretched. He is nude to the waist and does not wear a headdress. His feet rest on the north pole. Cetus is intersected by the autumnal equinoctial colure such that only his tail appears. Corona Borealis is drawn as two simple concentric rings. Cygnus is placed upside-down north of Aquila and faces to the west. Delphinus is drawn as a fish with his head cocked at an odd angle. Draco is intersected by the autumnal equinoctial colure such that only its head and half its body are presented. Hercules is upside down with his eastern foot touching Draco’s head. He is facing to the east.The orientation of his hands suggests that his back is facing the viewer. He is nude to the waist and kneels on his western knee. He stretches his eastern hand out in front of him towards Lyra and raises a club in his western hand behind his head. Lupus is a dog-like animal held by the eastern hand of Centaurus upside-down by its heels. Lyra is drawn as a lyre with a U-shaped frame. Ophiuchus is nude apart from a conical hat. Ophiuchus holds Serpens. Pegasus is placed upside down and is depicted as the front half of a horse, without any evidence of wings. Pisces are joined by a line at their mouths. They are swimming back to back and in opposite directions. Piscis Austrinus swims upside down to the east, with his mouth connected to the stream of Aquarius. Sagitta is grasped by the talons of Aquila, the arrow pointing to the west. Sagittarius is drawn as a centaur, holding a bow and arrow with his western hand before him. Scorpius is drawn as a scorpion with two front claws, eight legs, and a segmented tail. Serpens is a snake encircling the body of Ophiuchus. Ursa Minor is facing to the west and is drawn as a bear with a long tail. Unidentified: south of the tail of Piscis Austrinus is an image drawn as two concentric rings. comme nts: The image of a ring south of the tail of Piscis Austrinus could be either Corona Australis, which should be below the forefeet of Sagittarius, or more likely the configuration Anonymous II discussed in Section 2.3. For the manuscript, see McGurk 1973.

H2. ABERYSTWYTH, NATIONAL LIBRARY OF WALES, MS 735 C, f. 5r (Fig. 3.2) France (Limoges?), early eleventh century. The hemispheres appear among a miscellaneous collection of texts (ff . 1r–9v) with verses, and excerpts from Cicero and Macrobius. The hemispheres are arranged on one page with the summer hemisphere on top of the winter hemisphere. The two hemispheres are joined at their north poles such that in the summer hemisphere south is at the top and north at the bottom and in the winter hemisphere north is at the top and south at the bottom. cartog raphy: Each hemisphere is framed by a circle that represents the equinoctial colures. There are no internal divisions within the maps to signal the zodiacal band, the solstitial colures, or any of the other main celestial circles. constellations: The presentation is in globeview. Of the 47 Aratean constellations 42 are presented in these maps: Libra is presented by the claws of Scorpius and Ara, Corona Australis, Lupus, and Sagitta are missing. All the constellations seem to be presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged, but it is difficult to determine the orientation of the figures in many instances. descriptions (summer hemisphere): Argo Navis is drawn as a partly visible ship with two steering oars and sails attached to a mast. Aries is split between the two hemispheres by the vernal equinoctial colure. His back half appears on this map. Auriga is nude and has one small goat on his outstretched eastern arm and an unidentifiable object (possibly the kids) in the crook of his western arm. Bootes is split between the two hemispheres by the vernal equinoctial colure. The edge of the map intersects his chest so that his body below the chest and his legs appear in this hemisphere. Cancer has a round body, two claws and six legs, and faces to the east (towards Leo). Canis Maior is a dog running to the west. Canis Minor is a dog running to the west. Centaurus runs to the east and holds a bow in his hands. His forefeet and the bow are cut by the

209

The descriptive tradition in the Middle Ages autumnal equinoctial colure. Cetus is split between the two hemispheres by the vernal equinoctial colure. It is drawn as a sea monster with claws on his front legs, facing east. Corvus faces forward and stands near the tail of Hydra, pecking at its body. Crater is drawn like an egg-cup and is placed on the middle of Hydra. Draco is split between the two hemispheres by the autumnal equinoctial colure. Its tail curls around the head of Ursa Maior, ending near its forelegs. Eridanus is drawn as a kind of a curl which starts at the eastern shin of Orion and flows off the end of the map into a very large urn (?). Gemini are nude, face each other, embracing with both arms. Hydra is drawn like a snake. Its head is below the front feet of Leo and its tail below Virgo. Leo is lion with his head held high and his tail upwards. Lepus is a hare running to the west. Orion is nude, raising his western hand and holding a small stick or sword in his eastern hand. Perseus is nude and holds the Gorgon’s head in his outstretched southern hand. His other hand is cut off by the vernal equinoctial colure.Taurus is depicted as the front half of a bull, with both of his front legs bent. Triangulum is a triangle between Perseus and Aries’s back. Ursa Maior is drawn as a bear with a short tail. Virgo is nude and faces the viewer. She has no attributes. Her feet extend past the boundary of the sphere. descriptions (winter hemisphere): Andromeda is drawn upside-down. She is nude and faces the viewer. Aquarius is nude, faces the viewer and holds an urn upside-down in his northern hand.The stream pouring from it flows under his feet into the mouth of Pisces. Aquila is a bird flying northwards to the east. Aries is split between the two hemispheres by the vernal equinoctial colure. The front half of Aries appears here on the winter hemisphere, including his forelegs and his curly horns. Delphinus is drawn as a fish with his head facing towards the north. Bootes is split between the two hemispheres by the autumnal equinoctial colure so that both shoulders and his raised western hand appear in this hemisphere. He is upside down, naked and holds a knobbly club in his raised western hand. Capricornus has two short, curved horns and a corkscrew tail. His front legs are bent. Cassiopeia is upside-down and sits on a square

seat with a low back. She is dressed in a long robe and wears no head covering and her western arm is outstretched and her eastern arm raised. Cepheus stands upside-down, is nude and has his arms down by his side. His feet are close to the north pole. Cetus is split between the two hemispheres by the vernal equinoctial colure. Its tail appears below Aries. Corona Borealis is a simple circle. Cygnus is a bird flying to the south-west. Draco is split between the two hemispheres by the autumnal equinoctial colure. Its head forms an S-shape, with Ursa Minor being enclosed by the curl. Hercules is upside-down. His lower body is in profile, but his upper body faces the viewer. He raises his western hand at the elbow and holds a piece of cloth in his eastern hand in front of him. His head is west of that of Ophiuchus. Lyra is a lyre drawn with a U-shaped frame. Ophiuchus is nude and faces the viewer. The snake held by Ophiuchus encircles his body. Ophiuchus’s feet rest on the back of Scorpius. Pegasus is depicted as the front half of a horse, without any evidence of wings. He is upside-down. Pisces are joined by a line at their mouths. They are placed at oblique angles to one another. Piscis Austrinus is a fish swimming to the east. It is connected by his mouth to the stream of Aquarius. Sagittarius is a centaur, holding a bow and arrow with his western hand before him. Scorpius is drawn as a scorpion with two front claws, six legs, and a curved tail. Serpens is held by Ophiuchus and encircles his body. Ursa Minor is drawn as a bear with a short tail. comments: There are some illegible textual notations at the top, in the middle, and at the bottom of the folio. For the manuscript, see McGurk 1973.

H3. DRESDEN, SÄCHSISCHE LANDESBIBLIOTHEK—STAATSUND UNIVERSITÄTSBIBLIOTHEK, MS DC. 183, f. 8v (Fig. 3.3) West Francia, early ninth century. The hemispheres follow the text Descriptio duorum semispheriorum and precede the chapter Arati genus of the Revised Aratus latinus (ff. 13r–31r).The hemispheres

210

Appendix 3.1 Catalogue of medieval hemispheres are arranged on one page with the summer hemisphere on top of the winter hemisphere. In each hemisphere north is at the top and south at the bottom. cartog raphy: The circle that frames each hemisphere represents the equinoctial colures.The vertical line passing through the middle of each map and the north and south equatorial poles represents the solstitial colure. In the summer hemisphere there are five straight lines perpendicular to the summer solstitial colure representing the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle. When expressed as fractions of the diameter of the map, the distances of these five horizontal lines from the north pole measure 0.08, 0.18, 0.45, 0.58, and 0.80 respectively. In the winter hemisphere, there are only three straight lines perpendicular to the winter solstitial colure representing the ever-visible circle, the Tropic of Cancer, and the Equator. The lines corresponding to the Tropic of Capricorn and the ever-invisible circle are not drawn. When expressed as fractions of the diameter of the map, the distances of these three horizontal lines from the north pole measure 0.20, 0.41, and 0.62 respectively. In addition to these straight lines, there are in each hemisphere two arcs (or sections of circles) that represent the northern and southern boundaries of the zodiac. The zodiacal band is divided into twelve segments. In the summer hemisphere the upper and lower boundaries of the zodiac intersect the solstitial colure at distances of 0.18 and 0.39 from the north pole respectively (distances expressed as fractions of the diameter of the map). The line corresponding to theTropic of Cancer is tangential to the upper boundary of the zodiacal band. In the winter hemisphere the upper and lower boundaries of the zodiac of the winter hemisphere intersect the solstitial colure at distances of 0.13 and 0.34 from the south pole, respectively (distances expressed as fractions of the diameter of the map). constellations: The presentation is in globeview. Of the 47 Aratean constellations, only 36 constellations are present in these maps. In the summer hemisphere are non-Aratean additions of the ivy leaf presented as a vase-like object and an anomalous

depiction of Capricorn. The following constellations do not appear: Ara, Corona Australis, Corona Borealis, Cygnus, Eridanus, Lepus, Lyra, Perseus, Sagitta,Triangulum, and Ursa Minor. Most constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Exceptions are Ophiuchus, Sagittarius, and possibly Orion and Bootes. de scriptions (summer hemisphere): Argo Navis is drawn as a partly visible ship with a trefoil at one end, seven oars, a little steering house and two shields on deck. Aries has curled horns and a long tail. It is leaping to the west while looking back over his shoulder to the east. He has a lacy ring around his body. Auriga wears a short tunic and cape around his shoulders. He holds a sword in his western hand and raises his other hand. Cancer is facing to the west. He has eight legs and two eyes on his shell. His shell is scalloped on the eastern side. Canis Maior is a dog with a long tail, drawn as if he were running vertically up the summer solstitial colure. Canis Minor is a dog leaping to the east. Centaurus appears partly in this hemisphere. Only the upside-down rear half of the horse’s part is depicted, such that the rear hooves touch the ever-visible circle. Cetus is drawn as a sea monster with front legs and a cork-screw tail. Corvus is a bird facing westwards, placed on Hydra, near the middle. Crater is drawn as a goblet, placed on the middle of Hydra, below Leo. Draco is drawn as a complete snake. Gemini are nude, walking to the east with their inner arms resting on each other’s shoulders. Hydra is drawn like a snake with its head below Cancer and its tail belowVirgo. Leo is a lion, standing to the west with his tail upwards. Orion wears a knee-length tunic and a Phrygian cap. He holds a cloth in his western hand and a sword horizontally in his eastern hand. Taurus is depicted as the front half of a bull, facing to the east, with one front leg bent under and the other extended in front of him. Ursa Maior faces to the west and is drawn as a tiny bear. Virgo appears to be a male figure. He wears a long dress and holds a branch in his raised western hand. Ivy leaf is north of the Tropic of Cancer, above Leo. The object is shaped as a vase with water pouring

211

The descriptive tradition in the Middle Ages from the top. Anomalous Capricorn is below the Tropic of Capricorn and to the west of the summer solstitial colure and to the east of Cetus. It is drawn with one long horn, a beard, and a corkscrew tail. descriptions (winter hemisphere): Andromeda is upside-down and dressed in a long robe with sleeves that hang down from her elbows like tubes. Her arms are outstretched. Aquarius is nude apart from a cape around his shoulders. He holds an upturned urn in front of him that pours water into a stream. Aquila is standing upside down and faces to the east with wings spread out. Bootes is dressed in a tunic and has a cloth covering his western arm. He holds a sword in his eastern hand. Capricornus faces west, has a single horn and a tail with a curl at the end. Cassiopeia is upside-down, wears a long dress and sits on a seat with outstretched hands. On both sides, there are branches or trees more commonly found accompanying Andromeda. Centaurus stands to the east, holding Lupus at its feet in his outstretched eastern hand. In his other hand he holds a spear at the end of which is another animal hanging by its feet. Cepheus is upside down and has his arms raised. He wears a short tunic and a long cloak around his shoulders. Delphinus is a wormlike creature, with its head facing toward the south. Draco is presented by a long tail-part, north of the ever-visible circle. Hercules is upside-down. He is kneeling on his western knee. He is nude but has a cloak over one of his shoulders.The cloak covers his eastern arm so that is looks like a piece of cloth. He holds a club in his western hand behind him. Libra is drawn as a figure in a long robe, holding a pair of scales in the western hand. Lupus is an animal held at its feet by the outstretched eastern hand of Centaurus. Ophiuchus is confined to the segment of the zodiacal band holding Scorpius. He stands with both feet on the back of Scorpius. Serpens wraps around his waist and curls through his legs. Pegasus is depicted as the front half of a winged horse, upside-down, facing west. Pisces are swimming back-to-back in the same direction and are joined by a line at their mouths. Piscis Austrinus swims to the east, with his mouth connected to a stream,

which does not connect to Aquarius. Sagittarius is a nude male archer, standing to the west, holding a bow with his western hand in front of his body. Scorpius is drawn as a scorpion, with two claws and a curved tail. Ophiuchus is standing on his back. Serpens is held by Ophiuchus and its head faces him. comments: For the manuscript, (damaged during World War II), see Schnorr von Carolsfield 1882, Band I, pp. 334–5.

H4. MONZA, BIBLIOTECA CAPITOLARE, MS B 24/163 (228), f. 67r (Fig. 3.4) Lombardy (Monza?), twelfth century. The map follows the imperfect ending of Boethius, In topica Ciceronis. It consists only of the winter hemisphere on one page with north at the top and south at the bottom. cartog raphy: The circle that frames the map represents the equinoctial colures. The vertical line passing through the middle of the map that ends at the ever-visible and ever-invisible circles represents the winter solstitial colure. Perpendicular to this colure, there are five straight lines representing the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle. When expressed as fractions of the diameter of the map, the distances of these five horizontal lines from the north pole measure 0.14, 0.31, 0.50, 0.71, and 0.87, respectively. In addition to these straight lines, there are two arcs (or sections of circles), which represent the northern and southern boundaries of the zodiac. The zodiacal band is not divided into segments.The upper and lower boundaries of the zodiac intersect the solstitial colure at distances from the south pole of 0.26 and 0.35, respectively (with distances expressed as fractions of the diameter of the map). constellations: The presentation is in globeview. Of the Aratean constellations usually presented in the winter hemisphere Sagitta are missing. Most constellations are presented face-on, with the left and

212

Appendix 3.1 Catalogue of medieval hemispheres right characteristics as defined by Hipparchus’s rule interchanged. Exceptions are Hercules and Aquarius. descriptions (winter hemisphere): Andromeda is upside-down. Her eastern foot passes over the edge of the map. Although she is nude, there are no evident signs of being either male or female.She faces the viewer with her arms outstretched on either side. She has no attributes. Her head touches the body of Pegasus. Aquarius is nude except for a cape around his shoulders. He holds an upturned urn in his extended eastern hand in front of him that pours water. Aquila is a bird flying to the west with its head towards the north. Ara is drawn as a footed cup with five tongues of flame coming from it.Aries is intersected by the vernal equinoctial colure such that only his front part with his head, front legs, and shoulders appears just west of the boundary of the hemisphere. He runs to the west and turns his head backwards to the east. His legs are stretched in front of him as if he were leaping. Bootes is intersected by the autumnal equinoctial colure such that only his upper body appears just east of the boundary of the hemisphere. He is upside-down. He is dressed in a toga and holds a knobbly club in his raised western hand. Capricornus faces west, has a pair of short, curved horns and a corkscrew tail. Cassiopeia appears upsidedown. She wears a long dress and is shown in a seated posture, but there is no evidence of a throne. She stretches out her arms on either side. Centaurus is intersected by the autumnal equinoctial colure such that only his eastern hand holding Lupus appears just east of the boundary of the hemisphere. Cepheus appears upside-down with his arms held down by his sides. His feet extend over the edge of the map outside of its outer perimeter. He is nude and faces the viewer. Cetus is intersected by the autumnal equinoctial colure such that the large curl of its tail appears to the west of the boundary of the map. Corona Borealis is represented by a leafy circlet. Corona Australis is in front of Sagittarius’s feet. It is represented by a leafy circlet. Cygnus is upside-down with wings spread out and feet extended to the east. Delphinus has a single large horn. Its belly is upwards and its tail touches the Equator. Draco is north of the ever-visible circle except for its head which is just below it. Hercules appears upside-

down and kneels towards the east on the ever-visible circle. The Tropic of Cancer passes through his raised club and the top of his head. His lower body is in profile and his upper body faces away from the viewer. He is nude, kneels on his western knee and holds a club in his western hand behind his head. Between his legs, below his eastern hand, is something that may be a part of a lion’s skin. Lyra is presented as an upside down lyre. Lupus appears horizontally in the hand of Centaurus with its feet pointing upwards. Ophiuchus is nude and faces the viewer. He holds Serpens so that it makes an X-shape across his chest. Both his feet rest on the back of Scorpius. Pegasus appears upside down as the front half of a winged horse, facing to the west. Its body ends in a curl. Perseus is intersected by the autumnal equinoctial colure such that only his western arm appears west of the boundary of the hemisphere. He holds a knobbly club. Pisces is in the zodiacal band. Only one of the fishes is visible, swimming to the west.There is a feature south of the zodiacal band and cut by the vernal equinoctial colure which may represent the tail of the other fish. Piscis Austrinus is depicted as an upsidedown fish and swims to the east. Sagittarius is presented as an archer.The figure is holding an arrow and bow with his western hand to the west of his body. He is nude to the waist, but wears a long skirt and faces the viewer. Scorpius is to the east of the autumnal equinoctial colure. It is drawn as a scorpion with two large claws and a curl in its tail. Ophiuchus rests both feet on his back. Serpens is a snake held by Ophiuchus. Its head faces upwards. Ursa Minor is a small bear nestled within the curve of Draco’s body. comments:The map is on the last folio, but it is not an insertion. It is part of a quire of 12 of which the second leaf is missing. This page presumably held the summer hemisphere. For the manuscript, see McGurk 1966, p. 52.

H5. PARIS, BIBLIOTHÈQUE NATIONALE DE FRANCE, MS lat. 12957, ff . 60v–61r (Fig. 3.5a–b) West Francia (Corbie?), early ninth century. The hemispheres follow the text Descriptio duorum semispheriorum (f. 60v) and precede the chapter Arati genus (ff.

213

The descriptive tradition in the Middle Ages 61r–61v) of the Revised Aratus latinus (ff . 57r–74v). The hemispheres are arranged on two pages (f. 60v: winter hemisphere, f. 61r: summer hemisphere) with north at the top and south at the bottom of both hemispheres. cartog raphy: Each hemisphere is framed by a circle that represents the equinoctial colures.The vertical line passing through the middle of the maps and the north and south equatorial poles represents the solstitial colure. In the summer hemisphere there are four straight lines perpendicular to the colure representing the ever-visible circle, the Tropic of Cancer, the Tropic of Capricorn, and the ever-invisible circle.The line corresponding to the Equator is oblique to the colure.When expressed as fractions of the diameter of the map, the distances of the four horizontal lines from the north pole measure 0.09, 0.22, 0.61, and 0.81, respectively.The oblique Equator intersects the colure at a distance of 0.45 from the north pole. In the winter hemisphere there are four straight lines perpendicular to the colure, representing the ever-visible circle, the Tropic of Cancer, the Equator, and the Tropic of Capricorn.The line corresponding to the ever-invisible circle is not drawn.When expressed as fractions of the diameter of the map, the distances of these four horizontal lines from the north pole measure 0.17, 0.39, 0.61, and 0.81, respectively. In addition to these straight lines, there are in each hemisphere two arcs (or rather sections of circles), which represent the northern and southern boundaries of the zodiac.The zodiacal band is divided into 12 segments. In the summer hemisphere the upper and lower boundaries of the zodiac intersect the summer solstitial colure at distances from the north pole of 0.22 and 0.40, respectively (with distances expressed as fractions of the diameter of the map). The line corresponding to the Tropic of Cancer is tangential to the northern boundary of the zodiacal band. In the winter hemisphere the upper and lower boundaries of the zodiac intersect the winter solstitial colure at distances from the south pole of 0.19 and 0.35, respectively (with distances expressed as fractions of the diameter of the map). The line corresponding to the Tropic of Capricorn is tangential to the southern boundary of the zodiacal band.

constellations: The presentation is in globeview. Of the 47 Aratean constellations, only 38 constellations are present in these maps. In the summer hemisphere are non-Aratean additions of the ivy leaf and an anomalous depiction of Capricorn. The following constellations do not appear: Corona Australis, Corona Borealis, Cygnus, Eridanus, Lepus, Lyra, Sagitta, Scorpius, and Triangulum. Most constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Exceptions are Gemini, Orion, and Sagittarius. descriptions (summer hemisphere): Argo Navis is drawn as a partly visible ship with an ornament at the bow, six normal oars, a little steering house, and two shields on deck. From a mast sails or vanes blow to the west. Aries has horns and a long tail. It is leaping to the west while looking back over his shoulder to the east. Auriga wears a tunic and cape around his shoulders. He holds a sword in his western hand and raises his other hand. Cancer is facing the west. He has two claws, six legs, and two eyes on his shell. His shell is scalloped on the eastern side. Canis Maior is a dog drawn as if he were running vertically up the summer solstitial colure. He has a long tail. Canis Minor is a dog, leaping to the west. Centaurus appears partly on this hemisphere. Only the rear half of the horse’s part is depicted. Cetus has been drawn as a sea monster with a dog’s face, front legs, and a corkscrew tail. Corvus is a bird facing westwards, placed on Hydra near the tail. Crater is drawn as a goblet, placed near the middle of Hydra, below Leo. Draco is drawn as a complete snake. Gemini are nude, walking to the west with their inner arms resting on each other. They are seen from the rear. Hydra is drawn like a snake, with its head below Cancer and its tail below Virgo. Leo is a lion, standing to the west with his tail upwards. Orion is seen from the rear. He wears a knee-length tunic. A cape covers his western shoulder, arm, and hand. He holds a long sword in his eastern hand. Perseus is nude, kneeling to the west, holding Medusa’s head in his western hand in front of his body and a raised sword in his other hand behind him. Taurus is depicted as the front half of a bull,

214

Appendix 3.1 Catalogue of medieval hemispheres facing to the east, with one front leg extended in front of him. Ursa Maior is drawn as a jumping hare with a short tail.Virgo wears a long dress and holds something (a branch?) in her raised western hand. Ivy leaf is shaped as a leaf. It is above Leo.Anomalous Capricorn is to the east of Cetus. It is drawn with one long horn, a beard, and a corkscrew tail. It faces west and its tail touches the summer solstitial colure. descriptions (winter hemisphere): Andromeda is upside-down and dressed in a long robe with sleeves that hang down from her elbows like tubes. Her arms are outstretched and her hands rest on piles of rock or trees on both sides. Aquarius is nude apart from a cape around his shoulders. He holds an upturned urn in front of him that pours water into a stream flowing to the mouth of Piscis Austrinus. Aquila is standing upside-down and faces to the east with wings spread out.Ara has an unfamiliar structure consisting of two rows of three small squares and a vertical line connecting the two rows. Bootes is dressed in a tunic, has a cape covering his western arm, and holds a sword in his raised eastern hand. Capricornus faces west, has a single horn and a tail with a curl at the end. Cassiopeia is upside-down, wears a long dress and sits on a square seat with outstretched hands. Centaurus is cut by the boundary of the map and passes through his belly and rear part. He holds Lupus at its feet in his outstretched eastern hand. In his other hand he holds a spear at the end of which another animal is hanging by its feet. Cepheus is to the east of the winter solstitial colure. He is placed upside-down and so that the ever-visible circle passes through his head and hands. Cepheus has his arms raised. He wears a tunic and a long cloak around his shoulders. His feet are on the belly of Ursa Minor. Cetus is cut by the boundary of the map and his rear part is presented as a snaky tail. Delphinus is a worm-like animal with its head facing towards the south. Draco is partly shown by the greater part of the long tail-part of a snake. Hercules is depicted upside-down. He is nude but has a cloak over one of his shoulders.The cloak covers his eastern arm so that is looks like a piece of cloth. He holds a club in his western hand behind him. Libra is drawn as a (female) figure in a long robe, holding a pair of

scales in its western hand. Lupus is an animal, held at its feet by the outstretched western hand of Centaurus. Ophiuchus is nude and confined to the eighth segment of the zodiacal band (usually but not here holding Scorpius). He holds Serpens which wraps around his waist. Pegasus is depicted as the front half of a winged horse, upside-down, facing west. Pisces are swimming back-to-back in the opposite direction and are joined by a line at their mouths. Piscis Austrinus swims to the east, with his mouth connected to the stream of Aquarius. Sagittarius is a nude male archer, facing away from the viewer, holding an arrow and bow with his western hand in front of his body. Serpens wraps around the waist of Ophiuchus who holds it by his hands. Ursa Minor is depicted as an animal underneath the feet of Cepheus. comments: For the manuscript, see Le Bourdellès 1985, pp. 75–6.

H6. PARIS, BIBLIOTHÈQUE NATIONALE DE FRANCE, MS nouv. acq. lat. 1614, f. 81v (Fig. 3.6) West Francia (Tours?), 9th century. The hemispheres follow the text Descriptio duorum semispheriorum (ff. 81r–81v) and precede the chapter Arati genus (ff. 82r–82v) of the Revised Aratus latinus (ff . 77r–93v).The hemispheres are arranged on one page with the summer hemisphere on top of the winter hemisphere. In each hemisphere north is at the top and south at the bottom. cartog raphy: Each hemisphere is framed by a pair of concentric circles that represent the equinoctial colures.A pair of close-set vertical lines passes through the middle of each hemisphere and the north and south equatorial poles, representing the solstitial colure. In the summer hemisphere there are four straight lines (all as double lines) perpendicular to this colure, representing the ever-visible circle, the Equator, the Tropic of Capricorn, and the ever-invisible circle.The line corresponding to the Tropic of Cancer is not drawn.When expressed as fractions of the diameter of the map, the distances of the four horizontal

215

The descriptive tradition in the Middle Ages lines from the north pole measure 0.13, 0.51, 0.68, and 0.85 respectively. In the winter hemisphere there are three straight lines (all double lines) perpendicular to the colure, representing the ever-visible circle, the Tropic of Cancer, and the Equator. The lines corresponding to the Tropic of Capricorn and the everinvisible circle are not drawn. When expressed as fractions of the diameter of the map, the distances of these three horizontal lines from the north pole measure 0.17, 0.33, and 0.51 respectively. In addition to these straight lines, there are in each hemisphere two arcs (or rather sections of circles also drawn as double lines), which represent the northern and southern boundaries of the zodiac. The zodiacal band is divided into twelve segments.The upper and lower boundaries of the zodiac in the summer hemisphere intersect the summer solstitial colure at distances from the north pole of 0.26 and 0.44, respectively (with distances expressed as fractions of the diameter of the map).The upper and lower boundaries of the zodiac in the winter hemisphere intersect the winter solstitial colure at distances from the south pole of 0.26 and 0.44, respectively (with distances expressed as fractions of the diameter of the map). conste llations: The presentation is in globeview. Of the 47 Aratean constellations, 37 are present in these maps. In the summer hemisphere are nonAratean additions of the ivy leaf and an anomalous depiction of Capricorn. The following constellations do not appear: Ara, Corona Borealis, Corona Australis, Cygnus, Eridanus, Lepus, Lyra, Sagitta, Scorpius,andTriangulum.Most constellations are presented face-on,with the left and right characteristics as defined by Hipparchus’s rule interchanged. An exception is Sagittarius. descriptions (summer hemisphere):Argo Navis is drawn as a partly visible ship with the head of a dog at the bow looking east, one steering and six normal oars, a little steering house, and two shields on deck. From a mast sails or vanes blow to the west. Aries has horns, a long tail and a ring around his body. He is leaping to the west while looking back over his shoulder to the east. Auriga wears a long dress. He holds a sword in his western hand and raises his other hand.

Cancer is facing to the west. He has two claws, six legs, and two eyes on his shell. His shell is scalloped on the eastern side. Canis Maior is a dog drawn as if he were running vertically up the summer solstitial colure. Canis Minor is a dog leaping to the west. Centaurus appears partly in this hemisphere, only the rear half of the horse’s part is depicted. Cetus has been drawn as a sea monster with a dog’s face, front legs, and a cork-screw tail. Corvus is a bird facing westward, placed on Hydra, near the middle. Crater is drawn as a goblet, placed not far from the head of Hydra. Draco is drawn as a complete snake. Gemini are nude, walking to the west with the eastern twin resting his hand on the other’s shoulder and the western twin apparently grabbing the other’s genitals. They are seen face on. Hydra is drawn like a snake. Its head is below Cancer and its tail belowVirgo. Leo is a lion, standing to the west with his tail down. Orion wears a knee-length tunic. A cape covers his western shoulder and arm. He holds a long sword in his eastern hand and an animal skin covers his western hand. Perseus is nude, holds Medusa’s head in his western hand in front of his body and a raised sword in his other hand behind him. Taurus is depicted as the front half of a bull, facing to the east, with both front legs extended in front of him. Ursa Maior is drawn as a tiny bear with a tail.Virgo wears a long dress and holds something (branches?) in her raised western hand. Ivy leaf is above Leo. It is shaped as a leaf. Anomalous Capricorn is to the east of Cetus. It is drawn with two horns and a corkscrew tail. It faces west and its tail touches the summer solstitial colure and the Tropic of Capricorn. descriptions (winter hemisphere): Andromeda is upside-down and dressed in a long robe with sleeves that hang down like tubes. Her arms are outstretched and her hands rest on piles of rock or trees on both sides. Aquarius is nude apart from a cape around his shoulders. He holds an upturned urn in front of him that pours water into a stream flowing to the mouth of Piscis Austrinus. Aquila is standing upside-down, and faces to the east with wings spread out. Bootes is dressed in a tunic and a cloth covers his western arm. He holds a sword in his raised eastern hand.

216

Appendix 3.1 Catalogue of medieval hemispheres Capricornus faces west, has a single horn and a tail with a curl at the end. Cassiopeia is upside-down and sits on a seat with outstretched hands. Centaurus stands to the east, holding Lupus by its feet in his outstretched eastern hand. In his other hand he holds a spear at the end of which another animal is hanging by its feet. Cepheus is placed upside-down and has his arms raised. He wears a tunic and a cape around his shoulders. His feet are on the belly of Ursa Minor. Cetus appears with his rear part on this hemisphere.This rear part is depicted as a snaky tail. Delphinus is drawn as a worm-like animal with its head facing towards the south. Draco is presented by the tail part of a snake. Hercules is depicted upside-down. He is nude but has a cloak over one of his shoulders. The cloak covers his eastern arm. He holds a lion’s skin in his eastern hand in front of him and a club in his western hand behind him. Libra is drawn as a figure in a long robe, holding a pair of scales in its western hand. Lupus is held at its feet by the outstretched eastern hand of Centaurus. Ophiuchus is confined to the eighth segment of the zodiacal band (usually but not here holding Scorpius). The man holds Serpens which wraps around his waist. Pegasus is depicted as the front half of a (probably) winged horse, upside-down. Pisces are swimming back-to-back in the opposite direction and are joined by a line at their mouths. Piscis Austrinus swims to the east, with his mouth connected to the stream of Aquarius. Sagittarius is a nude male figure, facing away from the viewer, holding an arrow and bow with his western hand in front of his body. Serpens wraps around the waist of Ophiuchus who holds it by his hands. Ursa Minor occupies the small space between the feet of Cepheus and the northern boundary of the hemisphere, to the east of the winter solstitial colure. It is depicted as a scorpion. comments: The text above the maps is the last line of Descriptio duorum semispheriorum: aliud semispherium. ipsa enim in medio iacet duobus semispheriis. There is a hole in the page above Leo. In the picture published by Cumont 1916, p. 12, fig. 4 and McGurk 1981, p. 327 this hole has been filled in.

H7. ST GALL, STIFTSBIBLIOTHEK, MS 250, p. 462 (Fig. 3.7) St Gall, last quarter of the ninth century. The hemispheres follow the text Descriptio duorum semispheriorum (pp. 461–62) and precede the chapter Arati genus (pp. 463–64) of the Revised Aratus latinus (pp. 447–522). The hemispheres are arranged on one page with the summer hemisphere on top of the winter hemisphere. In each hemisphere north is at the top and south at the bottom. The drawings are executed in brown ink.There are also holes through the sheet at the centre of both circles (equinoctial colures), indicating compass points. cartog raphy: Each hemisphere is framed by a circle that represents the equinoctial colures.The vertical line passing through the middle of the maps and the north and south equatorial poles represents the solstitial colure. In the summer hemisphere there are five straight lines perpendicular to the colure representing the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the everinvisible circle. When expressed as fractions of the diameter of the map, the distances of the five horizontal lines from the north pole measure 0.06, 0.19, 0.43, 0.65, and 0.92 respectively. In the winter hemisphere there are three straight lines perpendicular to the colure, representing the ever-visible circle, the Tropic of Cancer, and the Equator. The lines corresponding to the Tropic of Capricorn and the everinvisible circle are not drawn. When expressed as fractions of the diameter of the map, the distances of these three horizontal lines from the north pole measure 0.17, 0.41, and 0.56 respectively. In addition to these straight lines, there are in each hemisphere two arcs (or rather sections of circles), which represent the northern and southern boundaries of the zodiacal band. The zodiacal band is divided into 12 segments. The upper and lower boundaries of the zodiacal band in the summer hemisphere intersect the solstitial colure at distances of 0.19 and 0.39 from the north pole respectively (with distances expressed as fractions of the diameter of the map).The line corresponding to the Tropic of Cancer is tangential to

217

The descriptive tradition in the Middle Ages the northern boundary of the zodiacal band. The upper and lower boundaries of the zodiacal band in the winter hemisphere intersect the winter solstitial colure at distances from the south pole of 0.16 and 0.38, respectively (with distances expressed as fractions of the diameter of the map). constellations: The presentation is in globeview. Of the 47 Aratean constellations, 38 are presented in the maps. In the summer hemisphere are non-Aratean additions of the ivy leaf presented as a vase-like object and an anomalous depiction of Capricorn.The following constellations do not appear: Ara, Corona Borealis, Corona Australis, Cygnus, Eridanus, Lepus, Lyra, Sagitta, and Triangulum. Most constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Orion is an exception. descriptions (summer hemisphere): Argo Navis is drawn as a partly visible ship with a dog’s head at the bow, seven normal oars, a little steering house, and two shields on deck. From a mast sails or vanes seem to blow to the west.Aries has curled horns, a long tail, and a ring around his body. It is leaping to the west while looking back over his shoulder to the east. Auriga wears a tunic and cape around his shoulders. He holds a sword in his western hand and raises his other hand. Cancer is drawn as a crawfish facing the west. There are six legs and two eyes on his shell. Canis Maior is drawn as a dog with a short tail running vertically up the summer solstitial colure. Canis Minor is a large-sized dog leaping to the west. Centaurus appears with his rear part on this hemisphere. The boundary circle cuts through the middle of the horse’s body and the summer solstitial colure cuts off its hindfeet. Cetus has been drawn as a sea monster with a lion’s face, front legs, and a curl in its body. Corvus is a bird facing westwards, placed on the rear half of Hydra’s body. Crater is drawn as a water pot, placed on the front half of Hydra’s body. Draco is drawn as a complete snake. The border of the hemisphere passes through the tip of his tail. Gemini are dressed in short tunics and long capes and stand facing each other, gesturing towards each other with both hands. They are seen face on. Hydra is drawn

like a snake, with its head below Cancer and its tail below Virgo. Leo is a lion, standing to the west with his tail upwards. Orion is seen from the rear. He wears a knee-length tunic.A cape covers his western shoulder, arm, and hand. He holds a long sword in his eastern hand. Perseus wears a tunic and holds Medusa’s head in his western hand in front of his body and a raised sword in his eastern hand. Taurus is depicted facing to the east, as a complete bull with his tail upwards. Ursa Maior is drawn as a tiny bear with a short tail.Virgo wears a long dress and holds a sword in the raised right (western) hand. Ivy leaf stands on the Tropic of Cancer, and is shaped as a vase. Anomalous Capricorn is to the east of Cetus. It is drawn with two long horns and a curl in its tail. descriptions (winter hemisphere): Andromeda is upside-down and dressed in a long robe with sleeves that hang down from her elbows like a scarf. Her arms are outstretched and her hands rest on piles of rock on both sides. Aquarius wears a short tunic. He holds an upturned urn from which water streams. Aquila is standing upside-down, and faces to the east with wings spread out. Bootes faces the viewer. He wears a cloak covering his western shoulder and arm. He holds a sword in his raised eastern hand. Capricornus has two horns and a tail with a curl at the end. Cassiopeia is upside-down, wears a hat and a long dress, and sits on a square seat with outstretched hands. Centaurus holds Lupus at its feet in his outstretched eastern hand. In his other hand he holds a spear at the end of which another animal is hanging. Cepheus is placed upside-down. He raises his arms and wears a hat, a tunic, and a long cloak around his shoulders. His feet are on the belly of Ursa Minor. Cetus appears with his rear part in this hemisphere.This rear part is depicted as a huge snaky tail. Delphinus is drawn as a worm-like animal with its head facing towards the south. Draco appears with his rear tail-part in this hemisphere. Hercules is depicted upside-down and is nude save a cloak.The cloak covers his eastern arm so that it hangs down over his eastern arm like a piece of cloth. He holds a club in his western hand behind him. Libra is drawn as a figure in a long robe, holding a pair of scales in its western hand. Lupus in held at its

218

Appendix 3.1 Catalogue of medieval hemispheres feet by the outstretched western hand of Centaurus. Ophiuchus is confined to the zodiacal segment holding Scorpius.The man stands on the back of Scorpius facing the viewer and holds Serpens which wraps around his waist. Pegasus is depicted as the front half of a winged horse, upside-down. Pisces are swimming back-to-back in the opposite direction and are joined by a line at their mouths. Piscis Austrinus swims to the north-east. Sagittarius is a nude satyr, walking to the west and holding an arrow and bow with his western hand in front of his body. Scorpius is drawn as a scorpion with two claws and a curved tail. It faces to the west with Ophiuchus standing on his back. Serpens wraps around the waist of Ophiuchus. Ursa Minor is an animal occupying the space between the feet of Cepheus and the northern boundary of the hemisphere. comments: The text above the maps is the last lines of Descriptio duorum semispheriorum: habet quod subtus terra longitudinem aliud semispherium. ipsa enim in medio iacet duobus semispheriis. For the manuscript, see Von Euw 2008,Vol. 1, Kat. Nr. 120, pp. 449–54.

H8. ST GALL, STIFTSBIBLIOTHEK , MS 902, p. 76 (Fig. 3.8) St Gall, first and second half of the ninth century. The hemispheres follow the text Descriptio duorum semispheriorum (p. 75) and precede the chapter Arati genus (p. 77) of the Revised Aratus latinus (pp. 69–104). The hemispheres are arranged on one page with the summer hemisphere on top of the winter hemisphere. In each hemisphere north is at the top and south at the bottom.The bottom of the page has been cut so that nearly everything beneath the southern boundary of the zodiacal band in the winter hemisphere is lost. The drawings are executed in brown ink.There are also holes through the sheet at the centre of both circles (equinoctial colures), indicating compass points. cartog raphy: Each hemisphere is framed by a circle that represents the equinoctial colures.The vertical line passing through the middle of the maps and the north and south equatorial poles represent the

solsitial colure. In the summer hemisphere there are five straight lines perpendicular to the colure representing the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle. When expressed as fractions of the diameter of the map, the distances of the five horizontal lines from the north pole measure 0.06, 0.18, 0.45, 0.69, and 0.90 respectively. In the winter hemisphere there are three straight lines perpendicular to the colure, representing the ever-visible circle, the Tropic of Cancer, and the Equator. The lines corresponding to the Tropic of Capricorn and the ever-invisible circle are not drawn. When expressed as fractions of the diameter of the map, the distances of these three horizontal lines from the north pole measure 0.20, 0.42, and 0.66 respectively. In addition to these straight lines, there are in each hemisphere two arcs (or rather sections of circles), which represent the northern and southern boundaries of the zodiacal band.The zodiacal band is divided into 12 segments.The upper and lower boundaries of the zodiac in the summer hemisphere intersect the solstitial colure at distances of 0.18 and 0.40 from the north pole respectively (with distances expressed as fractions of the diameter of the map). The line corresponding to the Tropic of Cancer is tangential to the northern boundary of the zodiacal band. The upper and lower boundaries of the zodiac in the winter hemisphere intersect the winter solstitial colure at distances from the south pole of 0.11 and 0.28 respectively (with distances expressed as fractions of the diameter of the map). constellations: The presentation is in globeview. Of the 47 Aratean constellations, 35 are presented in the maps. In the summer hemisphere are non-Aratean additions of the ivy leaf presented as a vase-like object and an anomalous depiction of Capricorn. The following constellations do not appear: Ara, Corona Borealis, Corona Australis, Cygnus, Eridanus, Lepus, Lyra, Sagitta, and Triangulum. Centaurus, Lupus, and Piscis Austrinus have been cut off by the edge of the page. In addition to these constellations, there is also the image of a vase-like object in the summer hemisphere; and an anomalous

219

The descriptive tradition in the Middle Ages Capricorn and a snaky tail in the winter hemisphere. Most constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Exceptions are Orion, Sagittarius, and one of the Gemini. descriptions (summer hemisphere): Argo Navis is drawn as a partly visible ship with a dog’s head at the bow, seven normal oars, a little steering house, and two shields on deck. From a mast sails or vanes blow to the west.Aries has outward horns, a long tail, and a ring around his body. It is leaping to the west while looking back over his shoulder to the east. Auriga wears a tunic and cape around his shoulders. He holds a sword in his western hand and raises his other hand. Cancer is facing to the west. He has two claws, six legs, and two eyes on his shell. His shell is scalloped on the eastern side. Canis Maior is a dog with a long tail running vertically up the summer solstitial colure. Canis Minor is a leaping dog with a long tail. Centaurus appears with his rear part on this hemisphere. The boundary circle cuts through the middle of the horse’s body and the solstitial colure cuts of his hindlegs. Cetus has been drawn as a sea monster with a lion’s face, front legs, and a curl in its body. Corvus is a bird facing westwards, placed on the rear half of Hydra’s body. Crater is drawn as a water pot, placed on the front half of Hydra’s body. Draco is drawn as a complete snake. Gemini are nude and walk to the west. The western twin is a male shown in rear view, the eastern is a female figure in front view. They stretch their inner arms towards each other. Hydra is drawn like a snake, with its head below Cancer and its tail below Virgo. Leo is a lion, standing to the west with his tail upwards. Orion is seen from the rear. He wears a knee-length tunic. A cape covers his western shoulder, arm, and hand. He holds a sword in his eastern hand. Perseus wears a tunic and holds Medusa’s head in his western hand in front of his body and a raised sword in his other hand. Taurus is depicted as the front half of a bull with both front legs bent under. Ursa Maior is drawn as a tiny bear with a short tail.Virgo is drawn as a male figure. He wears a tunic and holds a sword in the raised western hand. Ivy Leaf stands on the Tropic of

Cancer. The object is shaped as a vase. Anomalous Capricorn is to the east of Cetus. It is drawn with two long horns and a curl in its tail which touches the summer solstitial colure. descriptions (winter hemisphere): Andromeda is upside-down and dressed in a long robe with sleeves that hang down from her elbows like tubes. Her arms are outstretched and her hands rest on piles of rock on both sides. Aquarius wears a short tunic. He holds an upturned urn from which water streams. Aquila is standing upside-down, and faces to the east. Bootes faces the viewer. He wears a cloak covering his western shoulder and arm. He holds a sword in his raised eastern hand. His eastern foot touches the Tropic of Cancer. Capricornus has two horns and a tail with a curl at the end. Cassiopeia is upside-down, wears a hat and a long dress, and sits on a square seat with outstretched hands. Cepheus is placed upside-down with his arms raised. He wears a hat, a tunic, and a long cloak around his shoulders. His feet are on the belly of Ursa Minor. Cetus appears with his rear part on this hemisphere, below Aquarius.The rear part is depicted as a huge snaky tail. Delphinus is drawn as a wormlike animal with its head facing towards the south. Draco is presented as the rear tail-part of a snake. Hercules is depicted upside-down. He is nude save a cloak.The cloak covers his eastern arm so that is hangs down over his eastern arm like a piece of cloth. He holds a club in his western hand behind him. Libra is drawn as a female figure in a long robe, holding a pair of scales in her western hand. Ophiuchus is confined to the zodiacal segment holding Scorpius. The man stands on the back of Scorpius facing the viewer and holds Serpens which wraps around his waist. Pegasus is depicted as the front half of a winged horse, upsidedown. Pisces are swimming with their backs up in the opposite direction and are joined by a line at their mouths. Sagittarius is drawn as a satyr, holding an arrow and bow with his western hand in front of his body. Scorpius is drawn as a scorpion with two claws and a curved tail, with Ophiuchus standing on his back. Serpens wraps around the waist of Ophiuchus. Ursa Minor is an animal occupying the space between the feet of Cepheus and the

220

Appendix 3.1 Catalogue of medieval hemispheres northern boundary of the hemisphere, to the east of the winter solstitial colure. comments: Centaurus, Lupus, and Piscis Austrinus have been cut off by the edge of the page.The bottom of the page has been cut so that a number of constellations in the winter hemisphere are lost. This loss must have occurred after the manuscript was copied into St Gall 250 as this part of the winter hemisphere is preserved in the later drawings. For the manuscript, see Von Euw 2008,Vol. 1, Kat. Nr. 119, pp. 44–449.

H9. VATICAN CITY, BIBLIOTECA APOSTOLICA VATICANA, MS Reg. lat. 1324, f. 23v (Fig. 3.9) France or Italy, fifteenth century. The hemispheres follow the text Descriptio duorum semispheriorum (f. 23r) and precede a blank page (f. 24r) followed by the chapter Arati genus (f. 24v) of the Revised Aratus latinus (ff. 21v–35r). The hemispheres are arranged on one page with the summer hemisphere on top of the winter hemisphere. In each hemisphere north is at the top and south at the bottom.The hemispheres drawn in pale grey-brown pen are very highly coloured in pink, blue, and green. Each section of the map has a different coloured background and the figures are coordinated to stand out from these. cartog raphy: The circle that frames each hemisphere represents the equinoctial colures. The vertical line passing through the middle of each map and the north and south equatorial poles represents the solstitial colure. In the summer hemisphere there are four straight lines perpendicular to the summer solstitial colure representing the Tropic of Cancer, the Equator, the Tropic of Capricorn and the ever-invisible circle.The line corresponding to the ever-visible circle is not drawn. When expressed as fractions of the diameter of the map, the distances of the four horizontal lines from the north pole measure 0.20, 0.41, 0.61, and 0.80, respectively. In the winter hemisphere, there are four straight lines perpendicular to the winter solstitial colure representing the ever-visible circle, the Tropic of Cancer, the Equator and the

Tropic of Capricorn. The line corresponding to the ever-invisible circle is not drawn.When expressed as fractions of the diameter of the map, the distances of these four horizontal lines from the north pole measure 0.20, 0.40, 0.60, and 0.80, respectively. In addition to these straight lines, there are in each hemisphere two arcs (or sections of circles) that represent the northern and southern boundaries of the zodiacal band. The zodiacal band is divided into twelve segments, presumably representing signs. In the summer hemisphere the upper and lower boundaries of the zodiac intersect the solstitial colure at distances of 0.17 and 0.37 from the north pole respectively (distances expressed as fractions of the diameter of the map). In the winter hemisphere the upper and lower boundaries of the zodiac of the winter hemisphere intersect the solstitial colure at distances of 0.17 and 0.37 from the south pole, respectively (distances expressed as fractions of the diameter of the map). There is one starry object and eight coloured circular dots marked in the summer hemisphere. The starry object is to the east of Orion and to the west of the summer solstitial colure, above the Tropic of Capricorn. There are three dots around the picture of the anomalous Capricorn to the west of the summer solstitial colure, between the Tropic of Capricorn and the ever-invisible circle.There is one dot in front of Canis Minor to the east of the summer solstitial colure, above the Tropic of Capricorn. The remaining four dots are around the head of Canis Maior to the east of the summer solstitial colure, between the Tropic of Capricorn and the ever-invisible circle. conste llations: The presentation is in globeview. Of the 47 Aratean constellations, only 36 constellations are present in these maps. In the summer hemisphere are non-Aratean additions of the ivy leaf presented as a vase-like object and an anomalous depiction of Capricorn. The following constellations do not appear: Ara, Corona Australis, Corona Borealis, Cygnus, Eridanus, Lepus, Lyra, Perseus, Sagitta, Triangulum, and Ursa Minor. All constellations are presented face-on, with the left and right

221

The descriptive tradition in the Middle Ages characteristics as defined by Hipparchus’s rule interchanged. descriptions (summer hemisphere): Argo Navis is drawn as a complete ship with two steering oars, a raised poop deck, a small building, and two shieldlike objects on deck. Aries has curled horns and a tail. He is looking back over his shoulder to the east. Auriga wears a short tunic and faces east. He holds a sword in his western hand behind him and raises his other hand. Cancer is facing to the west. He has two claws, eight legs, and two eyes on his shell. Canis Maior is a dog with a long tail running vertically up the summer solstitial colure. Canis Minor is a dog with a long tail running to the west Centaurus appears partly on this hemisphere. Only the upside-down rear half of the horse’s part is depicted. Cetus has been drawn as a sea monster with front legs and a corkscrew tail. Corvus is a bird facing westwards, placed on Hydra, near the tail. Crater is drawn as a goblet, placed on the middle of Hydra. Draco is drawn as a complete snake. Gemini are nude and appear to be female and male. They face each other and hold each other at arm’s length. Hydra is drawn like a snake. Its head is below Cancer and its tail below Virgo. Leo is a lion, standing to the west with one of his forelegs raised and his tail upwards. Orion faces the viewer and wears a short tunic. His short cape is draped over his western shoulder and arm so that it seems that he holds a cloth in his western hand. He has a club in his eastern hand. Taurus is depicted as the front half of a bull, facing to the east, with one front leg bent under and the other extended in front of him. Ursa Maior is drawn as a tiny bear.Virgo appears to be a female figure. She wears a long dress and holds a branch in her raised western hand. Ivy leaf is north of the Tropic of Cancer. It is shaped as a vase-like object. Anomalous Capricorn is to the east of Cetus. It is drawn with two horns, a beard, and a corkscrew tail. descriptions (winter hemisphere): Andromeda is upside-down and dressed in a short tunic and a long cape. Her arms are outstretched. Aquarius is nude and has long hair. He holds an upturned urn in front

of him that pours water into a stream. Aquila is an extremely large bird, standing upside down and faces to the east with wings spread out. Bootes faces the viewer. He is dressed in a tunic and has a cape covering his western shoulder and arm. He holds a club in his eastern hand. Capricornus faces west, has two horns and a corkscrew tail. Cassiopeia is upsidedown, wears a long dress and sits on a seat with outstretched hands. On both sides, there are branches or trees more commonly found accompanying Andromeda. Centaurus is a two-legged centaur, holding an animal at the neck in each of his outstretched hands. Cepheus is placed upside-down, sits on a throne with raised arms. He wears a crown on his head, a long robe, and a cape. Delphinus has a wormlike body and its head faces toward the south. Draco is presented as a long rear tail-part of a snake. Hercules is upside-down. His lower body is in profile and his upper body faces the viewer. He is nude but has an animal skin draped over his eastern arm. He holds an odd object (a ‘club’) in his western hand behind him. Libra is drawn as a female figure in a long robe, holding a pair of scales in her raised western hand. Lupus is an animal held by the outstretched eastern hand of Centaurus. Ophiuchus is confined to the zodiacal segment holding Scorpius.The figure of Ophiuchus is depicted as a female standing on the tail of Scorpius. She faces the viewer and holds Serpens which wraps around her waist and curls through her legs. Pegasus is depicted as the front half of a winged horse, upside-down. Pisces are swimming to the east with their backs uppermost and are joined by a line at their mouths. Piscis Austrinus swims to the west. Sagittarius is a bearded, two-legged centaur standing to the west and facing towards the viewer, holding a bow with his hands in front of his body. Scorpius is drawn as a scorpion, with two claws, six legs, and a tail. SerPens wraps around the waist of Ophiuchus and curls through the legs. comments: Despite the obvious stylistic distance between the two manuscripts, the hemispheres in MS Vat. Reg. lat. 1324 are close in composition to those in the Dresden manuscript (H3). For the manuscript, see Pellegrin II.1 1978, pp. 165–7.

222

Appendix 3.1 Catalogue of medieval planispheres of the map). The upper and lower boundaries of the zodiac in the winter hemisphere intersect the winter solstitial colure at distances from the south pole of 0.23 and 0.40, respectively (with distances expressed as fractions of the diameter of the map).

H10. VATICAN CITY, BIBLIOTECA APOSTOLICA VATICANA, MS gr. 1087, ff. 309v and 310r (Fig. 3.10a–b) Byzantium, fourteenth/fifteenth century. The maps are part of a collection of pictures following the Greek text known as the Fragmenta Vaticana Catasterismorum. The hemispheres are arranged on two pages (f. 309v: winter hemisphere, f. 310r: summer hemisphere) with north at the top and south at the bottom of both hemispheres. cartog raphy: Each hemisphere is framed by a pair of concentric circles that represent the equinoctial colures.A pair of close-set vertical lines passes through the middle of each hemisphere and the north and south equatorial poles, representing the solstitial colure. In the summer hemisphere there are five pairs of straight lines perpendicular to this colure, representing the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the everinvisible circle. When expressed as fractions of the diameter of the map, the distances of these five horizontal lines from the north pole measure 0.14, 0.32, 0.50, 0.68, and 0.88 respectively. In the winter hemisphere there are five pairs of straight lines perpendicular to the colure, representing the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle. When expressed as fractions of the diameter of the map, the distances of these five horizontal lines from the north pole measure 0.15, 0.32, 0.50, 0.67, and 0.85 respectively. In addition to these straight lines, there are in each hemisphere two arcs (or rather sections of circles also drawn as double lines), which represent the northern and southern boundaries of the zodiacal band.The zodiacal band in the summer hemisphere is divided into six segments. In the winter hemisphere only the division coinciding with the colure and the preceding one are clearly visible.The upper and lower boundaries of the zodiac in the summer hemisphere intersect the summer solstitial colure at distances from the north pole of 0.23 and 0.40, respectively (with distances expressed as fractions of the diameter

constellations: The presentation is in globeview. Of the 47 Aratean constellations, 44 are presented in these hemispheres. The following constellations do not appear: Corona Australis, Sagitta, and Triangulum. In the summer hemisphere one finds in addition the non-Aratean image of the ivy leaf. On the winter hemisphere is an unidentified image of two concentric rings east of Ophiuchus. Most constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Exceptions are Ophiuchus, Perseus, Bootes, Orion, and Centaurus. descriptions (summer hemisphere): Argo Navis is drawn as a partly visible ship with an ornament at the bow, two steering oars, and a little steering house. Aries has curly horns and a tail. He is leaping to the west while looking back over his shoulder to the east. He has a ring around his body. Auriga wears a short bodice and leggings and a cape around his shoulders. He wears a spiky crown and has one small goat in his outstretched eastern hand. Cancer is facing to the west. He has two claws and eight legs.There is a square on his back (presumably representing the Manger of the Aselli). Canis Maior is a dog with a very long tail, jumping to the west.There are rays of light emanating from his head. Canis Minor is a dog with a tail, leaping to the west. Centaurus appears partly on this hemisphere. Only the rear of the horse’s part is depicted. Cetus has been drawn as a sea monster with a pair of front legs and a corkscrew body.The shading on the rear section suggests that this part might be a later addition. Corvus is a bird facing westwards, placed on the rear half of Hydra’s body, at which he pecks. Crater is drawn as a wide-brimmed cup, placed near the middle of Hydra’s body. Draco is drawn as the rear half of a snake. Eridanus starts from the western foot of Orion, runs south across the everinvisible circle, and south of Lepus turns again north. It ends at the ever-invisible circle, just to the west of

223

The descriptive tradition in the Middle Ages the summer solstitial colure. Gemini are seen from the front.They are nude, each resting his inner arm on the other’s shoulder.The western twin holds a club down by his side. Hydra is drawn like a snake, with its head beneath Cancer and its tail beneath Virgo. Leo is a lion, jumping to the west with his tail upwards. Lepus runs to the west. Orion is seen from the rear. He wears a knee-length tunic and holds in his raised eastern hand a long sword.There is an empty scabbard at his waist. Perseus wears a helmet, a tight tunic, and a long cloak that flows out behind him. He holds Medusa’s head in his western hand in front of his body and a raised sword in his other hand behind him. Taurus is depicted as the front half of a bull, facing to the east, with one front leg extended in front of him. Ursa Maior is drawn as a bear with a short tail.Virgo is a winged female and wears a long dress. She holds an ear of sweet-corn in the eastern (left) hand and a pair of scales beneath her waist in her (right) western hand. Ivy Leaf is north of the Tropic of Cancer, above Leo. It is shaped as a leaf. descriptions (winter hemisphere): Andromeda is upside-down and dressed in a long robe with a shawl that hangs down from her elbows. Her arms are outstretched. Aquarius is nude apart from a cape around his shoulders and a Phrygian cap. He holds an upturned urn in front of him that pours water into a stream flowing to the mouth of Piscis Austrinus. Aquila is upside-down. It faces to the east. Ara has a double structure with flames on top. Bootes is dressed in a short tunic with a skin over his outstretched western arm. He holds a curved stick or crook in his raised eastern hand. Capricornus has long horns and a corkscrewed tail. Cassiopeia is upside down, wears a long dress and seems to sit on an obscured seat with outstretched hands. Centaurus is to the east of the autumnal equinoctial colure. The boundary of the map passes through the horse’s belly and back cutting the rear part of the horse off. He holds Lupus at its feet in his outstretched eastern hand. In his other hand he holds a staff with thyrsus. Cepheus is placed upside down and wears a rounded cap, a tunic, and a long cloak around his shoulders. His arms are outstretched. Cetus appears with his rear part on this

hemisphere. This rear part is depicted as a snaky tail with dots on it. Corona Borealis is shaped like a wreath. Cygnus is a bird flying down. Delphinus is drawn as a dolphin with its head towards the south. Draco is presented by the long head-part of a snake. Hercules is nude, depicted upside-down. He holds a skin over his extended eastern arm and a club in his western hand behind him. Libra is drawn as a nude figure with a scarf wrapped around its eastern shoulder and falling down by its side.The figure holds a pair of scales in its western hand. Lupus in an animal with a long tail, held at its feet by the outstretched western hand of Centaurus. Lyra is a lyre with a square frame. Ophiuchus is nude, and is seen from the rear. He holds the Serpens horizontally at his waist and the snake faces away from him. Both his feet are on the back of Scorpius. Pegasus is depicted as the front half of a winged horse, upside-down, facing west. Pisces are swimming with their backs up in the opposite direction and are joined by a line at their tails. Piscis Austrinus swims upside-down to the east, with his mouth connected to the stream of Aquarius. Sagittarius is presented as a satyr, striding to the west with a long cloth flowing out behind him. He holds an arrow and bow with his western hand before him. Scorpius has two front claws, eight legs, and a segmented tail. Serpens is wrapped around the waist of Ophiuchus who holds it by his hands. Ursa Minor is drawn as a bear with a short tail. unidentified: east of Ophiuchus is a ring-like image depicted as two concentric circles. comments: The image of a ring east of Ophiuchus may perhaps represent Corona Australis gone astray. Note that the image does not compare to the wreath representing Corona Borealis. However, on the planisphere in this manuscript is a ring-like feature below the forefeet of Sagittarius which certainly represents Corona Australis. The codex contains a epistle from Nicephoros Gregoras, a treatise of Theodoros Metochites, and a commentary by Theon on Books VIII– XIII of the Syntaxis matematica of Ptolemy; the Ptolemaic text itself and a series of drawings (ff. 300r–312r), followed by a set of astronomical fables (ff . 300, 311r–v and 312r), see Martin 1956, pp. 46–8,

224

Appendix 3.1 Catalogue of medieval planispheres who dates the manuscript to the fourteenth century while Rehm 1899a dates it to the fifteenth century.

H11. VATICAN CITY, BIBLIOTECA APOSTOLICA VATICANA, MS gr. 1291, ff. 2v and 4v (Fig. 3.11a–b) Byzantium (Constantinople), first half ninth century. The maps are included in a manuscript with Ptolemy’s Πρόχειροι κανόνες (Handy Tables).The hemispheres are arranged on two pages (f. 2v: summer hemisphere, f. 4v: winter hemisphere) with north at the top and south at the bottom of both hemispheres. Both hemispheres have a dark blue-black (‘midnight blue’) background with the circles marked in gold.The figures are drawn with white marking the highlights and a darker blue-black marking the lowlights and shadows. Whereas the constellation figures on the summer hemisphere are easy to read, the paint surface of the winter hemisphere has been badly rubbed, making legibility difficult.There are compass holes in the middle of each map, but no other signs of manufacture. Both maps are plagued with old wormholes.185 cartog raphy: Each hemisphere is confined to a circular area bounded by a blue painted surface. The boundary of this circular area represents the equinoctial colures. A vertical line passes through the middle of each hemisphere and the north and south equatorial poles, representing the solstitial colure. In the summer hemisphere there are five straight lines perpendicular to this colure, representing the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle. When expressed as fractions of the diameter of the map, the distances of these five horizontal lines from the north pole measure 0.13, 0.32, 0.50, 0.69, and 0.87 respectively. In the winter hemisphere there are five straight lines perpendicular to the colure, representing the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle. When expressed as fractions of the diameter of the 185 I am indebted to Kristen Lippincott for her personal examination of the hemispheres. The remarks on colour stem from her notes.

map, the distances of these five horizontal lines from the north pole measure 0.11, 0.30, 0.49, 0.67, and 0.85, respectively. In addition to these straight lines, there are in each hemisphere two arcs (or rather sections of circles), which represent the northern and southern boundaries of the zodiacal band.The zodiacal band is divided into twelve segments. The upper and lower boundaries of the zodiac in the summer hemisphere intersect the summer solstitial colure at distances from the north pole of 0.25 and 0.39, respectively (with distances expressed as fractions of the diameter of the map). The upper and lower boundaries of the zodiac in the winter hemisphere intersect the winter solstitial colure at distances from the south pole of 0.27 and 0.41, respectively (with distances expressed as fractions of the diameter of the map). constellations: The presentation is in globeview. Of the 47 Aratean constellations, 38 seem to be present but this number is uncertain because of damage to the winter hemisphere. Libra is represented by the claws of Scorpius and the following constellations do not seem to appear: Aquila, Corona Australis, Cygnus, Delphinus, Ophiuchus, Sagitta, Serpens, and Triangulum. The absence of some of these constellations may be due to paint loss, but it could as well be that they were never included in the map. Only the suggestion of a shape remains of the depiction of Centaurus in the winter hemisphere. In the summer hemisphere one finds in addition the non-Aratean image of the ivy leaf. In the winter hemisphere is an unidentified image of two concentric rings beneath the hindfeet of Sagittarius. Most constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Exceptions are Bootes, Hercules, Orion, and Perseus. descriptions (summer hemisphere): Argo Navis is drawn as a partly visible ship with an ornament at the bow, a mast, and two shields on deck. Aries leaps to the west while looking back over his shoulder to the east. He has a ring around his body. Auriga wears a long robe that merges with the horns of Taurus. He wears a spiky crown, carries a small goat in his outstretched eastern hand, and a stick in his western hand

225

The descriptive tradition in the Middle Ages behind his head. Cancer faces to the east, towards Leo. He has two claws, six legs, and two extra hindlegs. Canis Maior is a dog with a very long tail and a halo with rays around his head. Canis Minor is a dog with a long tail running to the west. Centaurus appears partly in this hemisphere.The boundary circle intersects the lower part of the horse so that only the hindlegs and tail of Centaurus are depicted. Cetus has been drawn as a sea monster with two small front legs. Corvus is a bird facing westwards, placed on the tail of Hydra. Crater is drawn as a wide-brimmed cup, placed in the middle of Hydra’s body. Draco is drawn as a section of a snake, without head or tail. Eridanus starts from the feet of Orion, runs south and below Lepus turns again north. It ends at the intersection of the ever-invisible circle and the summer solstitial colure. Gemini are seen from the front, and seem to be nude. Each rests his inner arm on the other’s shoulder.The western twin holds a lyre down by his side and the eastern twin rests his eastern hand upon a (T-shaped) stick down by his side. Hydra is drawn like a snake, with its head below Leo and its tail below Virgo. Leo is a lion, jumping to the west with his tail upwards. Lepus is a hare running to the west. Orion is seen from the rear. He wears a knee-length tunic and has a piece of cloth over his outstretched western arm. He holds in his raised eastern hand a long sword. Perseus rushes to the west showing his back to the viewer. He wears a tunic and a long cloak that flows out behind him. He holds Medusa’s head in his western hand in front of his body and a raised sword in his other, northern hand behind him. Taurus is depicted as the front half of a bull, facing to the east, with one front leg extended in front of him. Ursa Maior is drawn as a tiny bear. Virgo wears a long dress. She holds something in her eastern hand (the crossbar of a pair of scales?). Ivy Leaf is north of the Tropic of Cancer and Leo. It is shaped as a large leaf. descriptions (winter hemisphere): Andromeda faces the viewer, wears a head-band around her head and is dressed in a long robe. Her northern arm is stretched and the other one is down by her side. Aquarius is dressed in a short tunic, leggings, and a

pointed hat. He stretches his arms out. The eastern arm appears to have a long sleeve or holds a piece of cloth. He holds an upturned urn in his western hand in front of him that pours water into a stream flowing to the mouth of Piscis Austrinus. Ara is below the ever-invisible circle, close to the boundary of the map. It has a thin stick-like structure. Bootes is dressed in a short tunic and holds a curved stick or crook in his raised eastern hand. His western shoulder appears to be covered by a cloak. Capricornus has long horns, bent forefeet, a curve in its body and a trefoil tail. Cassiopeia is upside-down, wears a hat and a long dress, and seems to sit with outstretched hands. Centaurus is holding something (probably Lupus) in his outstretched eastern hand. There are traces of a staff carried by him. Cepheus is placed upside-down. He wears a rounded cap, a tunic, and a cloak around his shoulders. Corona Borealis is depicted as two concentric circles. Draco is the greater part of a snake. Hercules is nude, depicted upside-down. It seems that one arm is held upwards behind his head.The rest of the figure is lost. Lyra is drawn as a U-shaped lyre with its bridge towards the north. Pegasus is depicted as the front half of a horse, upside-down. Damage may have removed its wings. His belly touches the head of Andromeda. Pisces are swimming with their backs up in the opposite direction and are joined by a line at their tails. Piscis Austrinus swims upside-down to the east, with his mouth connected to the stream of Aquarius. Sagittarius is presented by a bearded centaur, leaping to the west with a cloth flowing out behind him. He holds an arrow and bow with his western hand before him. Scorpius has two front claws, six legs, and a segmented tail. His claws extend into the preceding segment of the zodiacal band. Ursa Minor is drawn as a bear with a short tail. unidentified: beneath the hindfeet of Sagittarius is an image drawn as two concentric rings. comments: In the centre of the winter hemisphere are traces of one or two constellations.These could be Aquila and/or Delphinus, but the map is too damaged to decide.The image of a ring beneath the hindfeet of Sagittarius represents perhaps Corona Australis. Obrist 2004, p. 211 claims that stars are marked on the maps by

226

Appendix 3.2 Catalogue of medieval planispheres white spots but these spots extends beyond the boundaries of the maps and therefore certainly cannot be stars! For the manuscript, see Boll 1899, pp. 110–138.

Exceptions are Hercules and Bootes. In a number of cases the bodies of the human constellation figures seem to twist so that ‘front’ and ‘back’ are difficult to determine.

APPENDIX . Catalogue of medieval planispheres

descriptions: Andromeda is nude to the waist, wears an ankle-length skirt, and from both arms trail pieces of rope.The orientations of her hands suggest that she is facing towards the viewer. Her head touches the truncated belly of Pegasus. Aquarius is dressed in a close-fitting skirt that falls to his feet. He raises his southern hand above his head and holds with his other hand an upturned urn that pours water into a stream flowing to the mouth of Piscis Austrinus. Aquila is a bird, standing upside-down and holding Sagitta in his claws.Ara has a bi-partite structure with three horizontal flanges acting as foot, middle, and top of the altar and flames on top. Argo Navis is a cut-off ship floating on water with sails attached to a mast. It has two steering oars. Aries has curly horns and a long tail. It leaps westwards while looking back over his left shoulder eastwards. Auriga holds a flail behind his body in his right hand and has one goat on his shoulder and two small goats on his outstretched left arm. Bootes is nude but carries a piece of cloth over his left shoulder and left arm. Cancer has two front claws and no legs. He faces eastwards (towards Leo). There are two animals (head, neck, and part of the back) on his shell, representing the Aselli. Canis Maior is a dog, jumping westwards. His tail and rear feet touch the stern of Navis. Canis Minor is a dog, crouching down westwards. Capricornus has two short curved horns, a beard, two curls in his body and a quatrefoil tail. His front legs are stretched in front of him. Cassiopeia is upside-down and sits on a square seat with a low back with outstretched arms. She is dressed in a long robe and wears a head covering. Centaurus is a bearded centaur, nude to the waist and without a cloak. He holds an animal on its back with its legs in the air in his outstretched left hand. Cepheus stands upside-down and dressed in a short tunic and leggings. He holds his hands by his sides with his palms held towards the viewer. He either has a turban-like covering on his head or has very round hair. Cetus is depicted as a classical sea monster, with

P1. ABERYSTWYTH, NATIONAL LIBRARY OF WALES, MS 735C, f. 10v (Fig. 3.12) France (Limoges?), early eleventh century. The map follows an empty page (f. 10r) and precedes another one (f. 11r); on ff . 11v–24v follows Germanicus, Aratea with scholia Basileensia. The planisphere and its drawings are executed in brown ink. cartog raphy: The planisphere has a grid consisting of five concentric circles centred on the northern celestial pole. From the centre to the outer border, they presumably represent the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle, successively.When expressed as a fraction of the radius of the Equator, the radii of the Tropics of Cancer and of Capricorn are 0.73 and 1.25, respectively. The radii of the evervisible and ever-invisible circles are 0.36 and 1.54, respectively. In addition, two eccentric circles have been drawn to represent the northern and southern boundaries of the zodiacal band. The ecliptic pole (that is, the centre of these boundary circles) is located inside the innermost circle representing the evervisible circle. When expressed as a fraction of the radius of the Equator, the distance of the ecliptic pole from the centre of the map is 0.26 and the diameter of the northern and southern boundaries of the ecliptic are 0.84 and 1.08 respectively. constellations: The presentation is in globeview. Of the 47 Aratean constellations, 46 are presented on the planisphere: Libra is represented by the claws of Scorpius.There is the additional depiction of the Aselli on the shell of Cancer. Many constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged.

227

The descriptive tradition in the Middle Ages claws on his front legs, wings, furry ears, and a trefoil tail. Corona Austrinus consists of two concentric circles. Corona Borealis consists of two concentric circles. Corvus is a westward facing bird, standing near the tail of Hydra and pecking at its body. Crater is a vase with two handles on a raised foot. It is placed on the middle of Hydra. Cygnus is a bird, flying southwards. Delphinus is drawn as a fish with his back towards the south. Draco is a serpent with three bends in its body. Eridanus is a stream with a watery pattern. Gemini are nude to the waist and wear long skirts wrapped around their lower bodies. They face each other, embracing with both arms. Hercules is upside-down. He is nude and faces away from the viewer. He kneels on his right knee, holds a rudimentary lion’s head in his left hand in front of him and raises a club in his right hand behind him. Hydra is drawn like a snake. Leo is a lion with his head and tail held high. Lepus is a hare, running westwards, directly south of Orion. Libra is presented by the claws of Scorpius. Lupus is an animal held by Centaurus. Lyra is drawn with a U-shaped frame. Ophiuchus is nude, and his back is turned to the viewer. He stands with both feet on the back of Scorpius. Orion wears a knee-length tunic and a cloak that completely covers his western arm and shoulder. He holds a crook horizontally in his other hand. There is a scabbard at his waist. He seems to be facing the viewer although his eastern hand suggests otherwise. Pegasus is only half of a horse without wings. He is upside-down. Perseus is nude to the waist. His front/back orientation is not clear. He holds Medusa’s head in his southern hand in front of his body and a hooked sword in his northern hand behind him. Pisces are swimming in opposite directions, with both of their backs turned to the south.A line shaped like a stream of water connects their mouths. Piscis Austrinus swims eastwards, with his mouth connected to the stream of Aquarius and his back turned to the north. Sagitta is an arrow in the feet of Aquila, pointing eastwards. Sagittarius is drawn as a satyr, holding a bow with his left hand before him. Scorpius has two long front claws, four visible legs (three on the south side), and a segmented tail. Serpens is a snake held by Ophiuchus.

Taurus appears as the front half of a bull, with his right leg bent and his left leg slightly advanced.Triangulum is a triangle. Ursa Minor is a bear with a short tail. Ursa Maior is a bear with a short tail. Virgo wears a long dress. She holds a plant (ear of wheat?) in her right hand. She faces the viewer. comments: The style of the constellation drawings is the same as that of the hemispheres H1. The iconography of the planisphere agrees with that of the hemispheres for the constellations Ara, Cancer, Eridanus, Scorpius, and Taurus. However, it differs for Aries (no belt), Auriga (standing), Bootes (with staff and piece of cloth), Hercules (no Lion’s head), Orion (crook), and Sagittarius (satyr).Andromeda,Aquarius, Gemini, and Perseus are now dressed. Aberystwyth NLW MS 735C and Vatican City MS gr. 1087 are the only two manuscripts containing both planispheres and hemispheres. McGurk 1973 believes that the closeness of the essential iconographic features of the Aberystwyth planisphere to the one in MS gr. 1087 should be seen as a measure of its antiquity. For the manuscript, see McGurk 1973.

P2. BASLE, UNIVERSITÄTSBIBLIOTHEK, MS AN. IV. 18, f. 1v (Fig. 3.13) Fulda, early ninth century. After the map comes a partial version of Aratus latinus (ff. 2r–9v).The next two pages (ff. 10r–10v) are blank and then follows Germanicus, Aratea with scholia Basileensia (ff. 11r–45v).The planisphere drawings are executed in light brown ink with the ecliptic and the northern and southern boundaries of the zodiacal band drawn in red. These three lines are now nearly invisible due to fading. cartog raphy: The planisphere has a grid consisting of concentric circles centred on the northern celestial pole. It appears as though the ever-visible circle is represented by a pair of concentric circles or band. The Tropic of Cancer, the Equator, and the Tropic of Capricorn are demarcated by a single circle and the ever-invisible circle is, again, marked by a pair of concentric circles or band. At the border of

228

Appendix 3.2 Catalogue of medieval planispheres the map there is an additional pair of concentric circles, which presumably is only decorative. When expressed as a fraction of the radius of the equator, the radii of the Tropics of Cancer and of Capricorn are 0.75 and 1.25, respectively. The radii of the pair presumably representing the ever-visible circle are 0.38 and 0.49, respectively, so their mean value is 0.44.The radii of the pair of supposed ever-invisible circles are 1.48 and 1.54, respectively, so their mean value is 1.51. In addition to these circles, there are traces of three other circles that are eccentric with respect to the northern celestial pole. These circles represent the ecliptic and the northern and southern boundaries of the zodiacal band. The ecliptic pole, which is the centre of these boundary circles, is located inside the innermost band representing the ever-visible circle. When expressed as a fraction of the radius of the Equator, the distance of the ecliptic pole from the centre of the map is 0.28, and the diameter of the ecliptic and the northern and southern boundaries of the zodiacal band are respectively 0.99, 0.87, and 1.13. Finally, there are two straight lines that intersect each other perpendicularly at the equatorial pole, which, presumably, represent the colures. constellations: The presentation is in globeview. Of the 47 Aratean constellations to be expected 43 are presented on the planisphere: Libra is represented by the claws of Scorpius and Aquarius, Sagitta, and Triangulum are missing. In addition, there is 1) an anomalous animal in the place where Aquarius should be and 2) a set of concentric circles, placed at the left foot of Orion representing the star group we label Anonymous I. Many constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged, but several are drawn in too sketchily to determine orientation. descriptions: Andromeda is dressed in a gown that seems to stop at her thigh and she has dark shoes. Her arms are held out to the sides. Aquila is a bird in profile. Ara is depicted as an H-shaped object. Argo Navis is the rear part of a ship with three shields on deck. It has two steering oars and a number of normal

ones.Aries is leaping west with his head turned back, facing over his shoulder. He has a long tail. Auriga kneels facing east. His arms are outstretched. Bootes is nude and appears to be facing the viewer. He holds a curved stick or crook upraised in his left hand. Cancer has two claws and six legs, and faces towards Leo. There are some lines trailing behind the Crab that may be indications of a tail of some sort. Canis Minor is drawn more like a rabbit or hare than a dog, with long ears and relatively short legs. Canis Maior is shaped like a dog, running westwards. Capricornus has two long, twisted horns, a corkscrewed body, and a tail. His front legs are stretched out in front of him. Cassiopeia is upside-down. She appears to be sitting and her arms are raised to either side.The contours of the throne are not clear. She wears a robe and seems to be wearing a head covering. Centaurus is a nude centaur, holding something (an animal?) in his left hand in front of him. Cepheus is upside-down. He appears to be naked, and has his arms outstretched to either side. Cetus is a very long sea monster. He appears to have short legs and a long, uncurled tail with a trefoil end. Corona Austrinus consists of two concentric rings, placed in front of Sagittarius’s forelegs. Corona Borealis consists of two simple concentric circles. Corvus is a bird standing near the tail of Hydra, facing towards Hydra’s head and pecking its body. Crater is a bowl, placed on the middle of Hydra. Cygnus is a bird flying southwards. Delphinus is a dolphin swimming westward. Draco is a snakelike animal with two bends in its body (shaped like an ‘S’) and its mouth is open. Eridanus is a ‘snaky’ stream without patterns.The Gemini are nude, without attributes and stand facing the viewer.They hold each other’s hands in such a way that they seem cojoined at the elbow. Each of their outer hands is raised. Hercules is placed upside-down. He is naked; his lower body is in profile (with the buttocks showing) and he lifts his left leg. The hand of his leading arm holds something which may be a lion’s head or skin. Hydra looks like a snake with a trefoil tail. Its head is south of Cancer and its tail below Virgo. Leo is a lion, with his head and tail held high. Lepus appears as a dog to the south-east of Orion. Lupus may be the

229

The descriptive tradition in the Middle Ages ‘something’ held by Centaurus. Lyra is represented by an H-shaped image. It consists of two beams or ‘horns’ connected by a crossbeam. Ophiuchus is nude and has his back to the viewer. Serpens wraps around his waist. Orion is nude. He is facing towards the viewer. A piece of cloth is wrapped around his right hand. Pegasus is only half of a horse. His truncated belly nearly touches the head of Andromeda. Perseus is dressed (with evidence of a short skirt-like garment) and faces the viewer. He holds the Medusa’s head in front of him in his right hand and something that may represent a stick in his left hand, which is raised above his head. Pisces are swimming in opposite directions. A line joins them at their mouths. Piscis Austrinus swims eastwards, with his back towards the north and his mouth connected to the stream emerging from an anomalous animal (replacing Aquarius). Sagittarius is a centaur, drawn in profile. He holds a bow with his left hand in front of him. Scorpius has two long front claws, six legs, and a segmented tail. Serpens is held by Ophiuchus and encircles his body, with its head facing towards him.Taurus is depicted as half a bull, looking towards Gemini. He has short horns. Ursa Minor is a bear with a long tail. Ursa Maior is a bear with a short tail.Virgo wears a long gown and appears to have two outstretched wings, but no arms. additional features : Anonymous I is a star group depicted as two concentric circles, east of the left foot of Orion and west of Lepus. There is an Anomalous Animal in the place of Aquarius, which looks most like a jumping dog. It is positioned with its belly to the north. His set of ears is connected to a stream that runs into the mouth of Piscis so, to that extent, it has one aspect that is faithful to the iconography of Aquarius. comments: The map was removed from the manuscript in 1987 and is now in a separate folder. Haffner 1977, p. 34, supposes that the original location of the planisphere within the manuscript is unknown. From the current state of preservation of the map, it seems that its separation from the manuscript was carried out to save the page from constant folding and refolding. If one compares older photographs of the map with its

current state, one can see there have been significant losses on a strip about 4 cm wide running in a straight line between the mouth of Piscis Austrinus and Lepus, vertically through Pegasus, Andromeda, and so on down to Orion and the two concentric circles.There is also indication of a second fold (with much less damage) running vertically from the tail of Scorpius, through Bootes, the forequarters of Leo, and the neck of Hydra. The two concentric circles near Orion compare well with the set of circles beneath Lepus on Kugel’s globe and the circlet of eight stars in this location on the Mainz globe, representing the star group we labelled Anonymous I. Its appearance on maps is quite rare, none of the other planispheres have anything quite like it. For the manuscript, see Haffner 1977.

P3. BERLIN, STAATSBIBLOTHEK ZU BERLIN-PREUSSISCHER KULTURBESITZ, MS lat. 129 (Phill. 1830), ff . 11v and 12r (Fig. 3.14) France (Laon), ninth century. The map is on the last two pages of the manuscript and follows after texts and tables of Dionysius on the computus (ff. 1r–10v).This manuscript was originally bound together with MS lat. 130 (Phill. 1832) which opens with texts of Bede.The planisphere covers two facing folii and the drawings are executed in a now faded brown ink. In two of the corners of the page, there are depictions of an antique figure dressed in a toga.The one on the left points to a circlet attached to the edge of the planisphere, which contains a bust of Sol-Apollo with rays coming from his head. Alongside, there is the accompanying text: ‘Sol quoque exoriens et cum se condit in undas [. . .].’ versi LX. (Virgil, Georgics, I, 438): ‘The Sun also at dawning and when she sinks deep/will give you signs: his signs are the most reliable of all’. Followed by ‘grandiaque effossis mirabitur ossa sepulcris’ (Virgil, Georgics, I, 497): ‘And marvel at the heroic bones he has interred’. The one on the right points to a crescent Moon with his right hand, which has the accompanying text: ‘Luna revertentis cum primum colligit ignis, sunt versi’ XI (Virgil, Geor-

230

Appendix 3.2 Catalogue of medieval planispheres gics, I, 427):‘When first at the new moon her radiance is returning’; and in the next line ‘[G]lau[co et] panope[ae et Inoo] Melicerta’ (Virgil, Georgics, I, 437): ‘And sailors ashore shall pay their vows for a safe return to Glaucus and Panope and Melicertes son of Ino’. cartog raphy: The planisphere has a grid consisting of five concentric circles centred on the celestial pole. From inside to outside, they presumably represent the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle.When expressed as a fraction of the radius of the Equator, the radii of the tropics of Cancer and of Capricorn are 0.70 and 1.29, respectively.The radii of the ever-visible and ever-invisible circles are 0.43 and 1.57, respectively. In addition, there are two eccentric circles. The centre of the largest eccentric circle is located inside the ever-visible circle, in the head of Draco. When expressed as fractions of the radius of the Equator, the distance from its centre to that of the map amounts to 0.21 and the radius of this eccentric circle is 1.20. The centre of the smallest eccentric circle is located in the head of Bootes.When expressed as fractions of the radius of the equator, the radius of this eccentric circle is 0.88. Finally, there is series of short lines, radiating from the outer edge of the map, which, if the lines were continued into the map, would come together at the northern celestial pole. At the border of the map, these lines are set at regular distances of 30° or, if one thinks in terms of zodiacal coordinates, they divide the map into 12 equal segments. constellations: The presentation is in globeview. Of the 47 Aratean constellations to be expected, 43 are presented on the planisphere: Sagitta, Crater, Corvus, and Corona Austrinus are missing. In addition, there is an anomalous bust below the middle of Hydra and in advance of Navis.There is also an additional bear drawn above Gemini and in advance of Auriga. Most constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Exceptions are Perseus and Sagittarius. Two constellations, Bootes and Orion, have their buttocks exposed, suggesting a

rear view, but their heads are twisted making their presentation face-on. descriptions: Andromeda wears a long robe and stretches her arms out on either side. She faces the viewer.The figure is labelled: Andromade. Aquarius is a nude male, who faces the viewer. He holds an urn in his hands. Aquila is a bird, standing upside-down with its head towards the south. Its wings are outstretched and it looks over its shoulder westwards. (The figure is now almost obscured by a tighter rebinding of the manuscript.) Ara has three feet and a single column ending in a circular top, with flames coming from the top. Argo Navis is depicted as the rear part of a ship. It has one large oar, five triangular decorations that may have been oarlocks, and a mast with tattered sails or pennants. Aries is upside-down, with his head towards the south. He has curled horns and a long tail. His head is turned over his shoulder looking backwards at Taurus.Auriga faces the viewer. He wears a long dress and has a long cloak draped over his left hand. He holds a stick upraised in his right hand. Bootes is dressed in a short tunic, which exposes his northern shoulder. He holds a sickle in his southern hand; his northern hand is covered by a piece of cloth. It is not clear whether he faces the viewer or not. Cancer faces towards Leo and has two claws and six (?) legs. Canis Maior is a jumping dog with a tail and, around his head, a halo with streams of light emanating from it. Canis Minor is a jumping dog with a tail. Capricornus has two long horns, a coil in his body and a trefoil tail. His legs are bent in front of him. Cassiopeia appears to be sitting, though there is no evidence of a throne. She is dressed in a long robe with long sleeves and her arms are raised to either side.There is an incorrect label (cepheys) on her head. Centaurus is a centaur, his human half is nude and is facing the viewer.A sort of cloak or cloth floats behind him from his right shoulder. He holds something (an animal?) in his left hand in front of him. Cepheus stands upside-down, facing the viewer. He is dressed in a short tunic, wears a hat and has his arms outstretched to the side. Cetus is a sea monster with pointed ears, paws on his front legs, and an oddlyshaped trefoil tail. There is a label (cetus) above his

231

The descriptive tradition in the Middle Ages neck. Corona Borealis is a wreath of circlets with ribbons that look like wings placed at the bottom. Cygnus is a bird, standing upside-down with its head towards the south. Delphinus looks like a classical dolphin with a trefoil tail. Draco has three bends in its body and a small head like a snake. Eridanus is depicted as a snake, complete with a head that faces towards Cetus. There is a label (heridanus) above his neck. Gemini are nude and face the viewer.They are standing and both raise their right hands as if pointing to their own heads. The eastern twin has a club or spear in his left hand; the western twin has something lumpy in his left hand.There is a label (gemini) above their heads. Hercules is upside-down. He is nude, kneeling and is facing the viewer. He has a skin hanging over his outstretched arm in front of him towards Lyra and club in other arm held behind him. (The figure is now almost obscured by a tighter re-binding of the manuscript.) Hydra looks like a very long snake. Leo is a lion, with his head held high and his tail lowered. Lepus is an animal leaping westwards. Libra looks like a female, wearing a long robe and holding a pair of scales in her right hand. Lupus may be the something held by Centaurus. Lyra consists of two beams or ‘horns’ and appear to be conflated with Corona Borealis. Ophiuchus is nude and faces the viewer. He stands with both feet on Scorpius. Serpens surrounds his waist. Orion wears a skirt that comes down to his knees and is covered with decorative drapery folds, so that it is difficult to determine if some of the curved line are intended to represent buttocks or not. His face, however, appears to be in profile. A cloak covers his following arm and flutters away from his body. He raises a sword vertically in his eastern hand. Pegasus is depicted as half a winged horse and is placed upside-down. Perseus stands upside-down. He twists his body, so that his back is towards the viewer. He wears a sort of cloak or cloth around his shoulders and holds a curved stick in his raised right hand.There is no Medusa’s head. He is in the location where one would expect Cassiopeia and there is an incorrect label (casiephia) above his head. Pisces are swimming in opposite directions. Piscis Austrinus swims eastwards, with his back towards the north. There is a label (piscis mag.). Sagittarius is a centaur

with his back turned to the viewer. He holds a bow and arrow before him. Scorpius has two front claws, six legs, and a segmented tail. It has Ophiuchus standing on its back. Serpens is a snake encircling Ophiuchus’s body and its head is facing towards him.Taurus is depicted as half a bull. He tucks his right leg under his body and extends his left one in front of him.Triangulum is a simple triangle. Ursa Minor is a bear with a very short tail. Ursa Maior is a bear with a very short tail.Virgo wears a long dress and holds a branch upraised in her right hand. There is a label (uirgo) above her head. anomalous features : There is an Anomalous Bear-like Animal east of Auriga. It faces westwards and may be the reminder of one of the goats belonging to the Charioteer. There is an Anomalous Bust of a bearded male figure placed to the south of Hydra and in advance of Argo Navis. comments: As far as the relative positioning of the constellations is concerned, this planisphere is the least accomplished of the whole series.The positions of Cassiopeia and Perseus have been interchanged, for example. Cygnus, between Pegasus and Andromeda, appears to have lost his way completely, Corona and Lyra have become conflated and Aries appears upsidedown. Aquila is in the wrong place, its correct position being to the rear of Delphinus and to the south of Lyra. The head of Cetus is placed below Taurus instead of Aries, and Ara is located below Sagittarius instead of Scorpius. Last, but not least, there are the anomalous features. If the anomalous bust does indeed represent Eridanus, it appears as a kind of ghostly memory from some other map or series of constellations. Not only is it placed in the wrong spot, but there is already a ‘correct’ version of the stream elsewhere in the map. Similar arguments apply to the anomalous bear-like feature. On the two eccentric circles: the largest eccentric circle seems to represent the southern boundary of the zodiacal band since its centre is located inside the ever-visible circle, in the head of Draco.The position of this centre is close to what one would expect for the ecliptic pole. The radius of this circle is 1.20, a value that fits the southern boundary of the zodiac

232

Appendix 3.2 Catalogue of medieval planispheres best.The smallest eccentric circle could be the missing northern boundary.The radius of this circle, 0.88, would support such a hypothesis. However the centre of this eccentric circle is close to that of the Milky Way centre seen on other planispheres.The radius of the Milky Way circle should be close to 1.00 and for that reason this alternative interpretation is also not without difficulty. In earlier literature the codices MS lat. 129/130 (Phill. 1830/1832) have been located at St.Vincent in Metz. However, as Boschen 1972 remarks, the notes in MS lat. 129 (Phill. 1830) referring to Metz were added in the eleventh and twelfth centuries. A reference to Laon in MS lat. 129 (Phill. 1830) make it likely that the manuscript comes from there (see also Contreni 1978, p. 125). For the manuscript, see Boschen 1972 and Kirchner 1926, p. 30.

ever-invisible circle. When expressed as a fraction of the radius of the equator, the radii of the Tropics of Cancer and of Capricorn are 0.70 and 1.40, respectively. The radii of the ever-visible and ever-invisible circles are 0.31 and 1.83, respectively. In addition, there are three other circles. Two of them are concentric and represent the northern and southern boundaries of the zodiacal band.The third is the Milky Way.The centre of the two concentric boundary circles, that is the ecliptic pole, is located inside the ever-visible circle, in the head of Draco. The Tropic of Capricorn touches the southern boundary circle of the zodiacal band.The Tropic of Cancer intersects the band.When expressed as fractions of the radius of the Equator, the distance of the ecliptic pole from the centre of the map amounts to 0.23. The radii of the boundaries of the zodiac are 0.87 and 1.18 and the radius of the Milky Way turns out to be 1.10.

P4. BERN, BURGERBIBLIOTHEK, MS 88, f. 11v (Fig. 3.15)

constellations: The presentation is in sky-view. Of the 47 Aratean constellations to be expected 43 are presented on the planisphere: Corona Austrinus, Lyra, Sagitta, and Triangulum are missing.All constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule. The only exception is Perseus.

St Bertin, before 1029, produced during the abbacy of Odbert (986–1008). The map follows a text by Germanicus, Aratea, with excerpts from Avienus and scholia from ps. Bede, De signis caeli (ff . 1r–11r).The map is drawn in full-colour, with orange, red-orange, blue, grey-blue, and green predominating.The background of the zodiacal band is orange and its northern and southern boundaries are marked in green, painted over a thin black line.All the other circles are drawn in green over a thin black line. There are pencil traces of a circle drawn along the top (Piscis Austrinus side) of the map. There are three compass holes: one in Ursa Minor (the north celestial pole), one in Draco’s mouth (the north ecliptic pole), and the third below the left elbow of Bootes (the centre of the Milky Way). cartog raphy: The planisphere has a grid consisting of five concentric circles centred on the northern celestial pole. From inside to outside they represent: the ever-visible circle which is differentiated from the others because it is both thicker and is coloured orange and framed by thin green lines), the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the

descriptions: Andromeda is nude, with shortcropped orange hair, facing the viewer. Both her wrists, which are held down, are tied with some rope. Aquarius is a nude male facing the viewer, who wears a grey-blue Phrygian hat and a red cape draped over his left shoulder. He holds an upturned greyish urn that pours water into a stream flowing towards the mouth of Piscis Austrinus. Aquila is an orange bird, with outstretched wings. His head is on the south side. Ara is a grey, stepped, three-story structure with orange flames on top. Argo Navis is a grey and blue ship with pale blue sails attached to a red-orange mast. It is cut-off at the west side. Aries is leaping westwards, while looking back over its shoulder towards Taurus. He is pinkish and has a short tail. Auriga is depicted facing the viewer and kneeling. He holds something that looks like a rod in his left hand and has two small goats on his outstretched right arm. He wears a light blue-grey shift with long sleeves. Bootes

233

The descriptive tradition in the Middle Ages is facing the viewer. He wears a short grey tunic that exposes his right shoulder. He raises both arms and holds an orange crook in his right hand. Cancer has two claws and eight pointy legs. It is orange with brown and white markings and faces eastwards. Canis Minor is blue, has a long tail and his mouth is open, with his tongue sticking out. Canis Maior is orange, has a long tail and leaps towards Canis Minor (westwards). Capricornus has two white horns and a series of curls in his brown body and a short, pointed tail. His front legs stretch in front of him. Cassiopeia is dressed in a long green robe that exposes her shoulders and has orange hair. She stretches her arms to either side and has no seat. Centaurus is nude to the waist. He has a brown animal’s skin draped over his left shoulder in such a way that it seems more an extension than covering his arm. His horse parts are light blue-grey and blue. He holds a brown animal with a short tail by its heels in his right hand in front of him. Cepheus is dressed in a short, light brown tunic, dark brown shows, and raises both his hands. Cetus is a large blue-grey sea monster, with a brown backbone, marked with white dots and a red-orange acanthus-like tail. He breathes orange-red flames. He has flippers on his front legs and two coils in his body. Corona Borealis consists of a simple orange ring with ribbons. Corvus is a brown bird with darker brown wings, standing near the tail of Hydra facing eastwards to the tip of Hydra’s tail and pecking at its body. Crater is an orange vase on a foot, placed on the first bend of Hydra. Cygnus is a pale grey/green bird with its wings spread. Delphinus is a grey fish with a trefoil tail, placed with his back towards the south. Draco has a green-grey body in four bends. It has two small horns/ears on its head. Eridanus is depicted as a nude sea god with flowing brown hair, visible from the waist upwards as if emerging from his stream. He holds a brown decorated urn out in front of him (towards Orion) so that the stream pours towards his body.The Gemini are nude and stand facing each other, each holding the elbow of the other’s inner arm. The southern twin has a slightly curved, brown staff in his right hand, so that its curved end rests near his feet. Hercules is nude and his left arm is

covered by a grey/green lion’s skin. He has orange hair. He holds a curved brown staff/club in his right hand. He faces the viewer and stands upside-down. Hydra is a snake with a green and grey body and two short ears on its head. Leo is a lion, grey-blue with white highlights, with his head and tail held high. Lepus is orange and placed in advance of Orion, leaping towards his right leg. Libra is a male figure wearing a short blue tunic, a green cape over his left shoulder, red stockings, and brown shoes. He faces the viewer. In his right hand, he holds a pair of whitish scales in front of Scorpius’s claws.The scales are placed in the zodiacal band. Lupus is a brown animal held by Centaurus upside down by its hindlegs. Ophiuchus is nude, faces the viewer, while standing in front of Scorpius. He holds a green snake in his hands which encircles his body. Orion is standing facing the viewer, wearing a short blue tunic with an orange cape hanging over his left shoulder. He is barefoot and has orange hair. He holds an orange curved stick aloft in his right hand and there is a scabbard (no sword visible) hanging at his waist. Pegasus is depicted as half a horse, white and winged. He is positioned upside-down. Perseus is nude, but wears a pale green cape over his shoulders and a brown and white Phrygian hat. He holds the Medusa’s head by its hair in his northern hand in front of him and raises a straight white stick vertically above his head with his southern hand.The orientation of his body is not clear: his left leg seems closer to the viewer, but the fingers of the hand holding the Medusa’s head are clearly visible. Pisces are two grey and grey-blue fish, swimming in opposite directions. Their mouths are tied by a cord. Piscis Austrinus swims eastwards, with his mouth connected to the stream of Aquarius. His body is blue and orange. Sagittarius is a centaur with a blue horse’s body, holding a golden bow and golden arrow with his left hand outstretched in front of him, pulling back the string of the bow with his right hand. Scorpius is brown with white highlights. He has two long front claws, no legs, and a curved tail. Serpens is held by Ophiuchus and encircles his body. Its head is facing away from Ophiuchus. Taurus is a complete, pinkish bull, lying down with both front legs stretched

234

Appendix 3.2 Catalogue of medieval planispheres out in front of him. Ursa Minor is an orange bear with a short tail. Ursa Maior is an orange bear with a short tail.Virgo is a female figure, facing the viewer. She is dressed in a blue dress covered by a green cloak. She holds a plant in her right (northern) hand. The Milky Way passes through the right (northern) arm of Cassiopeia and the hips of Auriga. It touches the head of the northern twin and Cancer and it continues through the horse part of Centaurus, the middle of Lupus, the flames of Ara, the middle of Sagittarius, and the feet of Aquila; it touches the feet of Pegasus and the left wing of Cygnus. comments:The Bern map has two ‘reversed’ images: Argo Navis and Corvus. Other peculiarities are that Perseus has the Gorgon head north of himself instead of south and Delphinus is south of Hercules and west of Cygnus instead of south of Cygnus and east of Aquila.Another deviation is that the Bears are not set on either side of the northern celestial pole, but the pole is in the body of Ursa Minor. Missing are Lyra and the small constellations Corona Australis and Triangulum. The codex was originally bound together with the Boethius text now in Bern MS 87. In 1004 both manuscripts were donated by Bishop Werinhars I of Strasbourg (1001–29) to his cathedral (f. 1v: Werinharius episcopus dedit santae Mariae (Strasbourg cathedral)). Stevens 1997, p. 434, states that MS 87 was written before 1004 at the monastery at Luxeuil. For other notes on the manuscript, see Obbema 1989, pp. 13–14; Homburger 1962, pp. 116–18; Munk Olsen 1982, p. 406.

the map. Five concentric circles are drawn in black and show signs of ‘flooding’.They all have a sheen to them, which suggests that they were originally silvered.The background of the zodiacal band is orange and its northern and southern boundaries are gilded. The circle marking the Milky Way is painted in red and has been gilded.A black dot between Bootes and Virgo marks its centre. cartog raphy: The planisphere has a grid consisting of five concentric circles centred on the celestial pole. From inside to outside they represent the evervisible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle. When expressed as a fraction of the radius of the Equator, the radii of the Tropics of Cancer and of Capricorn are 0.71 and 1.45, respectively.The radii of the ever-visible and ever-invisible circles are 0.33 and 1.89, respectively. In addition, there are three other circles.Two of them are concentric and represent the northern and southern boundary of the zodiacal band. The third represents the Milky Way. This latter circle is labelled in black: LACTEUS CIRCULUS. The centre of the two concentric circles, that is the ecliptic pole, is located inside the ever-visible circle, in the head of Draco.TheTropic of Capricorn touches the southern boundary circle of the zodiacal band; the Tropic of Cancer intersects its northern boundary. When expressed as fractions of the radius of the Equator, the distance between the ecliptic pole and the centre of the map amounts to 0.25. The radii of the boundaries of the zodiac are 0.88 and 1.18 and the radius of the Milky Way turns out to be 1.16.

St Bertin, produced during the abbacy of Odbert (986–1008).

constellations: The presentation is in sky-view. Of the 47 Aratean constellations to be expected, 44 are presented on the planisphere: Corona Austrinus, Lyra, and Triangulum are missing. All constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule. The only exception is Perseus.

The map precedes a text by Germanicus, Aratea, with excerpts from Avienus (ff. 20v–33r). The planisphere is fully coloured, with grey-blue, red-orange, pale brown, and pale green predominating. In the centre of Ursa Minor’s belly is a hole indicating the centre of

descriptions: Andromeda is nude, with shortcropped black hair, facing the viewer, and both her arms are held down by her sides. Aquarius is a nude male facing the viewer, who wears a brown Phrygian hat and a red cape with white highlights draped over

P5. BOULOGNE-SUR-MER, BIBLIOTHÈQUE MUNICIPALE, MS 188, f. 20r (Fig. 3.16)

235

The descriptive tradition in the Middle Ages his left shoulder. He holds an upturned blue urn that pours water into a black (silvered?) stream flowing towards the mouth of Piscis Austrinus. Aquila is a coloured red-orange bird, with his wings stretched out behind him. His back is on the south side. Ara is a dark blue, stepped, three-story structure (each step is highlighted in yellow) with red flames on top and red highlights in the base. Argo Navis is a dark grey and blue ship with pale blue sails attached to a redorange mast. It is cut-off at the west side.Aries is leaping westwards while looking back over his shoulder towards Taurus. He is pinkish with a long tail. Auriga is depicted facing the viewer. He holds a stick in his raised left hand and has two pale blue goats standing on his outstretched right arm. He wears a pale blue tunic with long sleeves. Bootes is facing the viewer. He wears a short blue tunic that exposes his right shoulder. He raises both arms and holds a blue crook in his right hand. He wears orange shoes and has one golden dot on his head. Cancer has two claws and six legs. It is brown and faces eastwards. Canis Minor is blue and has a long tail. He is leaping towards Orion and is chased by Canis Maior. Canis Maior is redorange and leaps towards Canis Minor (westwards). Capricornus has two long horns and two curls in his brown body. His front legs stretch in front of him towards Sagittarius. Cassiopeia is dressed in a long blue robe that exposes her shoulders and has black hair and brown shoes. She stretches her arms to either side. Centaurus is nude to the waist. He has a light brown animal’s skin draped over his left shoulder in such a way that it seems more an extension than covering his arm. His horse parts are pale blue. He holds a brown animal with a short tail by its heels in his right hand in front of him. Cepheus stands upsidedown. He is dressed in a short, mauve tunic. One of his legs is mauve and the other tan. He raises both his hands. Cetus is a large blue sea monster, with a black backbone, marked with gold dots and a pink acanthus-like tail. He breathes orange-red flames. He has flippers on his front legs and two coils in his body. Corona Borealis consists of a red-orange wreath with orange ribbons. It is marked by 12 small gold dots. Corvus is a brown bird standing near the tail of Hydra, facing eastwards to the tip of Hydra’s tail and

pecking at its body. Crater is a mauve vase, placed on the first bend of Hydra. Cygnus flies towards Hercules. Its wings are spread and it is coloured pale yellow. Delphinus is a two-toned blue fish with an orange trefoil tail with his back southwards. Draco has a green body with white and gilt dots and four bends in it. It has a horn on its head and its tail passes below the feet of Ursa Maior.There are four dots on the head and five on the body. Eridanus is depicted as a nude, pale green and blue sea god with long hair, visible from the waist upwards as if emerging from his stream. He holds his mauve urn out in front of him (towards Orion) so that the stream pours back towards him. Gemini are nude and stands facing each other, each holding the elbow of the other’s inner arm.The southern twin has a slightly curved, brown staff in his right hand, so that its curved end rests near his feet. Hercules is nude and his left arm is covered by a dark blue lion’s skin with brown dots. He faces the viewer and stands upside-down. He holds a curved brown staff/club in his right hand, resting it on his shoulder. He has brown hair and one dot on his head and three on his left thigh. Hydra is a snake with a blue body and with horns on its head. Leo is dark blue and leaps westwards, with his head held high. Lepus is orange and placed in advance of Orion. Libra is a male figure holding a pair of scales. He wears a short grey tunic and leggings and an orange cape over his left shoulder. He faces the viewer. In his right hand he holds a pair of red-orange scales in front of Scorpius’s claws. The scales are placed in the zodiacal band. Lupus is a brown animal held by Centaurus upside-down by its hind legs. Ophiuchus is nude, faces the viewer, while standing on the back of Scorpius. He holds a snake in his hands which encircles his body. Orion is standing facing the viewer, wearing a short, pale blue tunic and with a red-orange cape hanging over his left shoulder. He has blue hair. He holds a straight brown stick aloft in his right hand and there is a brown sword hanging at his waist. Pegasus is depicted as half a pinkish winged horse. He is positioned upside-down, with his back to the south and facing towards Aquila and Delphinus (westwards). He has a decorative band on his shoulder. Perseus is parallel to the Tropic of Cancer. He faces away from the viewer and his buttocks

236

Appendix 3.2 Catalogue of medieval planispheres are visible. He is nude, but wears a red cape with white highlights over his shoulders and a black Phrygian hat. He holds the Medusa’s head by its brown hair in his left (northern) hand in front of him and he raises a straight black (silvered?) stick vertically above his head with his right (southern) hand. Pisces are two blue and green fish, swimming in opposite directions, with both their backs to the north.Their mouths are tied by a dark red and green cord. Piscis Austrinus swims eastwards, with his back facing north and his mouth connected to the stream of Aquarius. His body is green and pale blue with red-orange fins and highlights. Sagittarius is a centaur with a pale blue horse’s body, holding a red bow and red arrow with his left hand outstretched in front of him, pulling back the string of the bow with his right hand. Scorpius is brown, has two long front claws, very thin legs, and a curved tail, whose tip curves upwards. Serpens is a pale blue and green snake with white dots, held by Ophiuchus. Taurus is a complete, pinkish bull, lying down with both front legs stretched out in front of him. Ursa Minor is a brown bear with a short tail. Ursa Maior is brown bear with a short tail.There are three or four flashes of gold on its body. Virgo is a female figure, facing the viewer. She is dressed in a long orange dress covered by light grey cloak. She has no wings, but holds a drooping, plant in her right (northern) hand and seems to raise her left hand. The Milky Way passes through the right, northern arm of Cassiopeia and the hips of Auriga. It touches the head of the northern twin and continues through the horse part of Centaurus, the hindlegs of Lupus, the middle of the human part of Sagittarius, the feet of Aquila, and the feet of Pegasus. comments: The sheen on the concentric circles suggests that they were originally silvered. This observation is supported by the fact that, at some point in the map’s history, it seems as though the fixative for the silver leaf on these lines flooded over their contours and also permeated through the page, leaving a stain on the reverse side of the page. Inspecting the application of silver on other areas of the planisphere (as well as in other illustrations within the manuscript), the fixative seems to have bled through each page where

it was applied.The celestial circles on the planisphere are the only instance where there is evidence of ‘flooding’. It may have been occurred when the fixative was still damp and the book was prematurely closed, with the weight of the other pages pressing when the book was closed. The Boulogne-sur-Mer map has two ‘reversed’ images: Argo Navis and Corvus. Other peculiarities are that Perseus has the Gorgon head north of himself instead of south and Delphinus is south of Hercules and west of Cygnus instead of south of Cygnus and east of Aquila.Another deviation is that the Bears are not set on either side of the northern celestial pole, but the pole is in the body of Ursa Minor. Missing are Lyra and the small constellations Corona Australis and Triangulum. On the manuscript, see Obbema 1989, pp. 11–13; Munk Olsen 1982, I, pp. 406–7.

P6. EL BURGO DE OSMA, ARCHIVO DE LA CATEDRAL, MS 7, f. 84v (Fig. 3.17) Spain, 1124–30. The map precedes a late twelfth century copy of the descriptive star catalogue De signis coeli, often referred to as ‘pseudo-Bede’.The constellations are lively coloured renderings with pink, yellow, and blue predominating. The five celestial circles are drawn in brown, the other circles in red. The northern celestial pole is marked in blue with a red circle drawn around it. cartog raphy: The planisphere has a grid consisting of five concentric circles, which are drawn in brown and are centred on the celestial pole. From inside to outside, they represent successively the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle. When expressed as a fraction of the radius of the Equator, the radii of the Tropics of Cancer and of Capricorn are 0.66 and 1.29, respectively.The radii of the ever-visible and ever-invisible circles are 0.36 and 1.57, respectively. In addition, there is one other circle drawn in brown, but not centred on the equatorial pole.This circle represents the ecliptic. It touches the Tropics of Cancer and Capricorn.The ecliptic pole is located inside the

237

The descriptive tradition in the Middle Ages ever-visible circle, below the head of Draco. When expressed as fractions of the radius of the Equator, the distance between the ecliptic pole and the centre of the map amounts to 0.29 and the radius of the ecliptic to 0.97. There is a series of 12 circles drawn in red, centred on the equatorial north pole. The innermost circle is just inside the Tropic of Cancer. The radii of the inner and outermost circle are 0.64 and 0.89. constellations: The presentation is in globe-view. Of the 47 Aratean constellations to be expected, 45 are presented on the planisphere: Libra is represented by the claws of Scorpius and Corona Austrinus is missing. The rendering of the constellations makes it often difficult to determine whether or not they are drawn face-on or presented from the rear. Those certainly drawn in rear view with the left and right characteristics as defined by Hipparchus’s rule are Andromeda, Bootes, Aquarius, and Orion (his body is seen from behind but his head has been turned). Exceptions seem to be Cepheus, Cassiopeia,Auriga, Perseus, and Virgo. descriptions: Andromeda is nude, has long hair and faces away from the viewer. She seems to stretch her right arm out to the side, but holds her left arm closer to her body.The figure is labelled near her left shoulder: Andromeda. Aquarius is nude, but has a cloak draped over his left shoulder and arm. He seems to be facing away from the viewer. With his right hand he holds an upturned blue urn that pours water into a stream flowing to the mouth of Piscis Austrinus. There is a label in the middle of the cloak: Aqr. Aquila is a bird standing upside-down on Sagitta. The figure is labelled, but the name is illegible. Ara is a blue and yellow inverted triangle, with red flames coming from the top. The label in the middle of the vase is illegible. Argo Navis is a complete ship with a steering house and sails (?). It has two steering oars that touch the ever-invisible circle. There is a label above the deck of the ship: Argo navis. Aries is blue, has curled horns and a long tail. He leaps westwards while looking back over his shoulder towards Taurus. There is an illegible label on Aries’s body. Auriga faces the viewer, wears a short, blue tunic with long sleeves, and stretches his arms to either side. He holds a harness in his right hand and a flail in his left hand.

In addition, there are two small goats on his outstretched right (western) arm. The figure is labelled below his arms: Auriga. Bootes appears to be facing away from the viewer. He wears a very short, blue tunic and there is a blue animal’s skin with two legs over his extended left arm.The figure is labelled: arctofilax. Cancer has two claws and six legs.There may be a label but, if so, it is illegible. Canis Maior is blue with an orange collar and an orange tongue. His tail touches Navis.There is an illegible label in the middle of the body. Canis Minor is blue and sticks his orange tongue out. There is a label below the body: Syrius and an illegible word above the dog. Capricornus has a flesh-coloured head with two short, straight horns and a beard. He has one curl in his blue body and a fish’s tail. His front legs stretch in front of him. There is a label in the middle of the body: CAPR. Cassiopeia is upside-down. She appears to stand, wearing a long blue robe and a blue head covering. She stretches her arms out to either side. There is a label beside her body but it is illegible. Centaurus is dressed in blue, and seems have a small orange cloak floating behind him. He holds an animal in his outstretched right hand.There may be a label but, if there is, it is illegible. Cepheus stands upside-down. He is dressed and has leggings of some sort, which seem to resemble a suit of armour. The figure is labelled: cefeus. Cetus is a sea monster with a flesh-coloured head and a blue body, swimming eastwards. It has one coil and a long tail. There is an illegible label on Cetus’s body. Corona Borealis consists of a white, wreathlike ring with two ribbons and a golden centre.There may be a label but, if so, it is illegible. Corvus is a blue bird with an orange head. It faces towards Hydra’s head and stands near the Hydra’s tail.There is an illegible label on Hydra’s body. Crater is a blue vase with orange decoration on its body and two handles. Cygnus is flying towards the south.The bird is labelled in the middle of its body: cignus. Delphinus is placed upside-down. He has a long, straight orange body and a pig-like face. There is a label along the back of the figure: delfin. Draco is blue, with orange bands set at intervals and three bends in its body. Its tail ends in front of Ursa Maior. Draco encloses Ursa Minor completely and Ursa Maior partially.There is an illeg-

238

Appendix 3.2 Catalogue of medieval planispheres ible label on Draco’s body. Eridanus is depicted as a stream, which starts below the western foot of Orion, makes a U-shaped detour and then ends to the south of Orion’s foot in a ‘source’ consisting of a kind of triangular shape (rock?). There is a long label in the middle of the stream but it is hard to read, possibly eridanus fluvius [. .] p[. .]dus. Gemini may be nude. They embrace each other. The figures are labelled: Gemini and an illegible name (appears to the right of the following twin). Hercules is upside-down.There is a lion skin but it is unclear how he carries it. The figure is labelled, but it is difficult to read. Hydra is a snake with its head directly south of Cancer, while its tail extends as far asVirgo. It is blue with orange bands set at intervals. There is a label in the body of Hydra below Crater: Ydrus. Leo leaps westwards, with his head and tail held high.There figure is labelled in the middle of its body: leo. Lepus is blue with an orange collar.There is a label in the middle of the body: lepus. Lupus is an animal held by Centaurus. It is scarcely visible. If there is a label, it is illegible. Lyra has a blue U-shaped frame, an orange horizontal bar at the top, three strings and a peculiar bathplug-like device hanging from it. The figure is labelled: lira. Ophiuchus is nude, and faces away from the viewer. He stands with both feet touching the back of Scorpius. The snake he holds encircles his body. The figure is labelled behind the man’s body: Serpentarius (?). Orion wears a blue, knee-length tunic. His body is twisted. He has a cloak that completely covers his western shoulder and arm. He holds a long staff in his eastern hand and a skin over his western hand.There is a white scabbard at his waist.There is a label in front of his head: Orion. Pegasus is depicted as half a blue horse with a pink head. There is vague evidence of wings. He is upside-down. There is an illegible label on Pegasus’s body. Perseus is dressed in a short blue garment, a Phrygian hat, and appears to be facing the viewer. His hands are enormous. The Medusa’s head is light blue and located below and in front of his right hand.The figure is labelled: Perseus. Pisces are a pair of orange fishes, swimming in opposite directions at an angle of about 120°.The southern one is roughly parallel with the Equator, to the south of Pegasus and with its back towards the north.The northern one is

between Pegasus and Aries, with its back to the south. There is a label below the bodies: pisces. Piscis Austrinus swims eastwards, with his back to the north. His mouth connects to the stream of Aquarius.There is a label in the middle of the body: Piscis. Sagitta is at the feet of Aquila. The arrow points eastwards. The figure is labelled: telum (?). Sagittarius is a half human and half fish-like creature. He holds a bow with his right and pulls the string with his left hand before him. The arrow touches the end of the tail of Scorpius. Blue leaves or fur cover the middle of the body; his body ends in a flesh-coloured ‘lobster’ tail.There is a label on the middle of the body: SAG. Scorpius has two very long front claws, six legs, and a very long tail. He has a blue and a long tail which extends towards the south. There is a label in the middle of the body: Sco and two illegible names written on the ends of the right and left claws. Serpens is a snake held by Ophiuchus. It encircles the body of Ophiuchus. It is labelled: anguis. Taurus is depicted as half a blue bull with curved horns. At least one of his legs is extended in front of him.There is a label above the body: taurus (?) and another between his horns which is illegible. Triangulum is a blue equilateral triangle.The figure is labelled: Deltoton. Ursa Maior is a blue bear with a short tail. The figure is labelled: arcturus maior. Ursa Minor is a blue bear without a tail. The figure is labelled: minor. Virgo is a female figure dressed in a long blue robe. She faces the viewer and stretches her right arm, which has a huge hand, out from her side so that it touches the Equator.There is a label, but it is difficult to read, possibly: Virgo. comments: The series of 12 circles drawn in red, centred on the equatorial north pole is not seen on other planispheres.Their significance is not clear. On the manuscript, see Avilés 2001, p. 59, note 140 and Rojo Orcajo 1929, pp. 706–10.

P7. LONDON, BRITISH LIBRARY, MS Harley 647, f. 21v (Fig. 3.18) English, ninth/tenth century. The map is part of material that was added to the first part of the manuscript (ff. 2v–17v), based on Cicero’s

239

The descriptive tradition in the Middle Ages translation of Aratus’s poem and scholia from Hyginus’s myths (dated 820–30). The pages preceding the map (ff. 20v–21r) are empty. The manuscript is known to have been at St Augustine’s monastery in Canterbury at the end of the tenth century. The planisphere is executed in brown ink. The drawings are very finely executed and are all labelled in a darker black-brown ink.There are three compass holes in the map.The first marks the northern celestial pole. The second, found in front of the lower jaw of Draco, marks the northern ecliptic pole.The third, in the right shoulder of Bootes, marks the centre of the circle of the Milky Way. inscription (appearing in the lower part of the hemisphere, within the outermost circle of the sphere, between the constellations Navis and Lepus): ‘ISTA PROPRIO SVDORE NOMINA VNOQVOQVE/ PROPRIA EGO INDIGNVS SACERDOS ET MONA/CHVS NOMINE GERVVIGVS REPPERI AC/SCRIPSI: PAX LEGENTIBVS’. (‘These proper names for each [of them] have I, the humble cleric and monk named Gervvigus, traced and written down with my own sweat. Peace [be] with the readers’.)186 cartog raphy: The planisphere has a grid consisting of five concentric circles centred on the northern celestial pole. From inside to outside, they represent the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the ever-invisible circle. When expressed as a fraction of the radius of the Equator, the radii of the Tropics of Cancer and of Capricorn are 0.65 and 1.31, respectively. The radii of the evervisible and ever-invisible circles are 0.32 and 1.64, respectively. In addition, there are three other circles. Two of them are concentric and represent the northern and southern boundaries of the zodiacal band.The third represents the Milky Way. The centre of the two concentric boundary circles, that is the ecliptic pole, is located inside the ever-visible circle, in front of the head of Draco. The Tropic of Capricorn more or less touches the southern boundary circle of the zodiacal band. The Tropic of Cancer touches the northern boundary.When expressed as fractions of the radius of 186 The English translation is made by Paul Kunitzsch (private communication, 12 April 2002).

the Equator, the distance between the ecliptic pole and the centre of the map amounts to 0.20.The radii of the boundaries of the zodiac are 0.86 and 1.13 and the radius of the Milky Way turns out to be 1.04. constellations: The presentation is in sky-view. Of the 47 Aratean constellations to be expected, 45 are presented on the planisphere: Corona Austrinus and Triangulum are missing. Most constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule. Exceptions are Auriga (but his head is turned) and Perseus. de scriptions: Andromeda is nude and stands facing the viewer with her arms outstretched to either side. Her wrists have ‘bonds’ attached to them. Her head is close to the cut-off of the body of Pegasus. There is an incorrect label surrounding her head: Deltoton. Aquarius is a male figure, facing the viewer. He is dressed in a short tunic, long cape, and Phrygian cap, he holds an urn out in front of himself with both hands.The stream from the urn flows into the mouth of Piscis Austrinus. The figure is labelled: Ganimedes, Vrna, and Aquarius. Aquila is upside-down and faces westwards.The figure is labelled: Aquila. Ara is a twostory structure, with a small step at its base. It has flames on top. The figure is labelled: ARA. Argo Navis is as half a ship with sails attached to a mast. There is one steering oar. On the very tip of the mast stands a small bird. The ship is reversed from the norm: its stern should be towards Canis Maior.The figure is labelled: Argo. Aries leaps westwards, while looking back over his left shoulder towards Taurus. He has crescentshaped horns, a long tail, and a ring around the body. The figure is labelled: Aries. Auriga is dressed in a short, loose tunic that is gathered at his waist with a belt. His body is turned away from the viewer. He holds a single-strip flail outstretched in his right hand. He has one goat on his left shoulder and two small goats on his outstretched left (eastern) hand. There is also a small goat kneeling in front of his left foot. His left foot touches the northern horn of Taurus.The figure bears multiple labels: Erichtonius (surrounding his head), Eduli (above his left shoulder), and Caprea (near the goats on his left hand). Bootes faces the viewer and wears a short tunic and holds a curved staff or crook

240

Appendix 3.2 Catalogue of medieval planispheres upraised in his right hand.The figure is labelled: Boetes. Cancer has a round body and faces westwards. He has two claws and six legs. A label appropriate for Lyra appears along the bottom edge of Cancer’s shell: lira orphei. Cancer’s own label appears in a text around Eridanus (see entry Eridanus below). Canis Maior is in advance of Canis Minor and runs westwards, with his tongue sticking out. His tail touches the sail of Argo Navis. The figure is labelled: Syrius. Canis Minor is a dog jumping westwards.The figure is labelled: Anticanis. Capricornus swims towards Sagittarius, with his two legs stretched in front of him. His marine posterior is shaped like a fish. It has two straight horns and a beard. The figure is labelled: Capricornus. Cassiopeia is dressed in a long robe and appears to be seated, though there is no evidence of a throne, and she stretches her arms to either side. The figure is labelled: Cassiephea. Centaurus is nude and faces eastwards. In his left hand is a spear and an animal’s skin, which flows behind him. In his right hand he holds a rabbit by its heels in front of him. The figure is labelled twice: Centaurus and Ciron. Cepheus is upside-down. He is dressed in a short tunic, a Phrygian cap, and there is a scabbard on his left hip, which hangs on a cord from his right shoulder. He stretches his arms to either side. The figure is labelled: Cepheus. Cetus is depicted as a classical sea monster. He faces eastwards and has claws on his front legs, one coil in his body, and an acanthus leaf tail. The figure is labelled: Coetus. Corona Borealis is a wreath with ribbons.The label for this figure mistakenly appears next to Lyra (see entry Lyra below). Corvus is bird standing on the tip of Hydra’s tail, facing eastwards.The figure is labelled: Coruus. Crater is a vase with two handles, placed on the middle of Hydra; it is labelled: Crater. Cygnus is depicted as an upside-down swan with its head towards the south flying westwards. It has a long curved neck and its wings outstretched. The figure is labelled: Cignus qui est Olor et Ornin. Delphinus is depicted as an upside-down dolphin, with its back to the south.The figure is labelled: Delphinus. Draco has four bends. Its tail passes below the feet of Ursa Maior. The figure is labelled: serpens. Eridanus is depicted as a bearded classical sea god. He holds with his right hand an urn from which a stream of water flows in front of him. The stream flows as far as Cetus.In his left hand Eridanus

holds a reedy plant. The figure is accompanied by a rather bizarre label: Cancer qui et eridanus. Gemini are nude and stand facing the viewer, embracing each other with their inner arms.The northern twin carries a spear in his left hand and the southern twin has a club in his right hand, whose end rests at his feet.The figures are labelled: Gemini. Hercules is standing upsidedown. He faces the viewer, but walks in profile eastwards. He is nude, carries a lion’s skin on his left arm and holds a club in his right hand close to his body.The figure is labelled: Herculis (surrounding his hips) and pellis leonis (in front of the skin). There is also another label encircling his head: Serpens qui et. Hydra looks like a snake extending from the front of Leo to the end of Virgo.The figure is labelled: Hydra. Leo runs westwards, with his head and his tail held high.The figure is labelled: Leo. Lepus is a hare running westwards. The figure is labelled: Lepus. Libra is a male figure holding a pair of scales, who faces the viewer. He wears a short tunic and a long cloak which covers his upraised left hand. He swings the scales out to his right side so that they extend towards Scorpius. The figure is labelled: Libra. Lupus is depicted as an animal held by Centaurus upside down by its heels. It is not labelled. Lyra is a lyre with horns, a square base, and five strings. It is placed upside-down. The label for Corona Borealis mistakenly appears next to Lyra: Corona (an appropriate label for Lyra appears on the other side of the map, below Cancer). Ophiuchus is nude, faces the viewer in profile as he turns westwards. He stands with both feet on the back of Scorpius.The snake he holds encircles his body with the snake’s head facing away from him, towards the north. Ophiuchus is labelled: Serpentarius. Orion faces the viewer. He wears a knee-length tunic and a cloak that completely covers his left arm and shoulder. He holds a curved club upraised in his right hand. There is a scabbard with sword and a travelling bag at his left hip hung from a strap from his right shoulder. The figure is labelled: Orion. Pegasus is depicted as half a winged horse. He is upside-down. The figure is labelled:Equus and beneath it qui et Pegasus written in a later hand. Perseus is nude, with his back to the viewer. He has a cloak draped over both his shoulders and a Phrygian hat. He holds the Medusa’s head in his left hand down by and to the north of his

241

The descriptive tradition in the Middle Ages knees. There is a hooked sword upraised in his right hand. Perseus is labelled: Perseus and the head of Medusa is labelled: Medusa. Pisces are swimming in opposite directions, their bodies parallel to one another, with both their backs towards the north. A line connects their tails.The figures are labelled: Pisces. Piscis Austrinus swims eastwards, with his back facing toward the north and his mouth connected to the stream of Aquarius. The figure is labelled: Piscis. Sagitta is shown as an arrow placed below the feet of Aquila (but the eagle is not standing on it), pointing westwards. The figure is labelled: Sagitta. Sagittarius is depicted as a centaur, leaping westwards. He holds his bow out in front of his body with his left hand and appears to pull back its string with his right hand (but this section of the page has suffered losses).The figure is labelled: Arcitenens. Scorpius has two front claws, three visible legs on his southern side, and a curved tail. He faces towards Sagittarius (eastwards, so is reversed from his proper position). The figure is labelled: Scorpius. Serpens is a snake held by Ophiuchus.There are traces of an inscription between the head of the Serpens and Corona Borealis. It is illegible, perhaps because of an attempt to remove it.Taurus is depicted as half a bull, facing eastwards. His left leg is tucked under his body and the right one extends in front of him. The figure is labelled: Taurus. Ursa Maior is a bear with a tail, standing inside the fourth bend of Draco and it is looking outwards that is, eastwards and is back to back with Ursa Minor. His nose in the wrong direction: it should be facing into Draco’s bend. The figure is labelled: arctophylax. Ursa Minor has suffered losses. It is clearly a bear, but the contours are vague. It is inside the third bend of Draco and is back to back with Ursa Maior.There are two labels in front of the Bear’s nose: Helix (written correctly with regard to the orientation of the page) and, written upsidedown relative to the other label, arcturus. His nose seems to be in the wrong direction: it should be facing into Draco’s bend. Virgo is a winged, female figure, who faces the viewer and wears a long robe. She is placed parallel to the zodiacal band, with her head towards Leo. She holds a bushy plant outstretched in her right (northern) hand and caduceus in her left (southern) hand.The figure is labelled: Virgo.

The Milky Way passes through the northern arm and hip of Cassiopeia, the hips of Auriga, and the head of the northern one of the twins. It touches Cancer and Hydra on the south side and it continues through the legs of Centaurus (just below the belly), the middle of Lupus, the middle of Sagittarius, the body of Aquila, Sagitta, the feet of Pegasus, and the southern wing of Cygnus. comments: There has been what appears to be water damage to the map in the past. In particular, there are areas of loss in the centre of the ever-visible circle and along a relatively wide band stretching from the Sagittarius and Delphinus at the top of the map to Gemini and Cancer in the lower middle section of the map. At the top of the page, there is a gloss on Ursa Maior: ‘Callisto gentiles finxerunt In ursam versam [. .]/ [. . .] fabul[. . .] claramque Licaonis Arcton’. The expression ‘claramque Licaonis Arcton’ seems to come from Virgil, Georgics, Book I, 136–138: ‘Tunc alnos primum fluvii sensere cavatas;/navita tum stellis numeros et nomina fecit,/Pleiadas, Hyadas, claramque Lycaonis Arcton’. This map has a number of ‘reversed’ images: Ursa Maior and Ursa Minor, Cancer, Scorpius, Argo Navis, and Corvus.The reversal of Scorpius causes a disconnection between the scales and his claws (Libra). Other peculiarities are that Perseus has the Gorgon head north of himself instead of south, and that Delphinus is south of Hercules and west of Cygnus instead of south of Cygnus and east of Aquila.Another deviation is that the Bears are not set on either side of the northern celestial pole, but the pole is in the body of Ursa Minor. On the manuscript, see Saxl III, 1, pp. 149–51, and Bischoff 2004, pp. 111–12.

P8. MUNICH, BAYERISCHE STAATSBILIOTHEK, Clm 210, f. 113v (Fig. 3.19) Salzburg, 818–20. The planisphere is part of the Salzburg Compilation of 810–818: Liber calculationis in three blocks.The map is placed between the first (ff . 112v) and second block (ff . 114r–129r). The first two chapters of the second

242

Appendix 3.2 Catalogue of medieval planispheres block are 1) Excerptum de astrologia (ff . 114r–115r) and 2) De ordine ac positione stellarum in signis (ff. 115r–121r) which is illustrated by coloured drawings. The planisphere is executed in colour, with orange, brown, black, and white predominating. The background colour to the page is dark olive green and the painterly figures stand out against it—as if against a dark night sky. Some of the circles are marked very lightly in whitish green, including the circle identified here as the (misplaced) Equator. The northern and southern boundaries of the zodiacal band are marked in orange and the Milky Way is highlighted in bright white. At the edge of the map there is a bright orange border. cartography :The planisphere has a grid consisting of four concentric circles centred on the celestial pole. From inside to outside, they successively represent the ever-visible circle, the Tropic of Cancer, the Tropic of Capricorn, and the ever-invisible circle. When expressed as a fraction of the radius of the (misplaced) Equator, the radii of the Tropics of Cancer and of Capricorn are 0.65 and 1.41, respectively. The radii of the ever-visible and ever-invisible circles are 0.35 and 1.63, respectively. In addition, there are four eccentric circles.Two of them represent the northern and southern boundaries of the zodiacal band.The other two circles represent the Milky Way and the (displaced) Equator. The centre of the two boundary circles, that is the ecliptic pole, is located inside the ever-visible circle. The Tropic of Cancer touches the northern boundary circle of the zodiacal band. The Tropic of Capricorn touches the southern boundary circle of the zodiacal band.When expressed as fractions of the radius of the (displaced) Equator, the distance of the ecliptic pole from the centre of the map amounts to 0.27. The radii of the boundaries of the zodiac are 0.91 and 1.15 and the radius of the Milky Way is equal to 1.00. There also appear to be some ‘ghost lines’ or false starts on the map. For example, there is a pale white line running slightly inside of the circle of the Milky Way, which can be seen most clearly beneath the body of Hydra and near the body of Cancer, but it doesn’t seem to continue past this point.

constellations : The presentation is in sky-view. Of the 47 Aratean constellations to be expected, 43 are presented on the planisphere: Corona Austrinus, Lepus, Sagitta, and Triangulum are missing. In addition, there is a tiny leaf-like object between Cancer and Gemini. All constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule. descriptions: Andromeda wears a long, orange robe and stretches her arms to either side.The figure is labelled: ANDROM (with a line over the M). Aquarius is nude, except for his black shoes. He faces towards the viewer. He holds an upturned urn in front of his body that pours water into a stream that flows north. Another ‘stream’ starts at the middle of his back and flows towards the mouth of Piscis Austrinus. Aquila is upside-down. He has his wings outstretched and his head is turned backwards. Ara is a brown and white, square, three-story structure with flames on top. Argo Navis is a partly-visible, brown ship, without sails. It has five oars. Aries is a large white ram with orange and black markings. He leaps westwards while looking back over his left shoulder, eastwards. He has horns and a long tail.Auriga stands facing the viewer and wears a short, brown tunic that leaves his right shoulder exposed. His right hand is extended in front of him and his left hand rests on his hip. Bootes faces the viewer and holds both arms out to the side. In his left hand he holds an orange sickleshaped crook. He is dressed in a short orange and white tunic that seems to leave his shoulders and chest exposed. The figure is labelled in orange: BOOTES. Cancer is a black flea-like crab with two large front claws and six legs, and faces eastwards. Canis Maior is a white dog with a long tail. He runs westwards. Canis Minor is a white dog with a very long tail that curves upwards at the end. Capricornus has a white body and two large, curved white horns. There is one coil in his body and a long tail that ends in a trefoil. Cassiopeia is dressed in a long white and orange robe and has black hair. She stretches her arms to either side. There is an incomplete orange label near her knees: CAS [. .]. Centaurus faces eastwards. He is nude, but he seems to carry a cloth or skin,

243

The descriptive tradition in the Middle Ages which flows behind him. He holds a brown animal by its heels in his right hand in front of him, and a stick in his left hand.The figure is labelled in orange: CENTAUR (with a line over the R). Cepheus is facing the viewer and stretches his arms out to the sides. He is dressed in a short orange, white, and black tunic with black and white leggings and black hair. Cetus is a sea monster, swimming eastwards. It turns its head back over its shoulder westwards. It has a dog-like face and, possibly, wings on his shoulders, one coil in his body, paws for feet, and a long tail that ends in a feathered crescent. Corona Borealis consists of a black, leafy wreath with ribbons. Corvus is a black bird, facing backwards towards the tail of Hydra and pecking at its body. Crater is an orange vase hovering above the first bend of Hydra. Cygnus is an upside-down white swan with wings outstretched to either side. Delphinus is depicted as a long-bodied white fish (somewhat like a pike), with an orange and brown back and with straight stick-like fins. He is is upside-down.The figure has an orange label: DELPHINUS. Draco is black and white with orange dots and has four bends in its body. Its tail passes below Ursa Maior, ending beneath her hindfeet. Eridanus is depicted as an orange stream or cord. Gemini are nude and stand facing the viewer, embracing each other with their inner arms. Hercules stands upside-down. He is nude, may carry a lion’s skin on his left arm, and holds a long stick in his right hand, resting it on his right shoulder. There is a label, but it is mostly illegible: HE[. .]CU[. . .]. Hydra is a black and white snake, with its head south of Leo and its tail below Libra.The figure is labelled in orange: HYDRA. Leo leaps westwards with his head and tail held high. He has a white and orange body and an orange tongue hanging out. He is set within the zodiacal band. Libra is a pair of scales, set within the zodiacal band with the pans placed towards Virgo’s feet instead of the claws Scorpius. Lupus is a brown animal held by Centaurus. Lyra is a U-shaped lyre with three strings.There is a label, but it is mostly illegible: L [...]. Ophiuchus is nude, faces the viewer. He does not stand on Scorpius. The Serpens passes in front of his body. There is an orange label: SERPENT (line over T). Orion is facing the viewer. He wears a short brown tunic, which

exposes his right shoulder and has a cloak that completely covers his left arm and shoulder. He holds a curved staff in his right hand and there is a white scabbard on his left side. The figure is labelled in orange: ORION. Pegasus is depicted as half a brown horse without wings. He is upside-down. Perseus is nude, faces the viewer and holds Medusa’s head in his extended left hand. There is an orange label near his feet: PERSEUS. Pisces are swimming in the same direction (towards Aries), and both their backs face to the south. Piscis Austrinus is a white and orange fish with a black backbone that swims upside-down, with its back towards the south. Its mouth is connected to the stream of Aquarius. Sagittarius is depicted as a centaur, leaping westwards. He holds his bow in his outstretched left hand and pulls back its string with his right. His human part appears to be nude. Scorpius is black, with two long claws, no legs, and a segmented tail. Serpens is held by Ophiuchus. Its raised head is close to Corona Borealis.Taurus is depicted as half a white and orange bull, facing eastwards, with his right leg stretched out in front of him and his left one bent under his body. Ursa Maior is a black bear, looking into the third bend of Draco. It is back-toback with Ursa Minor. Ursa Minor is a black bear, looking into the second bend of Draco. Virgo is a female figure without wings. She faces the viewer and wears a long orange and white dress, exposing her left leg. She holds a leafy plant in her right hand. additional features: There is a tiny leaf-like object is set in the zodiacal band between Cancer and above the head of the left twin. The Milky Way bisects Cassiopeia from her head to her feet, bisects Auriga from his head through his left foot, and passes through the left arm and head of the advanced twin. It touches the southern legs of Cancer and passes below the feet of Centaurus. It continues through the middle of Sagittarius, the feet of Aquila, the forefeet of Pegasus, right hand of Andromeda, and left hand of Cepheus. comments: Whereas our analysis of the cartographic details of the map relies on North’s drawing of the circles in this map (north 1975, p. 180), we do not agree with his conclusion that stereographic

244

Appendix 3.2 Catalogue of medieval planispheres projection was used in constructing the map. For a full discussion of the issues involved, see Section 3.2. I have identified the eccentric circles on the map as the (misplaced) Equator because 1) its size is what would be expected for the Equator and 2) the Equator is the only circle missing. Next to a misplaced Equator, the Munich planisphere has Libra depicted as a pair of scales, Cetus looking backwards over its shoulder, Aquarius with a stream coming from both his urn in front and from his back.The leaf-like object between Cancer and Gemini could be the tail of Cancer or perhaps a remainder of an attribute carried by one of the twins. On the manuscript, see Rück 1888, pp. 5–7.

P9. VATICAN CITY, BIBLIOTECA APOSTOLICA VATICANA, MS Reg. lat. 123, f. 205r (Fig. 3.20) Ripoll, before 1056. The map is included in an astronomical compendium, consisting of four books on respectively the Sun (ff. 1r-74r), the Moon (ff. 74v–110v), Nature (ff. 128r–150v), and Astronomy (ff. 153r–233v). The latter book contains extracts from Hyginus, De Astronomica, set within sections of astronomical commentaries by Isidore, Bede the Venerable, ‘Aratus’, and others. The chapter immediately preceding the map (f. 204v) is HYGINI FABULA DE ANTICANO PROCYONE.CXVIIII. The chapter immediately following the map is (f.205v):ISIDORI DE ERRORE GENTILIUM. CXXI. The drawings are executed in a fine, light brown ink with stars marked as red dots. The outer circumference of the map, the ever-visible circle, the Tropic of Cancer, and the ‘misplaced Equator’ have been silvered, but this seems to have worn off .There is a compass hole at the middle of the map, marking the north pole in the middle of Draco’s body. There is a second hole in the thickest part of the first bend of Draco’s neck and a third one beneath the last star in Draco’s tail.There seems to have been another hole at the middle of the ‘misplaced Equator’, right outside the Tropic of Cancer, but this seems to have been filled in.

inscription (at the top of the map f. 205r): MACROBII AMBROSII. DE CIRCULIS SIGNIFERIS. CXX cartog raphy: The planisphere has a grid consisting of four concentric circles centred on the celestial pole. From inside to outside, they represent the evervisible circle, the Tropic of Cancer, the Tropic of Capricorn, and the ever-invisible circle. In addition, there are four other circles. Two of them represent the northern and southern boundaries of the zodiacal band. The Tropic of Cancer touches the northern boundary circle of the zodiacal band. The Tropic of Capricorn touches the southern boundary circle of the zodiacal band. The other two circles represent respectively the Milky Way and the (misplaced) Equator.When expressed as a fraction of the radius of the (misplaced) Equator the radii of the Tropics of Cancer and of Capricorn are 0.55 and 1.46, respectively.The radii of the ever-visible and ever-invisible circles are 0.32 and 1.72, respectively. The centre of the two boundary circles (that is, the ecliptic pole) is located just inside the ever-visible circle. When expressed as fractions of the radius of the (misplaced) Equator, the distance between the ecliptic pole and the centre of the map amounts to 0.27.The radii of the boundaries of the zodiac are 0.83 and 1.16 and the radius of the Milky Way is equal to 1.00. constellations: The presentation is in sky-view. Of the 47 Aratean constellations to be expected, 42 are presented on the planisphere: Corona Austrinus, Delphinus, Eridanus, Sagitta, and Triangulum are missing. There is an additional bird drawn south of Hercules. All constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule. Some constellations have a number of stars represented by red dots. descriptions: Andromeda wears a short dress and stretches her arms to either side.Aquarius is nude and faces towards the viewer. He holds an upturned urn in front of his body (but it does not pour out water). Instead, there is another stream that starts at the middle of his back, and connects to the mouth of Piscis Austrinus. He has four stars marked.Aquila is upsidedown. He has his wings outstretched and his head is

245

The descriptive tradition in the Middle Ages turned eastwards. Ara is a very simple two or threestory set of boxes with no flames. Argo Navis is just the body of a partly-visible ship. Its curved end faces eastwards. It has four stars. Aries leaps westwards, while looking back over his left shoulder eastwards. He has small horns and a long horse’s tail. His head seems to be dislocated from his body as it rests on the intersection between the northern boundary of the zodiacal band and the ‘misplaced Equator’. It has eight stars. Auriga is is facing the viewer. He wears a short tunic. He has a number of stars but it is difficult to say how many. Bootes is dressed in a short tunic with long sleeves. He faces the viewer and holds his right hand down by his side. He holds his club within his raised left hand. Cancer is a crayfish-shaped with two large front claws and six legs. It has two stars. Canis Maior is a dog running westwards. It has seven stars, with one clearly placed in the mouth. Canis Minor is a dog with a long tail that curves upwards at the end. It has three stars. Capricornus has two horns and one coil in his body. His front legs stretch in front of him. It has six stars. Cassiopeia is dressed in a long robe, stretches her arms to either side, and appears to be seated, though there is no evidence of a chair. She has no stars. Centaurus wears a shirt and carries two animals by their heels in both his outstretched hands. It has 12 stars. Cepheus is upside-down. He is facing the viewer and stretches his arms out to the sides. He is dressed in a short tunic. Cetus is a sea monster. It swims eastwards, but turns its head back over its shoulder towards westwards. He has a dog-like face and one coil in his body, paws for feet and a long feathery tail. He is marked by 11 stars. Corona Borealis consists of a circle of nine dots. Corvus is a bird facing backwards towards the tail of Hydra, but does not stand on his body. Crater is an urn without handles, sitting on the first bend of Hydra. It has two stars in the rim. Cygnus is an upside-down bird, with outstretched wings to either side. Draco has three bends in its body. Its tail passes below Ursa Maior, ending beneath her hind feet. It has eight large stars (consisting of one central dot surrounded by other dots) in its body. Gemini are dressed in tunics that fall to their knees.Their chests may be bare as they seem

to have pronounced breasts.They have no attributes. The left twin has five stars and the right twin has four stars. Hercules stands upside-down. He is nude, carries a decapitated bearded head in his left hand and holds a small club extended behind his body in his right hand. Hydra is a snake with its head south of Cancer and its tail south of Virgo. It has five stars. Leo is a lion with his head and tail held high. It has six stars. Lepus is a hare facing westwards. It has two stars. Libra is depicted as a pair of scales, with the pans placed towards Virgo’s feet and the handle held in Scorpius’s mouth. Lupus is presumably presented by the eastern one of the two animals held by Centaurus. Lyra is a square lyre. Ophiuchus is nude, faces the viewer. He does not stand on Scorpius, but hovers to the north of it. He holds a snake that wraps around his body. Orion is facing the viewer, with his right hand holding a straight stick/sword horizontally. He wears a short tunic and has a cloak that completely covers his left arm and shoulder. He is marked by eight stars. Pegasus is depicted as half a horse, without wings. He is upside-down. He has four stars. Perseus is nude and faces the viewer. He holds a male and bearded Medusa’s head by the hair in his extended left hand. His right hand is empty. Pisces are swimming in opposite and both their backs faces towards each other. They have each three stars. Piscis Austrinus swims upsidedown, with its back towards the south. Its mouth is connected to the stream of Aquarius. It has four stars. Sagittarius is depicted as a centaur, leaping westwards. He holds his bow in his outstretched left hand and pulls back its string with his right. His human part is nude. He has four stars. Serpens is a snake in the hands of Ophiuchus. Scorpius is shaped like a paisley, with two long front claws, no legs, and a curled tail. It has five stars. Taurus is depicted as a half bull, facing eastwards, with his both legs stretched out in front of him. He has five stars. Ursa Maior is a bear with a short tail, looking into the third bend of Draco. It is back-to-back with Ursa Minor. It has three large stars (consisting of one central dot surrounded by other dots) in its body. Ursa Minor is a bear with a long curved tail, looking into the second bend of Draco. It has three large stars (consisting of one central dot sur-

246

Appendix 3.2 Catalogue of medieval planispheres rounded by other dots) in the body and three dots in the tail.Virgo is a female figure without wings, wearing a dress. She faces the viewer and holds both her hands in front of her. She has six stars. additional features: There is an anomalous bird south of Hercules, presumably an erroneous image for the missing Delphinus. It has three stars. The Milky Way bisects Cassiopeia from her head to her feet, grazes Auriga’s head, passes through the left wrist and waist of the right twin and through the head of the left twin. It passes through the legs and chest of Centaurus. It continues through the middle of Scorpius, touches the bow and arrow of Sagittarius, Aquila’s feet rest upon it and it passes through the right hand of Andromeda and left hand of Cepheus. comments: On f. 118r is a 19-year cycle beginning in 1056 with a note in red (see Viré 1981, p. 174) suggesting a date of production before 1056. Hyginus (Viré 1992), p. xviii, says 1056 (except for ff. 118v– 125v, which are a little later and f. 128r–v and f. 151 r–v which are twelfth century), from Monastery of St Maria in Ripoll, transcribed by Oliva, abbot of Santa Maria de Ripoll and illustrated by a monk named Arnaldi. On ff . 182v–183r one has an ‘EXCERPTUM DE ASTROLOGIA MACROBII AMBROSII. LXXXV ’ including the Aratean text ‘Duo sunt extremi vertices mundi quos appellant polos—ad ipsum usque decurrit accipiens’. (Excerptum de astrologia Arati, cf. Maass, pp. 309–12) which is followed by an ‘INCIPIT EPITOME PHENOMENON VERSIBUS XII. LXXXVI ’ which includes the poem ‘XII De sideribus by Priscianus ‘Ad boreae partes arcti vertuntur et anguis’ (Riese 1869), vol. 1, no. 679. Next to a misplaced Equator, the planisphere shares with Munich Clm 210 Libra depicted as a pair of scales, Cetus looking backwards over its shoulder, Aquarius with a stream coming from both his urn in front and from his back. There are three birds drawn on this planisphere, two of which represent Aquila and Cygnus, the third one is an anomalous bird.The idea that the latter is an erroneous image for the missing Delphinus is based on the fact that it is placed south of Hercules. In this same location one finds Delphinus on the related map Munich Clm 210. It seems as

though the artist began adding large stars, consisting of one central dot surrounded by smaller dots (Dra, UMa, UMi), a technique also applied in some of the drawings of the individual constellations in this manuscript, and then realized these large stars would not fit within each constellation. Thus he continued using small dots. It is worth noting that stars are included in a few of the northern constellations (Dra, UMa, UMi, Auriga Pegasus, and the anomalous bird), the zodiacal constellations (except Libra) and in all southern constellations.The dots do not seem to correspond to the number or placement of the stars described in the accompanying star catalogue of Hyginus’s Book III. On the manuscript, see Saxl I 1915. pp. 45–59; Pellegrin II.1 1978, pp. 35–8;Viré 1981, p. 174.

P10. VATICAN CITY, BIBLIOTECA APOSTOLICA VATICANA, MS gr. 1087, f. 310v (Fig. 3.21) Byzantium, fourteenth/fifteenth century. The maps are part of a collection of pictures following the Greek text known as the Fragmenta Vaticana Catasterismorum. The planisphere is executed in ink. There is a small compass hole in the centre of the ever-visible circle which appears in the middle of Draco’s body. There is a double-line marking the periphery of the map. cartog raphy: The planisphere has a grid consisting of five concentric circles centred on the northern celestial pole. From inside to outside, they represent the ever-visible circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the everinvisible circle. When expressed as a fraction of the radius of the Equator, the radii of the Tropics of Cancer and of Capricorn are 0.62, and 1.37, respectively. The radii of the ever-visible and ever-invisible circles are 0.30 and 1.70, respectively. In addition to the five circles, there are two straight lines, representing the colures, which intersect each other perpendicularly at the equatorial pole. constellations: The presentation is in globeview. Of the 47 Aratean constellations to be expected,

247

The descriptive tradition in the Middle Ages 44 are presented on the planisphere: Libra is represented by the claws of Scorpius, Sagitta and Triangulum are missing. Most constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Exceptions are Perseus, Hercules, Ophiuchus, Orion, and Centaurus. descriptions : Andromeda is dressed in a long robe that exposes her arms and she has the tube-like extensions falling from her forearms. Her arms are held outstretched at shoulder height, with her wrists tied with ropes. Aquarius is facing the viewer and dressed in a short tunic and leggings. He also wears a cloak draped on his left shoulder and a Phrygian cap. He raises his right hand and,with his left hand,he holds an upturned urn that pours water into a stream that flows into the mouth of Piscis Austrinus. Aquila is standing upsidedown, facing eastwards. Ara is shaped like a candlestick, set on three small feet,with flames coming from the top. Argo Navis is drawn as the rear part of a ship with a house on deck. It has two steering oars and five normal oars.Aries has curly horns and a short tail. He turns his head back over his shoulder in the direction of Taurus. He has a ring around his body. Auriga is kneeling and faces eastwards. He wears a long robe, a spiky crown, and has one small goat on his outstretched left (eastern) arm. His right foot touches the left horn of Taurus. Bootes is oriented towards the viewer. He is dressed in a short tunic and holds a curved stick or crook in his left hand, the top of which rest upon his shoulder. Cancer has a round body, two large claws, and eight legs. It faces eastwards. Canis Maior is a dog placed vertically on the solstitial colure. Around his head, there is a halo with streams of light emanating from it. Canis Minor a dog running westwards. Capricornus has two short horns, a beard, one curl in his body and a tail that has two fins. His right front leg stretches in front of him and his left leg is bent under his body. Cassiopeia is upside-down. She appears to be seated, though there is no evidence of a chair, and is dressed in a long robe, which seems to keep her arms exposed. She may wear a head covering and her arms are stretched out to either side. Centaurus is nude and bearded, but he carries an animal’s skin tucked under

his left arm, which flies outwards and behind his left shoulder. He also carries something like a thyrsus or plant in his left hand, which is visible above his left shoulder. In his outstretched right (eastern) hand, he holds a dead animal with a long tail by its heels. Cepheus stands upside-down. He is dressed in a short tunic with a mid-calf cape and a ‘bobble-cap’ and stands, facing the viewer, with his arms outstretched to either side. Cetus is depicted as a classical sea monster with claws on his front legs, a beard, one curl in his body, and a tail. He sticks his tongue out as he faces eastwards. Corona Austrinus consists of two simple, concentric circles, placed between the front feet of Sagittarius. Corona Borealis consists of two simple concentric circles. Corvus faces forward and stands near the tail of Hydra, above its body. Crater is a cup on a raised foot and is placed on the middle of Hydra. Cygnus is an upside-down bird. It flies with outstretched wings southwards. Delphinus is a dolphin. Draco has two bends in its body. Its tail passes in front of Ursa Maior. Eridanus is a stream without patterns. It starts below the left foot of Orion, makes an ‘S’shaped series of curves and ends on the ever-invisible circle. Gemini are nude and stand facing the viewer, embracing each other with their inner arms. It appears as if they both have something like sticks in their outer hands. Hercules is upside-down. He is nude and has a skin on his outstretched left arm in front of him. He raises a club in his right hand behind his head. Hydra is depicted as a snake and has its head to the south of Cancer and its tail stretches as far asVirgo. Leo is a lion, with his head and tail held high. Lepus is a hare, facing westwards. Lupus is held by Centaurus upside-down by its heels and has a very long tail. Lyra is depicted as a lyre with horns and a cross bar and five strings. Ophiuchus is nude. His back is towards the viewer. He stands with both feet on Scorpius, holding the Serpens horizontally at his waist. Orion is with his back towards the viewer. He wears a knee-length tunic and has a cloak draped so that it completely covers his left arm and shoulder. He holds a pointed sword in his raised left hand.There is a scabbard at his waist. Perseus is nude, save the cloak that flows from his shoulders, and faces away from the viewer (with his

248

Appendix 3.3 Northern and southern medieval hemispheres buttocks clearly showing). He holds Medusa’s head by the hair in his left hand in front of his body. He raises a small object (stick or knife?) in his right hand behind his head. Pegasus is depicted as half a winged horse. He is upside-down. Pisces are swimming at an angle of 60°, with their backs towards each other. They are connected at their tails by a cord. Piscis Austrinus swims eastwards, with his back to the south. His mouth is connected to the stream of Aquarius. Sagittarius is depicted as a centaur. He is nude, but has a long, animal skin flowing out behind him. He holds a bow with his left hand and pulls back its string with his right. His front legs overlap Corona Austrinus. Scorpius has two long front claws, ten legs, and a very long straight segmented tail. Serpens is held by Ophiuchus, and his head is facing towards him.Taurus is depicted as half a bull, with both of his front legs bent. Ursa Maior is a bear seemingly without tail, placed to the south of Draco’s tail. It has a humped back. It is back-to-back with Ursa Minor. Ursa Minor is a bear with a short, upturned tail, looking into the second bend of Draco’s body. Virgo is a winged, female figure, dressed in a long gown, facing the viewer. She holds a pair of scales down by her side in her right hand. comments : The codex contains a epistle from Nicephoros Gregoras, a treatise of Theodoros Metochites, and a commentary by Theon on Books VIII–XIII of the Syntaxis matematica of Ptolemy; the Ptolemaic text itself and a series of drawings, followed by a set of astronomical fables, see Martin 1956, pp. 46–8, who dates the manuscript to the fourteenth century while Rehm 1899a dates it to the fifteenth century.

APPENDIX . Northern and southern medieval hemispheres BERNKASTEL, CUSANUS STIFT, MS 212, ff. 24r/v Astronomical compendium, fourteenth century? The pair of hemispheres is in the middle of a copy of the AlfonsineTables.The northern and southern hemi-

spheres are on two subsequent pages, executed in light brown ink with stars marked as red dots in a few constellations. constellations: The presentations of both hemispheres are in globe-view. Of the 47 Aratean constellations, 19 are presented on the northern, 13 on the southern, and 9 are divided over both hemispheres. Libra is represented by the claws of Scorpius. Auriga, Cassiopeia, Delphinus, and Sagitta are missing on the northern and Corona Australis on the southern hemisphere. Most constellations are labelled.All constellations are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged. Stars are marked as red dots in Ursa Minor, Draco, Bootes, Corona Borealis, Ophiuchus, Serpens, Triangulum, Leo, Virgo, and the northern claw of Scorpius. I. The northern hemisphere cartog raphy: The circle that frames the map represents the Equator. The straight lines running through the north equatorial pole in the middle of the map represent the northern sections of the equinoctial and solstitial colures. Centred on the equatorial pole are two circles representing the ever-visible circle, labelled circulus articus, and the Tropic of Cancer, labelled circulus tropicus. When expressed as fractions of the radius of the Equator, the radii of these two circles are 0.36 and 0.73, respectively (measured along the equinoctial colures). In addition to the straight lines and circles, there are a number of arcs (or sections of circles) two of which represent the northern and southern boundaries of the zodiacal band.The upper and lower boundaries of the zodiac intersect the summer solstitial colure at distances of 0.61 and 0.88 from the north pole, respectively. descriptions: Andromeda, labelled andromeda, is dressed in a long robe. Aquila, labelled Aquila, is standing upright, south of Lyra, facing east. Aries, labelled Aries, has curly horns and a tail. He is standing to the west while looking back over his shoulder to the east. He is divided over the hemispheres. The main part of his body is in the northern hemisphere. The vernal equinoctial colure passes through the

249

The descriptive tradition in the Middle Ages hind part of the body. Bootes, labelled boetes, is dressed in tunic and holds a staff downwards in his right hand. Cancer, labelled cancer, has two claws, three legs on both sides, and a short tail. His claws are facing to the right, towards Leo. Canis Minor, labelled procion [. . .] canis, is a dog divided over the hemispheres. The Equator cuts through his neck. Cepheus, labelled cepheus, is standing upside down, wearing a tunic and a cap, with his arms outstretched. His head is north of the tail of Cygnus. Corona, labelled corona, is a ring with 13 little circles of which 8 have a red dot in them, presenting stars. Cygnus, labelled cignus, is an upsidedown bird, flying south. Crater, labelled vrna, is a simple vase resting on the Equator. Draco, not labelled, is a snake-like animal with three bends which encircle both bears in the wrong way. The tip of the tail ends below the forefeet of Ursa Major.There are 12 red dots of which 6 are in the head, presenting stars. Gemini is labelled Gemini. The twins have curly hair and seem to wear tunics. The eastern twin holds a lance in his left hand and touches the western twin with his right hand. The western twin may carry an attribute but if so, it cannot be identified. Hercules, labelled hercules, is a nude male. He has a club in his raised right western hand and a lion skin in his other hand in front of him. His lower body is in profile and his torso appears to the viewer. He is upside-down. Hydra, labelled ydra, is divided over the hemispheres. The Equator cuts through his neck. Leo, labelled Leo, is a leaping lion with his tail raised. Libra, not labelled, is presented by the Claws (of Scorpius).The northern claw is in the northern hemisphere.The remainder of Scorpius is in the southern hemisphere. The autumnal equinoctial colure cuts through the tip of the Claw. Lyra, labelled lira, is a lyre with strings. Ophiuchus, labelled serpentarius, is nude and facing the viewer. He is divided over the hemispheres. The Equator cuts through his legs. He holds the Serpens, not labelled, with both hands. There are seven red dots in Ophiuchus. Orion, labelled orion, wears a knee-length tunic and a hat. He has a sword in his raised left hand and in his right hand he holds a piece of cloth. He is divided over the hemispheres. The equator cuts through his waist and his sword. Pegasus, labelled equus, is a winged horse facing west. His head

and the top of his wing are cut by the Equator. The cut-off parts are in the southern hemisphere. Perseus, labelled perseus, is dressed in a tunic and wears a hat. He holds Medusa’s head in front of his body in his right hand and a curved sword in his raised left hand behind his head. Pisces, not labelled, are divided over the hemispheres.The northern Fish is in the northern hemisphere, with its head pointing north. The fishes are connected at their mouths by a line. Scorpius is divided over the hemispheres. His claws are cut off by the Equator, such that only his northern claw is in the northern hemisphere. Serpens has wrapped itself around Ophiuchus’s body.The tail of Serpens ends on the Equator.There are 20 red dots in Serpens.Taurus, labelled taurus, is a full bull facing east. His forefeet are cut by the Equator and his hindlegs rest on it.Triangulum, labelled triangulum (?), is between the hind part of the body of Aries and the feet of Perseus.There are three red dots, one in each corner, presenting stars. Ursa Minor, not labelled, is a bear with a short tail located inside the first bend of Draco and faces outwards. Ursa Maior, not labelled, is a bear with a short tail located inside the second bend of Draco and faces outwards.Virgo, labelled Virgo, is a winged female in a long dress. She is divided over the hemispheres.The Equator cuts through her lowered hands, her middle, and the tip of her western wing. II. The southern hemisphere cartog raphy: The circle that frames the map represents the Equator.The straight lines running through the south equatorial pole in the middle of the map represents the southern sections of the equinoctial and solstitial colures. Centred on the equatorial south pole, there are two circles, not labelled, representing the ever-invisible circle and the Tropic of Capricorn. When expressed as fractions of the radius of the Equator, the radii of these two circles are 0.36 and 0.73, respectively (measured along the equinoctial colures). In addition to the straight lines and circles, there are a number of arcs (or sections of circles, also drawn with paired lines) two of which represent the northern and southern boundaries of the zodiacal band.The upper and lower boundaries of the zodiac intersect the win-

250

Appendix 3.3 NORTHERN AND SOUTHERN MEDIEVAL HEMISPHERES ter solstitial colure at distances of 0.63 and 0.88 from the south pole respectively. descriptions: Aquarius, labelled Aquarius, is a nude figure with curly hair. Over his eastern, left shoulder and his left arm is a cape. He holds in his western, right hand an upturned urn that pours water into a stream flowing to the mouth of Piscis Austrinus. Ara, labelled ara (?), consists of the disc supported by three legs. Argo Navis, labelled navis argo, is a complete ship with two steering oars. Aries, labelled ps Ari[...], is divided over the hemispheres. His belly and feet are in the southern hemisphere.The vernal equinoctial colure passes through the hind part of the body. Canis Maior, labelled canicula, is a dog facing west. Canis Minor, labelled ps anticanis, is a dog divided over the hemispheres.The main part of his body is in the south hemisphere. Capricornus, labelled capricornus, has a corkscrewed tail.The winter solstitial colure passes through his body, just behind his shoulders and neck. Centaurus, labelled centaurus, is drawn as a centaur. His torso is nude. He holds an animal, labelled bestia, by its hindfeet in his left hand in front of him and a long stick with decoration on both ends in his right hand.The autumnal equinoctial colure passes through his head, the torso, and his right hand. Cetus, labelled cetus, is a big fish with two horns, without front legs or a corkscrew body. The vernal equinoctial colure cuts his body behind the head. Corvus, labelled corvus, is standing on Hydra’s body, facing west in the direction of the tail at which he pecks. Eridanus, labelled Eridanus fluvius(?), is a river, which starts between the feet of Orion, runs staight south, crosses the Tropic of Capricorn, and ends on the ever-invisible circle. Hydra, labelled ps ydre, is divided over the hemispheres.The Equator cuts through his neck.The lower part of his body meanders southwards. Lepus, labelled lepus, is a hare facing west. Ophiuchus is divided over the hemispheres. His feet should be in the southern hemisphere but only one foot above Scorpius’s back is drawn. Orion, labelled ps Orionis, is divided over the hemispheres. The Equator cuts through his waist and his sword. Pegasus is divided over the hemispheres. His head and the top of his wing are in the southern hemisphere.There is text close to the Equa-

tor north of it which is illegible. Pisces, not labelled, are divided over the hemispheres.The southern fish is upside-down.The fishes are connected at their mouths by a line. Piscis Austrinus, labelled (illegible), swims eastwards, with his mouth connected to the stream of Aquarius. The winter solstitial colure passes through his head. Sagittarius, labelled (but the label is at the cut-off of the page and hard to read), is a centaur striding west. His human part has a curly head and holds a bow with his left hand and an arrow before him. Scorpius, labelled scorpius, is divided over the hemispheres. He is drawn as a scorpion with claws cut off by the Equator, such that only the northern claw is in the northern hemisphere. He has a long tail. Virgo, is divided over the hemispheres. The lower part of her dress is in the present hemisphere comments: The manuscript contains a collection of astronomical treatises, most of which are part of the mathematical tradition and do not link to the present maps which clearly belong to the descriptive tradition. Below the northern hemisphere is the Hebrew and Greek alphabet. On the manuscript, see Marx 1905, pp. 203–8; Krchňák 1964, p. 169.

DARMSTADT, LANDESBIBLIOTHEK , MS 1020, f. 61r Possibly St Jacob-Lüttich, before 1150. The set of hemispheres is part of a collection of astronomical texts (ff . 59r–66v) which follows after a collection of computus texts.The maps are in the middle of a poem which starts on f. 60v: Inc.: ‘Summa meae cartae brevis est divisio sperae’ and ends on f. 61v: Expl.: ‘Hec ita Gerbertus cui testis et auctor Higinus’. f. 61r: northern and southern hemispheres: the northern and southern hemispheres are drawn on one page. The drawings are executed in light brown ink with details of the constellations marked in red. Alongside the hemispheres are two texts:

251

‘Inde p(ro) funda patent hinc sensib(us) abdita lucent’ (Here secrets become plain, here shine things hidden from the senses)

The descriptive tradition in the Middle Ages ‘Q(uod) mente(m) refugit solet ars reserare figuris’ (What escapes the mind, art uses to disclose through (painted) figures)187

constellations: The presentation of the northern hemisphere is in globe-view, that of the southern hemisphere in sky-view. Of the 47 Aratean constellations, 22 are presented on the northern, 15 on the southern, and 8 are divided over both hemispheres. Libra is represented by the claws of Scorpius. Corona Australis is missing on the southern hemisphere. Most constellations in the northern hemisphere are presented face-on, with the left and right characteristics as defined by Hipparchus’s rule interchanged, except perhaps Hercules which is uncertain. Most constellations in the southern hemisphere are also presented face-on, but since this map is in sky-view the left and right characteristics are as defined by Hipparchus, except perhaps Aquarius which is uncertain. I. The northern hemisphere cartog raphy: The circle that frames the map represents the Equator. The straight lines running through the north equatorial pole in the middle of the map represent the northern sections of the equinoctial and solstitial colures. Centred on the equatorial pole, there are two circles representing the ever-visible circle and the Tropic of Cancer. When expressed as fractions of the radius of the Equator, the radii of these two circles are 0.38 and 0.68, respectively. In addition to the straight lines and circles, there are a number of arcs (or sections of circles) two of which represent the northern and southern boundaries of the zodiacal band.This zodiacal band is divided into compartments of unequal sizes, which represent the zodiacal signs. The beginnings of the signs of Aries and Libra are west of the respective equinoctial colures, and the beginning of the sign of Cancer is west of the summer solstitial colure. The upper and lower boundaries of the zodiac intersect the summer solstitial colure at distances of 187 I are indebted to Paul Kunitzsch for the translation (letter 15 December 2005).

0.55 and 0.80 from the equatorial pole respectively. The other arc of a circle represents the Milky Way. The centre of the circle which this arc is located is on the autumnal equinoctial colure at a distance of 0.68 from the north pole and its diameter is 1.10. This arc intersects the vernal equinoctial colure at a distance of 0.42 from the north pole and each of the solstitial colures at a distance of 0.88 from the north pole. descriptions: Andromeda is dressed in a long robe. Her head touches the body of Pegasus. The vernal equinoctial colure passes through the lowest folds of her robe. Aquila is upright, facing east. The winter solstitial colure cuts through its body. The Equator runs through his tail and right wing. The tip of that wing is in the southern hemisphere. Aries has curly horns and a tail. He is looking back over his shoulder to the east. His body is cut by the Equator, placing the lower part of his body in the southern hemisphere. The vernal equinoctial colure passes through the horn and the head on the rear (western) side of the turned round head.Auriga wears a short bodice and leggings, with a cape around his shoulders. His left foot rests on the head of Taurus. In his raised left hand he holds a goat and in his other hand a smaller one. Bootes is dressed in a tunic without attributes. His head is on the autumnal equinoctial colure. His arms seem twisted. Cancer is a crawfish with two claws and no legs. His claws are facing east, towards Leo. The summer solstitial colure cuts through its tail. Canis Minor is below Cancer and east of Orion. His hind feet rest on the Equator. Cassiopeia is upside down and dressed in a long gown, with one hand raised and the other placed in her lap.She is sitting on a square seat.Cepheus is standing upside-down, wearing a tunic and a cap, with his arms outstretched.The ever-visible circle cuts through his body at his breast. His head touches the tail of Cygnus. His feet are below the tail of Ursa Minor. Corona is a ring with 10 dots. Cygnus is an upside-down bird, flying south. The winter solstitial colure cuts through its right western wing and its head. The Tropic of Cancer cuts through its head (at the intersection with the colure). Delphinus is a dolphin with its head towards the north. Draco is a

252

Appendix 3.3 NORTHERN AND SOUTHERN MEDIEVAL HEMISPHERES snake-like animal with two bends which encircle the heads of the bears. Its own head is just below the evervisible circle and grazes the winter solstitial colure below the forefeet of Ursa Minor. The tip of the tail ends below the forefeet of Ursa Maior. Gemini wears a tunic and each twin is resting his arms on the other’s shoulder.There are no attributes. Hercules is a nude male with a cape round his shoulder. He has a club in his raised western hand, behind his head. His lower body is in profile and his torso appears facing the viewer. He is upside-down.The Tropic of Cancer cuts through his head and his club. Leo is a lion leaping to the west with its tail down. Libra is represented by the Claws (of Scorpius) which are cut off by the Equator. The remainder of Scorpius is in the southern hemisphere. The autumnal equinoctial colure passes through the ends of the claws. Lyra is a lyre with strings. Ophiuchus is nude and facing the viewer.The Equator cuts through his legs, placing the lowest parts of his legs in the southern hemisphere. He holds the Serpens with both hands. Orion wears a knee-length tunic and a hat. He is standing with a sword in his raised eastern hand. He faces west and his right hand is pointing to his breast. The Equator cuts through his waist, placing the lower part of his body in the southern hemisphere. Pegasus is a winged horse, cut off in the middle of his body. He is upside-down. His neck and the tip of his wings are cut by the Equator. The cut-off parts are in the southern hemisphere. Perseus is dressed in a tunic. He holds the Medusa’s head in front of his body in his right hand and a curved sword in his raised left hand behind his head. The vernal equinoctial colure passes through his sword, and his head. Pisces are divided over the hemispheres. The northern fish is in the northern hemisphere, below the shoulder of Andromeda, with its head pointing north. Sagitta is an arrow north of Aquila, pointing east.The winter solstitial colure cuts through the end part. Serpens has wrapped itself around Ophiuchus’s body. The Tropic of Cancer cuts through the neck of Serpens. Taurus is a bull, cut-off in the middle of its body. One of his forefeet is cut by the Equator. The corresponding paw is in the southern hemisphere. Triangulum is between Andromeda and Aries. The

vernal equinoctial colure passes through the middle. Ursa Minor is a bear with a short tail. Its head is inside the first bend of Draco. Ursa Maior is a bear with a short tail. Its head is inside the second bend of Draco. The summer solstitial colure cuts through his body at his shoulder.The ever-visible circle grazes his hindfeet. Virgo is a female and wears a long dress, without wings.The Equator cuts through her lowered right hand and her middle.The lowest part of her dress is placed in the southern hemisphere. The Milky Way circle passes on the northern hemisphere through the body of Aquila, the tip of Sagitta, the tip of Cygnus’s eastern wing, the legs of Cassiopeia, Perseus’s left arm and leg, the middle of Auriga, the shoulders of both Gemini, and the legs of Canis Minor. II. The southern hemisphere cartog raphy: The circle that frames the map represents the Equator. The straight lines running through the south equatorial pole in the middle of the map represent the southern sections of the equinoctial and solstitial colures. Centred on the equatorial pole, there are two circles representing the ever-invisible circle and the Tropic of Capricorn.The radii of these two circles are 0.33 and 0.64, respectively. In addition to the straight lines and circles, there are a number of arcs (or sections of circles, also drawn with paired lines) two of which represent the northern and southern boundaries of the zodiacal band. This zodiac is divided into 12 compartments of unequal sizes, which represent the zodiacal signs. The beginnings of the signs of Aries and Libra (represented by the Claws of Scorpius) are west of the respective equinoctial colures, and the beginning of the sign of Capricorn west of the winter solstitial colure. The upper and lower boundaries of the zodiac intersect the winter solstitial colure at distances of 0.55 and 0.82 from the south pole respectively. The other arc of a circle represents the Milky Way. The centre of the circle of which this arc is a part is located on the vernal equinoctial colure at a distance of 0.44 from the south pole (where a clear hole can be seen) and its diameter is 0.94.This arc intersects the vernal

253

The descriptive tradition in the Middle Ages equinoctial colure at a distance of 0.48 from the south pole and each of the solstitial colures at a distance of 0.84 from the that pole. descriptions: Aquarius is nude. He holds in his southern hand an upturned urn that pours water into a stream flowing to the mouth of Piscis. Ara is an elongated altar with flames on top. It rests on the ever-invisible circle. Argo Navis is the rear part of a ship with a rudder. The bottom of the ship rests on the ever-invisible circle and the rudder is below it. Aries is divided over the hemispheres (see also above). Canis Maior is a dog-like animal. His neck is on the summer solstitial colure. Capricorn has a corkscrewed tail. The winter solstitial colure passes through his neck and front legs. Centaurus is a centaur. His torso is nude but he has a band around his middle. He holds an animal with a short tail by its neck in his right hand in front of him.The autumnal equinoctial colure passes through his head, torso, and front legs. Cetus is a big fish, without front legs or a corkscrew body. The vernal equinoctial colure cuts his body in the middle. Corvus faces forward to the head of Hydra, standing on the tail of Hydra’s body, at which he pecks. Crater is a wide-brimmed wine cup, placed on the first half of Hydra. The Equator passes grazes the top of cup. Eridanus is a river, which starts at the western (left) foot of Orion, crosses the Tropic of Capricorn, and ends on the ever-invisible circle. Hydra looks like a snake-like animal. Its head is on the summer solstitial colure, south of the Equator, and north of the head of Canis maior. Its tail extends almost to above the head of Centaurus. Lepus is a hare between Orion’s legs. Lupus is an animal with a short tail held in Centaurus’ right hand. Orion is divided over the hemispheres. Pisces are divided over the hemispheres. The southern fish is in the southern hemisphere; its head points in the direction of Aquarius. Piscis swims upside-down, with his mouth connected to the stream of Aquarius. Sagittarius is a centaur with a hat, striding west. He holds a bow with his left hand and an arrow in the other hand before him. Scorpius has two front claws, six legs, and a tail.The feet of Ophiuchus are standing on his back. His claws are cut off by the Equator, placing

the ends of his claws in the northern hemisphere. The autumnal equinoctial colure passes through the southern claw. In the southern hemisphere one finds also, at the border of the map, the legs of Ophiuchus, the skirt of Virgo, a paw of Taurus, the tip of the wing of Aquila, and the head and the tip of the wing of Pegasus.The main parts of these constellations are located in the northern hemisphere. The Milky Way circle passes on the southern hemisphere through the body of Sagittarius, the flames of Ara, the middle of Lupus, the horse’s part of Centaurus, grazes the stern of Navis, and passes through the head of Hydra. comments: Globe-view versus sky-view: a conceptual error made in the process of constructing the southern map is that the zodiacal constellations are placed in the same order (anti-clockwise) as in the northern map. In order that the orientation of the northern map (globe-view) is maintained, the order of the zodiacal constellations in the southern map must be reversed to clockwise, since it is south of the Equator. This was not done and as a result the southern map shows the order of the constellations as it is seen in the sky (sky-view). Differences in radii between the two hemispheres: the radii of the ever-invisible circle and the Tropic of Capricorn in the southern hemisphere (respectively 0.33 and 0.64) are not equal to the corresponding circles in the northern hemisphere (respectively 0.38 and 0.68). Instead they appear to be close to their complements, that is 0.33 is close to 1–0.68 (= 0.32) and 0.64 is close to 1–0.38 (= 0.62). It may well be the copyist/maker (?) in the process of constructing the southern hemisphere (perhaps by the mirror image of the northern hemisphere) measured the distances from the Equator instead of from the pole.

APPENDIX . Medieval pictures of globes Drawings of a celestial globe appear in the following six manuscripts with the text Revised Aratus

254

Appendix 3.4 Medieval pictures of globes latinus. Four globe drawings (G1–G4) are in manuscripts dating to the ninth–tenth century, two (G5–G6) occur in the only two known Renaissance copies of Revised Aratus latinus, see McGurk 1966, p. xiv.

G1. PARIS, BIBLIOTHÈQUE NATIONALE DE FRANCE, MS lat. 12957, f. 63v (Fig. 3. 27) West Francia (Corbie?), early ninth century. Drawing in sepia ink of a celestial globe showing 10 constellation figures.The double line of the meridian ring is in red.The stand consists of six columns with Corinthian orders/capitals supporting the horizon ring and one central support for the meridian ring. The two columns in the background and the central support are decorated. The straight part of the horizon ring passes in front of the meridian ring.The north pole is indicated by a clamping screw. The zodiacal band is divided into three compartments with images for Aries, Taurus, and Gemini. Three images (Perseus (?),Auriga, Ursa Maior (?)) are above the zodiacal band. A snaky figure (Eridanus (?)) is below the zodiacal band and above the horizon ring, while the images below the horizon ring represent the hind legs of Canis Maior and Navis. In addition there is a animal below Ursa Maior which is intersected by the horizon ring, which might be a reminiscence of Leo or Canis Minor. All the human figures are nude. Aries has a ring around its middle; Taurus is a whole animal facing to Aries; Gemini, both drawn in front view, are connected by an extended arm; Perseus (?) is seen from behind and has a cloth over his left arm and a stick raised in his right hand; Auriga is seen from behind, has two goats on his extended right arm, and a flail in his left hand; Ursa Maior (?) has a long tail; Eridanus (?) is a snake; Navis, with two steering oars, has a building and two shields on its deck. There is a compass point in the middle of the meridian ring. For the manuscript, see Le Bourdellès 1985, pp. 75–6.

G2. ST GALL, STIFTSBIBLIOTHEK, MS 902, p. 81 St Gall, first half of the ninth century. The drawing of the celestial globe is the same as G1 except for the following differences. The meridian ring passes here in front of the horizon ring, and the a clamping screw is lacking. All columns supporting the stand are decorated and the Corinthian orders/ capitals have been changed. The four columns in front are distinguished from the two in the back and on the sides by their decoration. One of the twins is seen here from behind; Perseus (?) is now drawn in front view and Auriga holds a sword in his left hand. For the manuscript, see Von Euw 2008,Vol. 1, Kat. Nr. 120, pp. 446–9.

G3. ST GALL, STIFTSBIBLIOTHEK , MS 250, p. 472 (Fig. 3. 28) St Gall, last quarter of the ninth century The drawing of the celestial globe is the same as G2. For the manuscript, see Von Euw 2008,Vol. 1, Kat. Nr. 120, pp. 449–54.

G4. DRESDEN, SÄCHSISCHE LANDESBIBLIOTHEK—STAATSUND UNIVERSITÄTSBIBLIOTHEK, MS Dc. 183, f. 13r West Francia, first quarter of the ninth century (damaged in 1945). The drawing of the celestial globe is the same as G1 except for the following differences. The meridian ring passes here in front of the horizon ring.The four columns in front are decorated and the two at the back not. The Corinthian orders/capitals have been changed.The goats on Auriga’s right arm are gone, as is the animal below Ursa Maior.A picture of the globe is in Thiele 1898, p. 43, fig. 7. For the manuscript, see Schnorr von Carolsfeld 1882, Band I, pp. 334–5.

255

The descriptive tradition in the Middle Ages G5. VATICAN CITY, BIBLIOTECA APOSTOLICA VATICANA, MS Reg. lat. 1324, f. 27r

G6. GOTTWEIG, STIFTSBIBLIOTHEK, MS 7 (146), f. 6r

France, fifteenth century.

North Italy, fifteenth century.

The drawing of the celestial globe is the same as G4 except for the following differences. The columns supporting the (pink) horizon ring are not decorated and their Corinthian orders/capitals have been adapted. Below the (blue) horizon ring three semicircles have been added inside the meridian ring, which seem to belong to the sphere. The support for the meridian ring is drawn as a continuation of Navis. Aries is without ring, the twins embrace. For the manuscript, Pellegrin II.1 1978, pp. 165–7.

The drawing of the celestial globe is the same as G4 except for the following differences. Auriga is kneeling and Ursa Maior is here presented as a rabbit. The six columns supporting the horizon ring and the central support for the meridian ring are marble-like decorated. Their orders/capitals are changed. For the manuscript, see Kerscher 1988, pp. 34–6 and a picture of the globe on p. 45, Fig. 46.

256

chapter four

islamic celestial cartography

T

he astronomer, mathematician, and geographer Abū’l-Rayḥān al-Bīrūnī (973–1048) opens his treatise Kitāb fī tasṭīḥ al-ṣuwar wa tabṭīḥ alkuwar (The Book of the Projection of the Constellations and Making Spheres Plane) with the words:1 ‘Acquaintance with the complete constellations comprising the observed stars, from among those with which the heaven is decorated and which are made signs for those observing carefully the heavens and indications for those who wander on dry land or sea, is of no little advantage or utility in both parts of the science of heavenly bodies.’2

To promote the knowledge of the celestial sphere he describes various methods to map the stars on ‘the surfaces of flat planes’, and in this way tried to circumvent the problems with globes that were either too big for transport or too small for showing sufficient detail.3 His treatise exemplifies the great interest of Islamic scientists in mathematical methods to project the sphere on a plane. Foremost among the methods he describes is stereographic projection which is used in the construction of astrolabes.The plane astrolabe is 1 On al-Bīrūnī generally, see Kennedy DSB vol. 2. On the book, see also Richter-Bernburg 1982. 2 Berggren 1982, p. 48. A German translation is in Suter 1922, p. 80. 3 Berggren 1982, p. 50.

a flat device for imitating the daily motion of the Sun and the stars above the local horizon.4 Invented in Greece under circumstances as yet unknown, the astrolabe was transmitted to the Middle East in the eighth century where its design and construction was further developed. The tenth-century bibliographer Ibn al-Nadīm, famous for his Kitāb al-Fihrist (The Catalogue, an index of Arabic books completed in 987–88), recounts that astrolabe making centred on the city Ḥarrān and from there spread over the Middle East.5 The earliest extant text on the astrolabe is written by Abū Jacfar Muḥammad ibn Mūsā al-Khwārizmī (born before 800, died after 847) who was a member of the ‘House of Wisdom’, an institution set up under the ‘patronage of the Abbasid caliph al-Ma’mūn (reigned 813–33).6 Another early text, on the construction of the astrolabe, is by the astronomer Aḥmad ibn Muḥammad ibn Kathīr al-Farghānī, who also worked for al- Ma’mūn.7

4 There is an extensive literature on the astrolabe.The reader could consult for example King 2005 and also the introductions to catalogues such as Gunther 1931/1976, Gibbs 1984, Turner (A) 1985, Stautz 1999,Van Cleempoel 2005, and Pingree 2009. 5 King 1996, p. 166. 6 Charette and Schmidl 2004. On al-Khwārizmī generally, see Toomer DSB vol. 7. 7 Al-Farghānī (Lorch 2005).

islamic celestial cartography The oldest extant dated astrolabe is shown in Fig. 4.1. It was made by the Bagdad instrument maker Nasṭūlus who according to Ibn al- Nadīm was one of the leading astrolabe makers of his time.8 At the back of the astrolabe, on the throne, is the inscription:‘Constructed by Nasṭūlus in the year 315’, that is 927/28.9 Although astrolabes were made long before the present instrument, this dated example has all the characteristics of the earlier Islamic tradition in astrolabe making. It has a diameter of 173 mm and consists of a mater with a throne and rim, a rete with pointers for 17 stars, and a single plate for latitudes 33° and 36°. Numerals are written in abjad notation, as on most early Islamic instruments. A circular

Fig. 4.1 The astrolabe made by Nasṭūlus, dated 927/28. (© The al-Sabah Collection, Dar al-Athar al-Islamiyyah, Kuwait.)

suspension ring is attached to it.The rete is shaped by the ecliptic, the Tropic of Capricorn, an arc of the Equator, and dagger-like pointers. A straight bar connects the ecliptic with the tropic. This simple design makes it easy to use the instrument. Astrolabes based on different projections were also explored. In al-Bīrūnī’s list of methods, there are two more projections that were used for the construction of astrolabes. One of these is called cylindrical projection—nowadays known as orthographic projection. Its construction involves circles and ellipses which are fairly easy to draw.10 The other method mentioned by al-Bīrūnī, known as polar azimuthal equidistant projection, was applied in the construction of the melon-shaped astrolabe, so called because oblique circles on the sphere do not remain circles when projected onto the plane but acquire an oval shape. Elements of orthographic and equidistant projections were used in the medieval maps discussed in Chapter 3, where it is shown that these projections were not yet fully understood. How to construct the oval circles of a melonshaped astrolabe was first described by Aḥmad ibn ‘Abdallah Ḥabash al-Ḥāsib (mid-ninth century), another mathematician and astronomer who was associated with the Abbasid court in Bagdad and who moved with the court to Samarra in 838.11 Ḥabash al-Ḥāsib was a resourceful scientist and the breadth of his achievements is clear from the many works known by his hand. In addition to the treatise on the melon-shaped astrolabe several zīj’s have been attributed to him but only one has survived. A zīj is a work with tables and introductions on how to use them, for solving astronomical problems of all sorts.

8 On Nasṭūlus, see Brieux and Maddison 1974; King 1978; King and Kunitzsch 1983. 9 King 1995b, pp. 79–83, esp. p. 83.

258

10 Puig 1996. 11 Kennedy et al. 1999.

ISLAMIC CELESTIAL CARTOGRAPHY Ḥabash’s Zīj is seen today as his most important work.12 Ḥabash’s treatise on the construction of the common, stereographic astrolabe is not extant but is mentioned in the literature. Fortunately his treatise on the celestial globe and its operation has survived.13 It is said that Muḥammad ibn Ibrāhīm al-Fazārī (fl. second half of the eighth century), a mathematician and astronomer who at the request of the caliph al-Manṣūr worked with an as yet unidentified Indian astronomer on an Arabic translation of a Sanskrit astronomical text, made both the common and the melon-shaped astrolabe, but this cannot be confirmed.14 Al-Farghānī appears not to have valued the melon-shaped astrolabe.15 The construction of the ovals of a melon-shaped astrolabe is indeed not easy, since it cannot be drawn simply by using a ruler and compass.This may explain why no example of the instrument has been found. Al-Bīrūnī himself seems to have rejected the polar azimuthal equidistant projection because

the later European maps discussed in Chapter 5, unacceptable. A noteworthy practical, but non-mathematical, method of mapping the stars in al-Bīrūnī’s list of projections, is the one attributed to the Persian astronomer Abu’l-Ḥusayn ‘Abd al-Raḥmān ibn ‘Umar al-Ṣūfī (903–86). It is said that for making the constellation images in his Kitāb ṣuwar al-kawākib (Book on the Constellations of the Fixed Stars) al-Ṣūfī placed ‘thin paper on the sphere and then drew the figures on it’.17 According to al-Bīrūnī this is not a bad approximation as long as the areas involved are small. Considering the impact of al-Ṣūfī on celestial cartography in general this method will be discussed in more detail below. Of all the mappings discussed, al-Bīrūnī’s globular projection oriented on a plane through the poles seemed to be his preference. Berggren associated this projection with Ptolemy’s second map projection, but Kennedy and Debarnot have argued, rather convincingly, that it may have been designed as a close approximation to ‘only the representation of one of the two halves of the azimuthal equidistant projection.18 the zodiac is possible, either the northern or the Despite al-Bīrūnī’s discussion of the various southern, and the annexation of the other half to it possibilities of mapping the stars, not one mediis useless because of the wideness of the distances every time you increase a little bit in the sphere, eval celestial map is known today to have been and overstepping the acceptable limit by its like- made in the Muslim world.19 This cannot be ness in that’.16 explained by a lack of interest in mathematical Such presentations—he says—have the disad- problems related to projecting the surface of the vantage that the zodiacal constellations are sphere on a plane, as the many texts on the astroincompletely presented since these extend south labe testify. Indeed, the astrolabe was the most of the ecliptic forming the boundary circle. popular instrument of the Middle Ages both in Al-Bīrūnī considered the distortions that arose the Islamic world and in Europe. Stautz mentions by extending them across the border, as done in that today about 700 copies or parts thereof have 12 13 14 15 16

Charette 2007. Lorch and Kunitzsch 1985. Pingree 1970. Al-Farghānī (Lorch 2005). Berggren 1982, p. 52.

17 Berggren 1982, p. 53. 18 Berggren 1982, p. 73; Kennedy and Debarnot 1990. 19 In the seventeenth century a few maps were copied from examples made in Western Europe, see Savage-Smith 1992, pp. 65–70.

259

ISLAMIC CELESTIAL CARTOGRAPHY been preserved.20 Mathematicians and astronomers from the Eastern and Western parts of the Islamic World made the most of it in terms of its practical value to solve problems in finding the hours of prayers and the direction of Mecca. They also developed various new forms such as seen in mixed astrolabes in which stereographic projections from different points of view, northern and southern, are combined.21 Al-Bīrūnī published an extensive work on all forms of astrolabes, including many unusual types, that had already been developed in his time, in his Kitāb fī istīcāb al-wujūh al-mumkina fī ṣancat al-asṭurlāb, a treatise known in several manuscripts but not yet published.22 The universal astrolabe was invented by the well-known instrument maker and astronomer working in Toledo, Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Tujībī al-Zarqālluh (died 1100), who used the orthographic projection on the back of his universal instrument.23 An exhaustive treatment of all the variant ways in astrolabe making was compiled by Abū cAlī al-Ḥasan al-Marrākushī (second half of the thirteenth century), an astronomer from the western part of the Islamic world who had moved to Cairo.24 It is hard to accept that celestial maps were never made in the Islamic world during the Middle Ages.They may have either been lost or are still hidden in one of the many manuscripts that need to be catalogued. But it is not too farfetched to conclude that celestial maps were not a dominant mode for modelling the celestial sphere in Islamic astronomy. Another story can 20 Stautz 1999, p. 11. 21 Lorch 1994; Charette 2003, pp. 66–79. 22 Kennedy et al. 1999, pp. 5 and 184. 23 On al-Zarqālluh, see Puig 2007. On the universal astrolabe, see Puig 1987; on orthographic projection, see Puig 1996. 24 Charette 2003.

be told about globes. Like the astrolabe, the celestial globe was transmitted from Greece to the Middle East. Evidence of the early influx of Greek astronomical artefacts is apparent in the celestial ceiling painting in a building in the desert 80 km east of Amman (Jordan), nowadays known as Quṣayr cAmra built around 705–15. This unique document in celestial cartography is discussed before the main topic of this chapter, Islamic globes, is taken up.

. THE CELESTIAL CEILING OF QUṢAYR C AMRA In 1898 the Reverend Dr Alois Musil of the University of Olmütz in Moravia discovered a building in the desert 80 km east of Amman (Jordan), nowadays known as Quṣayr cAmra, the castle of cAmra.25 This country residence or hunting lodge, a recent view of which is shown in Fig. 4.2, is believed to have been built in the first half of the eighth century. From an arthistorical point of view the building stands out for its many wall paintings, which together constitute a unique document on Islamic workmanship in the early Middle Ages.26 Of interest to the present study is the celestial map that is drawn on the inner sphere of the cupola of the bath house (calidarium). Already at the time of its discovery the wall painting in the bath house was in a bad state. A recent picture is shown in Fig. 4.3. The celestial map was studied in detail in 1932 by Saxl and Beer, using photographs taken by a British expedition led by K.A.C. Creswell.27 They both could identify 33 Ptolemaic

260

25 Musil et al. 1907. 26 Fowden 2004. 27 Saxl 1932 and Beer 1932; Creswell 1932.

4.1 THE CELESTIAL CEILING OF QUṢA YR CAMRA

Fig. 4.2 View of the buildings in Quṣayr cAmra. (Photo from Vibert-Guigue and Bisheh 2007, Plate 89a. Courtesy of the Institut Français du Proche-Orient, Amman.)

constellations or parts thereof. They disagreed about one: Saxl thought he could connect a fragment with Cepheus, which Beer identified as Cassiopeia.28 Saxl believed that the model used in painting the ceiling decoration in Quṣayr c Amra could be connected to celestial maps. This idea was taken over in 1985 by Savage-Smith. In discussing the ceiling decoration in Quṣayr c Amra she takes north examination of the Carolingian planisphere Munich Clm 210 as a standard: ‘Although the fresco at Qusayr ‘Amrah predates the Carolingian map by a century, it seems certain

at this point that the extant Western manuscripts of planispheric celestial maps produced by stereographic projection represents a much older, continuous tradition of mapping that reached Syria by the early eighth century along a route at present unknown.’29

As I have shown in Section 3.2, north’s idea that medieval planispheres were based on stereographic projection cannot be maintained. In 1998 a Franco-Jordanian project was carried out under the supervision of ClaudeVibertGuigue to collect new documentary material of the mural paintings of the buildings in Quṣayr

28 Saxl 1932, p. 290; Beer 1932, p. 298.

29 Savage-Smith 1992, pp. 12–70, esp. p. 16.

261

ISLAMIC CELESTIAL CARTOGRAPHY

Fig. 4.3 The ceiling painting of the bath house (calidarium) in Quṣayr cAmra. (Photo: Claude Vibert-Guigue.) See also Plate IV.

‘Amrah.30 From data obtained during this mission Brunet, Nadal, and Vibert-Guigue identified more Ptolemaic constellations.31 They added Perseus and Auriga to those already identified by

30 Vibert-Guigue and Bisheh 2007. 31 Brunet et al. 1998, p. 106;Vibert-Guigue and Bisheh 2007, Plates 74–82.

Saxl. In all, 35 of the classical 48 Ptolemaic constellations can thus be identified: 15 north of the zodiac (Ursa Minor, Ursa Maior, Draco, Cepheus, Bootes, Hercules, Lyra, Cygnus, Perseus, Auriga, Ophiuchus, Serpens, Aquila, Delphinus, Andromeda),9 in the zodiac (Gemini, Cancer, Leo,Virgo, Scorpius, Sagittarius, Capricornus, Aquarius, Pisces), and 11 south of the

262

4.1 THE CELESTIAL CEILING OF QUṢA YR CAMRA represent circles of constant ecliptic longitude.34 3. A series of concentric circles is centred on the centre N of the cupola and is parallel to the upper border of the frieze marking the lower edge of the cupola. The serrated motif at the top edge of the frieze is made out of units corresponding to 1/60 of a circle, that is 6°.35 The total number of concentric circles (or fractions thereof) is 13 of which in Scheme 4.1, again for the sake of clarity, only 4 have been marked (dotScheme 4.1 Types of circles drawn on the vault of ted lines).36 These parallel circles can represent Quṣayr cAmra. either circles of constant altitude or circles of constant declination. In the former case the cenzodiac (Cetus, Orion, Lepus, Canis Minor, Navis, tre of the cupola would coincide with the zenith Hydra, Crater, Corvus, Centaurus, Ara, Corona of the local horizon of Quṣayr cAmra (geoAustralis).32 In addition to these, there is an image graphical latitude about 32°). In such a local setof an ivy leaf covering a group of stars above ting one would, however, see only half the Leo’s tail, discussed in detail in Section 3.1. celestial sky visible at one time. The presence of The constellations drawn on the inner surface the whole zodiacal band shows that the artist of the vault are arranged with respect to a number tried to draw a complete view of the sky, in of circles which relate to certain coordinate grids which case the parallel circles represent circles of on the celestial sphere. These circles are of three constant declination and the centre N of the kinds as indicated in Scheme 4.1. cupola the celestial north pole. 1. Two concentric circles, drawn as full lines in Scheme 4.1, are centred on a point P at a small The relative positions of the zodiacal constelladistance from the centre N of the hemispherical tions in the zodiacal band show that the celescupola. All zodiacal constellations are located tial sky is presented on the concave surface of within these two circles, indicating that they the vault in globe-view, that is, the ordering represent the upper and lower boundaries of the of the constellations is as usually seen on a conzodiac and that P represents the ecliptic north vex globe and not as seen in the concave sky. Vaults presenting such a ‘globe turned inside pole. 2. Twelve sections of circles pass through P out’ are not uncommon.The Renaissance vault and divide the zodiac into twelve parts, each in the Sala del Mappamondo at Caparola is a of 30°.33 For the sake of clarity only two of them have been drawn in Scheme 4.1. These circles 32 Missing are Corona Borealis, Cassiopeia, Sagitta, Equuleus, Pegasus, Triangulum, Aries, Taurus, Libra, Eridanus, Canis Maior, Lupus, Piscis Austrinus. 33 Brunet et al. 1998, p. 102.

34 The name ‘latitude circle’ is used in some publications but it is confusing.Therefore we shall use the full expression circles of constant ecliptic longitude for them. 35 Brunet et al. 1998, p. 103. 36 Beer 1932, p. 303, recognized only 10 parallel circles but Brunet et al. 1998, p. 112,Table 2, list 13.

263

ISLAMIC CELESTIAL CARTOGRAPHY striking example that is based on a set of globe gores by the French globe maker François Demongenet.37 The presentation in globe-view seen in the vault in Quṣayr cAmra suggests strongly that a (pictorial) model such as a planar map or a globe was used for the construction of the vault’s mapping. The question of the vault’s model is of interest not only for the history of celestial cartography and globe making but also for the prevailing ideas of transmission of astronomical knowledge. Before discussing this, questions concerning the iconography, the date and construction will be addressed.

4.1.1 Iconography Saxl published an extensive analysis of the iconography based on a comparison of constellation drawings taken from a number of Greek-Roman sources and two later thirteen-century EastIslamic globes. The Greek-Roman material included the Farnese globe, the hemispheres in Vatican City MS gr. 1291, and the planisphere in Vatican City MS gr. 1087 discussed in respectively Sections 3.1 and 3.2.38 Saxl noticed that ‘on comparing the various figures of our fresco with the usual stellar representations of the GrecoRoman period, one is astounded by the extreme similarity of the two’.39 Typical examples are the nakedness of the Gemini and the ivy leaf.Actually, Saxl concluded that the attitude of three constellation images, Cepheus, Bootes, and Orion, did not fit into the Greek-Roman tradition but echoed

37 The constellations of the Sala del Mappamondo, Villa Farnese at Caparola are illustrated in Sesti 1991, pp. 121–213. Its art-historical aspect is discussed in Lippincott 1990. The relation with the globe gores of Demongenet is mentioned in Dekker 1999, pp. 69–74, esp. p. 74, note 16. 38 Saxl 1932, p. 290. 39 Saxl 1932, p. 290.

instead the style of the late Middle Ages in the East exemplified by the two Islamic globes. Of special interest are his remarks on Sagittarius, which on the fresco is drawn looking backwards with respect to the direction in which he is going (Fig. 4.4). Such a presentation is not unusual in occidental sources. In a now lost book with constellation images by cUtārid ibn Muḥammad al-Hāsib (ninth century) Sagittarius is reported by al-Ṣūfī as looking backwards towards the east.40 Note that on the fresco of Quṣayr cAmra Sagittarius is heading eastward and looking westward. Also conspicuous in the presentation of Sagittarius is that the garment flutters illogically ahead of Sagittarius in the direction he is going.41 As Saxl noted, the garment should flutter behind him opposite his direction of motion. I shall come back to this inconsistency later. The oriental trend observed in the style of the constellation images made Saxl decide that the artist based his drawing on examples from an oriental edition of a classical Greek manuscript in which some of the images were orientalized.

4.1.2 Can the model be dated? Alongside Saxl’s iconographical study, Beer published an astronomical analysis of the celestial vault of Quṣayr cAmra.42 By adjusting the photographs taken by the British expedition it was hoped that a detailed analysis would become possible. For the sake of comparing the pictures of the cupola with a presumably suitable standard, a map of the whole sky for the epoch ad 700 was constructed in the equidistant projection, in which right ascensions are conserved and parallels to the

264

40 Al-Ṣūfī (Schjellerup 1874), pp. 30–1. 41 Saxl 1932, p. 294. 42 Beer 1932, pp. 296–7.

4.1 THE CELESTIAL CEILING OF QUṢA YR CAMRA

Fig. 4.4 Sagittarius on the ceiling painting in Quṣayr cAmra, with on the left the tail of Scorpius and on the right, in front of Sagittarius’s feet, Corona Australis. (Photo from Vibert-Guigue and Bisheh 2007, Plate 137a. Courtesy of the Institut Français du Proche-Orient, Amman.) See also Plate IV.

Equator are presented proportionally to their distance from the north pole (see Fig. 4.5). A comparison of the vault’s mapping with Beer’s reference map showed that the two agree only in part. For example, the vault’s winter solstitial colure passes through Lyra and the human part of Sagittarius as it should in ad 700. However, the vault’s summer solstitial colure passes through Orion and Lepus whereas in 700 it should pass through Gemini and Canis Maior. Clearly, Orion and Lepus are displaced about 25° from their expected positions in 700. Although Beer considered it therefore ‘unreasonable to try to date the painting from an

astronomical comparison of stellar positions’, he deduced along another route a date between ad 500–1000, consistent with that generally accepted for the building as a whole, and he maintained that date in his later more general paper on astronomical dating.43 The reader is left more or less in the dark about his arguments:

265

‘There is no space for a detailed discussion of the various attempts made for this purpose ( ...). Nevertheless the relative position of equator and ecliptic allow us to make a rough estimate of the date.44 43 Beer 1932, p. 303; Beer 1967, p. 187. 44 Beer 1932, p. 303.

ISLAMIC CELESTIAL CARTOGRAPHY

Fig. 4.5a Beer’s reference map for 700 ad (from Beer 1932, p. 299, Fig. 354).

A comparison of Beer’s Fig. 354 and Fig. 356, especially in regard to the position of the point of intersection (γ), shows a change caused by the ‘Precession’, which leads back to a date between A.D. 500-1000.’ From Beer’s drawings (see Fig. 4.5 a-b) it is clear that he identified the equinoxes as the points of intersection between the circle he had identified as the map’s Equator and the circles of constant

longitude for respectively 0° and 180°.45 Both points appear to lie on the southern boundary of the zodiacal band whereas one would have expected them to be situated somewhere in between the zodiacal boundaries because the equinoxes lie by definition also on the ecliptic in

266

45 Beer 1932, figure 356 on p. 301.

4.1 THE CELESTIAL CEILING OF QUṢA YR CAMRA

Fig. 4.5b Beer's interpretation of the system of circles and his reconstruction of the missing coordinates on the ceiling painting (from Beer 1932, p. 301, Fig. 356).

the middle of the zodiacal band. In order to identify the Equator among the many parallel circles, Beer determined the mean declination (for ad 700) of a series of stars on or near each of them.46 Unfortunately this method is dependent on the chosen epoch of 700. Because of this, the date of the vault’s mapping arrived at by Beer 46 Beer 1932, pp. 302–3.

cannot be relied upon.Yet, for a long time Beer’s dating has received the benefit of the doubt since no better data were available. Beer had to make his analysis from rather unmanageable photographic material, the perspective distortions of which he believed to have eliminated by means of an ‘aerotopograph’.Yet from a methodological point of view a more lucid analysis is certainly desirable.

267

ISLAMIC CELESTIAL CARTOGRAPHY New quantitative data were collected during the above mentioned Franco-Jordanian mission from tracings of the frescos on transparent plastic sheets which served to make a new astronomical analysis of the celestial map.47 Brunet et al. presented data on the positions of each identifiable constellation depicted on the inner surface of the cupola.48 These positions were expressed by two coordinates: λQ and hQ. The first coordinate, λQ, measures the mean distance of a constellation with respect to the circles of constant ecliptic longitude drawn on the cupola and the second one, hQ, is the mean angular distance of the constellation from the upper border of the frieze marking the lower edge of the cupola.49 The data used by Brunet et al. have been reproduced here in Table 4.1. In the first column the abbreviated name of the constellation is given. This is followed in columns 2–3 by the values of hQ and λQ. Next we added in column 4 the corresponding averaged Ptolemaic longitude λPt which Brunet et al. calculated at the same time. In columns 5–8 some related data are provided which are discussed below. To evaluate the measured data Brunet et al. assume that the transfer of the constellations from the model sphere to the cupola would be governed by the relation λQ = λS

(4.1)

where λS is the averaged ecliptic longitude of the same constellation on a presumed model sphere.This assumption is based on the idea that 47 Brunet et al. 1998, p. 98. 48 The positions of the constellations were expressed in weighted averages of the stars belonging to a constellation. 49 Note that these coordinates should not be confused with the well known longitude λ and declination δ commonly used for marking a position on the celestial sphere.

the artist measured λS on a globe at his disposal and used this value to locate the constellations correctly with respect to the circles drawn on the vault. If correct, one can determine the differences between the averaged longitudes of the constellations on the model and the corresponding averaged Ptolemaic values: ∆λ = λS − λPt = λQ − λPt

Since the longitudes of the stars increase slowly in time by precession, ∆λ could in principle be used for dating the model. The differences ∆λ calculated by Brunet et al. are listed in Table 4.1 column 5. It appears then that the vault’s averaged longitudes λQ are in the mean in excess of the averaged Ptolemaic values λPt by 18.1°, with a standard deviation of 19.7°. Such excessive values cannot be caused by precession and tell us that the locations of the vault’s constellations are influenced by a number of systematic errors other than precession. In order to pursue this matter in more detail Brunet et al. determined the distribution function of the deviations ∆λ from their mean value = 18.1°, that is of ∆λ -. On the basis of this distribution function the constellations were divided into three groups.We have included these deviations ∆λ - in Table 4.1 (column 6) to show how the division into (three) groups depends on the (increasing) values of ∆λ -. One group has deviations ∆λ - which differ more than one standard deviation (19.7°) from the mean value (18.1°). On the one (negative) side one has UMi, And, Per, Cep, and Dra with deviations varying from -46.9° to -27.1° and on the other (positive side) are UMa and Aqr with deviations of respectively 25.5° and 28.7°.These deviations reflect serious misplacements and for this reason these constellations are excluded from further analysis.

268

4.1 THE CELESTIAL CEILING OF QUṢA YR CAMRA Table 4.1 Basic data of the celestial map in Quṣayr cAmra Const

hQ

lQ

lPt

∆l = lQ-lPt

∆l -

Gr 1

Gr 2

UMi And Per Cep Dra Aql Ara Cen Del Lyr Cap Sgr Ser Oph Cyg Cet Sco CMi CrA Psc Crt Her Gem Boo Crv Hya Com Ori Navis Vir Leo Cnc Lep Aur UMa Aqr

84.5 55.4 62.6 67.5 72.5 37.0 14.0 11.2 34.2 42.2 23.2 19.8 33.8 33.5 46.8 16.0 19.8 28.5 8.0 33.4 20.8 49.0 44.8 39.5 18.8 19.9 48.7 34.1 14.9 32.8 35.0 45.0 11.1 62.3 71.1 29.9

73.0 333.5 15.0 344.6 41.5 260.5 237.5 190.1 294.1 270.1 289.6 264.9 230.9 238.5 307.5 9.7 251.1 110.6 281.7 7.8 183.3 249.8 108.6 212.4 199.0 156.2 179.7 90.7 159.5 183.6 170.5 136.2 90.6 100.1 148.8 350.9

101.8 1.3 31.1 354.5 50.5 262.2 237.7 189.3 289.1 263.3 281.6 255.9 220.5 227.0 295.3 354.4 231.9 85.0 253.1 339.0 153.0 218.9 77.2 180.2 166.3 123.3 145.9 56.7 125.3 148.8 134.3 99.5 53.4 62.8 105.2 304.1

-28.8 -27.8 -16.1 -9.9 -9.0 -1.7 -0.2 0.8 5.0 6.8 8.0 9.0 10.4 11.5 12.2 15.3 19.2 25.6 28.6 28.8 30.3 30.9 31.4 32.2 32.7 32.9 33.8 34.0 34.2 34.8 36.2 36.7 37.2 37.3 43.6 46.8

-46.9 -45.9 -34.2 -28.0 -27.1 -19.8 -18.3 -17.3 -13.1 -11.3 -10.1 -9.1 -7.7 -6.6 -5.9 -2.8 1.1 7.5 10.5 10.7 12.2 12.8 13.3 14.1 14.6 14.8 15.7 15.9 16.1 16.7 18.1 18.6 19.1 19.2 25.5 28.7

— — — — — X X X X X X X X X X X X

— — — — —

— —

X X X X X X X X X X X X X X X X X — —

hQ, λQ and λPt are taken from Brunet et al. 1998, their Table 1.

Brunet et al. divided the remaining data on statistical grounds into two groups, as is indicated in Table 4.1 in columns 7 and 8.50 This division seems to be supported by the division in the 50 Brunet et al. 1998, pp. 109–10.

cupola. Group 1 consists of 12 constellations, most of which are pressed together in the area between the eastern and southern window of the cupola and have longitudes λQ within the range of 220°–310°. There are two exceptions: Centaurus on the north side of the east window

269

ISLAMIC CELESTIAL CARTOGRAPHY and Cetus on the south side of the western window. Both constellations seem to have been pushed backwards by the presence of the window. Group 2 consists of 17 constellations, most of which have longitudes λQ within the range of 0°–220°. Here there are also two exceptions: Hercules and Corona Australis which lie between the eastern and southern window.The deviating position of Corona Australis is probably caused by that of Sagittarius (see Fig. 4.4), the horse’s part of which is below Scorpius, contrary to what is described by Ptolemy. It looks as if the horse’s part of Sagittarius was mirrored in order to gain space in the narrow region between the eastern and southern window. This idea is supported by Sagittarius’s garment, which should flutter behind him opposite to his direction of motion but in the vault flutters illogically ahead of him in the direction he is going.51 Saxl thought that all this was not an invention of the artist, but if the horse’s part of Sagittarius was indeed mirrored in order to gain space, as I believe to be the case, it was his doing. Had the horse’s part of Sagittarius been properly presented Corona Australis would have been found east of the winter colure instead of west of it as it is now. The artist consistently placed Corona Australis where it is expected, at the (mirrored) forefeet of Sagittarius (see Fig. 4.4). The mean values for these two groups appear to differ significantly. The constellations in Group 1 differ in the mean from the averaged Ptolemaic values λPt by 8.0° with a standard deviation of 6.1°, those in Group 2 differ in the mean by 32.8° with a standard deviation of 3.2°. Thus Group 1 is on average displaced in longitude from Group 2 by about 25°. This difference is close to a whole sign which cannot be caused 51 Saxl 1932, p. 294.

simply by pressing the constellations together. Brunet et al. assumed, not unreasonably, that the constellations of Group 2 were unintentionally but systematically forwarded by 30°. Thus their next step was to reduce the longitudes of the constellations in Group 2 by 30° and then to recalculate the mean excess of all the constellations in both groups with respect to Ptolemy. The final result is that the vault’s longitudes are found on the average in excess of the Ptolemaic values by the amount of 5.0° ± 5.3°.52 In Table 4.2 the several calculations of the mean values and the corresponding standard deviations have been summarized. In the first column the groups are listed and in the next the number of constellations in each group. This is followed by the mean value of the differences λQ-λPt and the corresponding standard deviations. An asterisk (†) means that the longitudes of

Table 4.2 Mean values () and standard deviations (St Dev) of the excess of longitudes with respect to Ptolemy for selected groups of constellations Groups

n

St Dev

All constellations Group 1 + 2 Group 1 Group 2 Group 2† Group 1 + 2†

36 29 12 17 17 29

18.1 22.6 8.0 32.8 2.8 5.0

19.7 13.0 6.1 3.2 3.2 5.3

† means that the longitudes λQ listed in Table 1 are corrected by 30º.

52 Brunet et al. 1998, p. 109, mention a mean value of 4.8º. We could not reproduce this but found 5.0º instead which is not very different. Please note that they mention an error of the mean of ± 1.0º which is related to the standard deviation of 5.3º listed by us by the factor √ 29 = 5.4 where 29 is the number of constellations included in the mean value.

270

4.1 THE CELESTIAL CEILING OF QUṢA YR CAMRA the constellations in Group 2 have been reduced by 30°. Of their final result Brunet et al. claim: ‘This value is significantly different from zero and can be explained only by a correction of precession applied to Ptolemy’s longitudes.With the rate of 1° per century indicated by Ptolemy himself, the difference found gives the epoch of the model used by the painter [as] 620 ± 100.’ 53

The question that forces itself upon us is how we can be sure that the final mean value of 5.0° ± 5.3° of the deviations of the longitudes from the corresponding Ptolemaic values can only be explained by precession. It seems clear that the longitudes of Group 2 appear to have been systematically forwarded by 30°, but is this really the only systematic error in the data other than precession? For example, all longitudes of the constellations in Group 1 are assumed to have remained undisturbed in the transfer process. One can see quite easily that the contrary is the case by examining the longitudinal distances between subsequent zodiacal constellations and comparing them with Ptolemy’s values (Table 4.3). These relative distances are independent of precession and therefore a good measure of the reliability of the data. In the range from Pisces toVirgo (Group 2) the relative distances between subsequent zodiacal constellations compare well with those of Ptolemy, but those in the opposite range from Virgo to Pisces (that is, around the winter colure where most of the constellations in Group 1 are located) have distances that are very much disturbed. Scorpius is pushed back with respect to Virgo by about 15° and Sagittarius by about 25°.This latter value is maintained for Capricorn. Aquarius is placed so that it appears to be pushed forward with

53 Brunet et al. 1998, pp. 109–10.

Table 4.3 Distances in longitudes between zodiacal constellations Distance between

Vault

Ptolemy

Vault-Pt Remarks

Psc-Gem Gem-Cnc Cnc-Leo Leo-Vir Vir-Sco

100.8 27.6 34.3 13.1 67.5

98.2 22.3 34.8 14.5 83.1

2.6 5.3 -0.5 -1.4 -15.6

Sco-Sgr Sgr-Cap Cap-Aqr

13.8 24.7 61.3

24.0 25.7 22.5

-10.2 -1.0 38.8

Aqr-Psc

16.9

34.9

-18.0

Window interferes with zodiac

Window interferes with zodiac

respect to Virgo by about 12°, a difference compensated by locating Pisces such that its distance to Virgo is only 6° from what is to be expected. The data in Table 4.3 show beyond doubt that the locations of the constellations in Group 1 are greatly disturbed.This is not very suprising since the lowest part of the zodiac is centred on the winter solstitial colure which happens to be placed between the eastern and southern windows. Some interference can thus be expected, implying that constellations are pushed together and that systematic errors other than precession cannot be excluded for the data in Group 1. It is thus clear that the locations of the constellations in both groups have serious systematic errors other than precession. Those of Group 1 are not sufficiently regular that one can hope to correct for them in a reliable manner.Therefore one should dismiss the constellations in Group 1 in the procedure followed by Brunet et al. for deriving a date. Those of Group 2 have a mean value in excess of the Ptolemaic values by

271

ISLAMIC CELESTIAL CARTOGRAPHY 32.8° ± 3.2°. The greater part of the excess is most likely caused by a systematic error of a whole sign of 30°, leaving a small excess of 2.8° with respect to Ptolemy. With so many errors around it is hard to believe that this remaining excess of 2.8° represents a reliable estimate for the amount of precession between Ptolemy’s epoch and that of the model globe. It could easily derive from errors in the model itself or from inaccuracies in transferring the constellations from the model to the cupola. This conclusion contradicts the suggestions of Brunet et al. that the model maker was acquainted with precession and consequently that Ptolemy’s Almagest, in which precession was described for the first time in detail, was known in the Arabic world as early as the seventh century.There is in our opinion no sound reason to doubt the generally accepted opinion that the Almagest was first translated into Arabic at the turn of eighth century.54 The quantitative data of Brunet et al. reflect the overall inaccuracy of the vault’s celestial map and does not provide a sound basis for a precise dating. Despite all statistics the problem of dating the model remains unsolved and Beer’s first assessment that it is ‘unreasonable to try to date the painting from an astronomical comparison of stellar positions’ appears also today fully justified.

4.1.3 The parallel circles In order to relate the celestial map painted on the inner surface of the cupola to the model it is important to know which of the parallel circles represent which of the main celestial circles: the Equator, the tropics, and so on. To solve this problem Brunet et al. assumed that the value hQ of a constellation on the vault is in principle 54 Kunitzsch 1974, pp. 15–82.

related to the declination on the original model δS through the equation

(90° − h Q ) = ρ (90° − δ S )

(4.2)

where ρ is called the reduction factor.This relation is based on the assumption that the artist reduced the declinations of the model by a factor ρ to fit the map into the hemispherical cupola as shown in Scheme 4.2. Once ρ is known one can determine the sphere equivalents δS of the vault’s parallels from the corresponding values hQ and find out what circles they represent.Then also the geographical latitude used for the model globe or planisphere can be calculated from the ever-visible and invisible circle, presuming that these circles are represented. In order to determine the reduction factor ρ, Brunet et al. calculated declinations δC from the measured averaged values λQ and the theoretical averaged Ptolemaic latitudes βPt of the constellations. The idea behind this is that the ecliptic latitude is not affected by precession. By assuming that δC = δS and by correlating the values of hQ and δC, Brunet et al. obtained a value of the reduction factor ρ = 0.641 ± 0.022. The uncertainty in the value of ρ implies that the model’s ever-invisible circle is drawn for a geographical latitude between 34.8° and 44.4°. Using secondary arguments Brunet et al. in the end selected the value 0.625 = (5/8) for the reduction factor of the cupola and concluded from this that the original model was based on a globe designed for geographical latitude 36°. When the reduction factor is subsequently applied to the series of 13 parallel circles marked in the vault, a number of unconvincing interpretations of the meanings of some of them follow, the two most important ones of which are that: 1. The Equator is supposed to be represented by a belt bounded by values of hQ of 28.5 and

272

4.1 THE CELESTIAL CEILING OF QUṢA YR CAMRA

Scheme 4.2 Reduction of circles of constant declination on the sphere to circles on the cupola.

39.0, that is about 10° wide after the example of the zodiac instead of by a circle.55 2. The median of two particular parallels (with hQ equal to 53.5° and 59.5°) is identified with a so-called zenith-circle connecting stars that culminate in the zenith at Rhodes or any other place with a geographical latitude of 36°. This circle is also supposed to be represented as a belt, after the example of the zodiac.56

the ever-visible, and the ever-invisible circles. So many circles seem to hint towards a regular grid. Beer implicitly used this hypothesis in his analysis where he assumed that the declinations of these circles were multiples of 10°.57 As mentioned above, Beer tried to prove this thesis by using as a standard the declinations of the stars for the year ad 700. Considering the many errors in the positions of the constellations marked in the vault such an approach does not seem These particular interpretations of some of the convincing. vault’s parallels are not very convincing because As an alternative approach I have worked out no examples of globes and maps are known with a hypothesis similar to Beer’s but using a differthe Equator presented as a belt and no reference ent assumption, namely that the division of the is known in Antiquity to a zenith circle or belt scale in declination on the model sphere is the marking stars culminating in the zenith of a same as the one in right ascension. This means place. Finally, not every circle marked in the that the vault’s parallels would represent a series cupola has been explained by Brunet et al. which on the model sphere would be equivalent In their interpretation of the parallel circles, to multiples of 1p = 1/60 part of a circle = 6°, a Brunet et al. bypassed the most striking aspect of division that is also used in the serrated motif at the problem of parallels, namely that their the top edge of the frieze at the base of the number (13) is not restricted to the five wellcupola.58 As mentioned in Chapter 1, many known celestial circles: the Equator, the tropics, 55 Brunet et al. 1998, p. 116. 56 Brunet et al. 1998, p. 117.

57 Beer 1932, pp. 302–3. 58 Brunet et al. 1998, p. 103.

273

ISLAMIC CELESTIAL CARTOGRAPHY Table 4.4 Declinations PS and their equivalents in the vault, PQ nr

PS

PQ

TS

TS-PQ

1 2

66 54

74.25 66.00

75.2 67.8

0.9 1.8

3 4 5 6

42 36 30 24

62.50 59.50 53.50 49.50

60.4 56.7 53.0 49.3

-2.1 -2.8 -0.5 -0.2

7 8 9 10 11 12

18 12 6 0 -12 -24

46.75 41.00 39.00 32.50 28.50 18.75

45.6 41.9 38.2 34.5 27.1 19.7

-1.2 0.9 -0.8 2.0 -1.4 0.9

13

-54

0.00

1.1

1.1

Remarks Polar circle Ever-visible circle

Tropic of Cancer

Equator Tropic of Capricorn Everinvisible circle

TS: predicted values, calculated from PS by using eq. 4.3 and the reduction factor 0.617

antique sources on globes mention the use of a unit of 6°. Our method for analysing the data differs from that used by Beer because measured data for the parallel circles were published by Brunet et al. To each circle, numbered 1–13 for the sake of easy reference, I have allotted a value PS which is a multiple of 6°. These values are to be correlated to the measured values PQ published by Brunet et al.59 These data are summarized in Table 4.4. We assume that PS and PQ are linearly related as follows: (90° − PQ ) = ρ (90° − PS )

(4.3)

Using the method of least squares, a good correspondence is obtained between the data in 59 Brunet et al. 1998, my values PQ are equal to the values h in their Table 2 on p. 112.

columns (2) and (3) for a value of the reduction factor ρ = 0.617 ± 0.005 (see Scheme 4.3).60 The mean error of our reduction factor is 4 to 5 times less than that obtained by Brunet et al.61 With this reduction factor (= 0.617) one can calculate actual declinations TS and their difference with respect to the values measured by Brunet et al. (TS - PQ). One sees that the maximum deviation is 2.8°, in line with the dispersion of 2.3° found by the method of least squares. The present result is a good alternative to that of Beer and Brunet et al. because it is independent of any epoch and it has the advantage of explaining the presence of so many parallels in a natural way as a regular grid introduced by the artist. There is no need to presuppose belts or so-called zenith-circles. It also shows the intention of the painter to scale the map down with a reduction factor 0.625 (= 5/8) but owing to several causes a value of 0.617 was realized in the end. Our hypothesis implies that the painter used a standard size based on the unit of 6°.62 The main celestial circles presented on Greek and Roman maps and globes, the Equator, the tropics, the ever-visible and invisible circles, are all present on the inner surface of the cupola (cf. Table 4.4).63 The lower edge of the cupola corresponds to a declination of -54° which is the ever-invisible circle for a geographical latitude

60 If the last value of 54º is left out a mean value of p = 0.614 ± 0.006 is obtained.This reduction factor would imply that the vault’s circle at 0º is equivalent to the parallel of -56.6º, sufficiently close to -54º to include it in the statistics. 61 Compare the scatter in Scheme 4.3 with that of Brunet et al. 1998, p. 114, in their Fig. 9. 62 Assuming a diameter of the cupola of 260 cm, the unit of 1p = 1/60 part of a circle = 6º corresponds to 13.6 cm. 63 Geminus (Aujac 1975), V.46 pp. 28–9, described how to mark these circles on a globe.

274

4.1 THE CELESTIAL CEILING OF QUṢA YR CAMRA

Scheme 4.3 The relation between (90 º-PQ) and (90 º-PS).

of 36° which Geminus says was used in all globes made in Greece, despite the well-known fact that these circles vary from place to place.64 This latitude was also derived by Brunet et al., although by a less transparent method than that used here.Also of interest is that the circle representing the Equator intersects the circles of constant longitude for respectively 0° and 180° in points located in the middle of the zodiacal band, as one would expect.

4.1.4 On the model Although the analysis of the positional data is now as transparent as possible, a clear picture of the model used by the maker is still lacking. The

64 Geminus (Aujac 1975), XVI.12, p. 78.

constellations depicted on the inner surface of the vault occur all on medieval maps and most also on antique celestial globes. On both objects the main celestial circles centred on the north pole are drawn proportionally to their distance from the north pole. Only planispheres share with the vault’s map the characteristic property that the size of the Tropic of Capricorn exceeds that of the Equator. Some of the extant planispheres have the zodiac represented by two concentric circles around the ecliptic north pole and about half of the known medieval copies present the constellations as they are seen on a globe just as it is seen on the fresco. Saxl’s suggestion that the vault’s mapping is based on ‘a model of a flat surface’, seems to be supported by a number of iconographic details. The ivy leaf above the tail of Leo connects the

275

ISLAMIC CELESTIAL CARTOGRAPHY vault’s mapping with the hemispheres.65 Saxl did not distinguish between planispheres and hemispheres but we note that the ivy leaf does not feature in planispheres. Saxl was not aware that the ivy leaf was also drawn on an early Islamic globe.66 Another example is the deviating position of the head of Hercules with respect to that of Ophiuchus. This displacement was a common error in Antiquity: in eight of the ten known medieval planispheres and on two of the three antique globes Hercules is ahead of Ophiuchus, exactly as is seen on the vault. Saxl’s other feature of Ophiuchus standing with two feet on Scorpius is also not exclusively part of planar models.This feature is also seen on the recently discovered antique globes. Therefore, Saxl’s iconographic arguments in favour of planar models are not conclusive. Another possibility is that the artist employed a celestial globe. Medieval planispheres lack the circles of constant longitude emerging from the vault’s ecliptic pole. These circles are a standard feature of all later Islamic globes (see Section 4.4).67 It is on account of the vault’s circles of constant longitude that Brunet et al. assumed that the painter worked directly from a globe. The presence of circles of constant longitude in the cupola understandably draws the attention particularly to Islamic globes. However, this cannot be the whole story, because another very striking characteristic of Islamic globes, namely that all constellations are facing outwards, is absent. The constellations depicted in the vault are mostly seen from behind. This rather calls for a source in the Greek-Roman tradition. 65 Saxl 1932, p. 290. in Vatican City, MS gr. 1087 and Vatican City, MS gr. 1291. See also the discussion in Section 3.1. 66 Dekker and Kunitzsch 2008/9. 67 Savage-Smith 1985, p. 17.

In order to obtain a more complete picture I have listed in Table 4.5 for a number of features the correspondences between the vault and the origin of its possible model. For source material in the Greek-Roman tradition we used the globes described in Chapter 2 and the maps in Chapter 3.As a standard for Islamic globes, if any were common in this period, I have used the characteristics of the oldest surviving copies.68 Details suggest that these oldest surviving Islamic globes represent a tradition that precedes the one based on al-Ṣūfi, more commonly seen on later Islamic globes as discussed below. The first thing to note from Table 4.5 is that of the features listed in Column 1 only two are completely lacking in the sources connected with the Greek-Roman tradition and twelve are absent in the early Islamic globes.The absence of the tropics and ever-visible and invisible circles on early Islamic globes is a feature shared with later Islamic globes. The same holds for the use of units of 5° for dividing circles, used in early Islamic globes. This contrasts strongly with the Greek tradition of using units of 6° and the geographical latitude of 36° described in relation to globes by Geminus. The presence of these features in the vault seems to favour a Greek globe as its model. Among the striking positional and iconographic features of the vault’s constellations, there is actually only one, Ptolemy’s ivy leaf, that is seen on one of the early Islamic globes. However, it is also depicted in celestial hemispheres as Saxl has already pointed out. All these hemispheres show the sky as it is seen on a celestial globe and its prototype may therefore have been copied from a globe in the Greek-Roman tradition. Early Islamic globes are exclusive in

276

68 Dekker and Kunitzsch 2008/9.

4.1 THE CELESTIAL CEILING OF QUṢA YR CAMRA Table 4.5 Characteristics of Quṣayr cAmra’s map compared with other sources No Feature

QA

Greek-Roman Earliest Islamic

vault globes maps

globes

P RE S E N T A T I O N

1 2

globe view + seen from behind +

+ ±

± ±

+ –

–

–

+

–

–

–

[+]

–

–

+ + +

+ + +

+ – –

±

±

–

+ +

± ±

+ –

CONSTRUCTION

1 2 3 4 5 6 7 8 9

Circles of constant + longitude Equidistant grid + of parallels Scales based + on 6º Equator + Tropics + Ever-visible and + invisible circles Geographical + latitude 36º Ecliptic – Zodiac +

S T R I K I N G P O S I T I O N A L F E A T U RE S

1

2

Head of + Ophiuchus ahead of that of Hercules Ophiuchus with + feet on Scorpius

±

±

–

±

±

–

+ +

[–] ±

± ±

± –

+ +

± +

+ ±

– –

I C O N OG R A P HY

1 2 3 4

Ivy leaf Hercules with a club Lyra as a lyre Sagittarius as a centaur

+: present; – : absent; ±: is present on some maps and globes and absent on others

depicting Lyra not as a lyre but as a tortoise or a vase. But the Lyra on the vault is definitely not a tortoise nor a vase.

The presentation of Ophiuchus standing with both feet on Scorpius raises another question. Aratus describes Ophiuchus as standing upright and trampling Scorpius with both his feet—one placed on the beast’s eye and another on his chest as is regularly seen on planispheres and globes belonging to the descriptive tradition (see Section 2.3).69 A different configuration is described in the Ptolemaic star catalogue and depicted on the early Islamic globes. The image of Ophiuchus standing with both feet on Scorpius is thus typical for the Greek-Aratean tradition. Taking all evidence together we find that most details point to a Greek model globe in the descriptive tradition. Nevertheless, to the modern mind there remain two troubling questions on the vault in Quṣayr cAmra: the presence of great circles passing through the ecliptic poles and the boundaries of the signs and its presentation in globe-view. No Greek-Roman globes are known with graduated circles and circles of constant ecliptic longitude. This does not necessarily mean that such globes did not exist. We know too little of the development in production of globes in Antiquity. One cannot exclude the possibility that circles of constant longitude were added to globes and that such globes were graduated in right ascension and declination. If so, the design of constellations on such globes must have become mixed up with that of decorative globes illustrating Aratus’ Phaenomena.The tenthcentury astronomer al-Ṣūfi wrote that he has seen many globes from Ḥarrān. He criticized these globes which he calls ‘kurāt musawwarah’ (decorated globes) because their makers did not know the true positions or magnitudes of the

277

69 Aratus (Mair 1921), pp. 212–13.

ISLAMIC CELESTIAL CARTOGRAPHY stars.70 The seventh-century Byzantine author Leontinus reports that ‘la plupart des sphères dont on se sert actuellement, ne s’accordent pas en plusieurs choses avec celle de Ptolemée, ni dans la plupart avec celle d’Aratus’.71 The globes referred to by Leontinus may well have been known in the near east and have served as the example for the early phases of Islamic cartography.The presentation in globe-view is a problem of a different kind. At first sight it may seem logical to conclude from the vault’s presentation that a globe was used as a model. However, nothing is less evident. In order to present the mapping in globe-view one must, so to speak, turn the globe inside out before it is drawn on the inner surface of the cupola.This process was certainly not carried out directly. For the artist it would have been logical to make first a drawing, then to enlarge it, and subsequently paint it on the surface of the cupola. In this process a number of things could have happened: the images could have been turned round to make the globe look turned inside out and errors of the order of a whole sign of 30° could have been made. Perhaps one day new evidence will be found that can help to further elucidate how the mappings in Quṣayr cAmra were actually realized.

. THE ISLAMIC MATHEMATICAL TRADITION Abū l-Futūḥ Aḥmad ibn Muḥammad ibn al-Sarī Najm (Kamāl) ad-Dīn, called Ibn al-Ṣalāḥ, (died 1154) tells in his critique on the reliability of star positions in the Ptolemaic catalogue, that he read

70 Savage-Smith 1985, p. 23. 71 Halma 1821, pp. 65–74.

a book describing a Greek celestial globe (kitāb fī iqtiṣāṣ kura yūnānīya) on which the longitude of α Leo was 6° in excess of the corresponding Ptolemaic value.72 Assuming a Ptolemaic rate of precession of 1° in 100 years this would point to an epoch of this Greek globe of around ad 738. Other globes were mentioned by the historian and scholar ‘Alī ibn Yūsuf Ibn al-Qifṭī (d. 1248). In his Ta’rīkh al-ḥukamā’ (The History of Learned Men) al-Qifṭī remarks that Ibn al- Sanbadī saw in Cairo two globes, one of silver made by al-Ṣūfī and another one of brass which was attributed to Ptolemy: ‘this globe was taken from the Amīr Khālid ibn Yazīd ibn Mucāwiyah’, an Umayyad prince who died in 704.73 Al-Ṣūfī himself says that he examined a great and splendid globe made by cAlī ibn cĪsā (early ninth century?).74 Ibn al-Ṣalāḥ saw a globe from the city of Ḥarrān (kura min camal al-Ḥarrānīyīn), with Centaurus on it drawn with a lance.75 Another globe from Ḥarrān was made by Jābir ibn Sinān al-Ḥarrānī (ninth century), who was a famous instrument maker and the father of the astronomer al-Battānī, about whom more below.76 So there is ample evidence of globe making in Ḥarrān in the ninth century. 72 Ibn aṣ-Ṣalāḥ (Kunitzsch 1975), pp. 18 and 72–3; Kunitzsch 2005, p. 125 73 Savage-Smith 1985, p. 300, note 112; Kunitzsch 1974, p. 76, note 196. Ibn al-Qifṭī’s Arabic biographical dictionary, as it is preserved today, is only an extract, made in 1249/647, from a longer treatise titled Kitāb Ikhbar al-‘ulama’ bi-akhbar al-ḥukamā’ (Notices of Scholars with the Accounts of Learned Men) which is now lost, see Dietrich 1999. 74 Al-Ṣūfī (Schjellerup 1874), p. 31, refers to cAlī ibn cĪsā al-Ḥarrānī. Savage-Smith 1985, p. 18 and p. 300, note 86 says that al-Ḥarrānī has been added by the editors to the name of c Alī ibn cĪsā. Instead he would have been working in Baghdad and Damascus.A gloss in the Leiden manuscript h of the Arabic translation by al-Ḥajjāj refers as well to a globe made by cAlī ibn c Īsā, see Kunitzsch 1974, p. 77, note 197. 75 Kunitzsch 1974, p. 54, note 145 and p. 339. 76 Kunitzsch 1974, p. 77, note 197.

278

4.2 THE ISLAMIC MATHEMATICAL TRADITION

4.2.1 Star catalogues The impact of Greek science on the Muslim world was greatly influenced by the translation movement beginning in the eighth and continuing into the tenth century. Many books by famous Greek, Persian, and Indian authors were translated into Arabic during the reign of the caliph al-Ma’mūn. Among these books was Ptolemy’s Mathematike Syntaxis which was known by the Arabs as al-Majasṭī, and later became known in the Latin West as the Almagest. Not all books translated into Arabic have been preserved. For example,Aratus’s Phaenomena was translated in the first decades of the ninth century, possibly by the Jewish astronomer Abū c Uthmān Sahl b. Bishr b. Ḥabīb b. Hāni’, who was the court astronomer of Abu’ṭ-Ṭaiyib Ṭāhir ibn al-Ḥusain (159–207 H = 775/6–822/3), a general of the caliph al-Ma’mūn and governor of Khurāsān.77 Ibn al-Ṣalāḥ says that he knew five different translations of Ptolemy’s Mathematike Syntaxis, one Syriac and four Arabic versions: an old version made under the caliph al-Ma’mūn by one al-Ḥasan ibn Quraysh of whom nothing is known, a version by al-Ḥajjāj ibn Yūsuf ibn Maṭar and Sarjūn ibn Hilīyā al-Rūmī, completed in ad 827/28, another translation made by Isḥāq ibn Ḥunayn in about ad 880–90, and finally, a version of the translation of Isḥāq revised by Thābit ibn Qurra (d. 901).78 Of these Arabic translations only two have survived: the one by al-Ḥajjāj and the other by Isḥāq with revisions by Thābit.79

77 Honigmann 1950. 78 Ibn aṣ-Ṣalāḥ (Kunitzsch 1975), p. 15. An extensive review of all these Arabic translations is in Kunitzsch 1974, pp. 15–82. 79 These two translations have been edited in Kunitzsch I 1986.

Already under the patronage of the caliph al-Ma’mūn (813–33) a group of astronomers, known as the aṣḥāb al-mumtaḥan, (authors) of the revised (tables), had been invited to make observations to verify and where necessary adapt the parameters used by Ptolemy in the Almagest. These mumtaḥan observations showed that a number of the parameters had changed. For celestial cartography two of these parameters are of interest: the obliquity of the ecliptic and the rate of precession. Ptolemy uses a value for the obliquity of the ecliptic of 23° 51´ 20˝ whereas the astronomers of al-Ma’mūn measured a value close to 23° 35´.The Ptolemaic rate of precession of 1° in 100 years was also rejected but their opinions on the alternative varied somewhat. For example, the value of 1° in 66 years, determined by the mumtaḥan astronomers, was adopted by the astronomers al-Battānī and al-Ṣūfī in their star catalogues but the Egyptian astronomer and mathematician Ibn Yūnus (ca. 950, died in Cairo in 1009) determined a value of 1° in 70¼ Persian years (of 365 days).80 In order to control the variations in the obliquity of the ecliptic and in the rate of precession a new theory of precession was developed which became known as trepidation, on which more is said below. The star catalogues in the translations of the Almagest constitute the basic material for making celestial globes in the mathematical tradition. A number of astronomers produced separate catalogues for specific epochs using the new parameters for the rate of precession. One of the oldest in this series is a catalogue of 533 stars excerpted from the Ptolemaic star catalogue by Abū cAbd Allāh Muḥammad ibn Jābir al-Battānī 80 On al-Battānī and al-Ṣūfī, see Kunitzsch 1974, pp. 49–51; on Ibn Yūnus, see King DSB vol. 14 and King 2007.

279

ISLAMIC CELESTIAL CARTOGRAPHY (before 858–929), born in Ḥarrān, where his father—as mentioned before—was a famous maker of scientific instruments.81 Kunitzsch showed that al-Battānī’s catalogue, which is included in his most important astronomical work al-Zīj al-Ṣābi’, presented the star positions as recorded in the Syriac and the old Arabic versions.82 Al-Battānī adapted the positions to the epoch 880, by adding 11° 10´ to the corresponding values of the Ptolemaic longitudes. The star catalogue of al-Battānī was not of great influence in celestial cartography since it includes only 533 of the 1025 Ptolemaic stars. Of far greater importance is the star catalogue of al-Ṣūfī included in his Book on the Constellations of the Fixed Stars. For his verbal descriptions of the stars relative to the constellation figures al-Ṣūfī mostly followed the wording of the translation made by Isḥāq ibn Ḥunayn.83 The stellar positions are adapted to the epoch 964 by adding 12° 42´ to the corresponding Ptolemaic longitudes. Al-Ṣūfī’s Book on the Constellations stands out for a number of reasons and is discussed in more detail in the next section 4.3. Another Arabic version of the Ptolemaic catalogue was produced by al-Bīrūnī (epoch 1030, precession correction 13°). Al-Bīrūnī’s catalogue is based on a number of Arabic translations of the Almagest and on al-Ṣūfī’s Book on the Constellations.84 Al-Bīrūnī criticized al-Ṣūfī for not having corrected in his catalogue all the positions which he found at fault 81 On al-Battānī generally, see Hartner DSB vol. 1. 82 Al-Battānī’s work,‘al-Zīj al-Ṣābi’, was translated into Latin and Spanish, including a Latin translation by Plato of Tivoli (Plato Tiburtunus) in 1116 (De Motu Stellarum), see Nallino 1903, pp. 139–42 and 320–1. On al-Battānī’s use of older translations of the Almagest, see Ibn aṣ-Ṣalāḥ (Kunitzsch 1975), pp. 19 and 97–109. 83 Kunitzsch 1986a. 84 Kunitzsch 1974, pp. 52–3.

but, as Ibn al-Ṣalāḥ points out, al-Bīrūnī himself copied these erroneous positions without change.85 The scholar and scientist Naṣīr al-Dīn al-Ṭūsī (1201–74), the founder of a major observatory at Marāgha, wrote a recension of Ptolemy’s Almagest, called the Taḥrīr al-majasṭī for which he used the Almagest translation by Isḥāq with revisions byThābit.86 He also translated al-Ṣūfī’s Book on the Constellations into Persian. In a star list for the epoch 1232 (the year 601 in the Yezdejerd era) in the Īlkhānī Tables, the most famous astronomical work of al-Ṭūsī, the longitudes exceed the corresponding Ptolemaic values by 16° 45´.87 The precise background of the star catalogue drawn up for the epoch 1437 by the Samarkand prince and astronomer Ulugh Bēg (1394–1449) is not (yet) clear. Ulugh Bēg founded an observatory and assembled a number of astronomers there. Since the stellar longitudes are not simply adapted by adding a constant precession correction for the epoch 1437 the question has emerged whether these data were obtained by observation or compiled from older star catalogues. However, for 27 southern stars, which could not be observed at Samarkand, the longitudes were taken from al-Ṣūfī’s catalogue and adapted to 1437 by adding a value of 6° 59´, that is equivalent to an increase of 19° 41´ with respect to Ptolemaic longitudes. Most surviving copies of Ulugh Bēg’s catalogue are written in Persian, but a few Arabic editions exist. Kunitzsch has shown that the verbal descriptions of the stars relative to the constellation figures in Ulugh Bēg’s star 85 Ibn aṣ-Ṣalāḥ (Kunitzsch 1975), p. 39. 86 For al-Ṭūsī, see Nasr DSB vol.13, p. 514. On the edition of the Almagest, see Kunitzsch 1974, p. 26 and Ibn aṣ-Ṣalāḥ (Kunitzsch 1975), p. 115. 87 Kunitzsch 1992/93, p. 83.

280

4.2 THE ISLAMIC MATHEMATICAL TRADITION catalogue stem from al-Ṭūsī’s Persian translation of al-Ṣūfī’s Book on the Constellations.88 Before we turn our attention to books on the construction and use of globes, a few words must be said about the theory known as trepidation.89 This theory was developed by Muslim astronomers to account for the fact that a number of the parameters used by Ptolemy in the Almagest appeared to change in time. In order to explain the changes in the obliquity of the ecliptic and in the rate of precession a theory was developed in which the equinoxes were supposed to move forwards and backwards over the course of time. Ideas of such a motion but superimposed on a constant rate of precession were considered by al-Battānī and rejected on cosmological grounds.90 In the tenth century trepidation models were developed in the Kitāb Ḥarakāt al-Shams by Ibrāhīm ibn Sinān ibn Thābit ibn Qurra (908–46), the grandson of the mathematician and astronomer Thābit ibn Qurra.91 According to al-Bīrūnī the Persian astronomer Abū Jacfar al-Khāzin (900–71) included an explanation of the trepidation of the equinoxes in his Zīj al Ṣafā’iḥ.92 One of these early eastern theories, or a version thereof, was introduced in alAndalus where it was re-elaborated and provided with parameters which made it possible to produce tables for calculating corrections of precessions for arbitrary dates.93 One Andalusian model survives in the widely known Latin text Liber de motu octave spere (Book on the Motion of the Eighth Sphere). Its author is not 88 Kunitzsch 1998. 89 A good review of the historical problems associated with trepidation is in Chabás and Goldstein 2003, pp. 217–20 and pp. 256–66. 90 Ragep 1996. 91 Ibn Sinān (Saidan 1983). 92 Samsó 1977, p. 269; Samsó 1996, p. 600. 93 Samsó 1990/1994, pp. 2–3.

known, but the work may be by a member of the group of Toledan astronomers working for qāḍī Abū l-Qāsim Ṣācid al-Andalusī (1029–70).94 This group, in which the astronomer and instrument maker Ibn al-Zarqālluh seems to have had an outstanding position, is believed to have composed the tables which, although often accompanying the text Liber de motu octave spere, are independent from it.95 These tables appear to be based on a theory of accession and recession characterized by a period of 4057 Julian years and an amplitude of 10° 45´ centred on the year 604, such that before 410 bc the longitudes of the stars decrease and after 410 bc they increase until 1620, after which date the longitudes start to decrease again.96 These trepidation tables are also included in the Toledan Tables, an adaptation of the then available astronomical material (of al-Khwārizmī and al-Battānī), produced by qāḍī Ṣācid’s group of Toledan astronomers and known only through a Latin translation.97 The studies carried out so far on the models of accession and recession discussed among Andalusian astronomers show that opinions on trepidation were far from unified.98 All models had in common that the equinoxes were thought to move in a small circle causing them to access and recess under certain constraints. In some models the variation of the obliquity of the ecliptic was linked to the motion of the equinoxes, in others the obliquity varied independently. For the investigation of the theories of precession used by the various globe makers, the eastern models are no help for they lack

281

94 95 96 97 98

Richter-Bernburg 1987. Mercier 1996, p. 323. Mercier 1996, p. 304. Toomer 1968; Pedersen 2002. Samsó 1990/1994; Comes 1996; Comes 2001.

ISLAMIC CELESTIAL CARTOGRAPHY parameters that enable one to calculate precession corrections. The several models known in Muslim Spain could have been used by globe makers to adapt their star catalogues.

tic poles are characteristic of Islamic globe making and may have been introduced as part of the technique of marking stars on the globe by using their ecliptic coordinates. In the second book the use of the globe is elucidated in 14 4.2.2 Globe treatises chapters. Among the problems discussed are, Celestial globes are of great value in understand- for example, finding oblique ascensions and ing the celestial phenomena, but treatises from declinations of points on the ecliptic. Also Antiquity on their use are completely lacking. time-related matters, such as the length of the Instead there were many Aratean texts and scho- day in equal hours and the time of the day in lia, indicating that in Greek-Roman education temporal hours, formed part of the queries to be the descriptive tradition was the dominant mode. solved with a globe. Most, if not all of these probIn this tradition the globe served to demonstrate lems could also be found in treatises on the use ideas. Its function as a quantitative problem- of the astrolabe. 2. In chronological order Ḥabash’s treatise is solving device belongs to the mathematical trafollowed by the book written by Qusṭā ibn Lūqā dition.And so it happens that the first treatises on how to use globes stem from the Middle East. (ca. 820–912), a physician and scientist from BagA number of them have been edited and trans- dad who during his travels searched for Greek lated or their contents discussed. The following texts, and is known to have translated many discussion is based on this published, but no Greek and Syriac texts including books by Archimedes and Theodosius. His globe treatise doubt incomplete, material. Kitāb calā l-kura (Book on the Globe), is known in 1. Ḥabash al-Ḥāsib, the astronomer and math30 manuscripts but its precise background has ematician mentioned above in connection with not yet been clarified.100 One version is dedithe melon-shaped astrolabe, wrote a treatise Book cated to Ismācīl ibn Bulbul, the vizier of Caliph on the Sphere and its Use, the earliest extant examal-Muctamid and the patron of the translation of ple of its type.99 It consists of two books, the first the Almagest by Isḥāq ibn Ḥunayn. Another verof which describes very briefly in six chapters sion of the book is dedicated to Abū’l-Ḥasan how to construct a common globe. Such a globe c Abd Allāh ibnYaḥyā. Qusṭā’s book on the use of consists of a sphere mounted in a graduated the globe has 65 chapters. In setting up the globe meridian ring, which in turn is mounted in a the reader is told to raise the (equatorial) poles stand with a graduated horizon ring. On the above the horizon in proportion to the geosphere the Equator, the ecliptic, and six great cirgraphic latitude, an instruction missing in cles passing through the ecliptic poles and Ḥabash’s treatise. Qusṭā’s book differs also from through the beginning of the zodiacal signs are that by Ḥabash in that only a small selection of engraved. In all, 1022 stars are said to have been stars (as on the astrolabe) are marked. And in marked on the sphere as well as the lunar manchapter 53 Qusṭā discusses an interesting accessions.The great circles passing through the eclip99 Lorch and Kunitzsch 1985.

100 Worrell 1944, pp. 285–93; Lorch and Martínez Gázquez 2005, p. 10.

282

4.2 THE ISLAMIC MATHEMATICAL TRADITION sory shaped like a wooden peg and a graduated quadrant which served to find the altitude of the Sun. For this purpose the peg had to be attached to the globe at the appropriate position of the Sun for the time of the year and then the sphere had to be rotated on its polar axis until no shadow was visible at the foot of this peg.101 In chapter 55 it is explained how to determine the mundane houses after what north called the standard method (that is, dividing the ecliptic into arcs of equal rising times).102 3. Next to treatises on the use of the common Islamic globe a few more sophisticated discussions on the construction of the instrument are known. One of these was presented by al-Battānī, the astronomer from Ḥarrān. In his al-Zīj al-Ṣābi’ he describes a globe called bayḍa, meaning egg.103 It consists of a sphere which is mounted in a set of three mutual perpendicular rings representing the meridian ring, the horizon ring, and a third altitude ring which passes through the zenith and nadir and the east and west points of the horizon ring. This set of rings was mounted in an outer ring, passing again through the zenith and nadir. This latter ring is held by a suspension ring and has slots in which a gnomon can be inserted. Inside the meridian ring another altitude ring is added, which like the meridian ring passes through the zenith and nadir and the north and south points of the horizon ring.There are no echo’s of al-Battānī’s construction in the other globe treatises discussed here. 4. The treatise Fī sharḥ al-camal bi-l-kura (On the Explanations of the Operations with the Globe)

101 Lorch and Kunitzsch 1985, p. 74. 102 North 1986, pp. 4 and 9. 103 Savage-Smith 1985, pp. 18–20, gives a detailed description and a modern drawing of this globe.

written by the Persian astronomer al-Ṣūfī and dedicated to his patron Ṣamṣām al-Dawla, differs in many ways from those of Ḥabash and Qusṭā ibn Lūqā.104 It does not say much about the construction of globes, but from a number of problems, which al-Ṣūfī discusses, one can surmise that the meridian ring was pierced with holes and that a loose quadrant was among the auxiliaries. Kennedy suggests that the meridian ring has been pierced by radial holes corresponding to its graduation so that the ring can be set to a specific latitude.105 The treatise is divided into 3 books, with respectively 50, 55, and 52 (in all 157) chapters. Many of the problems in the first book are standard, but al-Ṣūfī often gives more than one solution. For example, al-Ṣūfī presents two ways of finding the altitude of the Sun. One method (section 1.8) is essentially the same as that described by Qusṭā ibn Lūqā and for the other method (section 1.4) a wooden gnomon is placed in a hole in the meridian ring. In this latter method the sphere is not rotated, instead the globe as a whole is first turned round in azimuth to locate the meridian ring in the plane of the Sun, and next the ring itself is turned in altitude to orient the device towards the Sun. In section 1.21 he explains how to determine the 12 mundane houses after the standard method. In the second book al-Ṣūfī discusses various methods for determining observationally the geographical latitude of a place and the local meridian. Some of these solutions require observations which, generally speaking, are more easily carried out with an astrolabe. His last book is devoted to the solutions of problems 104 Kennedy 1990. 105 For this, Kennedy 1990, p. 50 refers to a problem discussed in Section 1.4 which requires a hole, but not a series of holes in the meridian.

283

ISLAMIC CELESTIAL CARTOGRAPHY involving different localities and, for example, problems related to dawn and twilight. Al-Ṣūfī’s motive for using the globe for observation may have stemmed—as Kennedy underlines—from his interest as a practising astrologer.

in the Catalogue at the end of this chapter (IG6).

The globe treatise in Istanbul MS 3505 is in three parts. The first part deals with the construction of globes, the second part, consisting 5. Another more specialized treatise called of 111 chapters, discusses the uses of the globe Maqāla fī ittikhādh kura tadūru bi-dhātihā (The and in the last part the observational use of the Sphere that rotates by itself ) was written in the globe is considered.108 Next to the common first decade of the twelfth century by cAbd globe the author describes two other instrual-Raḥmān al-Khāzinī (early twelfth century), ments which can be identified as precession who worked at the court of the Saljūq ruler globes. The basic principle underlying precesSanjar ibn Malik-Shāh.106 The globe he sion globes is that the locations of the equatoemployed was a common globe without spe- rial poles are not fixed, but can move around cial features. Al-Khāzinī was especially inter- the ecliptic poles along a circle of radius ε, the ested in the mechanics of the moving sphere, obliquity of the ecliptic.Thus a precession globe hence the emphasis on mounting the globe can be set up for an arbitrary epoch.The author into a device designed to keep the globe in of the Risālat al-camal bi-l-kura claims that his step with the daily motion of the starry sky, so invention is the first of its kind.109 He does not that at any time the globe would show the sky mention that Ptolemy’s Almagest, book VIII.3, over head which is no sinecure. Al-Khāzinī’s includes the first known description of a premodel is special for its technical solution for cession globe.110 However that may be, the two moving the sphere, a problem that is outside designs for a precession globe presented in the globe treatise in Istanbul MS 3505 are certainly the scope of this study. 6. An intriguing globe treatise, entitled worth noting, considering that there is not one Risālat al-camal bi-l-kura, is conserved in an precession globe among the more than 200 undated manuscript in Istanbul, Ahmet III Islamic globes surviving today. Library MS 3505, ff . 1–97. According to The first solution for adjusting a globe to an Elkhadem this treatise was written by Mu’ayyid arbitrary epoch is simple. A series of holes is al-Dīn al-cUrḍī (early thirteenth century).107 made along the circles of radius ε around Al-cUrḍī was one of the instrument makers respectively the north and south ecliptic poles who worked under the supervision of Naṣīr (see Scheme 4.4).111 Each set of holes correal-Dīn al-Ṭūsī (1201–74) at the Observatory at sponds to the northern and southern equatoMarāgha, in today’s northern Iran. Al-cUrḍī is rial poles of a specific epoch. One set of holes known for his interest in Ptolemaic models. A in the series represents the north and south (common) globe made by al-cUrḍī’s son 108 Elkhadem 1992, p. 30. Muḥammad has been preserved and is described 106 Lorch 1980a; Abattouy 2007. 107 Elkhadem 1992.The attribution is on f. 1r (private communication 18 January 2011).

109 Elkhadem 1992, p. 36. 110 Toomer 1984, pp. 404–7. I shall discuss this Ptolemaic globe in detail in Chapter 5 in relation to the only surviving medieval copy. 111 Elkhadem 1992, p. 36.

284

4.2 THE ISLAMIC MATHEMATICAL TRADITION

Scheme 4.4 The first precession globe discussed in the treatise Risālat al-camal bi.

500 years. The model is therefore not really suitable to make adjustments in epoch of, say, a century. This restriction may be the reason why, at the end of the discussion of his newly invented globe, the author notes that one can substitute the series of discrete holes with two mobile rings attached to the body of the sphere such that they can rotate around it.112 Each ring is said to have a single hole which one can shift over the number of degrees corresponding to the interval between the required epoch and the time of construction.113 In other words, the holes represent the mobile north equatorial pole of the model. In Scheme 4.5 this model is illustrated.

equatorial poles (*NP and *SP in Scheme 4.4) corresponding to the epoch of the date of construction. All points and circles specific for this epoch are marked by an asterisk in Scheme 4.4. Once the poles for a specific epoch have been selected, the globe can be mounted and used as a common one.The model is not without restrictions, however. The Equator and the colures drawn on the sphere are only valid for the epoch of the date of construction because the locations of these circles change when the equatorial poles shift in position. Consequently the globe cannot be used at an arbitrary epoch for solving problems which require the location of the Equator. A more Scheme 4.5 The second precession globe discussed in the treatise Risālat al-camal bi. important limitation is that for a globe with a diameter of 30 cm the length of 1° along a 112 Elkhadem 1992, pp. 37–8. parallel with radius 23.5° around the north 113 Elkhadem 1992, p. 38: ‘On fait dans chaque cercle un ecliptic pole would be of the order of 1 mm. seul trou qu’on peut déplacer selon le nombre de degrés qu’on Assuming a rate of precession of 1° in 72 years, présume nécessaire pour un intervalle de temps donné. On fixe centres de ces deux trous sur le grand cercle qui passe par les holes of a diameter of 2 mm placed 5 mm apart les pôles de la ceinture zodiacale ainsi que par le degré nécessaire would correspond to a step in epoch of around pour le temps donné’. 285

ISLAMIC CELESTIAL CARTOGRAPHY One ring can rotate around the ecliptic poles. The holes in this ring, located at a radius ε from respectively the north and south ecliptic poles, can move in proportion to any amount of precession required. This first ring would represent a mobile solstitial colure. Since the interpretation of the second ring is uncertain I have draw it as a dotted line. I presume that this second ring passes through the mobile equatorial poles and thus is attached to the first ring at its holes.This second ring would then represent the meridian ring. If my interpretation is correct the model is similar to Ptolemy’s precession globe. An alternative interpretation of the text is seen in a drawing by Elkhadem in which the two rings are attached at their holes to the ecliptic pole, but by this construction one cannot shift the holes themselves along the circles of a radius ε around respectively the north and south ecliptic poles over the required interval.114 7. The last globe treatise to be mentioned here is that by Abū cAlī Ḥasan al-Marrākushī (second half of the thirteenth century), who wrote a comprehensive work on instrument making, including a spherical astrolabe.115 His interest in construction details is also apparent from his treatise on globe making.116 For example, his meridian ring has holes at intervals of 1° to make the sphere adjustable to geographic latitude. Note that this requires a fairly large globe because the circumference of a meridian ring with a diameter of, say, 30 cm is around 94 cm.The length of a unit of 1° is thus 2.6 mm, which is hardly enough to make a hole every degree. He proposed a special manner to lay out the main celestial circles and he

explained in detail how to mark the stars on the sphere by mounting the graduated meridian ring at the poles of the ecliptic. His globe was also equipped with a graduated quadrant. Al-Marrākushī knew five different treatises on the solid globe but found the one by Qusṭā ibn Lūqā the best.117 For setting up a globe to match it to the sky al-Marrākushī proposed the method for finding the altitude of the Sun with the help of a wooden peg described in chapter 53 of Qusṭā ibn Lūqā’s treatise and in chapter I.8 of al-Ṣūfī’s book. Unfortunately the globe book of al-Marrākushī has not yet been edited or translated and therefore an assessment of it is at present not possible. The summary given here on globe treatises is certainly not complete, but it shows that the globe received a lot of attention among astronomers. Its (un)suitability for making observations seems to have been a recurrent theme with early authors. But the globe was above all seen as a useful device for teaching and solving all sorts of practical problems connected with the celestial sphere.

. THE URANOGRAPHY OF ABU’LḤ USAYN ALṢŪFĪ  Al-Ṣūfī was born in 903 in Rayy, near modern Tehran. His scientific activities were connected with cAḍud al-Dawla and other members of the Iranian Buwayhid dynasty.118 Al-Ṣūfī seems to have followed the court in its travels, and observations were carried out in various places. He

114 Elkhadem 1992, p. 35, Fig. 3. 115 Charette 2003. 116 Sédillot 1844, pp. 110–14; Lorch 1980a, pp. 295–7.

117 Lorch and Kunitzsch 1985, p. 70. 118 Kunitzsch DSB vol. 13, pp. 149–50.

286

4.3 THE URANOGRAPHY OF ABU’L-Ḥ U SAYN AL-ṢU- fi- (903–86) became known in the Latin West by a number of names, but most often as Azophi.119 Al-Ṣūfī wrote various works on astronomy, all of which are written in Arabic. One book— mentioned before—is devoted to the use of the celestial globe, another to the use of the astrolabe.120 He is, however, best known for his Kitāb ṣuwar al-kawākib (Book on the Constellations of the fixed Stars) which he wrote for his patron cAḍud al-Dawla.121 In this book each of the 48 Ptolemaic constellations is introduced in great detail. The notes in the introduction to each constellation are always described from the perspective of the observer, never from the alternative perspective of a globe. The intention of his book is to serve in the first place astronomers who look at the sky. Al-Ṣūfī shows the depth of his knowledge in criticizing many of the stellar positions and magnitudes listed in the Ptolemaic star catalogue. He also discusses many indigenous Arabic star names and their identification with Ptolemaic stars. His detailed description of each constellation is concluded by a table of the locations of the stars inside the figure of the constellation, their longitudes, latitudes, and magnitudes. The organization of his catalogue entries is in close analogy to that of the Ptolemaic star catalogue. The wording of the descriptions in al-Ṣūfī’s entries mostly follows the corresponding entries in the Almagest translation by Isḥāq ibn Ḥunayn as revised by Thābit ibn Qurra.122 The values of the longitudes of the stars are adapted to the beginning of the year 1276, the era of Alexander (1 October 964) by adding 12° 42´ to those of Ptolemy. His stellar coordinates are not copied from one

particular version of Ptolemy’s star catalogue, they appear to have been chosen out of several catalogue versions, but the criteria he used are not known.123 The magnitudes of the stars are those observed by al-Ṣūfī himself. Each entry is supported by two drawings, one of the constellation as seen in the sky and another as it is seen on the sphere. Al-Ṣūfī displayed in many ways the gifted observer he was and this may explain his rather sceptical remarks about the observational efforts of his predecessors. In the introduction to the Book on the Constellations he explains that some astronomers observed only a few bright stars for determining the precession correction and that they—presumably deliberately—added small amounts (minutes says al-Ṣūfī) to the longitudes and latitudes of other stars to suggest that these too had been obtained by independent observation.124 An example of how he arrived at such a conclusion is his discussion of Sgr 23 (β1,2 Sgr), the Ptolemaic longitude of which is 17° 40´.125 In al-Battānī’s catalogue the position of this star to be expected is 28° 50´ since it is adapted to the epoch 880 by adding 11° 10´ to the corresponding value of the Ptolemaic longitude. Yet, al-Ṣūfī found in al-Battānī’s catalogue the value 28° 30´ instead. One could think that the difference of 20´ is the result of observation but had al-Battānī indeed observed the star—so al-Ṣūfī argued—he would have noticed that its brightness is not of the 2nd magnitude as Ptolemy says but less than the 4th magnitude. Al-Battānī did not mention this and clearly did not observe the star and therefore al-Ṣūfī concludes that

119 Kunitzsch 1986a, pp. 78–80. 120 Al-Ṣūfī’s treatise on the astrolabe is discussed in Kunitzsch 1990. 121 Al-Ṣūfī (Schjellerup 1874). 122 Kunitzsch 1974, p. 52 and his note 132.

287

123 Ibn aṣ-Ṣalāḥ (Kunitzsch 1975), Anhang III, pp. 109–11. 124 Al-Ṣūfī (Schjellerup 1874), p. 29. 125 Kunitzsch III 1991, p. 117.

ISLAMIC CELESTIAL CARTOGRAPHY al-Battānī changed the longitude of Sgr 23 artificially.126 Al-Battānī probably did not observe Sgr 23 (β1,2 Sgr), but there is no reason to assume that he deliberately changed its coordinates. It seems not to have occurred to al-Ṣūfī that star catalogues are abundant in copying errors and that other astronomers were less prompt than he in writing down observed deviations with respect to the Ptolemaic star catalogue.127 Al-Ṣūfī’s criticisms reflect more than anything else his own meticulous attitude as an observational astronomer.Al-Ṣūfī correctly described Sgr 23 (β1,2 Sgr) as a double star, with modern values for their magnitudes of respectively 4.01 and 4.29 (to be compared to 4.5 in al-Ṣūfī’s catalogue). And he was also right in estimating the magnitude of Sgr 24 (α Sgr) to be 4.5, the Ptolemaic value of which is less than 2. A modern astronomer wondered why this star Sgr 24 was called α, the Greek letter normally used for the brightest star in a constellation, for there are many brighter stars.128 Indeed, the label α for Sgr 24 shows that al-Ṣūfī’s corrections of Ptolemaic magnitudes had unfortunately not yet reached the West when Johann Bayer in 1603 introduced his notation of labelling the stars by letters of the Greek alphabet starting off with α for the brightest star, β for the next brightest, and so on.129

126 Al-Ṣūfī (Schjellerup 1874), pp. 29–30 and p. 181 for Sgr 23 and 24. 127 Paul Kunitzsch pointed out (private communication) that the difference of 30 vs 50n could be explained as a misreading or miswriting of the two abjad-letters for these two values, which he has observed on various occasions. 128 Dibon-Smith 1992, p. 178: ‘Curiously called α, for there are more than a half-dozen brighter stars’. 129 Bayer 1603.The stars Sgr 23 and Sgr 24 were too southern to be observed by Tycho Brahe, and therefore Bayer used their Ptolemaic data.

Whatever al-Ṣūfī’s opinions about his fellow astronomers may have been, his Book on the Constellations includes many astronomically conspicuous details. Next to describing quite a number of non-Ptolemaic stars, most of which unfortunately are only described and only occasionally presented in the drawings accompanying the constellations, al-Ṣūfī dismissed a number of Ptolemaic stars because he could not see them.These are Aur 14, Cen 30, Lup 11, and PsA 1e-6e. Although al-Ṣūfī rejected the stars Cen 30 and Lup 11 he retained the verbal descriptions of them, but dismissed their Ptolemaic coordinates because—as he notes—one does not observe a star in the places indicated by the Ptolemaic coordinates.130 Indeed there is only one bright star (Cen 29) below the belly of Centaurus, not two as listed in Ptolemy’s star catalogue. Neither can one confirm the Ptolemaic description of three stars in the tail of Lupus to which Lup 11 is said to belong. Savage-Smith claims that despite his criticism al-Ṣūfī included the six stars PsA 1e–6e in his Book on the Constellations, but in some manuscripts they are missing, and in others not.131 The same holds for globes. On the Malcolm globe IG5 these stars are missing but they are added on the Dresden globe IG6 (see Fig. 4.6).132 Of the group of stars PsA 1e–6e al-Ṣūfī remarks: ‘Selon ce qu’il [Ptolémée] a indiqué pour les longitudes et latitudes de ces étoiles, elles doivent être au sud de la 11e et de la 12e qui se trouvent sur les genoux du Capricorne. Il n’y a dans ce lieu [ ...] qu’une seule étoile mentionnée par nous à la description du Sagittaire, et quelques petites étoiles obscures dont l’éclat est estimée de sixième gran130 Al-Ṣūfī (Schjellerup 1874), pp. 249–50. 131 Savage-Smith 1997, catalogue entry no. 123, p. 212. 132 The globes IG1–IG10 are described in Appendix 4.1 at the end of this chapter.

288

4.3 THE URANOGRAPHY OF ABU’L-Ḥ U SAYN AL-ṢU- fi- (903–86)

Fig. 4.6 The external stars around Piscis Austrinus (PsA 1e–6e) on the celestial globe IG6. (Courtesy of the Staatliche Kunstsammlungen Dresden-Mathematisch-Physikalischer Salon Zwinger, Dresden.)

289

ISLAMIC CELESTIAL CARTOGRAPHY deur et qui sont disposées autrement qu’il ne les a decrites’.133

In the Ptolemaic star catalogue three stars (PsA 1e–3e) are said to be of the 3rd magnitude, two (PsA 5e–6e) of the 4th and one (PsA 4e) of the 5th magnitude. Next to a few faint stars of the 6th magnitude, which did not fit the pattern described by Ptolemy, al-Ṣūfī observed only one star of the 3rd magnitude, located between the star in the tail of Piscis Austrinus (PsA 11, γ Gru) and the one on the front left hock (Sgr 23 β1 Sgr). It is not clear how to identify al-Ṣūfī’s star of the 3rd magnitude. The most likely identification is α Ind because its brightness is around 3m and its right ascension in al-Ṣūfī’s days was 290° which is exactly between the right ascension of β1 Sgr (RA 272°) and γ Gru (RA 312°).134 However, the declination of α Indi (-50°) is more southern than that of β1 Sgr (-46°) and γ Gru (-42°), which may be the reason why it was not included in the Ptolemaic star catalogue. Worth mentioning also is the attention given to nebulous objects.Al-Ṣūfī recorded eight nebulae inclusive of those five which are labelled in the Almagest as nebulous.135 These five nebulae are in Perseus (Per 1), in Cancer (Cnc 1), in Scorpius (Sco 1e), in Sagittarius (Sgr 8), and in Orion (Ori 1). Al-Ṣūfī added three new ones, among which is the first record of the Andromeda Nebula, a well known nearby galaxy (M31).136 It is in the context of two Arabic indigenous star groups that the Andromeda nebula comes to the fore:

133 Al-Ṣūfī (Schjellerup 1874), p. 255. In the French translation of al-Ṣūfī’s star catalogue the stars Aur 14 and PsA 1e–6e have been completely left out. Thus his catalogue lists 1018 entries and the positions of only 1016 stars. 134 The identification was made in al-Ṣūfī (Schjellerup 1874), pp. 249–50. 135 Jones (K) 1975, pp. 5–9. 136 On the Andromeda Nebula, see also Kunitzsch 1987b.

‘The Arabs recognise two series of stars surrounding the figure of a large Fish below the throat of the Camel. These stars belong partly to this constellation [Andromeda] and partly to the northern Fish which Ptolemy describes as the twelfth figure of the Zodiac.These two series begin at a little Cloud situated very close to the 14th [star] which is found at the right side [of And] and which belongs to the three which are above the girdle.’137

In other words, the nebula is close to the star And 14 (ν And), the northernmost of the three stars in the girdle.The position of the nebula with respect to Andromeda is often recorded in the drawings accompanying the several versions of al-Ṣūfī’s book.138 In MS Marsh 144, p. 167, there are two fishes drawn on top of each other over the upper body of Andromeda.The smaller fish belongs to the Ptolemaic zodiacal constellation Pisces, the larger one represents the indigenous constellation of a large fish, with at its head a patchy object representing the Andromeda nebula.139 Another non-Ptolemaic nebulosity discovered by al-Ṣūfī is north of the two stars in the notch of Sagitta. It is an open cluster inVulpecula, now known as Collinder 399, but also referred to as Briocchi’s cluster.140 The third new nebulosity described by al-Ṣūfī is above the 37th star in Navis.141 The stars numbered 36–38 are hard to identify because of discrepancies in position but Jones has convincingly argued that the 37th star should be identified with Lac. II 5, described by LaCaille in 1751–52. It was later renamed as 137 The translation is from Jones (K) 1975, p. 8. 138 See for example, Wellesz 1959, fig. 11, and al-Ṣūfī (Schjellerup 1874), Plate II, fig.19a. Note that the drawings in al-Ṣūfī (Schjellerup 1874) are not photographic reproductions but have been copied by hand. 139 See for example Wellesz 1959, figs 10–12. 140 Al-Ṣūfī (Schjellerup 1874), p. 107, note 1. D.F. Brocchi was an American amateur astronomer who created a map of the object in the 1920s, see Collinder 1931. 141 Al-Ṣūfī (Schjellerup 1874), p. 255.

290

4.3 THE URANOGRAPHY OF ABU’L-Ḥ U SAYN AL-ṢU- fi- (903–86) IC 2391 and is now also known as the Omicron Velorum Cluster.142 Allen, in his Star Names, says on the Large Magellanic Cloud that ‘al-Ṣūfī mentioned it as Al Bakr, the White Ox, of the southern Arabs, and invisible from Bagdad, or northern Arabia’.143 This statement is a confused interpretation of a text connected with the star Suhayl, also known as Canopus (Navis 44 or α Car). Al-Ṣūfī says that the Arabs believe that there are below the feet of Suhayl (qadamā suhayl) some bright white stars, invisible in Iraq and Najd (the central region of the Arabian peninsula), which the inhabitants of Tihāma (latitude ca 15° N) call al-baqar (the Cows).144 Al-Ṣūfī adds that Ptolemy does not mention any of these stars (that is, the feet of Suhayl and the bright white stars) and that one cannot tell whether this record is right or wrong. The feet of Suhayl here referred to have been identified with the non-Ptolemaic stars β Dor and α Pic. Following several older Arabic sources, which put the stars al-acyār (or al-baqar according to al-Ṣūfī) behind the feet of Suhayl instead of below, the bright white stars have been identified with the ‘false cross’, located west of β Dor and α Pic consisting of the four Ptolemaic stars δκ Vel and ει Car.145 This ‘false cross’ is not in any way connected to the Magellanic Clouds which were not known in Antiquity and medieval times in the Arabic world. Among Arabic navigators they were called al-saḥābatān (the two clouds).146 They are mentioned by Aḥmad ibn Mādjid (end of fifteenth century) and Sulaymān al-Mahrī (early sixteenth century) in their books 142 Jones (K) 1975, p. 9. 143 Allen 1963, p. 295. 144 Al-Ṣūfī (Schjellerup 1874), p. 229; Kunitzsch 1961, p. 40, no. 23 and p. 49, no. 59. 145 Kunitzsch 1974b, pp. 41–2; Kunitzsch 1983, p. 109. 146 Kunitzsch 1974b, p. 50; Kunitzsch 1983, p. 109.

on navigation in the Persian Gulf and the Indian Ocean.147 In 1503 the Magellanic Clouds became known in the West through the explorations of Amerigo Vespucci in south America.148

4.3.1 Oxford, Bodleian Library, MS Marsh 144 Although the present study is focused on images of the celestial sphere as a whole, a discussion of the constellation drawings in al-Ṣūfī’s book is here in place since these drawings were very influential in globe making. The oldest copy of the Book on the Constellations of the Fixed stars is Oxford, Bodleian Library, MS Marsh 144, which was written by al-Ṣūfī’s son and is dated 400 H (= ad 1009–10). It is famous for its illustrations which were studied in detail by Emmy Wellesz in 1959.149 If the hypothesis—mentioned by al-Bīrūnī and discussed below—that these illustrations were copied from a globe is correct they embody an early Islamic celestial globe. It is therefore worthwhile examining the drawings in MS Marsh 144 in some detail and see first of all how they relate to the accompanying texts and second what they have to offer to the history of celestial cartography. As an example of the layout of the drawings I have chosen the images presenting the constellation Perseus in MS Marsh 144, pp. 110–11, shown in Figs 4.7a–b. I have added for the sake of reference a scheme showing the numbers of the labelled stars (Fig. 4.7). One drawing (Fig. 4.7a) is labelled on top: ‘Constellation of Barshāwush as seen in the sky’, the other (Fig. 4.7b) ‘Constellation of Barshāwush as seen on the

147 On Aḥmad ibn Mādjid, see Sourdel 1979; on Sulaymān al-Mahrī, see Tibbetts 1997. 148 Dekker 1990, pp. 537–40. 149 Wellesz 1959.

291

Fig. 4.7 Scheme of the stellar configuration of Perseus in Fig. 4.7a.

Fig. 4.7a Perseus as seen in the sky in the Bodleian Library, University of Oxford, MS Marsh 144, p. 111. (Courtesy of the Bodleian Library, Oxford.) See also Plate V.

Fig. 4.7b Perseus as seen on the sphere in the Bodleian Library, University of Oxford, MS Marsh 144, p. 110. (Courtesy of the Bodleian Library, Oxford.)

4.3 THE URANOGRAPHY OF ABU’L-Ḥ U SAYN AL-ṢU- fi- (903–86) sphere’.150 The stars belonging to the constellations are in MS Marsh 144 always marked in red and their numbers (referring to the listing in the corresponding catalogue entry) are in black. In order to distinguish the internal stars from stars located outside the figure, the reversed colour scheme is used for external stars: these are marked in black and labelled in red.This procedure is explicitly explained in the drawings of Perseus, where at the bottom of each drawing one reads: ‘Those marked in red (points) and inscribed in black belong to the figure, and those in black (points) and inscribed in red (numbers) are external’. In the introduction to the constellation al-Ṣūfī describes Perseus as a figure standing on his left leg and raising his right one. He is said to hold his right hand above his head and to carry in his left hand the head of al-Ghūl. All its stars are located between Cassiopeia (the sitting woman) and the Pleiades. In the drawing Perseus carries a straight sword in his right hand (Fig. 4.7a). In Greek mythology Perseus received the (hooked) sword,a sickle,from Mercury and decapitated Medusa with it.151 Like the sword the head of Medusa is a standard attribute of Perseus’s outfit, but whereas the head is explicitly mentioned in the Ptolemaic catalogue description, the sword is not. In al-Ṣūfī’s text Medusa’s head is substituted by the Demon’s Head, al-Ghūl. It explains why Perseus is not only called Barshāwush, but also ‘the Bearer of the Demon’s Head, al-Ghūl’. Since al-Ṣūfī’s text—following Ptolemy’s—does not mention a weapon, the sword in the drawings in MS Marsh 144 stems probably from a pictorial source.In describing the MilkyWay Ptolemy refers

150 The translations of the texts in the drawings of MS Marsh 144 discussed here and below are by Paul Kunitzsch. 151 Philips 1968.

to the hilt of a sword, suggesting that this weapon was part of the astronomical figure in Antiquity.152 In each drawing of Perseus a number of star names have been added.The brightest star of the constellation, Per 7 (α Per), received two names. One of these, janb barshāwush (the side of Perseus), reflects the Ptolemaic description of the star and underlies the later Latin name algenib.The second name, mirfaq al-thurayyā, refers to the elbow of al-thurayyā.153 In folk astronomy al-thurayyā was the head of a woman from which two arms radiated, one towards Cassiopeia and Perseus and the other towards Cetus.154 It is with respect to this female figure that other names added to the illustration of Perseus also have to be understood: the star Per 1 (τ Per) is on her wrist (micṣam al-thurayyā) and the stars Per 25 and 26 (ο and ζ Per) are in her shoulder-blade (cātiq al-thurayyā).155 Finally, in the drawing ‘as seen in the sky’ there is also a name for the brightest star in the Demon’s Head, Per 12 (β Per), ra’s al-ghūl, which is not an old Arabic name but derives from the Almagest.156 An interesting aspect of al-Ṣūfī’s description of Perseus are the frequent references to the Milky Way which as a rule is not depicted on Islamic globes.Al-Ṣūfī outlines the western border of the Milky Way by six stars: one in the shoulder (Per 3), one in the head (Per 5), the bright star on his side (Per 7), the star south of that (Per 10), one on the right calf (Per 20), and that on the right ankle (Per 21). Of these six stars two (Per 7 and 10) are said to lie just outside the Milky Way. Only one

152 Toomer 1984, p. 402. 153 Kunitzsch 1961, p. 77, no. 163. 154 Kunitzsch 1961, pp. 114–15, no. 306. Al-thurayyā is also the current Arabic name for the Pleiades. 155 Kunitzsch 1961, for Per 1 see p. 80, no. 169; for Per 25 and 26 see pp. 44–5, no. 41. 156 Kunitzsch 1974, p. 244, no. 141.

293

ISLAMIC CELESTIAL CARTOGRAPHY of the stars in the right knee (Per 17) is said to be in the middle of the Milky Way.157 It seems that in discussing the locations of the stars with respect to the Milky Way al-Ṣūfī was not guided by Ptolemy’s description of the Milky Way. Ptolemy defines a northern and southern boundary whereas al-Ṣūfī specifies only stars on the western border among which are two stars (Per 3 and 5) which Ptolemy places in the middle of the Milky Way.158 Al-Ṣūfī’s description may not be complete. For example, he mentions Per 17, but not the other stars in the right knee nor does he explain how a presumably eastern border runs through the constellation, and in this respect leaves his readers in the dark. Observation of a diffuse item such as the Milky Way is not easy and is doomed to be seen differently by different observers. The design outlined here for Perseus gives a clear idea of how the images of the constellations are composed but it does not tell how the drawings were made.The question that forces itself upon us is whether the formula ‘Constellation as seen on the sphere’ may be taken literally. A remark by al-Bīrūnī seems to answer this question: ‘I have heard Abū Sacīd Aḥmad b. cAbd al-Jalīl (al-Sijzī), the geometer, say about Abū’l-Ḥusayn al-Ṣūfī that he had placed thin paper on the sphere and wound it on its surface so that it fitted it neatly on its surface. Then he drew the figures on it and indicated the stars in accordance with their appearance on the transparency. And that is a (good) approximation when the figures are small but it is far (from good) if they are large.’159

If al-Bīrūnī’s story is true, and I can at face value see no reason why not, the cycle of constellation

images in manuscripts of al-Ṣūfī’s Book on the Constellations derive ultimately from a celestial globe. As explained below, the constellation Orion is suited best for a detailed discussion of this matter. In Figs 4.8a–b the two drawings of Orion in MS Marsh 144, pp. 325–26 are shown. In the drawing on the left side one has the constellation as seen in the sky and on the right as it is seen on the sphere. In all 38 stars are presented. For the sake of reference I have added again a scheme showing the numbers of the stars that are labelled (Fig. 4.8). The figure is in a kneeling position. Contrary to earlier Greek traditions Ptolemy placed the star Ori 38 under the right rear knee, and since the star Ori 35 is set in the left western foot a kneeling attitude of Orion is obtained. The extended sleeve on Orion’s raised western arm is not part of the Ptolemaic iconography. Ptolemy set the stars Ori 17–25 on a pelt on the left arm of Orion, whereas al-Ṣūfī mentions explicitly that these stars are on a curved line on the, presumably lengthened, sleeve.160 The label attached to this group of stars on the sleeve in the drawing in MS Marsh 144, ‘al-tāj wa-al-dhawā’ib ayḍan’, is an old Arabic name meaning crown, and also locks of hair.161 There are also names for two other groups of stars. The well-known stars in the girdle of Orion, Ori 26–28 (δ, ε, ζ Ori), are labelled collectively:‘al-minṭaqa wa-yuqālu lahu al-naẓm ayḍan’, meaning the girdle, also called the row.162 The three stars in the head of Orion, marked by three dots, were identified by al-Ṣūfī correctly with three stars (λ and φ1,2Ori), which stand close together and form the fifth lunar 160 Al-Ṣūfī (Schjellerup 1874), p. 206. 161 Kunitzsch 1961, p. 112, no. 295 and p. 53, no. 78. 162 Kunitzsch 1961, p. 77, no. 162 and p. 88, no. 202a/b.

157 Al-Ṣūfī (Schjellerup 1874), pp. 86–7. 158 Toomer 1984, p. 402. 159 Berggren 1982, p. 53.

294

Fig. 4.8 Scheme of the stellar configuration of Orion in Fig. 4.8a.

Fig. 4.8a Orion as seen in the sky in the Bodleian Library, University of Oxford, MS Marsh 144, p. 326. (Courtesy of the Bodleian Library, Oxford.)

Fig. 4.8b Orion as seen on the sphere in the Bodleian Library, University of Oxford, MS Marsh 144, p. 325. (Courtesy of the Bodleian Library, Oxford.)

ISLAMIC CELESTIAL CARTOGRAPHY mansion. He labelled the group after Ori 1 (λ Ori), ‘al-haqca’, which means the hair brush.163 Names have also been added for a few brighter stars. There are two names for the star on the left shoulder, Ori 3 (γ Ori): ‘al-mirzam’ and ‘al-nājidh’, which cannot be translated.164 Two star names are linked to the Arabic name ‘al-jawzā’’. This name belongs to a group of old names used for zodiacal constellations of Babylonian origin, but because the Arabs did not recognize this at the time of their introduction they associated ‘al-jawzā’’ with Orion. Thus the star on the right shoulder, Ori 2 (α Ori), is labelled ‘yad al-jawzā’’ (the hand of al-jawzā’) and the star on the left foot, Ori 35 (β Ori), ‘rijl al-jawzā’ al-yusrā’ (the left foot of al-jawzā’).165 Later, when the zodiac was introduced through translations of Greek astronomical texts, it was recognized that ‘al-jawzā’’ actually stood for the zodiacal sign Gemini and sometimes it is also used in this sense.166 Let me now turn to the construction of the stellar configurations in al-Ṣūfī’s manuscripts.The critical test to find out whether the stellar configurations in al-Ṣūfī’s manuscripts were copied from a globe would be to establish a dependence on latitude of the length of a degree. However, the absence of a scale does not allow this test. For a discussion of how the drawings were created, I have therefore chosen a graphical method. The first question to answer is to what extent the two drawings of Orion are mirror images of each other. This is examined in Fig. 4.9 where I have compared Orion as seen in the sky (Fig. 4.8a) to the mirror image of Orion as seen on the 163 Kunitzsch 1961, p. 64, no. 115a. 164 Kunitzsch 1961, p. 79, no. 166a/b and p. 84, no.185. 165 Kunitzsch 1961, for Ori 2 p. 116, no. 317a, and for Ori 35 p. 98, no. 251a. 166 Kunitzsch 1961, pp. 23–4.

globe (Fig. 4.8b). A grid is added in Fig. 4.9 to help observe small differences. The positions of the eyes and mouth, the length of the sword, and of the extended sleeve differ in the two views. Also the top garments differ because in both Figs 4.8a-b the right side of the clothing closes over the left side. This was apparently a convention because it is seen in most human figures such as Bootes, Hercules,Auriga, Perseus, and so on. The artist drawing the figures must have followed this routine automatically. Thus one can see that the constellation figure of Orion in the drawing as seen in the sky is not the perfect mirror image of that in the drawing as seen on the globe. In contrast with the constellation figures the stellar configurations in the two drawings are the precise mirror image of each other (compare Fig. 4.9). This supports the hypothesis that the drawings were constructed by first creating the stellar configurations and adding the figure afterwards, in keeping with the mathematical tradition. It suggests that, if al-Bīrūnī’s story is correct, it must have been only the stellar configurations that were copied from a globe. This seems all the more reasonable considering the plies and folds of the beautiful dresses of the constellation figures in MS Marsh 144. To test al-Bīrūnī’s story I have selected as a comparative standard the stellar configurations of Orion on the globes of Caspar Vopel (1536) and Gerard Mercator (1551).167 The choice of these two Renaissance globes has to do with the fact that they were constructed from globe gores, which are nearest to presentations copied on thin paper fitting closely the surface of the sphere.

167 ForVopel I used the gores described in Dekker 2010a; for Mercator I used the facsimile edition published by De Smet 1968.

296

4.3 THE URANOGRAPHY OF ABU’L-Ḥ U SAYN AL-ṢU- fi- (903–86)

Fig. 4.9 Orion as seen in the sky (left) compared to the mirror image of Orion as seen on the sphere (right).

And like al-Ṣūfī these Renaissance cartographers employed the Ptolemaic star catalogue, the use of which should in principle result in the same relative positions of the stars within a constellation. The use of Orion is primarily suggested because it is one of the few constellations confined to one gore. In Scheme 4.6 the stellar configurations of Orion in MS Marsh 144 (top left) and on the globe gores of Vopel (bottom left) and Mercator (bottom right) have been reproduced. Also the modern configuration generated by a computer program is added (top right).168 I have retained in the modern presentation only the stars rele168 Produced with the help of Chris Marriott’s SkyMap Pro, Version 8.

vant for the identification of the Ptolemaic configuration and added the Ptolemaic numbering. This latter configuration is a fairly good representation of what al-Ṣūfī would have seen in the sky. All configurations are orientated in Scheme 4.6 such that the horizontal coordinate corresponds more or less to ecliptic longitudes. Thus the Ptolemaic stars Ori 2 and Ori 23, having roughly the same southern latitude of respectively -17° 0´ and -17° 10´, lie more or less on the same horizontal line. Next the scale of each configuration was fixed by the distance in latitude between the stars Ori 17 and Ori 2. The horizontal lines added in Scheme 4.6 have been chosen to pass through the stars Ori 1, 11, 17, 27, 35, and 38 of Vopel’s Orion. In longitude the configurations are fixed by the vertical line through

297

ISLAMIC CELESTIAL CARTOGRAPHY

Scheme 4.6 Comparison of the configurations of Orion.Top left: in Oxford, MS Marsh 144, p. 325; top right: the modern configuration; bottom left: on Vopel’s printed globe; bottom right: on Mercator’s printed globe.

the star Ori 2. The other two vertical lines are again arbitrary and chosen to pass through the stars Ori 1 and 17 of Vopel’s Orion.The arbitrary grid of lines defined by Vopel’s configuration has been applied to the other groups to make it easy to expose deviations between them. A number of differences between the configurations depicted in Scheme 4.6 result from

variant readings occurring in star catalogues. For example, the latitude of Ori 1 varies in the Ptolemaic catalogues from -13° 30´ to -13° 50´, -16° 30´, -16° 50´, -18° 50´, to even -28° 50´.169 Mercator’s latitude of Ori 1 lies between the values of stars Ori 22 and Ori 23, with southern

298

169 Kunitzsch III 1991, p. 140.

4.3 THE URANOGRAPHY OF ABU’L-Ḥ U SAYN AL-ṢU- fi- (903–86) latitudes of respectively -15° 50´ and -17° 10´, suggesting that Mercator used a value of -16° 30´ or -16° 50´. Al-Ṣūfī’s and Vopel’s values are close to the latitudes of the stars Ori 5 and Ori 21, of respectively -14° 30´ and -14° 15´/14° 55´, suggesting that both used the value of -13° 50´ for Ori 1.This is also the value used in al-Ṣūfī’s catalogue entry. Another variant reading is used by Mercator for star Ori 3, for which two longitudes are quoted in the Ptolemaic star catalogue, 24° 0´ and 20° 20´. It is clear that al-Ṣūfī and Vopel used the former value and Mercator the latter and that variant readings can influence a configuration considerably. Generally speaking the agreement in longitude is less good than that in latitude. For example, in the stellar configurations of Vopel and Mercator the star Ori 11 (Ptolemy:Tau 1° 40´) is roughly on the same vertical as Ori 2 (Ptolemy: Tau 2° 0´) in agreement with the difference of 20´ in longitude between the two stars. In the configuration of al-Ṣūfī the star Ori 11 is to the west of Ori 2. This may be a copying error because the longitudes of Ori 11 and Ori 2 in the catalogue of al-Ṣūfī (Ptolemy + 12° 42´) are respectively Gem 14° 22´ and Gem 14° 42´ which is consistent with the above quoted Ptolemaic values. A conspicuous difference between the configuration in MS Marsh 144 and those of Vopel and Mercator is the orientation of the group of four stars Ori 13–16. Ptolemy says that these four stars lie on a straight line on the back of Orion and that is also the wording in al-Ṣūfī’s catalogue. The longitudes of these stars in the catalogue of al-Ṣūfī (Pt + 12° 42´) decrease in steps of about 1° from Gem 10° 12´ (no. 13), Gem 9° 2´ (no. 14), Gem 8° 2´ (no. 15), and Gem 6° 52´ (no. 16). Their latitudes decrease in steps of 20´ from -19° 40´ (no. 13), -20° 0´ (no. 14), -20° 20´ (no. 15), and

-20° ´ (no. 16).Thus the northernmost star in this group (no. 13) is also the easternmost one and the southernmost (no. 16) is the westernmost with the result that the row of stars is slightly inclined as is seen in all configurations in Scheme 4.6 except the one in MS Marsh 144. There the northernmost star of the group (no. 16) is the westernmost. It is hard to say how this difference came about. It is not the kind of error one would expect from al-Ṣūfī and it is not seen in globes. It could be a copying error that came about during the process of making a mirror image of the configuration.The correct orientation of these four Orion stars is seen for example in the drawing of Orion in globe view in Istanbul, Ahmet III Library, MS 3493, but other manuscripts show the same mistaken orientation of Ori 13–16 as in MS Marsh 144.170 It is clear that comparing stellar configurations is not a simple thing to do. As it is, I conclude that the disagreements between the stellar configurations in Scheme 4.6 do not confirm but at the same time do not exclude the possibility that the configurations depicted in al-Ṣūfī’s Book on the Constellations were ultimately copied from a globe. Actually, there are many passages in al-Ṣūfī’s descriptions in which he refers to differences between stellar configurations depicted on a globe (presumably one based on a Ptolemaic star catalogue) and those seen in the heavens. Cancer is a good example

170 For the image of Orion in Istanbul, Ahmet III Library, MS 3493, see Wellesz 1959, plate 18, fig. 45. Another correct example is the drawing of Orion as seen on a globe from a copy from the collections of the Library of Congress, which was produced circa 1730, and is an exact copy of a manuscript, now lost, prepared for Ulugh Beg of Samarkand (present-day Uzbekistan) in 1417 (820 A.H.), see http://www.wdl.org/en/ item/2484 [accessed 16 March 2012]. Incorrect orientations are seen in the images of Orion in Upton 1932/33, p. 19, fig. 47 and, for example, Al-Ṣūfī (Schjellerup 1874), plate III, fig. 35.

299

ISLAMIC CELESTIAL CARTOGRAPHY to illustrate such differences. In Figs 4.10a–b the two drawings in MS Marsh 144, pp. 256–57 are shown. I have added for the sake of reference again a scheme showing the numbers of the stars (Fig. 4.10). In all, nine stars inside the constellation are marked and four outside it.The main characteristic of Cancer is the nebulous group M44 (Cnc 1) known by the Greek as Praesepe and here labelled ‘al-nathra’, an old Arabic name meaning the tip of the nose (of Leo).171 Grouped around Praesepe are four stars, two of which (Cnc 4 and Cnc 5) are known as the Asses or Aselli.The two stars are labelled in the drawings ‘al-ḥimārayn’which is the genitive of‘al-ḥimārān’, the two donkeys.172 A third star name, ‘aḥad kawkabay al-ṭarf ’, refers to Cnc 2e (κ Cnc); it means ‘one of the two stars al-ṭarf ’ (the glimpse of Leo).The other star is λ Leo.173 Before considering the stellar configurations of Cancer in MS Marsh 144 I have reproduced in Scheme 4.7 two other configurations of this constellation with respect to a series of horizontal lines parallel to the ecliptic. The one on the left is copied again from the globe of Caspar Vopel. It shows all Ptolemaic stars in Cancer (Cnc 1–9 and Cnc 1e–4e). On the right is the modern configuration as it is seen in the sky, generated by a modern computer program, in which I have maintained only stars relevant for the identification of the Ptolemaic stars.174 The scheme illustrates a number of differences observed by al-Ṣūfī between the Ptolemaic configuration and that seen in the sky. In his

description of Cancer, for example, al-Ṣūfī notes that the Ptolemaic latitude of Cnc 9 (β Cnc) must be wrong because on the globe it is closer to Cnc 1 (M44, Praesepe) than Cnc 7 (ι Cnc), whereas in the sky it is at a greater distance from Cnc 1 than Cnc 7.175 How al-Ṣūfī concluded from this observation that the Ptolemaic latitude of star Cnc 9 is wrong is not clear, but Scheme 4.7 shows that it is certainly a correct conclusion. Compared to the modern configuration the Ptolemaic latitude of Cnc 1 is too small and the Ptolemaic latitude of Cnc 7 too large. In the catalogue entry al-Ṣūfī kept the erroneous Ptolemaic value for Cnc 9.176 Another example of a difference observed by al-Ṣūfī between the stellar configuration of Cancer as seen on the Ptolemaic globe and that in the heavens concerns the positions of the stars Cnc 3e (ν Cnc) and Cnc 4e (ξ Cnc).Al-Ṣūfī correctly assures his readers that on the globe the more advanced of the two stars over the nebula and to the rear of it (unformed star Cnc 3e) and the rearmost of these two (Cnc 4e) form a triangle with the star Cnc 7 (ι Cnc) whereas in the sky these three stars lie on a straight line (compare Scheme 4.7).177 Again al-Ṣūfī is right in his assessment that either the longitude or the latitude of one of these unformed stars is wrong. In modern studies it is usually assumed that the unformed stars Cnc 3e and Cnc 4e can be identified with ν and ξ Cnc only when the Ptolemaic latitudes of the two stars (respectively 4° 50´ and 7° 15´) are interchanged.178 In the catalogue entry of Cancer in al-Ṣūfī’s Book the latitude of Cnc 4e is 5° 10´. If this latter value had been plotted on the globe which al-Ṣūfī used in his comparison, Cnc 3e

171 Kunitzsch 1961, p. 88, no. 201. 172 Kunitzsch 1974, p. 275, no. 321. 173 Kunitzsch 1961, p. 114, no. 304a–b. 174 Produced with the help of Chris Marriott’s SkyMap Pro, Version 8.

300

175 176 177 178

Al-Ṣūfī (Schjellerup 1874), p. 149. Al-Ṣūfī (Schjellerup 1874), p. 151. Al-Ṣūfī (Schjellerup 1874), p. 149. Kunitzsch I 1986, p. 92, note 6.

Fig. 4.10 Scheme of the stellar configuration of Cancer in Fig. 4.10a.

Fig. 4.10a Cancer as seen in the sky in the Bodleian Library, University of Oxford, MS Marsh 144, p. 257. (Courtesy of the Bodleian Library, Oxford.)

Fig. 4.10b Cancer as seen on the sphere in the Bodleian Library, University of Oxford, MS Marsh 144, p. 256. (Courtesy of the Bodleian Library, Oxford.)

ISLAMIC CELESTIAL CARTOGRAPHY

Scheme 4.7 Configuration of Cancer. Left: on Vopel’s printed globe; right: the modern configuration as seen in the sky.

and Cnc 4e would still form a triangle with Cnc 7. A third example of perceptible positional errors concerns the unformed stars Cnc 1e (ο1,2 Cnc) and Cnc 2e (κ Cnc). Al-Ṣūfī notes that the Ptolemaic longitude of the star over the joint in the southern claw, Cnc 1e, must be wrong because the location of this star on the globe differs from that in the sky (compare Scheme 4.7).179 For the same reason he concludes that the longitude of the star to the rear of the tip of the southern claw, Cnc 2e, is wrong.180 In modern studies the unformed star Cnc 2e is usually identified with κ Cnc which implies an error in longitude of about 2°. No consensus exists on the identification of the unformed star Cnc 1e. If it is to be identified with π Cnc, there would be

an error in latitude of 2°. In some Ptolemaic catalogues the variant longitude 15° 10´ instead of 19° 40´ is mentioned for Cnc 1e.181 Then Cnc 1e would lie to the west of the star Cnc 6 (α Cnc, longitude 16° 30´) and would then possibly represent ο1,2 Cnc. In this case an error in longitude has to be assumed. The three examples discussed here show the outstanding quality of al-Ṣūfī’s work as well as its weak points. Structural features such as triangles instead of straight lines are easily observed but other deviations are harder to grasp. In neither case was al-Ṣūfī able to provide quantitative data for the observed differences. Ibn al-Ṣalāḥ mentioned that al-Bīrūnī severely criticized al-Ṣūfī for his lack of quantitative data, but that al-Bīrūnī

179 Al-Ṣūfī (Schjellerup 1874), p. 149. 180 Al-Ṣūfī (Schjellerup 1874), p. 149.

181 Kunitzsch III 1991, p. 97.

302

4.3 THE URANOGRAPHY OF ABU’L-Ḥ U SAYN AL-ṢU- fi- (903–86)

Scheme 4.8 Configurations of Cancer in Bodleian Library, University of Oxford, MS Marsh 144, pp. 256–57.

himself did nothing to improve the data in his own star catalogue.182 Ibn al-Ṣalāḥ argued that the differences observed by al-Ṣūfī could well be the result of copying errors and blamed him for not having taken a more critical look at the variant values occurring in the numerous versions of the star catalogue as he did himself.183 Since Ibn al-Ṣalāḥ himself corrected in Cancer only the longitude of Cnc 1e, his own approach did not identify the error in latitude of Cnc 9.184 This brings us to the next question. To what extent have the differences, to which al-Ṣūfī in the various passages refers, influenced the illustrations in his Book of the Constellations of the Fixed

182 Ibn aṣ-Ṣalāḥ (Kunitzsch 1975), p. 39. 183 Ibn aṣ-Ṣalāḥ (Kunitzsch 1975), pp. 21 and 38. 184 Ibn aṣ-Ṣalāḥ (Kunitzsch 1975), p. 60.

Stars. To answer this I have reproduced in Scheme 4.8 the stellar configurations of Cancer shown in Fig. 4.10. Both configurations have been turned round for easy comparison with those in Scheme 4.7. Although these configurations are not without copying errors one finds in both that the distance between the stars Cnc 1 (Praesepe) and Cnc 9 is larger than that between the stars Cnc 1 (Praesepe) and Cnc 7. Also the three stars Cnc 7, 3e, and 4e lie on a straight line in these drawings. Thus it is clear that the drawings of Cancer in MS Marsh 144 incorporate improved astronomical data observed by al-Ṣūfī, which is not found in the catalogue entry of Cancer. In addition to new positional data al-Ṣūfī also recorded a number of non-Ptolemaic stars. The constellation Ursa Maior in MS Marsh 144, p. 43

303

ISLAMIC CELESTIAL CARTOGRAPHY

304 Fig. 4.11 Scheme of the stellar configuration of Ursa Maior in Fig. 4.11a.

Fig. 4.11a Ursa Maior as seen on the sphere in the Bodleian Library, University of Oxford, MS Marsh 144, p. 43. (Courtesy of the Bodleian Library, Oxford.) See also Plate V.

4.3 THE URANOGRAPHY OF ABU’L-Ḥ U SAYN AL-ṢU- fi- (903–86) shown in Fig. 4.11 is a good example to illustrate this. For the sake of easy reference a scheme is added showing the numbers of the stars. Note that the artist switched the numbers 9 and 10. Since these numbers correspond to respectively UMa 10 and UMa 9, I have marked them with an asterisk.185 For reasons explained below I have also added an asterisk to the first external star (UMa 1e) below the tail. In addition to the red stars in Fig. 4.11, there are a number of black, unnumbered stars inside the figure.A text following the usual phrase on the colour scheme at the bottom of the drawing says: ‘and those in black without a letter are not mentioned by Ptolemy’. The best known part of the constellation Ursa Maior in Antiquity as well as today is the group of stars known as the chariot or wagon. It consists of seven stars of which four form a square. This group of stars, nos. 16–19, is labelled in the drawing in Fig. 4.11 by the old Arabic name ‘alnacsh’ which literally means ‘the bier’, but according to Kunitzsch the name of this asterism should not be translated in this way, because ‘Nacsh’ is probably a proper name in Arabic Antiquity.The remaining three stars in the tail, nos 25–27, are called ‘al-banāt’, meaning ‘the daughters’. Both names are part of the old Arabic asterism ‘Banāt Nacsh’, the stars of which coincide with those forming the Greek chariot.186 In addition to the group name, the stars nos 25–27 have been labelled individually in the drawings in MS Marsh 144: no. 25: ‘al-jawn’ (the black horse), no. 26: ‘al-canāq’ (the goat), and no. 27: ‘al-qā’id’ (the leader).187 The names of the pairs of stars

nos 23–24, nos 20–21, and nos 12–13 are connected through the leaps of the gazelles:‘al-qafza al-ūlā’ (the first leap), ‘al-qafza al-thāniya’ (the second leap), and ‘al-qafza al-thālitha’ (the third leap).188 Al-Ṣūfī identifies the gazelles with a group of stars in the head of Ursa Maior (UMa 1–6) and he adds the external stars UMa 3e, 4e, and 8e.The external stars UMa 5e–8e are counted among the young ones of the gazelles, hence the name ‘al-ẓibā’ wa-awlāduhā’ (the gazelles and their young ones).189 The first external star UMa 1e is marked by an asterisk in the reference scheme in Fig. 4.11, because in the drawing the star is actually not plotted. In its place at the edge of the drawing below the tail one finds the second part (al-asad) of its name ‘kabid al-asad’ written on a piece of paper pasted on. In the drawing of Ursa Maior as seen on the sky in MS Marsh 144, p. 44 there is still a trace of the star with its number, here also added on a piece of paper pasted on, now with the first part (kabid al-a) of its name.There also the last star in the tail, UMa 27, is marked on the piece of paper. The non-Ptolemaic stars plotted in the drawing of Ursa Maior include a number of individual stars and one group. One non-Ptolemaic star (g, 80 UMa) is next to the bright star UMa 26 (ζ UMa) in the middle of the tail. It is called ‘al-suhā’ (the overlooked one) because it is close to a bright star and could be used to test an observer’s vision.190 This star became known later in Europe as Alcor.191 Another non-Ptolemaic star is—as al-Ṣūfī says—located between UMa 19 (γ UMa) and UMa 22 (ψ UMa).This fairly bright

185 Al-Ṣūfī (Schjellerup 1874), p. 57, says that no. 9 is the northern of the two stars. 186 Kunitzsch 1961, p. 48, no. 55. 187 Kunitzsch 1961, p. 62, no. 106, p. 43, no. 33, and p. 91, no. 213.

188 Kunitzsch 1961, pp. 90–1, no. 212a–c, see also nos 211a–c. 189 Kunitzsch 1961, p. 120, no. 329 and p. 39, no. 21a . 190 Al-Ṣūfī (Schjellerup 1874), p. 50. MS Marsh 144, pp. 43–44; Kunitzsch 1961, p. 106, no. 271. 191 Kunitzsch 1986c, pp. 23–7.

305

ISLAMIC CELESTIAL CARTOGRAPHY star (3.7m) is easily identified as χ UMa. Al-Ṣūfī observed another star between this latter star and UMa 2e, which must be 67 UMa (magnitude 5.2), but this star is not marked in the drawing. Two more non-Ptolemaic stars are set inside a circular shape by the stars UMa 7-UMa11, UMa 14, and UMa 15 which Al-Ṣūfī labelled ‘al-ḥawḍ’ (the pond).192 The first of these is 16 UMa (magnitude 5.1), which forms a triangle with UMa 7 (τ UMa) and UMa 8 (23 UMa).The other nonPtolemaic star is described as forming a triangle with an obtuse angle with the stars UMa 9 (υ UMa) and UMa 10 (ϕ UMa), by which we can identify it as CS UMa (magnitude 5.2).193 In the drawing this obtuse angle is not observed. Close to UMa 22 (ψ UMa) a group of nonPtolemaic stars was observed in the form of a circle between the first leap (nos 23–24), the second leap (nos 20–21), and the square (nos 16–19).194 In the drawings these stars, known as ‘calā istidāra’ meaning in a round form, are marked in the hind leg as a circle of dots and in the reference scheme labelled ‘ring’, (see Fig. 4.11).195 How to identify these stars is not obvious. There is indeed a ring-like structure in the neighbourhood of ψ UMa (UMa 22), the five brightest stars of which are ω, 47, 55, 57, and 56 UMa, not counting ψ UMa. If this identification of the stars in the ring-like structure close to ψ UMa (UMa 22) is correct, it follows that four of the five stars marked in the drawing of Ursa Maior in Fig. 4.11 should lie east of ψ UMa instead of west because this is how these stars are situated with respect to ψ UMa. This difference

may have been the result of an error by which mirror images were confused, in the same way as may have happened to the four stars on the back of Orion discussed above. The present discussion of the stellar configurations presented in the drawings of Cancer and Ursa Maior in MS Marsh 144 shows that a number of the observations by al-Ṣūfī were recorded cartographically. It also elucidates his method for verifying Ptolemaic locations. One can imagine that al-Ṣūfī started off by copying stellar positions from a Ptolemaic globe on thin (transparent) paper. In order to compare them with the stellar configurations in the sky he could turn the transparencies round.Where possible he appears to have made corrections. This corrected diagram was apparently used for preparing the drawings to be included in his book, and perhaps also for making his own celestial globe. If this was the silver globe seen in the library in Cairo in 1043 which al-Ṣūfī made for his patron ‘Aḍud al-Dawla, it would have been unparalleled in globe making. However that may be, it is no wonder that the Book on the Constellations was very popular among globe makers. It was also of great use in popular astronomy in which the globe played an important educational role. As al-Ṣūfī explains, confusion could arise if a globe is used for studying the sky:

192 Al-Ṣūfī (Schjellerup 1874), p. 52. Kunitzsch 1961, p. 67, no. 122. 193 CS UMa is known also as HR 3870, HD 84335, SAO 27377, BD + 57 1231. 194 Al-Ṣūfī (Schjellerup 1874), p. 51. 195 Al-Ṣūfī (Schjellerup 1874), p. 51.

306

‘And when you look at these figures on a globe made [by an artisan], you will see them reversed because we are looking down at them, and we see their right side on the left and the left side on the right. But we see them in the sky as they truly are because we are looking up at them from the middle [centre] of the sphere. For each constellation we present two figures, one of them according to what falls on the globe and the other according to what is seen in the sky. In this way we have encompassed the two different conditions such

4.4 EXTANT GLOBES MADE BEFORE 1500 that no confusion will befall someone who contemplates this when he sees that what is on the globe is different from what is in the sky.When we wish to see the constellation as it is in truth, we should raise the page [on which the figures are drawn] above our heads and look at the second figure [i.e., the figure drawn as the constellation appears in the sky] from below; we will then see it according to what is in the sky.’196

century. Although such globes are outside the scope of the present book Savage-Smith discussed also many links to the Greek and Arabic predecessors.And, most importantly, in it she presented for the first time a catalogue listing all then known 132 globes. In 1991 Savage Smith could report 43 additional globes, bringing the total number of globes up to 175.198 Since then the number of Islamic globes has further increased to Thus to avoid confusion and to help a student more than 200.199 From the analysis of so many (his patron?) to bridge the gap between the globe globes Savage Smith arrived at a classification and the sky al-Ṣūfī added two pictures in his dividing the globes in three groups. book. The result is an extraordinary star atlas Class A consists of globes marked with about composed to suit the student in astronomy in 1000 stars and their constellation figures. These every respect, not only by clarifying the distincglobes with a more or less complete image of the tion between the celestial sphere and its main celestial sky form the core of our interest and model, the globe, but also by pointing out objects those made before 1500 are discussed in more of special interest in each constellation and furdetail below.They are described in the Appendix ther by transferring the names of the stars and labelled IG1–IG10. Class B includes globes belonging to the older traditional anwā’ culture on which only a selection of about 20–150 stars into the new mathematical tradition through are marked but there are no constellation figlabelling the indigenous star names. ures.200 An example of a Class B globe is shown in Fig. 4.12. It belongs to the collection of the Museum for the History of Science in Oxford, . EXTANT GLOBES has a diameter of 153 mm, and is dated 718 H MADE BEFORE  (=1318/19).201 It is made by cAbd al-Raḥmān In 1985 Emilie Savage-Smith published her well- ibn Burhān al-Mawṣilī. On this globe the folknown study on what she called Islamicate celes- lowing circles are engraved: the ecliptic, the tial globes. Her choice to use the label ‘Islamicate’ Equator, the great circles through the ecliptic served to express the fact that many globes are poles, and the polar circles centred on both the not part of the cultural domain of religious Islam ecliptic and equatorial poles.202 About 100 stars proper but ‘are often based on traditions taken are marked by inlaid silver points and labelled. over from other cultures and nurtured and devel- The stellar configurations of the lunar mansions oped by Muslims and non-Muslims alike’.197 Indeed, a central topic in her study is the pro198 Savage-Smith 1990/1991, p. 24; Savage-Smith 1992, duction of globes in Lahore in the seventeenth

196 The translation is from Goldstein and Hon 2007, pp. 2–3. 197 Savage-Smith 1985, p. vi.

p. 45. 199 Savage-Smith 1997, p. 168. 200 Savage-Smith 1985, p. 61. 201 Savage-Smith 1985, p. 247, no. 60. Oxford, Museum of the History of Science, Inv. no. 57–84/181. 202 Savage-Smith 1985, p. 30, Fig. 8.

307

ISLAMIC CELESTIAL CARTOGRAPHY examined here it coincides four times with the ecliptic (IG2, IG5, IG6, IG8), three times with the Equator (IG1, IG9, IG10), once with a meridian circle (IG4), once with a circle of latitude (IG7) and once it is along a great circle passing more or less through the Milky Way (IG3). On all globes but one the ecliptic and the Equator are uniformly divided into 1° with every fifth line longer; on IG4 every sixth line is longer.The ecliptic is divided into 12 sections of 30°. On the four oldest globes (IG1–IG4) the Equator is numbered continuously from 0°–360° and on the later globes (IG5–IG10) there are 3 segments of 100° and one of 60°. All globes have great circles passing through the ecliptic poles and the boundaries of the zodiacal signs. As a rule, polar circles centred either on the ecliptic or on the equatorial poles, as well as the Tropic of Cancer and Capricorn, are absent on these earlier Class A globes. An exception is—again— globe IG4 which appears to have polar circles Fig. 4.12 Class B Islamic globe, Museum of the History of Science, Inv. no. 57–84/181. (Courtesy of the around its equatorial poles.203 The Latin names Museum for the History of Science, Oxford.) engraved on the horizon ring of this globe were added later and perhaps this holds also for the with their labels are also indicated on the globe. equatorial polar circle. The limited number of stars depicted on Class B 4.4.1 Epochs and dates globes recalls the model described in Qusṭā ibn Lūqā’s book discussed above. The last group, Usually the greater part of the 1025 Ptolemaic Class C, comprises globes which have only the stars are marked on the globes of Class A, with main celestial circles engraved on them. All sizes varying with the magnitudes of the stars. globes belonging to this group were made When marking the positions of the stars a after 1500. Savage-Smith believes that it was a maker would rely on one of the Arabic versions later development designed especially for of the Ptolemaic star catalogue discussed above. teaching. Sometimes one can identify the catalogue used From the characteristics of the ten Class A by the maker by tracing so-called variants occurglobes considered here the following picture ring in star catalogues, that is, deviations which emerges. Islamic globes made before 1500 consist of two hollow metal hemispheres joined 203 Savage-Smith 1985, p. 218, says that IG3 (her no. 2) has together on a great circle.The choice of the great equatorial polar circles and ecliptic polar circles, but I cannot circle is not standard. Among the ten globes confirm this. 308

4.4 EXTANT GLOBES MADE BEFORE 1500 in the course of time have become part of the Ptolemaic corpus through corruption of data and so on. For most surviving Ptolemaic catalogues and their translations such variants have been collated by Kunitzsch.204 For example, the majority of the deviating positions on the oldest globes in our list, IG1 and IG2, could be identified with variants recorded in a star catalogue belonging to the Maghreb branch of the Almagest translation by al-Ḥajjāj which was available in Spain when the globes IG1 and IG2 were made.205 Other Islamic globes have not been studied in enough detail to identify the star catalogue used by the makers. On two globes, IG3 and IG8, the stars entered on the sphere are numbered.206 This may reflect the influence of the star catalogue in al-Ṣūfī’s Book on the Constellations, since as a rule the stars are not numbered within the constellation entries prior to al-Ṣūfī. Star catalogues influenced by al-Ṣūfī’s, such as those produced by al-Bīrūnī and Ulugh Bēg, also have numbered stars. Sometimes precession corrections are engraved on globes. On IG3 and IG4 the correction is said to have been calculated with respect to Ptolemy’s Almagest. On globe IG3, made by Yūnus ibn al-Ḥusayn, the interval between the calculations of Ptolemy (epoch 137) and the year 540 H (= 1144/45) is said to be 15° 18´. On three other globes in our list (IG7, IG9, and IG10) the catalogue of al-Ṣūfī is mentioned explicitly as their source. On globe IG9, made by Jacfar ibn c Umar ibn Dawlatshāh al-Kirmānī, the stars are said to have been ‘drawn according to the Book of Constellations by Abū al-Ḥusayn cAbd al-Raḥmān al-Ṣūfī after adding to their longitudes for our 204 Kunitzsch III 1991. 205 Dekker and Kunitzsch 2008/9. 206 Destombes 1960, p. 449; Makariou and Caiozzo 1998, p. 106.

time 6° 3´ in the year 764 H and 732 Yazdijird and 1674 (in the era) of Alexander’.In other cases,where there is no record of the precession correction, it can be determined by comparing longitudes of the stars with corresponding Ptolemaic values. How globe makers calculated their precession corrections is not known, but an examination of the data engraved on the globes shows that the use of a precession rate of 1° in 66 years was most popular. In order to demonstrate this we have collected some relevant data in Table 4.6. In the first column the number of the globe is mentioned, then follows an event date engraved on the globe. In the third column the precession correction with respect to either Ptolemy’s catalogue or al-Ṣūfī’s is listed as it is engraved on the globe and in the last column we have added precession corrections that have been determined by comparing the stellar longitudes plotted on the globe with corresponding values in the Ptolemaic star catalogue and subsequently calculating the mean value of the differences. The data in Table 4.6 have been plotted in a graph (Scheme 4.9) for the dated globes IG1, IG3, IG4, IG5, IG7, IG9, and IG10.The precession correction is shown as function of the dates engraved on them. Since the precession correction is not engraved on the dated globes IG1 and IG5, I have used the values listed in column 4 in Table 4.6. For comparison purposes I have also added to the graph first, the parameters of the star catalogue of al-Ṣūfī (epoch 964 and precession correction with respect to Ptolemy 12° 42´, marked in the graph by a black square ▪), and second a line marking the increase of the precession correction in time, using a rate of 1° in 66 years. It is very clear from the graph in Scheme 4.9 that the precession corrections engraved on the globes IG3, IG4, IG7, IG9, and IG10 correspond well to the date indicated by the line marking a

309

ISLAMIC CELESTIAL CARTOGRAPHY Table 4.6 Summary of the dates and the precession correction on early Islamic globes No.

Inscription

IG1

478 H (1085)

Data engraved on the globe

IG2 IG3 IG4 IG5 IG6

540 H (1144/45) 622 H (1225/26) 674 H (1275/76)

15° 18´ in excess of Ptolemy 16° 46´ in excess of Ptolemy

IG7 IG8 IG9

684 H (1285/86)

5° in excess of al-Ṣūfī

764 H (1362/63)

6° 3´ in excess of al-Ṣūfī

IG10

785 H (1383/84)

6° [2]3´ in excess of al-Ṣūfī

Measured precession correction in excess of Ptolemy 14° 5´ 14° 5´ ± 2’ 14° 1´ 14° 3´ ± 3’

(Destombes 1956) (Dekker and Kunitzsch 2008/9) (Destombes 1956) (Dekker and Kunitzsch 2008/9)

16° 32´ ca. 16° 17° 51´ 17° 33´

(Destombes 1956) (Destombes 1956) (Destombes 1956) (Oestmann 2002)

17° 56´ 18° 20´ 18° 20´

(Destombes 1956) (Gunther/Knobel 1923) (Destombes 1956)

rate of 1° in 66 years. For example, on globe IG3 the precession correction is 15° 18´. With a rate of 1° in 66 years this precession correction is equivalent to 1010 years, suggesting an epoch around 137 + 1010 = 1147, in good agreement with the year 540 H (= 1144/45) engraved on the globe.This shows that most dates and precession corrections engraved on the globes are consistent with each other and that globe makers used the rate of 1° in 66 years for a very long time. This is perhaps not so suprising, considering that even on the most recent globes in our list (IG9 and IG10) the precession correction is given with respect to the catalogue of al-Ṣūfī (epoch 964). Anyway, one can exclude the possibility that the epoch was determined by observing a few bright stars. This practice common among astronomers cannot be substantiated by the present group of globes. Not always does the year mentioned on a globe represent the epoch.The oldest globe, IG1, for example, is dated 478 AH (29 May 1085).The longitudes of the stars exceed on the average the corresponding Ptolemaic values by 14° 5’± 2’. Scheme 4.9 Precession corrections plotted as a function of dates.

4.4 EXTANT GLOBES MADE BEFORE 1500 If this excess in longitude of 14° 5’ is converted into a date by using the rate of precession of 1° in 66 years, one obtains for the epoch of the globe IG1 the year 1066–67. This result can be compared with some data related to astrolabe star lists. For example, the longitudes of the stars in a star list, dated 1066–67 and attributed to Ibn al-Zarqālluh (d. 1100), exceed the corresponding Ptolemaic longitudes by 14° 7’.207 It shows that the date engraved on globe IG1 does not represent the epoch of the globe’s star positions but its date of construction. In the graph in Scheme 4.9 this disagreement between the construction date and the epoch is clear from the fact that the point representing the globe lies to the right of the line representing a correction of a rate of 1° in 66 years. Since the difference between the date and the epoch is small, the point concerned does not deviate much. This cannot be said of the point in the graph in Scheme 4.9 referring to globe IG5.According to Destombes the stellar longitudes on this globe differ on average by about 16° from the corresponding Ptolemaic values.208 With a rate of 1° in 66 years this precession correction is equivalent to 1056 years, indicating an epoch of 1193, predating the date 674 H (= 1275/76) engraved on the globe by a period of a lifetime. One possibility suggested by Destombes is that the maker increased the longitudes of al-Ṣūfī by using the Ptolemaic rate of 1° in 100 years. However, if the maker did indeed use al-Ṣūfī’s catalogue it is very unlikely that he would have used the antiquated

207 Kunitzsch 1966, p. 133 gives a date of 1070 which is corrected in Kunitzsch 1980, esp. p. 196f, part II. On the record that Azarquiel made a globe, see Samsó 2005, p. 64. 208 Destombes 1956, p. 319. It is not known how Destombes derived the value of ca. 16°.The fact that it is a whole number may indicate that he measured the positions indirectly, say, from the planispheres which Dorn made of the globe.

Ptolemaic rate of 1° in 100 years. An alternative explanation is that the maker copied an earlier globe and simply engraved the date of production on the sphere. Another problematic situation applies to the globes IG9 and IG10.The value of 6° 3´ engraved on globe IG9 appears to agree well with the date on the globe (see the graph in Scheme 4.9), but this value is not supported by the longitudes of the stars themselves. By measuring the stellar longitudes Knobel found a precession correction of 5° 38´, which is 25´ less than the value engraved on the globe. Knobel’s value was confirmed by Destombes. It is hard to say how to interpret the difference of 25´. The globes IG9 and IG10 are by the same maker and the difference between the precession corrections of these two globes is 20´ which is equivalent to about 22 years.This agrees with the difference between the dates engraved on the globes (respectively 1362/63 and 1383/84). Therefore the maker seems to consider differences of the order of 20´ or more significant. More light on this problem could possibly be obtained by examining the stellar longitudes on the globe IG10, the more so since the precise value (in minutes) of the precession correction engraved on that globe is illegible. The remaining three globes, IG2, IG6, and IG8 are not dated.The longitudes of the stars marked on them differ according to Destombes on average by respectively 14° 3´, 17° 51´ and 17° 56´ from the corresponding Ptolemaic values.209 My own examination of the stars on IG2 gave a precession correction of 14° 3´ ± 3’ which is fully consistent with Destombes’s value. The precession correction of IG2 compares well with that of

311

209 Destombes 1956, pp. 319–20.

ISLAMIC CELESTIAL CARTOGRAPHY IG1 (14° 5’± 2’) which suggests that the two globes were made for the same epoch although not necessarily at the same time. The precession correction of 17° 56´ determined by Destombes for globe IG8 implies an excess with respect to al-Ṣūfī’s catalogue of 5° 14´, that is 14´ more than the value engraved on globe IG7 dated 684 H (1285/86), implying an epoch around 1300. Several examinations of the longitudes of the stars on IG6 are known. In 1805 Beigel made an attempt to date the globe and arrived at an epoch of 1289. Since Beigel’s date was close to 1279, Drechsler proposed the year 200 of the Djelali era as the epoch.210 Destombes derived at a date of 1304 for the precession correction of 17° 51´ mentioned above. Kunitzsch pointed out that with a rate of 1 in 66 years an excess of 1° with respect to al-Ṭūsī’s precession correction of 16° 45’ for the epoch 1232 (that is, a precession correction of 17° 45´) would result in an epoch of 1232 + 66 = 1298.And in case the excess is obtained by calculating it directly from Ptolemy’s epoch 137 a precession correction of 17° 45´ suggests an epoch of 137 + 66*17,75 = 1308.5. For these reasons he proposes an epoch of ca. 1305. 211 A recent study was carried out by Oestmann who obtained a precession correction of 17° 33´, which is 48’ in excess of al-Ṭūsī’s correction of 16° 45’ for the epoch 1232.212 Assuming a rate of 1 in 70 years Oestmann calculated an epoch of 1288 (= 1232 + 70*(48/60) = 1232 + 56). Oestmann’s precession correction is considerably less than Destombes’s value 17° 51´ mentioned above. Kunitzsch found it hard to accept such precise values since they suggest an unrealistic precision for marking the stars on a globe. It

210 Drechsler 1873, p. 5. 211 Kunitzsch 1992/1993, pp. 83–8. 212 Oestmann 2002, pp. 293–4.

should be kept in mind, however, that the precession corrections of Destombes and Oestmann present averaged values which do not indicate the precision actually achieved by the globe maker by plotting individual stars. Unfortunately neither Destombes nor Oestmann indicated the uncertainty in their results and so it is hard to decide whether these are compatible with each other. However that may be, the precession corrections of 17° 33´ and 17° 51´ obtained for IG6 are respectively 9´ less and greater than the value engraved on globe IG7, whose stars are said to be 5° in excess of al-Ṣūfī’s, that is, a precession correction of 17° 42´.A difference of 9´ is equivalent to about 10 years, and since IG7 is dated 684 H (1285/86), the epoch of the Dresden globe IG6 will probably lie between 1275 and 1295, although a date around 1300 cannot be excluded.

4.4.2 Constellation design For obvious reasons the study of Islamic constellation design has mostly been focused on al-Ṣūfī’s Book on the Constellations.213 Constellation drawings such as in MS Marsh 144 are of great artistic strength, yet the iconography of these images did not come out of the blue. Underlying all iconography in the mathematical tradition are the descriptions of the locations of the stars within a constellation in the star catalogues, thus defining a Ptolemaic iconography. It has been suggested that Ptolemy himself used pictorial sources for his descriptions and that he may have had access to a globe.214 The Ptolemaic iconography determines in the first place the shape of a constellation, which results automati213 Wellesz 1959; Savage-Smith 1992, pp. 54–60; Makariou and Caiozzo 1998. 214 Kunitzsch 1974, p. 76.

312

4.4 EXTANT GLOBES MADE BEFORE 1500 cally when, following the recipe described by Ptolemy, globe makers first plotted the stars using their coordinates and then drew the constellations in keeping with the descriptions.215 Then the basic structure of the iconography of, say, the images in MS Marsh 144, is not necessarily very different from that seen on later maps and globes in the mathematical tradition discussed in Chapter 5. Most differences are based on the one hand on variants in the Ptolemaic descriptions resulting from their transmission through series of translations and on the other hand on variations in mythological interpretation and style depending on the artist’s knowledge and tastes prevailing in the period in which the globe was made. A good example to illustrate this is the constellation nowadays called Hercules. Ptolemy and before him Eudoxus and Aratus described this constellation as a kneeling figure with one foot above the head of Draco. There is no clear mythology connected with this kneeling figure and no attributes are associated with it.The figure depicted on the Farnese globe discussed in section 2.6 is typical for this early iconography. Later this kneeling figure was connected in certain Greco-Roman traditions with the mythology of Hercules and as such he is shown on the Mainz globe and on early medieval planispheres (see sections 2.4 and 3.2, respectively). On most of these mappings he is still on his knees with one foot above the head of Draco, but now he has a club in the one (western) hand and a lion skin in the other (eastern) hand. In the Arabic translation of the Ptolemaic star catalogue by Isḥāq as revised by Thābit, which was used by al-Ṣūfī, the constellation is still described as a man kneeling in keeping with

Ptolemy’s description.216 The oldest image of this kneeling figure in the mathematical tradition is that in MS Marsh 144, pp. 81–2. The drawing in Fig. 4.13a shows the constellation as seen on the sphere, to which I have added, again for the sake of easy reference, a scheme showing the numbers of the stars (Fig. 4.13). Since the figure is upside-down south is on top and north is at the bottom of the drawing. The constellation is made out of 29 stars, of which one is not numbered in the figure because it is shared with Bootes (Boo 9). This unnumbered star is in the foot of the kneeling leg and it is labelled: ‘this one is the ninth of the constellation of Bootes, on the end of the staff, common between the two’. The one external star above the western arm with a scimitar (Her 1e) is labelled in the drawing as usually ‘Outside the figure’. The first star of the constellation, the one in the head, Her 1 (α Her), received the Arabic name,‘kalb al-rāc ī’ (the shepherd’s dog).217 It is—as al-Ṣūfī notes—a star often marked on astrolabes. The most conspicuous Arabic name in the constellation is ‘al-nasaq al-sha’āmī’, the northern row, a name often engraved on eastern Islamic globes.218 It refers to a group consisting of three stars on the arm with the scimitar (Her 2, 3, and 4) and six stars on the outstretched arm (Her 5, 6, 7, 8, 9, and 10). Two stars belonging to the neighbouring constellations Lyra (Lyr 7 and 9) and Serpens (Ser 3 and 4) are also part of the northern row.These northern-row stars lie on a straight line and fix the position of the outstretched arms of the kneeling figure.As an aside, I note that the Arabs also knew a southern row which al-Ṣūfī identifies with a number of star of

216 Kunitzsch I 1986, pp. 45–8. 217 Kunitzsch 1961, p. 73, no. 142. 218 Kunitzsch 1961, p. 86, no. 192a.

215 Manitius 1963, vol. 2, pp. 72–4;Toomer 1984, pp. 405–6.

313

ISLAMIC CELESTIAL CARTOGRAPHY

Fig. 4.13 Scheme of the stellar configuration of Hercules in Fig. 4.13a.

the Serpent (Ser 7–10, 12) and Ophiuchus (Oph 7, 8, 12, 13, and 19).219 On the two oldest globes IG1 and IG2 the kneeling figure is depicted without any attribute (see Figs 4.21a and 4.22a), but in MS Marsh 144 he is armed with a sickle (Fig. 4.13) and this is the way he is engraved on most eastern Islamic celestial globes (see Figs 4.23a and 4.24c).220 Makariou and Caiozzo presume that al-Ṣūfī’s image in Fig. 4.13a developed from the Greco-Roman image of Hercules, and that in this process his club has been replaced by a scimitar and his lion’s skin has disappeared.221 I think that this assumption is incorrect and that instead al-Ṣūfī’s image developed from the kneeling figure without any attributes, to which al-Ṣūfī added a scimitar.

219 Al-Ṣūfī (Schjellerup 1874), pp. 99–100. Kunitzsch 1961, p. 86, no. 192b. 220 Wellesz 1959, p. 8 and Savage-Smith 1985, p. 143. 221 Makariou and Caiozzo 1998, p. 103.

Fig. 4.13a Hercules as seen on the sphere in the Bodleian Library, University of Oxford, MS Marsh 144, p. 81. (Courtesy of the Bodleian Library, Oxford.)

However that may be, adornments such as scimitars, clubs, and lion skins do not hide the basic Ptolemaic attitude of a kneeling figure with one foot above the head of Draco and its arms aligned along the stars of the northern row.Any deviation from this Ptolemaic pattern is easily recognizable. By following the catalogue descriptions to the letter it is not always possible for the artist to draw a figure with normal proportions. Artistic adjustments are frequently seen on globes of all times and are not considered as deviating from the Ptolemaic norm. In this sense we can say that most constellations on the globes are drawn in agreement with the Ptolemaic iconography. However, not all constellations conform to the Ptolemaic standard. Some miss only a garment;

314

4.4 EXTANT GLOBES MADE BEFORE 1500 others have attributes not listed in the Ptolemaic star catalogue. Al-Bīrūnī refers in his Kitāb altafhīm to certain lawāzim (that is, attributes that were needed to complete some of the constellation figures), which are not mentioned explicitly in the Ptolemaic descriptions and on which no stars were placed but which were known to the Arabs from other (literary) traditions. Examples are the sword (sayf ) of Perseus and the vessel ( jarra) held by Aquarius.222 In her study of the iconography of the drawings in manuscripts of al-Ṣūfī’s Book of the Constellations Wellesz distinguished two groups: A is exemplified by the drawings in MS Marsh 144, and B is associated with the simpler iconography of the drawings in MS Fatih 3422.223 She further suggested that the iconography of the constellations on the earlier western globes IG1 and IG2 followed that of group B. SavageSmith’s statement that the constellations on globe IG1 conform to the basic designs as described by al-Ṣūfī but are drawn in a style that differs from the eastern globes, ignores the fact that globe IG1 (and IG2 as well) represent an iconographic tradition that is not at all associated with al-Ṣūfī’s designs.224 To underline such differences and to define at the same time a number of typical Islamic constellation characteristics a summary account of a selection of constellations follows. Ursa Minor: in ancient Greek sources the Bears tend to be presented back to back as described by Aratus in his Phaenomena.225 On the Mainz globe, the Kugel globe, and on the later Renaissance globes the bears are indeed back to

222 223 224 225

Kunitzsch 1974, p. 78, note 199. Wellesz 1959, pp. 22–3. Savage-Smith 1985, p. 24. Aratus (Kidd 1997), pp. 74–5, ll. 25–30.

back with the unavoidable result that the tail of Ursa Minor, outlined by the three stars UMi 1–3, points upwards (see Figs 2.8 and 2.13). If however Ursa Minor is drawn with its belly turned towards Ursa Maior, the tail formed by UMi 1–3 hangs down. In the Ptolemaic tradition the back and belly of the Lesser Bear are not specified, thus both ways of drawing Ursa Minor’s tail are consistent with the Ptolemaic description. On most Islamic globes Ursa Minor is drawn with its belly turned towards the Ursa Maior with its tail down. On globes IG1 and IG2 the shape of the tail of Ursa Minor is somewhat obscured by the body, but it is easily seen that it would hang down had it been drawn as a long tail (see Fig. 4.21a). In MS Marsh 144, pp. 34 and 35 and on globes IG3–IG8 Ursa Minor is also depicted with its tail down (see for example, Fig. 4.23a).226 However, on the Islamic globe IG9 the bears are drawn in the Greek way back to back such that Ursa Minor’s tail points upwards, showing perhaps some late GreekRoman impact.227 Bootes: the most important attribute of Bootes mentioned in the Ptolemaic star catalogue is a staff (a κολλόροβοϛ) held in his right hand which is marked by the stars Boo 8–10 and Boo 15. Al-Ḥajjāj translated κολλόροβοϛ as the truncated pineapple (i.e. conus) and Isḥāq as revised by Thābit as a shepherd’s staff or curved stick.228 On globes IG1 and IG2 Bootes is depicted without a staff which is not in keeping with either the Greek or the Arabic Ptolemaic tradition. In MS Marsh 144, pp. 69–70, and on globes IG5 and IG6 Bootes holds a stick (see Figs 4.17 and 4.23a),

226 For an Islamic example, see Wellesz 1959, fig. 18. 227 See the picture in Gunther 1923, vol. 2, between p. 248 and p. 249. 228 Kunitzsch I 1986, pp. 40–3.

315

ISLAMIC CELESTIAL CARTOGRAPHY more or less in agreement with the descriptions of Isḥāq as revised by Thābit and al-Ṣūfī. Lyra: in the translation by al-Ḥajjāj Lyra is introduced as ‘the constellation Lyra, that is al-nasr al-wāqic, that is the tortoise’.229 Isḥāq as revised by Thābit uses this name for the brightest star Lyr 1. This interpretation is probably based on some pictorial source, such as a Greek lyre with a resonance body in the shape of the shell of a tortoise as it is seen on the Farnese globe (Fig. 2.18), since the Greek text of the Ptolemaic star catalogue does not contain a clue in that direction. On globes IG1 and IG2, Lyra is depicted as a tortoise (see Figs 4.21a and 4.22a).230 The Arabic translations could have been the source for drawing Lyra as a tortoise, but it is more likely that the image belongs to an older iconography used on Islamic globes. Al-Ṣūfī mentioned that he had seen globes on which Lyra was drawn as a tortoise.231 The tortoise is seen in some manuscripts belonging to the oriental branch of manuscripts of al-Ṣūfīs Book on the Constellations.232 More often Lyra is presented as a vase or a pot, as in MS Marsh 144, p. 87 and on globes IG5 and IG6 (see Figs 4.21a and 4.24d). This Islamic image derived from a not understood image of a lyre occurring on some, possibly Greek, globe or other source.

Fig. 4.14 Perseus on the celestial globe IG2. (Courtesy of the Bibliothèque nationale de France, Paris.)

Perseus: in Greek mythology Perseus is a figure with a hooked sword holding Medusa’s head.233 The hooked sword is part of the image of Perseus on the early Western globes IG1 and IG2. The

attribute he holds in his other hand, a unique three-headed form, does not recall Greek illustrations nor any known Islamic source (see Figs 4.14 and 4.21b). If the three-headed form on IG1 and IG2 stands for three Gorgons their mythology might have been misinterpreted by Arabic globe makers.234 If not, the present threeheaded figure forms as much a mystery as the enigmatic name al-tlhb engraved on IG2 which appears only in the translation by al-Ḥajjāj.235 On

229 Kunitzsch 1974, p. 177; Kunitzsch I 1986, pp. 48–9. 230 The tortoise on IG2 is rotated by about 90° compared to that on IG1, but otherwise the images are the same. 231 Al-Ṣūfī (Schjellerup 1874), p. 77. 232 Kunitzsch 1986c, Exkurs I, pp. 47–8. 233 Philips 1968.

234 One possibility is that the three-headed form is an early artistic formula used to show one and the same head from three sides: twice in profile and once face-on. 235 Dekker and Kunitzsch 2008/9, p. 158, note 12.

316

4.4 EXTANT GLOBES MADE BEFORE 1500 The Ivy Leaf (Leo): Ptolemy describes in his star catalogue a group of three external stars forming the angular points of a triangle (Leo 6e–8e). The three stars belong to the nebulous mass called Πλόκαμος (lock of hair) located between the edges of Ursa Maior and Leo. In the description of the last star (Leo 8e) belonging to the lock of hair, it is added ‘in an ivy-leaf ’.238 As explained in Chapter 3 the addition should be understood as an alternative description of the three stars of the lock of hair.The figure of an ivy leaf is well established in the pictorial tradition in Antiquity. It is seen on the cupola of Quṣayr c Amra and on a number of medieval hemispheres.239 The ivy leaf is also engraved above the tail of Leo on globe IG2 (see Fig. 4.16) around the three unformed stars of Leo (Leo 6e–8e). This image could in principle have been inspired by the text in the Almagest translation by al-Ḥajjāj, which was used by the maker of globe IG2, but it Fig. 4.15 Drawing of Perseus on of the celestial globe is more likely that a pictorial source served for IG5. (reproduced from the hemisphere published by the transmission of the image. In MS Marsh 144, Dorn 1830, Plate A.) pp. 267–68 the stars are drawn as external stars and are not part of an separate image.This is also the Florence globe IG1 the three-headed form the case on globes IG1 and IG3. However on has the conventional Arabic label ‘the Carrier of three globes (IG5, IG6, and IG7) the stars are the Head of the Desert Demon’. In MS Marsh placed in a kind of leaf or branch held byVirgo in 144, p. 110–11 (see Fig. 4.7) Perseus holds a her northern hand. This branch should not be straight sword and carries indeed the head of confused with Spica which is in Virgo’s southern Ghūl, the desert demon, which is introduced in (left) hand.240 On globes IG5 and IG6 the form in the Arabic translations for Medusa’s head.236 The the northern hand is labelled: ‘al-hulba’ (hair), attributes of Perseus on the Eastern globes IG3, which according to al-Ṣūfī is the Arabic name IG5 (see Fig. 4.15), IG6 (see Fig. 4.24a) and IG7, used for the multitude of stars inside the triangle agree generally with those depicted in MS Marsh 144. Usually the sword is held above the head, but on globe IG3 Perseus’s sword is placed 238 Toomer 1984, p. 368; Kunitzsch 1974, p. 284, no. 355. behind his head.237 c 236 Kunitzsch I 1986, p. 54. 237 For this, see the picture in Guye and Michel 1970, p. 210, fig. 198.

239 For the ivy leaf in Quṣayr Amra, see Section 4.1. For medieval hemispheres with an ivy leaf above Leo, see Section 3.1. 240 Makariou and Caiozzo 1998, p. 105, seem to confuse the northern branch with the one connected with Spica.

317

ISLAMIC CELESTIAL CARTOGRAPHY (Leo 6e–8e), which itself is called ‘al-ḍafīra’ in the Arabic translations of the Ptolemaic catalogue.241 On IG6 quite a number of fainter stars are part of al-hulba (see Fig. 4.17).Why al-hulba is placed in the northern hand of Virgo is not clear, but it shows that globes IG5, IG6, and IG7 are part of the same iconographic tradition.

Fig. 4.16 Ivy leaf on the celestial globe IG2. (Courtesy of the Bibliothèque nationale de France, Paris.)

Fig. 4.17 Ivy leaf on the celestial globe IG6. (Courtesy of the Staatliche Kunstsammlungen Dresden-Mathematisch-Physikalischer Salon Zwinger Staatlicher mathematisch-physikalischer Salon, Dresden.)

Libra: as mentioned more than once in this study, the image of Libra in Antiquity was varied. It was seen as the Claws of Scorpius, as a pair of scales, and as a figure carrying a pair of scales.The Ptolemaic presentation as Claws is seen for example on the Kugel globe discussed in section 2.3, Fig. 2.6. It occurs also on a number of medieval planispheres analysed in section 3.2. On the Farnese globe, however, Libra is drawn as a pair of scales (see Fig. 2.18). In the Arabic translation by al-Ḥajjāj Libra is introduced as the Scales whereas Isḥāq as revised by Thābit speaks of both the (Ptolemaic) Claws and the Scales. For the Scales the translators may have been guided by a pictorial source such as that depicted on the Farnese globe, replacing in the descriptions of the locations of the stars the northern and southern ‘Claw’ by the northern and southern ‘Scale’. In the version by Isḥāq as revised by Thābit Libra is also called az-zubānayān, an indigenous Arabic name meaning the two claws of Scorpius, and identified with the stars α β Lib as 16th lunar mansion.242 In MS Marsh 144, p. 235 Libra is drawn as a pair of scales and this is how the constellation is commonly presented on most Eastern Islamic globes. On the two Western globes IG1 and IG2, however, Libra is drawn as a figure seated in an oriental fashion and holding a small pair of scales in his right hand (see Figs 4.18 and 4.24).

241 Kunitzsch 1961, p. 65, no. 117a. Al-Ṣūfī (Schjellerup 1874), p. 154. 242 Kunitzsch I 1986, p. 105, note 1. Kunitzsch 1961, p. 118, no. 322a.

318

4.4 EXTANT GLOBES MADE BEFORE 1500 stars of Libra lie in the Claws of Scorpius and the Claws extend over a range in longitude of about 30° preceding the body of Scorpius. In the Arabic cartographic tradition this space is now occupied by either the figure holding a pair of scales or by a balance, and the claws of Scorpius are pressed into a narrow space preceding the main body,with short claws as the result (see for example Fig. 4.24c). Sag ittarius: the shape of this constellation is discussed in the Epitome attributed to Eratosthenes where it is explained that ‘the Archer does not Fig. 4.18 Libra on the celestial globe IG2. (Courtesy appear to have four legs but to be standing and of the Bibliothèque nationale de France, Paris.) shooting a bow—and no centaur used a bow’.244 In the Ptolemaic catalogue and its Arabic translaThis image was described in detail by al-Ṣūfī tions Sagittarius is always described as a centaur. while discussing the location of the star Lib 5: The image of Sagittarius as an archer is seen on ‘Personne depuis Ptolémée n’a fait de cette figure un exa- some medieval hemispheres (see section 3.1). men attentif, ni déterminé la position de l’étoile en question, On globes IG1 and IG2 Sagittarius is a human afin de la mettre à la place qui lui convient; et comme il y archer (Figs 4.19 and 4.21e). In the translation by avait de l’incertitude parmi les astronomes, qui ne la trou- al-Ḥajjāj the position of the star Sgr 27, which vaient point placée sur les globes conformément aux indicaPtolemy places on the right hind lower leg, is tions de Ptolémée, et que de plus on n’avait pas dessiné la somewhat obscurely described as ‘in the lower figure de la balance, ils tracèrent eux-mêmes la figure d’un homme, et disposèrent les étoiles partout où elles se présen- arm’, a characterization that may well have been taient sur cette figure; puis ils lui mirent à la main une petite inspired by an image as seen on globes IG1 and IG2.245 In the absence of a horse’s part the four balance sur laquelle ne se trouvait aucune étoile.’243 stars Sgr 28–31 are here placed in a kind of garThis description fits exactly Libra’s image as ment floating behind him.More often Sagittarius engraved on the globes IG1 and IG2. It suggests is presented as partly human and partly equine that the image of the figure carrying a pair of scales on Islamic globes as it is in al-Ṣūfī’s Book on the is part of an older iconography. It is not encounConstellations. The stars Sgr 12–17, which accordtered on the few antique globes that survive today, ing to Ptolemy belong to the northern and but one finds a figure carrying a pair of scales in the southern cloak attachment, are placed in two medieval planispheres belonging to the ivy leaf ribbons of the head band, in keeping with the tradition (group III) discussed in Chapter 3. description by Isḥāq as revised by Thābit.246 Scorpius: in the Arabic iconographic tradition Scorpius is drawn as a scorpion with very short claws, a format that deviates from the usual 244 Eratosthenes (Pàmias and Geus 2007), pp. 156–9; Ptolemaic iconography. In a Ptolemaic context the Condos 1997, p 183; Charvet and Zucker 1998, p. 133. 243 Al-Ṣūfī (Schjellerup 1874), pp. 166–7.

245 Kunitzsch I 1986, p. 110: al-Ḥajjāj has: ‘Der Stern auf dem hinteren [Teil] des rechten Unterarms’. 246 Wellesz 1959, p. 392.

319

ISLAMIC CELESTIAL CARTOGRAPHY Islamic iconographic deviation from the Ptolemaic standard is the replacement of the pelt by an extended sleeve, as seen in the image of Orion in MS Marsh 144 (Fig. 4.8). Al-Ṣūfī mentions explicitly that the stars Ori 17–25 are on the sleeve.248 This image is seen on all Eastern Islamic globes discussed here (see for example Figs 4.23b and 4.24a). On globes IG1 and IG2, however, Orion has no sleeve extension. The stars Ori 17–25 are placed on some form that could represent the Ptolemaic ‘pelt’ (see Figs 4.21c and 4.22b). Fig. 4.19 Sagittarius and Ara on the celestial globe IG2. (Courtesy of the Bibliothèque nationale de France, Paris.)

Capricornus: the classical form of Capricornus is that of a goat with two legs and a fish-tail and that is how the constellation is depicted in all classical sources and on Eastern Islamic globes (compare Fig. 4.24d).The image presented on the early Western globes IG1 and IG2 is that of an ordinary goat with four legs, looking backwards in the eastern direction (Figs 4.19 and 4.21e).The goat’s attitude reminds one of that of Aries and it could have been inspired by it. However that may be, the backwards looking Capricorn is a unique example of designing this constellation. Orion: in the Ptolemaic tradition Orion has a staff (κολλόροβος) in the right hand and a pelt on his left arm (Ori 17–25). In the Arabic translations by al-Ḥajjāj and Isḥāq as revised byThābit the same attributes are mentioned, except that al-Ḥajjāj translated κολλόροβος as the pineapple and Isḥāq tells that the pelt is wrapped around the left hand.247 On most globes Orion is drawn with a club or stick in his right hand. The most typical

247 Kunitzsch I 1986, pp. 126 and 129.

Centaurus: the most striking attribute of Centaurus in the Greek tradition is the thyrsus, a long stick with a pine cone at the end and entwined with ivy and wine shoots, comprising the stars Cen 8–11. Ibn al-Ṣalāḥ tells us that in the Arabic translations there are three renderings of the Greek thyrsus.249 In the Syriac translation of the Almagest the stars Cen 8–11 are located ‘on the shield’ (calā al-turs), a description also encountered in the translation by al-Ḥajjāj.250 In the Arabic translation by al-Hasan ibn Quraysh (that is, the old translation made under the caliph al-Ma’mūn) the same stars are described as being ‘on the lance’ (calā al-ḥarba), whereas in the translation by Ishāq these stars Cen 8–11 are described as being on a ‘vine-branch’ (qaḍīb al-karm). Ibn al-Ṣalāḥ even saw the thyrsus represented as a lance on a globe made in Ḥarrān. On globe IG1 Centaurus holds a long lance-like stick with a small triangle at the end surrounded by a shieldlike oval structure (Fig. 4.21d). On IG2 a small additional ornament is attached to the triangle (Fig. 4.22b). The stick and the shield-like oval structure depicted on globes IG1 and IG2 seem

248 Al-Ṣūfī (Schjellerup 1874), p. 206. 249 Ibn aṣ-Ṣalāḥ (Kunitzsch 1975), p. 71. Dekker and Kunitzsch 2008/9, p. 173. 250 Kunitzsch 1974, p. 339.

320

4.4 EXTANT GLOBES MADE BEFORE 1500 to reflect a combination of two old traditions, that of a lance and that of a shield surviving in the translation by al-Ḥajjāj. On Eastern globes Centaurus holds a bunch of leaves in his right hand, meant to represent the vine branch (Figs 4.23b and 4.24c).This particular shape as a bunch of leaves is another typical Islamic characteristic in constellation design, seen already in the image of Centaurus in MS Marsh 144, pp. 401–2. Ara: Savage-Smith notes that ‘on all Islamic globes studied, but one, it [Ara] is depicted as a censer upside down with flames going toward the southwest’.251 Indeed, on globes IG1 and IG2 Ara is drawn as an upside-down square box on feet with a lid in an oriental shape on top and a long handle to hold it (see Figs 4.19 and 4.21e). This image recalls the Islamic cast bronze incense burner of the eighth century from Iran in the collection of the Länsmuseet Gävleborg in Gävle (Fig. 4.20) and the eleventh century example from Spain (al-Andalus) in the collection of the Metropolitan Museum of Art in New York.252 The image of Ara on IG1 and IG2 expresses literally its Arabic name. Summing up the discussion above, the globes studied here represent two major iconographic traditions.The oldest of these is seen on theWestern globes IG1 and IG2. The iconography of their constellation images includes many echoes from an early Eastern Islamic tradition of globe making. In this tradition, the constellations are marked by a simple and realistic approach, the characteristics of which are seen neither in early Greek sources nor on later Eastern Islamic globes.And although there are many variants to the Ptolemaic iconography, 251 Savage-Smith 1985, p. 209. 252 Länsmuseet Gävleborg in Gävle, inventory number GM 9699, described in Bott 1993, vol. II, pp. 819–20. A similar eleventh-century Andalusian incense burner is inThe Metropolitan Museum of Art, New York (Inventory number (67.178.3ab)).

Fig. 4.20 Incense burner of the eighth century from Iran. (Courtesy of the Länsmuseet Gävleborg, Gävle.)

the constellations on these two globes display well Ptolemy’s advice to make them as simple as possible, a feature which enhances the astronomical importance of the globes and which is rarely seen on later Eastern globes. How the early iconography tradition came to survive in the two Western globes is not hard to imagine. With the expansion of the Islam from the early eighth century on, Arabic science was transmitted not only in an eastern but also in a western direction, to north Africa and the Iberian peninsula.253 Astronomical instruments, such as globes and astrolabes, and books on astronomy were part of the stream of culture that was imported into Spain, to fill the library of, say, the court in Cordoba. Astronomers working in alAndalus quickly absorbed and expanded the new Arabic astronomy.254 In the second half of the tenth century the Arabic translation of the star

321

253 Kunitzsch 2005; Lowney 2006. 254 Samsó 1990/1994.

ISLAMIC CELESTIAL CARTOGRAPHY catalogue by al-Ḥajjāj and the al-Zīj al-Ṣābi’ of al-Battānī had reached Muslim Spain. The Almagest and al-Battānī’s astronomical works were known to the astronomer Maslama al-Majrīṭī (d. 1007).255 One can assume that globe makers in eleventh-century al-Andalus at least could dispose of the material displayed in the Almagest (notably the version of al-Ḥajjāj) and in the work of al-Battānī. The variant iconography employed on globes IG1 and IG2 suggests that an additional illustrated source was available in Spain. It is unlikely that this other source was the now lost book with constellation images by cUṭārid ibn Muḥammad al-Ḥāsib (ninth century) reported by al-Ṣūfī.256 In this book Sagittarius is drawn looking backwards towards the east, a feature not seen on the globes considered here. It excludes the relevance of cUṭārid’s book for the study of globes.The Book of the Constellations of al-Ṣūfī is first attested in al-Andalus in the twelfth century.257 Besides, some of the images, especially the Libra figure carrying a small pair of scales and the stick and the shield-like oval structure held by Centaurus, seem to reflect an early iconography in globe making, predating the time of al-Ṣūfī (964) and originating in the Middle East. Against this backdrop it does not seem unlikely that a globe from the striving globe industry of ninth-century Ḥarrān circulated in eleventh-century Spain and provided the ‘variant’ iconography one finds on IG1 and IG2.258 Such an early eastern globe may also 255 Ṣācid al-Andalusī 1985, p. 169, ll. 2–3 (referring to Maslama al-Majrīṭī, d. 1007). Kunitzsch 1966, p. 17. 256 Al-Ṣūfī (Schjellerup 1874), pp. 30–1. 257 Abraham ibn cEzra (mid-twelfth century); cf. Millás Vallicrosa 1947, p. 76 etc. 258 Samsó 2005, p. 63, states that the celestial globe was known in al-Andalus in the tenth century. He probably refers to a description of a globe rather than a material specimen.

have been the source of some of the names engraved on IG1 and IG2. The other major iconographic tradition is seen on the Eastern globes (IG3–IG10).This tradition is closely connected with al-Ṣūfī’s Book of the Constellations.The drawings in MS Marsh 144 are probably typical for globes in al-Ṣūfī’s own time, leaving aside the fact that the artist working on this manuscript could have added artistic refinements while using a flat surface. Whatever the case may be, the impact of al-Ṣūfī’s work on globe making is visible in many ways.The number of star names engraved on Eastern globes includes many of the indigenous Arabic names listed and identified by al-Ṣūfī. For example, the names of the stars or star groups in Ursa Maior engraved on globes IG3–IG6 recalls those labelled in the drawings in MS Marsh 144 (Fig 4.10) discussed above. Unfortunately the nomenclature of the Eastern globes has not yet been subject of a detailed comparative study.Four globes,IG3–IG6, have about 70 star names, and IG7 has names for 55 star or groups. Globe IG8 has around 145 names, inclusive those of the zodiacal signs and the non-zodiacal constellations, suggesting nearly a hundred star names. Globe IG9 has about 36 star names next to names of the zodiacal signs and the non-zodiacal constellations. This could hold for IG10, but this has yet to be confirmed. A number of globes are tied closer together for one reason or other. For example, three globes, IG5–IG7, are connected by the branch in Virgo’s northern hand.According to Destombes the iconography of the constellations on globe IG8 compares well with IG5 and IG6 and could therefore also be counted in this subgroup of the second major tradition. The iconography of the earliest Eastern globe IG3 is based on figures with simple outlines. Yet, it is not difficult to recognize many

322

appendix 4.1 Islamic Globes with Constellation Images made before 1500 characteristic features of Islamic constellation design as, for example, Perseus carrying the head of Ghūl, Orion with an extended sleeve, and Centaurus holding a bunch of leaves. Simple drawings without elaborate dresses also characterize the constellations on the later globes IG9 and IG10 which are distinguished by having the bears drawn back to back as in the Greek-Roman tradition. These globes deserve further study.This also applies to globe IG4 of which no good photographic documentation has been published.

appendix . Islamic globes with constellation images made before 1500

globes on published accounts and photographs, especially those provided in Savage-Smith 1985.

IG1. FLORENCE, MUSEO DI STORIA DELLA SCIENZA (Inv. no. 2712) Ø sphere 22 cm; made in Spain,Valencia. Date: 478 AH (= 29 May 1085). Provenance: Acquired in the nineteenth century by Meucci, formerly part of the Belluomini Collection. Maker(s): Ibrāhīm ibn Sacīd al-Sahlī al-Wazzān and his son Muḥammad. This instrument maker lived in Toledo and Valencia. In addition to the present globe he made astrolabes of which six are known. An inscription is located in a circular decorative band centred on the south pole and continuing along the part of the solstitial colure within this band:

Below I have listed all known Class A globes made before 1500, numbered here IG1–IG10.The transcription and translations of the inscriptions were made by Paul Kunitzsch. The description of globes IG1–IG2 are based on personal inspection, those of the other

Fig. 4.21a North polar region on the celestial globe IG1. (Photo: Franca Principe –Museo Galileo, Florence.)

323

‘ṣanaca hādhihi l-kura dhāt al-kursīy li-dhī l-wizāratayn al-qā’id al-aclā Abī cĪsā ibn Labbūn - adāma llāhu cizzahu wa-ta’yīdahu -cabduhu Ibrāhīm ibn Sacīd al-Sahlī al-Wazzān f ī Balansiya maca Muḥammad ibnihi fa-waḍaca al-kawākib al-thābita fīhā calā ḥasab acẓāmihā wa-aqdārihā fa-tammat fī

Fig. 4.21b The region centred on the vernal equinoctial colure on the celestial globe IG1. (Photo: Franca Principe–Museo Galileo, Florence.)

ISLAMIC CELESTIAL CARTOGRAPHY

Fig. 4.21c The region centred on the summer solstitial colure on the celestial globe IG1. (Photo: Franca Principe–Museo Galileo, Florence.)

Fig. 4.21d The region centred on the autumnal equinoctial colure on the celestial globe IG1. (Photo: Franca Principe–Museo Galileo, Florence.)

Fig. 4.21e The region centred on the winter solstitial colure on the celestial globe IG1. (Photo: Franca Principe–Museo Galileo, Florence.)

Fig. 4.21f South polar region on the celestial globe IG1. (Photo: Franca Principe–Museo Galileo, Florence.)

324

appendix 4.1 Islamic Globes with Constellation Images made before 1500 awwal Ṣafar cām tcḥ li-hijrat < ...> ṣalla llāhu calayhi wasallam taslīman’. (There has made this globe with stand for the holder of the double office of vizier, the supreme commander-in-chief Abū cĪsā ibn Labbūn - may God prolong his power and his support -, his servant Ibrāhīm ibn Sacīd al-Sahlī al-Wazzān in Valencia together with his son Muḥammad. He put the fixed stars on it according to their magnitudes and sizes. It was finished on the first of Ṣafar of the year 478 of the emigration (of the prophet), may God bless him and give him peace.)

Construction: The brass sphere consists of two hemispheres fixed to each other at the Equator.There are holes at the north and south ecliptic poles and at the north and south equatorial poles.The globe is mounted at the equatorial poles in a modern graduated brass meridian ring, supported by a modern brass stand. Cartog raphy: Language Arabic (Kūfic script/abjad numbering). There are great circles passing through the ecliptic poles and the boundaries of the signs.The Equator is graduated (0°–360°; numbered every 5°, division 1°). The ecliptic is graduated (12 times 0°–30°; numbered every 5°, division 1°); it is provided with labels for the names of the 12 signs of the zodiac. Close to the north pole, in the hind part of Ursa Minor, there is a label for the north pole. Also the south pole is labelled. Astronomical notes: In all, 1017 stars have been marked on the globe. The stars are presented by stamped circles whose sizes vary with the magnitudes of the stars. Of the 48 Ptolemaic constellations only 47 are drawn and labelled; the picture and the name of Crater are lacking.There are names for 26 stars. comments:The longitudes of the stars plotted on the globe exceed on the average the corresponding Ptolemaic values by 14° 5’ ± 2’ (see Dekker and Kunitzsch 2008/9, Table II.1, p. 190). A detailed description of the nomenclature by Kunitzsch is in Dekker 2004, pp. 112–18.The present globe and the globe IG2 described below are the earliest surviving Arabic-Islamic globes in general and the only surviving globes known to have been made in Muslim Spain. These globes are also the earliest surviving copies with positions taken from a Ptolemaic star catalogue, especially from one belonging to the Maghreb branch of the Arabic

translation by al-Ḥajjāj available in Spain from the second half of the tenth century onwards. For details see Dekker and Kunitzsch 2008/9, where also a discussion of the iconography can be found. On the maker, see Mayer 1956, pp. 50–2. For pictures, see Figs 4.21a–f . Reconstructions of the mapping in the form of globe gores were published by Meucci 1878. Literature: Meucci 1878; Millás Vallicrosa 1931, p. 55f; Destombes 1956, p. 319; Destombes 1958, p. 96; Savage-Smith 1985, p. 217, no. 1; Dekker 2004, pp. 112–18; Dekker and Kunitzsch 2008/9.

IG2. PARIS, BIBLIOTHÈQUE NATIONALE DE FRANCE (Inv. no. Ge A 325) Ø sphere 19 cm; made in Spain. Not signed, not dated. Construction: The brass sphere consists of two hemispheres fixed to each other at the ecliptic.There are traces of later repairs such as rests of solder close to the ecliptic. There are two short axes at respectively the north and south equatorial poles. A modern brass axis passes through the north and south ecliptic poles. This axis is fixed by bolts and is used to mount the globe in a modern graduated brass meridian ring (not numbered, division in units of 5°, subdivided in 1°). It is not possible to say whether there were originally holes at the ecliptic poles or whether these have been made for the modern axis used for mounting the globe erroneously into the meridian ring.The meridian ring with the globe fits badly into a brass stand consisting of four rising brass quarter-circles, which through recent fastenings support an original brass horizon ring and join at the top of the central column of a modern brass pedestal with four feet. The horizon ring has a scale for azimuth (twice 0°–180°; numbered every 5°, division 1°). Cartog raphy: Language Arabic (Kūfic script/abjad numbering). There are great circles passing through the ecliptic poles and the boundaries of the signs.The Equator is graduated (0°–360°; numbered every 5°, divided into units of 5° and subdivided into 1°).The ecliptic and equatorial poles are not labelled. The

325

ISLAMIC CELESTIAL CARTOGRAPHY

326 Fig. 4.22a Reproduction of the hemisphere north of the ecliptic of the celestial globe IG2 published by Jomard 1854.

Fig. 4.22b Reproduction of the hemisphere south of the ecliptic of the celestial globe IG2 published by Jomard 1854.

appendix 4.1 Islamic Globes with Constellation Images made before 1500 ecliptic is graduated (12 times 0°–30°; numbered every 5°, division 1°); it is provided with labels for the names of the 12 signs of the zodiac.

An inscription is located near the south equatorial pole, south of Sagittarius: ‘hādhihi al-kura tashtamil calā jamī c al-kawākib al-madhkūra fī Kitāb al-majasṭī bacda tasyīrihā ḥasab al-mudda (written above) allatī bayna raṣd Baṭlamyūs wa-sanat th-m li-l-hijra wa-huwa y-h daraja wa-y-ḥ daqīqa. ṣancat [or ṣana cahu] Yūnus ibn al-Ḥusayn al-Aṣṭurlābī sanat th-l-ṭ.’ (This globe contains all the stars mentioned in the book Almagest, after processing them according to the interval between the observation of Ptolemy and the year 540 H ( = 1145– 46), i.e. 15° 18´. The work of Yūnus ibn al-Ḥusayn al-Aṣṭurlābī (in the) year 539 (H = 1144–45)(or also possible:Yūnus ibn al-Ḥusayn al-Aṣṭurlābī has made it)).

Astronomical notes: In all, 1002 stars have been marked on the globe by stamped circles whose sizes vary with the magnitudes of the stars. All 48 Ptolemaic constellations are drawn. In addition, there is above Leo’s tail an ivy leaf.The Pleiades are presented by a cloud of dots.There are names for the 48 Ptolemaic constellations, two subgroups (the ivy leaf and the Pleiades) and for 27 stars. Comments: The longitudes of the stars plotted on the globe exceed on the average the corresponding Ptolemaic values by 14° 3’ ± 3’ (see Dekker and Kunitzsch 2008/9, Table II.1, p. 190). A detailed description of the nomenclature, the iconography and the relation of the present globe to IG1 is in Dekker and Kunitzsch 2008/9. For pictures, see Fig. 4.14 (Perseus), Fig. 4.16 (ivy leaf), Fig. 4.18 (Libra and Centaurus), Fig. 4.19 (Sagittarius and Ara). Reconstructions of the mapping of this globe in stereographic and equidistant projection were published by Jomard 1854, his figs 1–4, of which two are reproduced here, see Figs 4.22a–b. More illustrations are published in Dekker and Kunitzsch 2008/9, Figs 1–10. Literature: Sédillot 1844, pp. 116–41; Destombes 1956, pp. 318–19; Destombes 1958, pp. 96–7; Savage-Smith 1985, p. 236, no. 34; Dekker and Kunitzsch 2008/9.

IG3. PARIS, MUSÉE DU LOUVRE, DEPARTMENT OF ISLAMIC ART (Inv. no. MAO 824) Ø sphere 17.5 cm; made in the eastern part of Islamic world (Iran?). Date: H 540 (= 1145–46). Provenance: purchased 1985; formerly collection Marcel Destombes who bought the globe in 1958; the globe is said to have been in Bombay in 1930. Maker : Yūnus ibn al-Ḥusayn al-Aṣṭurlābī. Nothing is known of this maker but it is clear that he—like other globe makers—produced astrolabes as well.

Construction: The brass sphere consists of two hemispheres fixed to each other along a circle which follows the Milky Way (not itself marked on the sphere).There are traces of later repairs.The meridian ring is missing.The globe rests in a modern brass stand consisting of four columns, which support a brass horizon ring. Cartog raphy: Language Arabic (Kūfic script/abjad numbering). There are great circles passing through the ecliptic poles and the boundaries of the signs.The Equator is graduated (0°–360°; numbered every 5°, divided into units of 5° and subdivided into 1°).The ecliptic and equatorial poles are labelled.The ecliptic is graduated (12 times 0°–30°; numbered every 5°, division 1°); it is provided with labels for the names of the 12 signs of the zodiac. Astronomical notes: There are about 1025 stars presented by inlaid silver discs whose sizes vary with the magnitudes of the stars. The stars are numbered following the order in which they are described within constellations.The names of the 48 Ptolemaic constellations and of 72 stars or star groups are engraved. There are labels of the 28 lunar mansions. The longitudes of the stars plotted on the globe exceed, according to the inscription, the corresponding Ptolemaic values by 15° 18´. Comments: This is the oldest surviving globe from the Middle East. Savage-Smith 1985, p. 218, mentions the presence of polar circles which I could not confirm. For pictures, see Destombes 1958, p. 300 Plate I (Virgo) and p. 303 Plate 2 (inscription); Guye and

327

ISLAMIC CELESTIAL CARTOGRAPHY Michel 1970, p. 210, fig. 198; Makariou 1998, p. 70, PlateVI and p. 102, III.56 (same as PlateVI) and III. 57; King 2005, p. 30, fig. 3.3. Literature: Destombes 1958; Destombes 1960; Savage-Smith 1985, pp. 217–18, no. 2; Makariou 1998, p. 80, nr. 52 and p. 102.

IG4. NAPLES, MUSEO NAZIONALE Ø sphere 22 cm; made in Egypt or Syria? Date: 622 H (= 1225). Formerly in the Museum Borgiano,Velletri. Maker : Qayṣar ibn Abī al-Qāsim ibn Musāfir al-Abraqī al-Ḥanafī. This globe maker was born in H574 (1178/9) in Upper Egypt and died in H649 (1251) in Damascus. He became famous as a mathematician, astronomer, and architect. He later entered the service of Ayyubid al-Malik al-Muẓaffar Maḥmūd of Ḥamāh, Syria.While there he built towers in Hama and a mill on the Orontes. Two inscriptions259 in naskhī script and damascened with silver are located near the south equatorial pole, south of Aquarius and Piscis Austrinus: ‘bi-rasm khizānat mawlānā al-sulṭān al-malik al-kāmil al-cālim al-cādil nāṣir al-dunyā wa-l-dīn Muḥammad ibn Abī Bakr Ayyūb cazza naṣruhu’. (By order of the treasury of our lord, the sultan, al-Malik al-Kāmil, the learned one and just one, protector of this world and the religion, Muḥammad ibn Abū Bakr Ayyūb, may his superiority be prevalent) and ‘bi-rasm Qayṣar ibn Abī al-Qāsim ibn Musāfir al-Abraqī al-Ḥanafī bi-sanat 622 hijrīya bi-ziyādat y-w daraja m-w daqīqa calā mā fī al-majasṭī ’. (By order (or: in the draft) of Qayṣar ibn Abī al-Qāsim ibn Musāfir al-Abraqī al-Ḥanafī in the year 622 Hijra ( = 1225) with the addition of 16° 46´ to what is in the Almagest).

construction: The brass sphere consists of two hemispheres, fixed to each other along a meridian circle near the solstitial colure.The sphere is mounted into a graduated meridian ring (divided into 6°, subdivided into 1°). The meridian ring rests in a brass stand consisting of four concave legs, which support

a brass horizon ring. The horizon ring is graduated (numbered every 6°, divided into 6°, subdivided into 1°). The constellation figures are damascened with copper and many star names are damascened with silver. Cartog raphy: Language Arabic (naskhī script/abjad numbering). There are great circles passing through the ecliptic poles and the boundaries of the signs.The Equator is graduated (0°–360°; numbered every 6°, divided into units of 6° and subdivided into 1°).The ecliptic and equatorial poles are labelled.The ecliptic is graduated (12 times 0°–30°; numbered every 6°, division 1°); it is provided with labels for the names of the 12 signs of the zodiac. The polar circles are drawn. Astronomical notes: There are about 1025 stars presented by inlaid silver discs in five different sizes varying with the magnitudes of the stars. A magnitude table is marked on the globe.The names of the 48 Ptolemaic constellations and of many stars and star groups are engraved.The longitudes of the stars plotted on the globe exceed, according to the inscription, the corresponding Ptolemaic values by 16° 46´. Comments: There are labels in European form of Arabic numerals along the ecliptic every 30°, and along the Equator at 100°, 200°, 300°, and 360°. Savage-Smith notes that the constellations also have a Latin label. This and other features, such as the magnitude table, suggest that the globe has undergone later modifications. For pictures, see the poor reconstruction of the mapping of this globe published by Assemani 1790 and King 2005, p. 30, fig. 3.2. On the maker, see Mayer 1956, pp. 80–1. Literature: Assemani 1780; Savage-Smith 1985, pp. 218–19, no. 3.

IG5. LONDON, BRITISH MUSEUM, DEPARTMENT OF ORIENTAL ANTIQUITIES (Inv. no. ME OA 1871.3) Ø sphere 24 cm; made in Mosul, north of Bagdad.

259 The inscriptions are taken from Assemani 1790, p. Kiiiv.

Date: 674 H (= 1275–76).

328

Fig. 4.23b Reproduction of the hemisphere south of the ecliptic of the celestial globe IG5 published by Dorn 1830, Plate B.

appendix 4.1 Islamic Globes with Constellation Images made before 1500

329 Fig. 4.23a Reproduction of the hemisphere north of the ecliptic of the celestial globe IG5 published by Dorn 1830, Plate A.

ISLAMIC CELESTIAL CARTOGRAPHY Provenance: brought to India by the ancestors of the leader of the Bohora community. Presented to Sir John Malcolm (1769–1833) who deposited the globe with the Royal Asiatic Society of Great Britain and Ireland in 1839. In 25 February 1871 it was purchased by the British Museum. Maker : Muḥammad ibn Hilāl.Very little is known of this globe maker who according to the inscription was an astronomer from Mosul, an important city in northern Iraq, famous in the first half of the thirteenth century for its skilled metalworkers. An inscription is located south of Piscis Austrinus: ‘ṣancat [or ṣana cahu] al-faqīr ilā allāh tacālā Muḥammad ibn Hilāl al-Munajjim al-Mawṣilī fī sanat kh-c-dhijrīya’. (The work of [or also possible: has made it] the one in need of God - may He be exalted - Muḥammad ibn Hilāl alMunajjim [the Astronomer] al-Mawṣilī [from Mosul] in the year 674 of the hijra [ = 1275–76]).

Construction: The brass sphere consists of two hemispheres fixed to each other at the ecliptic. The stars are presented by inlaid silver dots.There are holes at the north and south ecliptic poles and at the north and south equatorial poles. The globe rests in a brass stand consisting of four rising brass quarter-circles, which support a brass horizon ring and join at the top of a four-legged pedestal with an eight-lobed base connected by cross bars. Its horizon ring is graduated in units of 1° and marked by four compass directions in naskhi script.Two of the brass rising quarter-circles have an extension shaped as a bird, the meaning of which is not clear.The other quarter-circle is marked by a series of holes, presumably for setting the globe to latitudes. Cartog raphy: Language Arabic (Kūfic script/abjad numbering). There are great circles passing through the ecliptic poles and the boundaries of the signs.The Equator is drawn and graduated (thrice 0°–100° and once from 300°–360°; numbered every 5°, division 1°). The ecliptic is drawn and graduated (12 times 0°–30°; numbered every 5°, division 1°); it is provided with labels for the names of the 12 signs of the zodiac. Close to the equatorial north pole, in the hind part of Ursa Minor, there is a label for the north pole and close to the equatorial south pole one for the south pole.

Astronomical notes: There are about 1000 stars presented by discs whose sizes vary with the magnitudes of the stars. In addition to the names of the zodiacal signs, there are names of 36 non-zodiacal constellations and of about 70 stars or star groups. The tiny non-Ptolemaic star above the bright star in the middle of the tail of Ursa Maior,‘the overlooked one’, is marked on the globe and labelled. The six external stars described by Ptolemy around Piscis Austrinus (PsA 1e–6e) are omitted. Comments: Destombes studied the longitudes of 70 stars and found that they, on average, exceed the corresponding Ptolemaic values by around 16°. A detailed description of the iconography is in Pinder-Wilson 1976. The stand with labels in naskhī script is probably not contemporary with the globe. The devices at two of the quarter circles are comparable to those seen in the drawings in Assemani 1780 (IG4). Pinder-Wilson 1976 published photographs of all the constellations on the globe. Reconstructions of the mapping of this globe were published by Dorn 1830, see Fig. 4.23a and Fig. 4.23b. Literature: Dorn 1830; PinderWilson 1976; Savage-Smith 1985, pp. 219–20, no. 4.

IG6. DRESDEN, STAATLICHER MATHEMATISCHPHYSIKALISCHER SALON (Inv. no. E II 1) Ø sphere 14.6 cm; Observatory at Marāgha,Azerbaijan. Date: ca. 1300. Provenance: Purchased in 1562 by the Elector August of Saxony from Nicholaus Valerius, mathematician of Coburg. Maker: Muḥammad ibn Mu’ayyad al-cUrḍī. This globe maker was the son of Mu’ayyid al-Dīn al-cUrḍī (ca. 1200–ca. 66), one of the leading astronomers working at the observatory at Marāgha founded by Naṣīr al-Dīn al-Ṭūsī (1201–74). Muḥammad was also a member of the observatory staff. An inscription is located between the head of Ursa Maior and Auriga:

330

‘ṣancat [or ṣana cahu] Muḥammad ibn Mu’ayyad al-cUrḍī’. (The work of Muḥammad ibn Mu’ayyad al-cUrḍī [or

appendix 4.1 Islamic Globes with Constellation Images made before 1500 also possible: Muḥammad ibn Mu’ayyad al-cUrḍī has made it]).

the six external stars described by Ptolemy around Piscis Austrinus (PsA 1e–6e) are marked (see Fig. 4.6).

Construction: The brass sphere consists of two hemispheres fixed to each other at the ecliptic.The seam has been broken.The globe is supported by a brass frame consisting of four rising quarter-circles, which support a graduated brass horizon ring (twice 0°–90°; 90°–0° beginning at the east point; numbered every 5°, division 1°) and marked by two compass directions: east and west. There is also a brass frame consisting of two semicircles, which join at the top and rest on the horizon ring. One semicircle serves as a meridian ring (twice 0°–90° beginning at the horizon ring; numbered every 5°, division 1°) and the other as a zenith circle (twice 0°–90° beginning at the horizon ring; numbered every 5°, division 1°). There is a device to suspend the frame. Some names are inlaid with gold, others with silver.The lines marking the equator are inlaid with gold, the other circles with silver.

comments: A detailed description of the nomenclature is in Drechsler 1873. A copy of this globe in the collection of Rudolf Schmidt,Vienna is described by Kunitzsch 1992/3. For pictures, see the reconstructions of the mapping published by Drechsler 1873 reproduced here (Figs 4.24a–d). Photographs of the globe itself are in Muris and Saarmann 1961, preceding p. 33 and Fauser 1973, p. 41. On the maker, see Mayer 1956, pp. 72–3. Literature: Drechsler 1873; Savage-Smith 1985, p. 220, no. 5; Oestmann 2002.

Cartog raphy: Language Arabic (Kūfic script/abjad numbering).There are great circles passing through the ecliptic poles and the boundaries of the signs. The Equator is drawn and graduated (thrice 0°–100° and once from 300°–360°; numbered every 5°, division 1°).The ecliptic is drawn and graduated (12 times 0°–30°; numbered every 5°, division 1°); it is provided with labels for the names of the 12 signs of the zodiac.There are holes at the ecliptic and equatorial poles. The ecliptic poles are labelled above the head of Draco and below the end of Eridanus.The equatorial poles are labelled below the tail of Ursa Minor and below Corona Australis. Astronomical notes: In all, 997 stars have been identified on the globe.The stars are represented by discs whose sizes vary with the magnitude of the stars. In all 130 names are engraved, among which are in addition to the names of the zodiacal signs names of 36 non- zodiacal constellations and of about 76 stars or star groups. The tiny non-Ptolemaic star above the bright star in the middle of the tail of Ursa Maior, ‘the overlooked one’, is marked on the globe and labelled.There are about 11 stars placed in a kind of leaf or branch held by Virgo in her northern hand, labelled: al-hulba (see Fig. 4.17), which according to al-Ṣūfī is the Arabic name used for the multitude of stars inside the triangle (Leo 6e–8e) called ∏λόκαμος (lock of hair) by Ptolemy. On this globe also

IG7. LONDON, THE KHALILI FAMILY TRUST (Inv. no. SC121) Ø sphere 13.4 cm; made in Province Ṭabaristān in northern Iran. Date: 684 H (= 1285–86). Provenance: allegedly brought from India for sale in London. Maker: Muḥammad ibn Maḥmūd ibn c Alī al-Ṭabarī, also called Muḥammad ibn Maḥmūd al-Aṣṭurlābī. Few particulars are known of this instrument maker of whom one other instrument, a brass horary quadrant, is known. He may have come from the provinceTabaristan in northern Iran.His father Maḥmūd ibn cAlī made astrolabes,witness of which are the records of two now lost astrolabes. An inscription is located north of Auriga: ‘ṣancat [or ṣana cahu] Muḥammad ibn Maḥmūd ibn cAlī al-Ṭabarī. (The work of Muḥammad ibn Maḥmūd ibn c Alī al-Ṭabarī’ (or also possible: Muḥammad ibn Maḥmūd ibn cAlī al-Ṭabarī has made it)).

Another inscription is located south of Ara, Sagittarius, Piscis Austrinus, and Aquarius: ‘rusimat hādhihi al-kawākib min kitāb al-ṣuwar li-Abī al-Ḥusayn al-Ṣūfī bacd al-ziyāda calā aṭwālihā li-zamāninā h daraja wa-taṣḥīḥ mā jarā fīhi sahwan wa-taṣḥīf calā al-mutarjimīn wa-dhālika fī sanat 684 wa-katab 260 Muḥammad ibn 260 Part of the word is cut out by a hole representing the south equatorial pole.The word could be wa-kataba or wa-katabahu.

331

ISLAMIC CELESTIAL CARTOGRAPHY

Fig. 4.24a Reproduction of three globe segments (longitudes 0º–90º) of the celestial globe IG6 published by Drechsler 1873,Tafel I.

Fig. 4.24b Reproduction of three globe segments (longitudes 90º–180º) of the celestial globe IG6 published by Drechsler 1873,Tafel II.

Maḥmūd al-Aṣṭurlābī’. (These stars were drawn after the Book of Constellations by Abu ’l- Ḥusayn al-Ṣūfī,after increasing their longitudes 5 degrees to correspond to our time, and the correction of what has happened in it261 of negligence and slips of the pen is left to those who interpret it.

And that is [or was] in the year 684 [ = 1285–86], and the inscriptions [are by] Muḥammad ibn Maḥmūd al-Aṣṭurlābī).

Construction:The brass sphere consists of two hemispheres fixed to each other at the ecliptic latitude circle

261 Either al-Ṣūfī’s Book or the present work on the globe.

332

appendix 4.1 Islamic Globes with Constellation Images made before 1500

Fig. 4.24c Reproduction of three globe segments (longitudes 180º–270º) of the celestial globe IG6 published by Drechsler 1873, Tafel III.

Fig. 4.24d Reproduction of three globe segments (longitudes 270º–360º) of the celestial globe IG6 published by Drechsler 1873,Tafel IV.

passing through the first points of Gemini and Sagittarius. The meridian ring, horizon ring, and stand are missing.

5°, division 1°). The ecliptic is drawn and graduated (12 times 0°–30°; numbered every 5°, division 1°); it is provided with labels for the names of the 12 signs of the zodiac.There are holes at the ecliptic and equatorial poles.

Cartography: Language Arabic (Kūfic script/abjad numbering).There are great circles passing through the ecliptic poles and the boundaries of the signs. The Equator is drawn and graduated (thrice 0°–100° and once from 0°–60°; numbered every

astronomical notes: In all, around 1000 stars are represented by inlaid silver dots whose sizes vary with

333

ISLAMIC CELESTIAL CARTOGRAPHY the magnitude of the stars. In addition to the names of the zodiacal signs, there are names of 32 non-zodiacal constellations, 55 stars and star groups, and 28 lunar mansions. The tiny non-Ptolemaic star above the bright star in the middle of the tail of Ursa Maior,‘the overlooked one’, is marked on the globe and labelled. The six external stars described by Ptolemy around Piscis Austrinus (PsA 1e–6e) are omitted.The number of stars for each constellation varies. For example, Draco has 26 instead of 31 stars and Corona Borealis no stars at all. Comments: Savage-Smith 1997, no. 123, p. 212, and note 7, did not notice in the inscription the dot under ‘j’ in ‘al-mutarjimīn’ (those who interpret) and has instead ‘al-mutaraḥḥimīn’ (those who are compassionate) and thus gives a slightly different translation. On p. 212 she claims that 1022 stars are indicated on the globe, yet she also notes that the number of stars are sometimes in error.This means that the number is less than 1022, which is why I have reduced her number to about 1000 stars.At one stage this globe was brought to India where it was copied.This copy has a sphere of cast brass. It was acquired in Cairo in 1892 and is now in Paris, Musée du Louvre Department of Islamic Art, inv. no. OA 6013, see Makariou 1998, p. 80, no. 54, and Savage-Smith 1985, pp. 221–2, no. 6. For pictures, see Savage-Smith 1997, pp. 212–21 and Savage-Smith 1992, p. 56. Photographs of the copy in the Louvre are in Makariou 1998, pp. 104–5, ill. III.58, III.59 and III. 60, and in Savage-Smith 1985, p. 28, fig. 6. On the maker, see Mayer 1956, pp. 72–3. Literature: Savage-Smith 1997, pp. 212– 13; Savage-Smith 1990/1991.

Construction: The brass sphere consists of two hemispheres fixed to each other at the ecliptic.There are square holes at the ecliptic and equatorial poles. The globe is supported by a modern pedestal stand. Cartog raphy: Language Arabic (Kūfic script/abjad numbering). There are great circles passing through the ecliptic poles and the boundaries of the signs.The Equator is drawn and graduated (thrice 0°–100° and once from 300°–360°; numbered every 5°, division 1°). The ecliptic is drawn and graduated (12 times 0°–30°; numbered every 5°, division 1°); it is provided with labels for the names of the 12 signs of the zodiac.There are labels for the ecliptic and the equatorial poles. Astronomical notes:The stars are represented by inlaid silver discs whose sizes vary with the magnitude of the stars. In all 930 stars have been identified. The stars are numbered within the constellations. There are 145 names of zodiacal signs, non-zodiacal constellations, star groups, and stars. Comments: Destombes 1956, p. 320, determined for 800 stars that the longitudes plotted on the globe exceed on the average the corresponding Ptolemaic values by 17° 56’. For a picture, see Makariou 1998, p. 106, ill. III.60. Literature: Destombes 1956, p. 320; Savage-Smith 1985, pp. 236–7, no. 35; Makariou 1998, p. 80, no. 53.

IG9. OXFORD, MUSEUM FOR THE HISTORY OF SCIENCE (Inv. no. 44790) Ø sphere 16.5 cm; made in Kirmān in south-east Persia. Epoch: 764 H (= 1362–63).

IG8. PARIS, MUSÉE DU LOUVRE, DEPARTMENT OF ISLAMIC ART (Inv. no. MAO 825)

Provenance: Lewis Evans Collection; bought in 1922 from Oercy Webster in London.

Ø sphere 21 cm; Marāgha, Sultanye or Tabriz, Azerbaijan. Not signed, not dated. Provenance: Bequest 1987. Formerly in the collection of Marcel Destombes who purchased the globe in 1953 from the Chadenat Collection, no. 6804.

Maker: Jacfar ibn cUmar ibn Dawlatshāh al-Kirmānī. This globe maker from Kirmān was a member of a family of astrolabists. In addition to the two globes listed here (nos IG9 and IG10) at least five astrolabes made by him are known. An inscription is located south of Sagittarius and Piscis Austrinus:

334

appendix 4.1 Islamic Globes with Constellation Images made before 1500 ‘rusimat hādhihi al-kawākib min Kitāb al-ṣuwar li-Abī al-Ḥusayn cAbd al-Raḥmān al-Ṣūfī bacda al-ziyāda calā aṭwālihā li-zamāninā w j fī sanat dh-s-d al-hijrīya wa-dh-l-b al-Yazdijirdīya wa-gh-kh-c-d al-Iskandarīya, ṣancat [or ṣanacahu] Jacfar ibn cUmar ibn Dawlatshā[h] al-Kirmānī’. (These stars were drawn according to the Book of Constellations by Abū al-Ḥusayn cAbd al-Raḥmān al-Ṣūfī after adding to their longitudes for our time 6° 3´ in the year 764 H [ = 1362–63] and 732 Yazdijird and 1674 (in the era) of Alexander, work of [or has made it] Jacfar ibn c Umar ibn Dawlatshāh al-Kirmānī).

Construction: The brass sphere consists of two hemispheres fixed to each other at the Equator.There are holes at the equatorial poles, and also at points along the solstitial colure on both sides of the equatorial poles at a distance equal to the obliquity of the ecliptic. One set of these latter holes represents the ecliptic poles, the meaning of the other set is unknown. At the ecliptic poles are removable pins. The globe is supported by a four-legged brass stand consisting of two rising semicircular arcs, which support a brass horizon ring, which is graduated (twice 0°–90°; 90°–0° starting from the east point; numbered every 5°, division 1°) and marked by four compass directions. There is no meridian ring. One of the semicircular arcs has a series of holes at 10° intervals for inserting of a pin. Cartog raphy: Language Arabic (Kūfic script/abjad numbering). There are great circles passing through the ecliptic poles and the boundaries of the signs.The Equator is marked and graduated (thrice 0°–100° and once from 300°–360°; numbered every 5°, division 1°). The ecliptic is drawn and graduated (not numbered, division 1°); it is provided with labels for the names of the 12 signs of the zodiac. There are labels for the ecliptic poles and for the equatorial poles. Astronomical notes: In all, about 1025 stars have been marked on the globe. The stars are represented by inlaid silver discs whose sizes vary with the magnitude of the stars.The names of 48 Ptolemaic constellations and of about 50 stars are engraved. The tiny non-Ptolemaic star above the bright star in the middle of the tail of Ursa Maior, ‘the overlooked one’, is marked on the globe and labelled.

Comments: Savage-Smith 1985, p. 222, notes that the inscription is engraved over another one which was partially erased.The older inscription says that the globe was made by Jacfar for a certain Muḥammad ibn Aṣīl. Gunther 1923, vol. 2, pp. 247–9, lists the names of the constellations and the stars. For pictures, see Gunther 1923, vol. 2, between pp. 248 and 249; Mayer 1956, plate XI. Savage-Smith 1985, p. 31, fig. 9; Nasr 1976, p. 123, Plate 80. On the maker, see Mayer 1956, pp. 53–4 and Pingree 2009, p. xix. King 2005, p. 1018, lists four globes said to have been made by this maker but the globes he numbers c and d are according to Savage-Smith (pp. 248–9, nos 61 and 62) made by the son Muḥammad ibn Jacfar al-Aṣṭurlābī, see Mayer 1956, pp. 53 and 68. Since these globes have no constellation images they are not included in my list. Literature: Gunther 1923, vol. 2, pp. 247–9; Savage-Smith 1985, pp. 221–2, no. 7.

IG10. ISTANBUL, KANDILLI OBSERVATORY, HISTORY OF SCIENCE MUSEUM (Inv. no. 763) Ø sphere 14.4 cm; made in Kirmān in south-east Persia. Epoch: 785 H (= 1383–84). Maker: Jacfar ibn cUmar ibn Dawlatshāh al-Kirmānī. This globe maker from Kirmān was a member of a family of astrolabists. In addition to the two globes listed here (nos IG9 and IG10) at least five astrolabes made by him are known. An inscription is located beneath Sagittarius and Piscis Austrinus: ‘rusimat hādhihi al-kawākib bi-ziyādat w- < ...> calā al-Ṣuwar Abū al-Ḥusayn cAbd al-Raḥmān al-Ṣūfī fī sanat dh-f-h al- hijrīya, ṣancat [or ṣanacahu] Jacfar ibn cUmar ibn Dawlatshāh al-Kirmānī’. (These stars were drawn with the addition of 6 ° [?]262 to [ ...]263 Constellations [by] Abū al-Ḥusayn cAbd al-Raḥmān al-Ṣūfī in the year 785 Hijra [ = 1383-84], work of [or: has made it] Jacfar ibn cUmar ibn Dawlatshāh al-Kirmānī.)

262 Value of the minutes in the increase of 6° [?] has been obliterated. 263 The text is either wrong or defective.

335

ISLAMIC CELESTIAL CARTOGRAPHY construction:The brass sphere consists of two hemispheres fixed to each other at the Equator.There are traces of repairs along the Equator.There are holes at the ecliptic and equatorial poles, and at points along the solstitial colure away from the equatorial and ecliptic pole by distances equal to one and two times the obliquity of the ecliptic, respectively.The stand is missing. cartog raphy: Language Arabic (Kūfic script/abjad numbering). There are great circles passing through the ecliptic poles and the boundaries of the signs.The Equator is marked and graduated (thrice 0°–100° and once from 300°–360°; numbered every 5°, division 1°). The ecliptic is drawn and graduated (not numbered, division 1°); it is provided with labels for the names of the 12 signs of the zodiac. There are labels for the ecliptic poles and for the equatorial poles.

Astronomical notes: In all, about 1025 stars have been marked on the globe. The stars are represented by inlaid silver discs whose sizes correspond to the magnitude of the stars. The names of the 48 Ptolemaic constellations and of an unknown number of stars are engraved. comments: Savage Smith gives a diameter of 114.3 mm, but Dizer and Meyer 1979 mention 144.3 mm. I have used the latter value. IG10 is very close to IG9 and like that globe based on the star catalogue of al-Ṣūfī. For pictures, see the photograph in Al-Hassan et al. 2002, p. 263. According to Savage-Smith there is a description of the globe in Dizer and Meyer 1979 with six pictures, but I have not been able to confirm this. On the maker, see Mayer 1956, pp. 53–4 and Pingree 2009, p. xix. Literature: Savage-Smith 1985, pp. 222–3, no. 8.

336

chapter five

the mathematical tradition in medieval europe

. THE MATHEMATICAL TRADITION: THE ISLAMIC LEGACY

found testifying to this first stage of transmission. Only one early eleventh-century Latin astrolabe text, the Sententie astrolabii, appears to include fragments translated from an Arabic he transmission of knowledge from Muslin work.2 Further, most early Latin texts are conSpain to the Latin West started with the fusing, not to say wrong, and it is not clear what introduction of the astrolabe at the turn of the help they could offer a reader apart from feedtenth century. This is why the astrolabe is often ing his imagination. Studies of extant early artefacts are rarely conseen as foreshadowing the spread of Islamic sciclusive in establishing their past history and more ence in Latin Europe, and it is for that reason the best studied medieval scientific instrument. often than not differences in opinion prevail, Many scholars, starting with Bubnov in 1899, especially where an interesting object such as the have collected and studied sources which could astrolabe discovered and first described by shed light on the assimilation of astrolabe knowl- Destombes is concerned.3 Many scholars conedge in Latin Europe.1 Despite their efforts a sider this astrolabe to have been made in the great deal of uncertainty still exists about the tenth century thus representing the earliest trace channels through which the knowledge needed of the instrument in Latin Europe.Another early for the construction and use of the instrument astrolabe in the collection of the National Maritime Museum, shown in Fig. 5.1, illustrates was transferred. In the study of written sources it is generally clearly the transmission from Muslim Spain to assumed that the diffusion started with a rather the Latin West. The instrument may have been primitive translation of an Arabic treatise copied in Paris around 1223 (or 1233) from an which was subsequently reworked and astrolabe of Spanish-Islamic origin, that was improved. Yet, no manuscript has so far been made there in 1070 or there about.4 Seen against

T

1 Bubnov 1899; Millás Vallicrosa 1931; Bergmann 1985; Kunitzsch 1997; Borrelli 2008.

2 Kunitzsch 1987a. 3 Stevens et al. 1995. 4 Dekker 2000.

the mathematical tradition in medieval europe

5.1.1 Alfonsine astronomy Among the many works translated in the twelfth century is the Latin translation of the Almagest made around 1175 by Gerard of Cremona from the Arabic versions circulating in Muslim Spain.6 Gerard’s translation became very influential in the Middle Ages and was printed in 1515. In the thirteenth century a group of Jewish and Christian scholars composed a series of works comprising translations, adaptations, and original texts in Spanish (or better old Castilian) under the supervision of King Alfonso X of Castile, a patron of literature and learning who reigned from 1252 until 1284.7 Not all texts survive intact. For example, only the canons (sets of instruction for use) of the Castilian Alfonsine Tables survive.8 These Tables, written in Toledo around 1270, served to calculate the positions of the planets. Other texts such as the Libros del saber Fig. 5.1 Medieval astrolabe, ca. 1230. (Courtesy of the National Maritime Museum Greenwich, de astronomía, also written in Castilian on astroInventory number AST0570.) nomical instruments, and related texts are completely preserved.9 In the Libros del saber one this background, it is no coincidence that the finds in the first book a description of the 48 shape of the rete of this astrolabe (Fig. 5.1) fits Ptolemaic constellations and their stars which— well into the style of astrolabes made in the secalthough not a direct translation—is based preond half of the eleventh century in Northern dominately on al-Ṣūfī’s Book on the Constellations Spain, with characteristics such as prayer niches of the Fixed Stars (see Section 4.3).10 It includes on the outer frame and the style of the pointers.5 many of al-Ṣūfī’s indigenous star names and his It is not difficult to understand that instruments coordinate tables,but the longitudes are increased were among the first transmitters of new mathby the Alfonsine value 17° 8´. The epoch menematical knowledge to the Latin speaking world. tioned is not the beginning of the reign of King An instrument is the sort of curiosity that attracts Alfonso X of Castile (1252), but the year 1256.11 the attention of a wider audience, whereas tables in learned treatises may turn people off. From 6 For the Arabic-Latin tradition of the Ptolemaic star catathat point of view it is all the more remarkable logue, see Kunitzsch 1974. A modern scholarly edition has that so few globes have survived from the Middle been published in Kunitzsch II 1990. 7 Samsó 1987; Chabás and Goldstein 2003, pp. 1–8. Ages. 8 Chabás and Goldstein 2003, pp. 19–94.

5 Gunther 1931/1976, pp. 252–6.

9 Rico y Sinobas 1863; Samsó 2007. 10 Kunitzsch 1986a, pp. 65–6; Samsó and Comes 1988; Chabás and Goldstein 2003, pp. 234–6. 11 Chabás and Goldstein 2003, p. 235.

338

5.1 THE MATHEMATICAL TRADITION: THE ISLAMIC LEGACY I shall return to this the Alfonsine value 17° 8´ in more detail below. Al-Ṣūfī’s work on uranography was also transmitted along another line, which is known as the Ṣūfī Latinus corpus, consisting of eight manuscripts with a specific type of illustrated star catalogue.12 The oldest representative of this group of manuscripts is Paris, Bibliothèque nationale de France, MS Arsenal 1036. The star catalogue of this corpus is Gerard’s Latin translation from the Arabic adapted to al-Ṣūfī’s epoch 964 by adding 12° 42´ to the longitudes of the stars.And for each constellation there is a drawing that stems from an Arabic al-Ṣūfī manuscript.Through these illustrations al-Ṣūfī’s iconography left its traces in the Latin West.13 A star catalogue in the translation of Gerard of Cremona with longitudes exceeding the corresponding Ptolemaic ones by 17° 8´ is also usually included in the Parisian Alfonsine Tables, so-called because they were written in Paris.14 Although the precession correction is the same as that used in the catalogue in the Libros del saber, the epoch of the latter (1256) is slightly later than that of the Parisian Alfonsine star catalogue, which is said to be the Alfonsine epoch of June 1252. The Parisian Alfonsine Tables, written around 1320 and first printed in 1483, are a reworking of the earlier and now lost Castilian Alfonsine Tables.15 Although the lines of transmission from Spain to Paris are far from clear it must have been from Toledo that the Parisian astronomers learned about the idea of accession and recession.The theory presented in chapters 49–50 of the Toledan Alfonsine canons refer to a model

by Arzarquiel and differs from the oldest Latin text in the Liber de motu octave spere (Book on the Motion of the Eighth Sphere).16 Both early theories differ in turn from the most common theory of precession used in the Middle Ages included in the Parisian Alfonsine Tables. This latter Parisian theory includes precession tables based upon two components: a motion of accession and recession characterized by a period of 7000 years, an amplitude of 9°, and a motion of a constant rate of precession with a period of 49,000 years.17 Application of the Parisian precession tables predicts that in June 1252 the longitudes of the stars will have increased with respect to Ptolemy (ad 137) by 15° 22´ 9˝.18 Or to put it another way, the Parisian precession tables predict that the stellar longitudes in June 1252 exceed the Ptolemaic ones by 17° 8´ only if the Ptolemaic epoch was ad 16 instead of ad 137. A number of modern scholars have tried to explain this difference. One suggestion is that the Alfonsine astronomers made an error in their calculation (adding instead of subtracting), another that they did not know the precise value of the Ptolemaic epoch (ad 16 instead of ad 137).19 The most promising explanation so far is that by Chabás and Goldstein who suggest that the Alfonsine correction of 17° 8´ came into being within the framework of the catalogue for the epoch 1256 in the Libros del saber which goes back to al-Ṣūfī’s star catalogue for the epoch 964 and a precession correction of 12° 42´. Using al-Ṣūfī’s rate of precession of 1° in 66 years, the difference 4° 26´ between the precession corrections 17° 8´

12 Kunitzsch 1965; Kunitzsch 1986a, pp. 66–77. 13 See for example Strohmaier 1984. 14 Kunitzsch 1986b. On the Alfonsine Tables see Poulle 1988 and Chabás and Goldstein 2003, pp. 243–90. 15 Chabás and Goldstein 2003.

16 Chabás and Goldstein 2003, pp. 89–90 and 217–21. 17 Mercier 1976; Mercier 1977; Chabás and Goldstein 2003, pp. 89–90 and 256–66. 18 Samsó and Castelló 1988, p. 116. 19 Poulle 1988; Samsó and Castelló 1988.

339

the mathematical tradition in medieval europe and 12° 42´ is equivalent to 292.6 years which agrees with the difference between the epoch 1256 and 964.20 Chabás and Goldstein further suggest that the Parisian astronomers borrowed the Alfonsine correction of 17° 8´ from the Libros del saber and used it for the Alfonsine epoch June 1252 independently of the Parisian precession tables.21 Gerard’s version of the Ptolemaic star catalogue adapted to epochs other than that of Alfonso X can be found in many medieval manuscripts. Often these catalogues are illustrated.22 The precession corrections in these later medieval star catalogues (for epochs later than 1252) are usually calculated with the Parisian precession tables through their excess with respect to the Alfonsine value 17° 8´. An example of an illustrated catalogue of special interest to this study is the one in Vienna, Österreichische Nationalbibliothek, MS 5415, ff . 217r–251v, which is adapted to the epoch 1424 by adding 1° 48´ to the Alfonsine value 17° 8´ for 1252 (f. 217r: ‘Et addunt super stellas verificatas per Alfoncium 1 gradum et 48 minuta in longitudine sed nichil in latitudine’).23 Thus in the star catalogue in Vienna MS 5415 the longitudes of the stars exceed the corresponding Ptolemaic ones by 18° 56´. Since it was obtained by adding to the Alfonsine value 17° 8´ for 1252 this latter value refers tacitly to a Ptolemaic epoch ad 16!24

20 Chabás and Goldstein 2003, pp. 234–5. 21 Chabás and Goldstein 2003, pp. 260–2. 22 Lippincott 1985, pp. 67–70. 23 Saxl 1927, p. 151. 24 Kremer 1980, p. 189, note 28, suggests that the value 19° 40´ used by Regiomontanus in his star catalogue for 1500 is not based on the Alfonsine trepidation theory, but this is not necessarily so. Regiomontanus’s value could have been obtained by counting from 1252 and adding to the Alfonsine value 17° 8´.

5.1.2 Globe treatises In the early corpus of astrolabe-related texts is a Latin fragment that is clearly a translation from the Arabic, Incipit de horologic seconded alkoram, id est speram rotundam, which some believe to describe a spherical astrolabe and others a celestial globe.25 Samsó proposed that it was related to Battānī’s bayda, but the text itself cannot discriminate between the various suggestions. The first complete text with instructions for making a (precession) celestial globe in the Latin West is included in Gerard’s translation of the Almagest. The oldest still extant globe made in medieval Europe, Cusanus’s globe discussed below in Section 5.2, was made following these instructions. Another text on the construction and use of the globe is part of the series of descriptions of astronomical instruments included in the Libros del saber.26 This Alfonsine globe treatise is a Castilian translation of Kitāb calā l-kura (Book concerning the Globe) written by Qusṭā ibn Lūqā, discussed in Section 4.2. The translators Yehūdah ibn Mosheh ha-Kohen and Johan Daspa revised their work in 1277, and it is this later version that is part of the Libros del saber. Preceding the 65 books by Qusṭā ibn Lūqā are four new chapters on the construction of the globe assumed to be the work of Isḥāq ibn Sīd, in which a number of technical details such as the advantages and disadvantages of the use of various materials such as wood, copper, and brass, are discussed.27 Following the 65 books is another newly written text by Don Mosheh on the use of auxiliaries such as a quadrant and a semicircular device for 25 Millás Vallicrosa 1931, pp. 288–90; Lorch 1980b, p. 161, note added in proof; Samsó 2005, p. 64. 26 Samsó 2005, pp. 66–79. 27 Savage-Smith 1985, pp. 80–1.

340

5.1 THE MATHEMATICAL TRADITION: THE ISLAMIC LEGACY finding the boundaries of the mundane houses after the prime vertical method.28 In Qusṭā ibn Lūqā’s treatise a method for determining the mundane houses is discussed in chapter 55 based on the standard method.29 The collection of treatises on instruments in the Castilian Libros del saber was translated in 1341 into Italian in Seville but never into Latin. The 65 chapters of Qusṭā ibn Lūqā’s globe treatise were also directly translated from the Arabic into Latin and Hebrew.The Latin translation by an unknown translator, the Liber in opera sphera uolubilis,is known from eight manuscripts.30 The Hebrew translation is by Jacob ben Makhir ibn Tibbon (ca. 1236–ca. 1305), also known as Profatius. Some of the Hebrew versions have a section on the construction of the globe. Profatius’s text was in turn translated into Latin by Stephanus Arlandi of Barcelona in 1301. He added also a chapter on globe making (at the end of his text).31 Thus in addition to a Castilian and an Italian version, two Latin translations were ultimately made of Qusṭā ibn Lūqā’s globe treatise. Another Latin treatise on the construction of the celestial globe, Tractatus de sphaera solida, circulated in the fourteenth and later centuries.32 Lorch has suggested from the style of writing that this treatise is also a translation from the Arabic, but an original has so far not been identified.The identity of the author of the Tractatus de sphaera solida is uncertain. Some suppose that the text is by Accursius of Parma, since his name is mentioned in the copy of the treatise in Florence, Bibliotheca Laurenziana MS Plut. 29.46: 28 29 30 31 32

Samsó 2005, p. 74. North 1986, pp. 4 and 9. The text is edited in Lorch and Martínez Gázquez 2005. Lorch and Martínez Gázquez 2005, pp. 14–15. Lorch 1980b; Chlench 2007.

‘Astrolabium sphaericum compositum anno domini 1303 Dominus Accursius de Parma fuit principium huius operis’.33 Lorch suspects that Accursius is the scribe of the Florentine text and that the other person often quoted in the treatise, John of Harlebeke, wrote it. His name occurs more often in copies of the treatise as for example in London, British Library, MS Arundel 268: ‘Tractatus de spera solida, sive astrolabio sperico, compositus a magistro Johanne de Harlebeke medico, anno domini 1303 Parisiis’.34 Very little is known about John of Harlebeke. He seems to have lived in the second half of the thirteenth century and was known as a priest and astronomer, and according to the text cited above worked in Paris as a physician.35 He is also mentioned as a monk of the Benedictine abbey of St Martin,Tournai.36 Of the two candidates, John of Harlebeke seems to have the best credentials.Whoever the author may be, there is general agreement that the text dates from 1303. It is known in more than 30 manuscripts and appears to have been most influential in medieval Europe.37 In the first decades of the sixteenth century three printed editions of the Tractatus de sphaera solida appeared.38 A German translation was made in the fifteenth century.39 This German translation is manifest to the growing interest in celestial cartography in Germanspeaking countries during the fifteenth century. Treatises on the construction and use of the astrolabe available to the medieval astronomer outnumber by far those on the construction of globes.The success of the astrolabe may explain 33 Chlench 2007, p. 60. 34 Chlench 2007, pp. 59–60. 35 Varenbergh 1888/1889. 36 Lorch 1980b, p. 155. 37 Chlench 2007, pp. 53–7, lists 28 manuscripts. 38 Two editions were published in 1518 and a third in 1531, see Chlench 2007, p. 51. 39 Chlench 2007, pp. 51–180.

341

the mathematical tradition in medieval europe the plea of John of Harlebeke in favour of the use of globe for solving astronomical problems in a prologue to the Tractatus de sphaera solida: ‘The root and basis of all astronomical theory, and also its immense prolixity and inexhaustible depth of ingenuity, take their beginning from things that are observed with appropriate instruments. It is agreed amongst all the authorities on this subject that without instruments there would be no way of discovering the motions of the celestial bodies. There is a great number of these instruments, but in this there generally seems to be agreement: that they all imitate the motion of the Heavens and are made in a likeness of it as if from the original, which not Man but God (may His name be blessed) has made. In the judgement of all those who philosophize aright, the Heavens are spherical. Hence, if it is also agreed that a copy is formed in a likeness to the original, it is plain that a spherical instrument is more similar to the spherical Heavens than all other instruments. In accordance with this, Ptolemy - being cognizant of the matter we have spoken of - made an armillary instrument with wonderful ingenuity [and described it] in the Almagest. The figure of the sphere is reflected in the form of this [instrument], but, contained only by the appropriate arrangement of circles, it had none of the stars in its composition - among the figures of the Heavens there is an empty space to mark the stars. By being so awkward, it is found unsuited to determine the daily configurations of the Heavens. Moreover, Ptolemy’s astrolabe is elaborated in the likeness of that sphere [sc. of the Heavens], for it should be conceived as a sphere spread out in a plane.The geometrical proofs in this are ingenious, but in conceiving it the mind is affected by tedium, because things that are seen directly in the sphere we must there [in the astrolabe] conceive obliquely. Nor are the figures [imagines] in the sky [accurately] portrayed. [The astrolabe] is also partly truncated: it does not represent stars that are south of the tropic of Capricorn - not from necessity, but

342

from custom and convenience. To place the latitudes of the planets in it is also difficult, if not impossible. It sometimes happens that the less experienced are misled in this matter and think that a planet in the East is above the Earth when it is below the Earth, and vice versa - and similarly for the other angle. In the judgement of the experienced the astrolabe is deservedly held, by virtue of its ingenuity, numerous uses, simple operation, and portability, as nobler and better than the other instruments of the venerable Ancients. The same Ptolemy mentioned a spherical instrument in the Almagest, and indicated that the stars are inscribed in it according to longitude and latitude and that the celestial figures and constellations are drawn on it. But he does not intimate how this instrument might be brought to perfection so that it could be put to everyday uses, i.e. [finding] ascendants, equations of the houses, and other things necessary in this application [i.e. astrology].We do not here set down the construction and uses of the astrolabe, as being sufficiently treated by the ancients. But what, by God’s mercy, has come to us of the construction and uses of the instrument called “sphera solida” or “spherical astrolabe” we treat with the Lord’s help - at the instance of some of my friends and for the use of those who might wish to look at this treatise. We treat first, the construction of this instrument with all its parts, and secondly its uses. The instrument will be easy enough to construct, handsome and delightful in appearance, and because of its many uses, much desired and soughtafter by the experienced. Of all other instruments it is the root and exemplar, except the two instruments that are called “perfect”- that is, they are universal - and other, imperfect, or particular, [instruments], such as the quadrant, cylinder, triquetrum, and shadow-instruments. Of these [latter] the everyday uses are few and they are, as it were, obtainable as parts of the perfect instruments. The Ancients have treated these carefully enough.

5.2 PTOLEMY’S PRECESSION GLOBE But enough of these things. We come now, by invoking divine help, to the book. The prologue ends.’40

could account for the disappearance of the evervisible and invisible circles. Indeed, these latter circles are not seen on the early Islamic globes After this prologue the globe is subsequently discussed in Section 4.4, but neither are polar described in the first part of nine chapters. It circles. Their introduction in the Tractatus de consists of a wooden sphere marked—as is pre- sphaera solida could have been inspired by the five scribed in most treatises—by a number of great terrestrial zones described by the author of the circles: the Equator graduated in 360º, the eclip- Tractatus de sphaera solida.43 In fact, the polar cirtic graduated twelve times 0º–30º and great cir- cles are relevant to understanding phenomena of cles through the ecliptic poles for every 30º. the climates and so on, and separate regions of Since such great circles through the ecliptic excessive cold from the temperate zones, and poles are found on many Arabic globes, their maps of these zones were common in the Middle prescription suggests that an Arabic globe or a Ages.44 Another interesting feature in John of treatise may have been one of the sources.41 Also Harlebeke’s globe treatise is the combination of the value of the obliquity of the ecliptic, 23º 33´, scales of the zodiac and the calendar scales on the is borrowed from an Arabic source.The sphere is horizon ring. This combination serves to find mounted in a meridian ring and set in a hemi- the place of the Sun in the zodiac on a certain spherical bowl with four vertical cords to sup- day of the year, which information is used in port the instrument’s particular mounting. In many applications of the globe. The author of some manuscripts the bowl is said to be placed the Tractatus de sphaera solida tells his reader that on a central piece instead of hanging on the four this information can be found on the back of astrolabes.45 Indeed, the zodiac with calendar is a cords.42 The construction is notable for a number of common element of Western Arabic and Latin points. There are two circles drawn around the astrolabes, but not of Islamic globes.46 The scales north and south pole with a radius ε, the obliq- on the horizon and the polar circles became uity of the ecliptic, which obviously represents standard features of Western globes. the north and south polar circles.Although polar circles became a regular feature in Western celes. PTOLEMY’S tial maps and globes these circles are properly PRECESSION GLOBE speaking not a meaningful part of celestial cartography. It is not known when the polar circles In 1444 Cardinal Nicolas of Cusa or Nicolas were first introduced in celestial cartography Cusanus (1401–64), a famous German polymath, and when they came to replace the ever-visible paid a visit to the Reichstag in Nuremberg and and invisible circles used in Antiquity.The means there bought a number of manuscripts and three to adjust the globe for geographical latitude instruments for the amount of 38 florins: 40 Lorch 1980b, pp. 155–6. 41 Savage-Smith 1985, pp. 19–21. 42 See for example Samhaber 2000, p. 28 who reproduced the illustration in Linz, Oberöstereichisches Landesmuseum, MS 3.

343

43 44 45 46

Chlench 2007, p. 112 and pp. 151–2. Stahl 1952, pp. 208–12; Obrist 2004, pp. 183–4. Chlench 2007, p. 98. King 1995a, p. 376.

the mathematical tradition in medieval europe ‘1444 Ego Nicolaus de Cusza, prepositus monasterii Treverensis dyocesis, orator pape Eugenii in dieta nurembergensi, que erat ibidem de mense Septembris ob ereccionem antipape felicis ducis Sabaudie factam Basilee per paucos sub titulo concilii, in qua dieta erat fridericus romanorum rex cum Electoribus, emi Speram Solidam magnam, astrolabium et turketum, Jebrum super almagesti cum aliis libris 15, pro XXXVIII florenis renensibus.’47

All three instruments—the solid globe, the astrolabe, and the torquetum—have been preserved in accordance with Cusanus’s wishes. His entire inheritance was bequeathed to a charitable institution that he had founded as a home for the aged in Bernkastel-Kues (St. Nikolaus Hospital). When Hartmann visited the place in 1913 he found next to the three instruments a small brass globe, which had clearly never been finished.48 In addition to a grid, there are the first 45 stars described in the Ptolemaic star catalogue on it, belonging to the constellations Ursa Minor, Ursa Maior, and Draco. Hartmann has measured their positions and compared them with the longitudes in the star catalogue of al-Ṣūfī. He showed that the stellar longitudes on the brass globe on the average exceed al-Ṣūfī’s precession correction by 4.6º ± 0.2º. Since al-Ṣūfī’s longitudes differ from the corresponding Ptolemaic ones by 12º 42´, the positions on the small brass globe appear to be consistent with those in the Alfonsine star catalogue (17° 8´ added to the Ptolemaic longitudes of the stars). This implies that the small globe could have been made any time after 1325, when the Alfonsine star catalogue was commonly appended to the Alfonsine Tables. From the style of the lettering, Hartmann has suggested the 47 Bernkastel-Kues, Cusanus-Stift MS 211, f. 1r.The citation is taken from Krchňák 1964, p. 109. See also Hartmann 1919, p. 8. 48 Hartmann 1919, pp. 42–50.

middle of the fifteenth century as the date of construction of this small globe. The other globe in Bernkastel-Kues, the ‘spera solida magna’, although now incomplete, is designed as a precession globe, very much after the model described in Ptolemy’s Almagest. It is described in Appendix 5.2 (WG1). In Ptolemy’s time, precession was a very novel feature, the understanding of which was crucial to discussing the main theme of the Almagest, the motions of the Sun and the planets. It is for this reason that Ptolemy included a description of a relevant demonstration model: ‘But we also wish to provide a representation [of the fixed stars] by means of a solid globe in accordance with the hypotheses which we have demonstrated concerning the sphere of the fixed stars, according to which, as we saw, this sphere too, like those of the planets, is carried around by the primary [daily] motion from east to west about the poles of the equator, but also has a proper motion in the opposite direction about the poles of the sun’s, ecliptic circle.’49

Cusanus’s globe is the only extant medieval artefact that recalls this description of Ptolemy’s precession globe. It deviates in construction from Islamic and later European globes which are made for a fixed epoch.50 The spera solida magna consists of a wooden hollow sphere, about 27 cm in diameter. The sphere is closed by a circular disc (Fig. 5.2) and covered by a thin layer of plaster and cloth.The maker did not follow Ptolemy in making ‘the colour of the globe in question somewhat deep, so as to resemble, not the daytime, but rather the nighttime sky, in which the stars actually appear’.51 Instead he painted the 49 Toomer 1984, p. 404. 50 Ptolemy’s precession globe is discussed in detail by Neugebauer 1975, pp. 890–2 and Savage-Smith 1985, pp. 8–10. 51 Toomer 1984, p. 404.

344

5.2 PTOLEMY’S PRECESSION GLOBE

Fig. 5.2 Construction detail of the sphere of Cusanus’s globe. (Reproduced from Hartman 1919, Plate XI.)

sphere with layers of white oil paint to smooth the surface. On the surface of the sphere in principle only two great circles are drawn. The first circle represents the ecliptic (see Fig. 5.3) which is divided into units of 1° by dots.The other (Fig. 5.4) is perpendicular to the ecliptic and passes through Sirius (α CMa).The intersection of this circle with the ecliptic is the fixed starting point for marking the stars on the sphere as explained by Ptolemy:

ecliptic towards its south pole recorded [in the star catalogue].’52

The choice of the brightest star Sirius (α CMa) as the reference star may seem obvious but one may well wonder how convenient this choice is from the point of view of globe construction.All longitudes in the star catalogue in the Almagest (fixed for the epoch 28 August 137) have to be reduced by subtracting Sirius’s longitude Gem 17° ⅔´. One is tempted to think that the choice ‘Since it is not reasonable to mark the solstitial and of Sirius was suggested by the fact that on equinoctial points on the actual zodiac of the globe Hipparchus’s globe the longitude of Sirius must (for the stars depicted [on the globe] do not retain have been close to Gem 15°. Later Ptolemy a constant distance with respect to these points), switched to another reference star, Regulus we need to take some fixed starting-point in the (α Leo), the longitude of which in the Ptolemaic delineated fixed stars. So we mark the brightest of star catalogue is Leo 2° ½´.53 them, namely the star in the mouth of Canis Major [Sirius], on the circle drawn at right angles to the ecliptic at the division forming the beginning of the graduation, at the distance in latitude from the

345

52 Toomer 1984, p. 405. 53 Neugebauer 1975, p. 890.

the mathematical tradition in medieval europe

Fig. 5.3 The ecliptic close to Aries on Cusanus’s globe. (Reproduced from Hartman 1919, Plate IV.)

circular recessed sections [thus created] into 180 Returning to Cusanus’s globe, the sphere is degrees.’54 mounted in a peculiar way that follows Ptolemy’s description of his precession model closely. At The thinner part of the ring fixed at the ecliptic the north and south ecliptic poles two brass cir- poles could then be used to mark the positions of cular discs are fixed by four nails. A brass ring is the stars on the sphere: attached to these discs such that it can rotate ‘Then, for each of the other fixed stars in the cataaround the sphere. Half of the ring is 8 mm thick, logue in order, we mark the position by rotating but the size of the other half is cut out such that the ring with the graduated recessed face about one side of the ring coincides precisely with a the poles of the ecliptic: we turn the face of its great circle through the poles (see Fig. 5.5).This recessed section to that point on the [globe’s] thinner ring through the ecliptic poles is divided ecliptic which is the same distance from the begininto units of 5° and subdivided into 1°, but is not ning of the numbered graduation (at Sirius) as the numbered.This ring is one of the pair that has to star in question is from Sirius in the catalogue; then we go to that point on the graduated face which be prepared as follows: ‘In the middle of the convex face of each ring we draw a line accurately bisecting its width. Using these lines as guides, we cut out one of the latitudinal sections defined by the line over half of the circumference, and divide [each of] the semi-

346

we have [thus] positioned which is, again, the same distance from the ecliptic as the star is in the catalogue, either towards the north or towards the

54 Toomer 1984, p. 405, and his note 181.

5.2 PTOLEMY’S PRECESSION GLOBE filled with red wax showing the stars in red against an originally white background. After having served as an auxiliary for locating the stars on the sphere, the ring attached to the ecliptic poles is next used for mounting the sphere. In two points of the brass ring, at a distance of about 24°, are provisions for fixing another larger brass ring that can rotate around these two points (Fig. 5.5). These provisions demonstrate that in this construction the smaller ring is supposed to represent the solstitial colure passing through the ecliptic and equatorial poles. Of the larger ring Ptolemy says: ‘Then we attach the larger of the rings, which will always represent a meridian, to the smaller ring which fits around the globe, on poles coinciding with those of the equator. These points [the poles of the equator] are, in the case of the larger, meridian [ring], attached, again, at the diametrically opposite ends of the recessed and graduated face (which will represent the [section of the meridian] above the earth); but in the case of the smaller ring, [which passes] through both poles, they will be fixed at the ends of the diametrically opposite arcs which stretch the 23; 51º of the obliquity from each of the poles of the ecliptic. We leave small solid pieces in the recessed parts of the rings, to receive the bore-holes for the attachments [of the pins representing the poles].’56

Fig. 5.4 The colure through Sirius (α CMa) on Cusanus’s globe. (Reproduced from Hartman 1919, Plate VI.)

south pole of the ecliptic as the particular case may be, and at that point we mark the position of the star; then we apply to it a spot of yellow colouring (or, for some stars, the colour they are noted [in the catalogue] as having), of a size appropriate to the magnitude of each star.’55

The maker of Cusanus’s globe did not number the ecliptic scale. For a globe with varying equinoxes and solstices this seems to make good sense although it is cumbersome to plot the stars without numbers. The maker also did not follow Ptolemy’s advice of using a yellow colour for marking the stars in a blue background. On Cusanus’s globe the stellar positions are indicating by small holes drilled into the sphere and

It is not difficult to see that Cusanus’s globe fits this Ptolemaic description well, even in the absence of the now lost larger meridian ring. Had it been there the globe mounted in its meridian ring could have been placed in a stand with a horizon ring and then would be ready for use. A user interested in demonstrating the heavenly phenomena in his own time would have to

55 Toomer 1984, pp. 405–6.

56 Toomer 1984, p. 406.

347

the mathematical tradition in medieval europe

Fig. 5.5 Detail of the mounting of Cusanus’s globe. (Reproduced from Hartman 1919, Plate VIII.)

determine the position of the solstitial colure passing through the ecliptic and equatorial poles as Ptolemy explains:

by the appropriate arc for the latitude in question, using the graduation of the meridian [to place the ring correctly].’58

‘Now the recessed face of the smaller of the rings must, clearly, always coincide with the meridian through the solstitial points. So on any occasion [when we want to use the globe], we set it to that point of the ecliptic graduation whose distance from the starting-point defined by Sirius is equal to the distance of Sirius from the summer solstice at the time in question (e.g. at the beginning of the reign of Antoninus, 12⅓° in advance57). Then we fix the meridian ring in position perpendicular to the horizon defined by the stand [of the globe], in such a way that it is bisected by the visible surface of the latter, but can be moved round in its own plane: this is in order that we may, for any particular application, raise the north pole from the horizon

The action to fix the meridian ring for a specific epoch has left its traces on Cusanus’s globe. Along the circle at a distance of about 24° from the north and south ecliptic poles one finds several holes, presumably indicating the equatorial poles for a number of epochs (Fig.5.6).Hartmann has carefully measured the positions of these holes which are schematically summarized in Scheme 5.1 following his example.59 One of the holes (A in Scheme 5.1) lies 12.4° east of the great circle through Sirius and, since the longitude of Sirius in the Ptolemaic star catalogue is Gem 17° ⅔´, this hole obviously represents the north equatorial pole for the epoch of the

57 This is the case when the required time is the Ptolemaic epoch.

348

58 Toomer 1984, p. 406. 59 Hartmann 1919, p. 30.

5.2 PTOLEMY’S PRECESSION GLOBE

Fig. 5.6 a–b Holes connected with the mounting of Cusanus’s globe. Left: Holes in the area around the north ecliptic pole; right: around the south ecliptic pole. (Photo: Elly Dekker.)

Almagest (ad 137).Two other holes (B and C in Scheme 5.1.) are shifted with respect to the great circle through Sirius 20.5° east and 3.3° west, respectively. The presumed solstitial colures through these holes are located respectively 8.1° east and 15.7° west with respect to the Ptolemaic solstitial colure through A. Around the points A and C are traces of a small circle and a series of points (Fig. 5.6) which were caused by the nails with which a circular disc was fixed to the sphere at the equatorial poles at A and C. Hartmann also found traces of the equators corresponding to the equatorial poles at A and C. These markings show that the equatorial poles A and C were actually used and must have had a particular interest for the maker or user of the globe.The absence of traces of a circular disc with nails around point B suggests that the hole at B was not used in the same way as those at A and C.

The interest in Ptolemy’s epoch (point A) does not require much explanation. For determining the epoch corresponding to hole C one needs to know which theory of precession was applied by the user. For example, with the method used by the Alfonsine astronomers for calculation the epoch of the star catalogue in the Libros del Saber, one finds an epoch by a simple calculation. The excess of 15.7° of the colure through point C with respect to Ptolemy’s exceeds that of al-Ṣūfī’s catalogue of 964 by 3º (12º 42´ = 12.7º). Using a constant rate of 1º in 66 years this difference of 3º is equivalent to 200 years, that is, an epoch of 1164 for point C. However, this epoch can be rejected because it violates a constraint indicated by the iconography of Perseus (Fig. 5.3). Already Hartmann noticed the peculiar helm worn by Perseus, and pointed out that this type came into use at the

349

the mathematical tradition in medieval europe

Scheme 5.1 The configuration of holes around the north ecliptic pole on Cusanus’s globe.

end of the thirteenth century.60Thom Richardson of the Royal Armouries has confirmed that ‘the “pointed top” group are first illustrated in 1285 and go on until about 1340’.61 The most common theory in use before 1444, the year in which Cusanus bought the globe, was the Parisian Alfonsine trepidation theory. This theory predicts an epoch of 1292 ± 50 for the solstitial colure 15.7° west (point C) of the

60 Hartmann 1919, p. 11. 61 Private communication Thom Richardson, Keeper of Armour and Oriental Collections. For the current thinking on this, with lots of illustrations of objects and art, see Southwick 2006.

Ptolemaic one (Point A) for ad 137.62 In assessing this epoch I have taken into account the fact that the uncertainty in the position of the holes according to Hartmann is ½°, which in terms of epochs is equivalent to about 50 years.63 Note that this epoch 1292 postdates the Alfonsine epoch 1252 while the excess of 15.7° associated with point C is less than 17° 8´, the value by which the longitudes in the Alfonsine star catalogue exceed the Ptolemaic ones. As explained in Section 5.1 above the value 17° 8´ agrees 62 Hartmann 1919, p. 33 gives a date of 1293. I calculated the date with the formula in Mercier 1977, pp. 58–9. 63 Hartmann 1919, p. 33.

350

5.2 PTOLEMY’S PRECESSION GLOBE effectively with the theory for the epoch ad 16. When counted from ad 16 the value of 15.7° west (point C) would correspond to an epoch of 1125 ± 50 which can be rejected for the reasons explained above. Indirectly this shows that the user had no copy of the Alfonsine star catalogue but used the copy of Gerard of Cremona in his translation of the Almagest and calculated the precession correction with respect to ad 137. An epoch between 1242 and 1342 predicted by the Parisian Alfonsine trepidation theory offers in my opinion the best prospects for interpreting point C. Considering that the Parisian Alfonsine precession theory was constructed around 1320, a date before 1320 is not likely. I think that one can exclude the possibility that the user intended to set the equatorial poles for the Alfonsine epoch at 1252 because then the value 17° 8´ would have been used.64 Thus the best assessment of point C is that it represents a date between 1320 and 1342 consistent with the range in dates indicated by Perseus’s helm mentioned above. About the epoch associated with point B one can only speculate. The absence of traces of the use of a circular disc around this hole could mean that it was created only after the meridian ring with the circular disc was lost. However that may be, Hartmann suggested that the pole at B was used to verify an old pre-Ptolemaic text since there are also traces on the surface of the globe of a number of parallel circles centred on pole B which seem to represent the tropics and the ever-visible and ever-invisible circles at geographical latitude 35º, but in the absence of other clues the meaning of pole B remains obscure.65 64 Hartmann 1919, p. 34. Zinner 1967/1979, p. 383 concludes that the globe is based on the Alfonsine star catalogue and dates the globe for different reasons to ca. 1400. 65 Hartmann 1919, pp. 32–3.

5.2.1 The constellations In the description of his solid globe Ptolemy gives the following instructions for drawing the constellations on the sphere after the stars have been marked on it: ‘As for the configurations of the shapes of the individual constellations, we make them as simple as possible, surrounding66 the stars within the same figure only by lines, which moreover should not be very different in colour from the general background of the globe.The purpose of this is, [on the one hand], not to lose the advantages of this kind of pictorial description, and [on the other] not to destroy the resemblance of the image to the original by applying a variety of colours, but rather to make it easy for us to remember and compare when we actually come to examine [the starry heaven], since we will be accustomed to the unadorned appearance of the stars in their representation on the globe too.’67

All constellation images on Cusanus’s globe are simple line drawings with very few elaborations, as Ptolemy’s instruction prescribes. When I examined the globe in 1992 it was difficult to make good photographs as a result of wear. I have therefore reproduced the pictures published by Hartmann in Figs 5.2–5.5 and 5.7–5.10. One should be aware that Hartmann did manipulate his photographs before publishing them. After enlarging his pictures he copied the constellation figures with a pencil and, after reducing these drawings to their original sizes, combined these drawings with the original photograph. Some of the drawings are incomplete. 66 In the translation of Toomer 1984, p. 406, the word ‘connecting’ is used instead of ‘surrounding’. This latter word is used by Manitius 1963, Band II, p. 74 and in my opinion is preferable in order to avoid confusion with modern usage to connect the stars inside a constellation by lines. 67 Toomer 1984, p. 406.

351

the mathematical tradition in medieval europe

Fig. 5.8 Ursa Maior and Leo on Cusanus’s globe. (Reproduced from Hartman 1919, Plate VII.)

Fig. 5.7 Auriga, Orion, Gemini, Cancer, and Canis Minor on Cusanus’s globe. (Reproduced from Hartman 1919, Plate V.)

The most striking examples are the absence of Bootes’s stick and the incomplete figure of Cygnus (compare my photographs in Figs 5.11–5.12 with Hartmann’s in Fig. 5.9). Despite these few shortcomings Hartmann’s pictures are good reproductions of the originals. As these pictures show, most human figures are nude, the exceptions being the female figures Andromeda and Virgo.The human figures seem to have very similar heads, hands, and curly hair, but there is some differentiation among their faces. Some human constellations, that is Bootes, Cassiopeia, Perseus, Auriga, and Orion, have their heads drawn in profile.The faces of others, such as Cepheus, Hercules,Andromeda, Gemini, Virgo, Aquarius, and Centaurus, are drawn full faced. Most animal constellations are drawn in

profile. These include Ursa Maior, Pegasus, Equuleus, Delphinus, Leo, Capricornus, Pisces, Hydra, Cetus, Lepus, Canis Maior, Canis Minor, and Lupus. Two constellations, Cancer and Scorpius, are as usual seen from above. Birds like Aquila and Cygnus are drawn in flight.Aries and Taurus have their heads turned to look backwards. Some animals, such as Ursa Minor and Ursa Maior, have scanty hair around the head and Cetus has some on the head and on his back, whereas Leo’s head and Aries’s fleece receive the full treatment.Wings are usually well worked out, not only in Cygnus and Aquila but also in the mythological figures Pegasus and Virgo. Finally the artist has a very characteristic way of drawing watery features, as for example his images of Aquarius’s stream of water (compare Fig. 5.2) and Eridanus. Since most human

352

5.2 PTOLEMY’S PRECESSION GLOBE

Fig. 5.9 Bootes, Ophiuchus, Serpens, Corona Borealis, Hercules, Draco, Lyra, and Cygnus on Cusanus’s globe. (Reproduced from Hartman 1919, Plate IX.)

Fig. 5.10 Centaurus, Lupus and Ara on Cusanus’s globe. (Reproduced from Hartman 1919, Plate X.)

the fact that contrary to earlier antique sources constellations are nude their design seems to and later Western globes, the Bears are not drawn have at first sight little to offer as far as dating is back to back (see Section 4.4). However, here concerned. However, the head gear of some of the agreement between Arabic iconography and the constellations is telling. As mentioned above that expressed on Cusanus’s globe ends. This Perseus’s helm was used between 1285 and 1340. becomes clear when the constellation figures on Also the hunting hat of Cepheus and Bootes Cusanus’s globe are compared with, say, the conpoints to the first half of the fourteenth stellation drawings presented in BernkastelKues, Cusanusstift, MS 207. According to century.68 A most conspicuous feature of Cusanus’s Krchňák, who examined the codices which globe is that all human constellations are pre- today are still kept in the Cusanusstift, this manusented in front view, a mode of constellation script was among the codices acquired in 1444 design common among Islamic globe makers. and may have the same provenance as the This would suggest that the model used by the globe.69 Bernkastel-Kues MS 207 dates to 1301–34 maker was an Islamic globe.This is supported by and according to Krchňák was written in 68 The hunting hat occurs in the Liederbuch Heidelberg (1300–44), f. 228, and in Bernkastel-Kues MS 207, f. 115v, see Krchňák 1964, p. 121, Fig. 1.

353

69 Krchňák 1964, p. 179.

the mathematical tradition in medieval europe

Fig. 5.11 Bootes on Cusanus’s globe. (Photo: Elly Dekker.)

Prague.70 On ff. 124v–135r is a cycle of constellation drawings which belongs to the star catalogue on ff . 116v–121v. This catalogue is part of the Ṣūfī Latinus corpus albeit of the augmented type.71 The drawings in MS 207 differ considerably from the main types but the connection with the Ṣūfī Latinus tradition is recognizable in many ways. Since Krchňák connects this codex with Cusanus’s globe a comparison is of interest. Below I have listed the images on the globe that deviate from those in the Ṣūfī Latinus tradition, as exemplified in Bernkastel-Kues MS 207. Ce pheus (Fig. 5.5) is naked and has no tiara but wears instead a medieval hat.The kneeling attitude is in line with the stellar configuration 70 Blume et al. in preparation, suggest alternatively ‘Mittelrhein (böhmisch?)’. 71 Kunitzsch 1986a, pp. 70–1.

Fig. 5.12 Cygnus on Cusanus’s globe. (Photo: Elly Dekker.)

described in the Ptolemaic catalogue. In MS 207, f. 125r he is also naked but here he wears a high cap in keeping with the Ṣūfī Latinus tradition. Bootes (Fig. 5.9) is standing as is expected from the Ptolemaic stellar configuration, with his western arm raised and a stick in his eastern hand. Apart from his hat, which is the same as that of Cepheus, and a girdle he is naked. In MS 207 f. 125v he is also naked but here he holds a sword in keeping with the Ṣūfī Latinus tradition. Corona Borealis (Fig. 5.9) is a crown with six petals, three of which are drawn on the outside and the other three on the inside of the ring. In MS 207 f. 125v it is a represented by a ring in keeping with the Ṣūfī Latinus tradition.

354

5.2 PTOLEMY’S PRECESSION GLOBE Hercules (Fig. 5.9) is a naked figure with a beard. His eastern foot is above the head of Draco and he kneels on the (western) knee in keeping with the ‘Kneeler’ described in the Ptolemaic catalogue. However, he carries the attributes of Hercules: the club in his raised western hand and a lion’s skin in his other outstretched hand. In MS 207, f. 125v this constellation is also naked but here the figure holds only a sickle in his raised left hand in keeping with the Ṣūfī Latinus tradition. Lyra (Fig. 5.9) is depicted as a musical instrument, the lyre. In MS 207 f. 126r Lyra is drawn as a vase in keeping with the Ṣūfī Latinus tradition. Perseus (Fig. 5.3) is drawn naked with a helm on his head. In his hand above his head he holds a curved sickle-like weapon with teeth. In his other hand he carries a female head, representing the decapitated head of Medusa. In MS 207, f. 126r Perseus is also naked but here he holds a sword and carries the head of Ghūl, the desert demon in keeping with the Ṣūfī Latinus tradition. Auriga (Fig. 5.7) is a naked figure with curly hair. On his right shoulder is the head of a goat and on his right wrist is a smaller goat. In MS 207, f. 126r Auriga is also naked but there are no goats and Auriga holds a rein in his hand in keeping with the Ṣūfī Latinus tradition. Virgo (Fig. 5.8) is a female figure with long hair and wings. She wears a long dress with a girded top. Her head is turned in profile to the north.The left hand is on her breast. In MS 207, f. 130r Virgo is also dressed but here she is drawn without wings in keeping with the Ṣūfī Latinus tradition. Libra (Fig. 5.10) is presented as the Claws of Scorpius as described in the Ptolemaic catalogue. In MS 207, f. 130v Libra is drawn as a pair of scales in keeping with the Ṣūfī Latinus tradition.

Orion (Figs 5.4 and 5.7) is a naked kneeling figure. He holds a shield in his raised western arm and carries a club in his raised eastern hand. He has around his middle a belt to which a sword in a scabbard is attached, as described in the Ptolemaic catalogue. In MS 207, f. 132r Orion is also naked but here he has a lengthened sleeve instead of a shield in keeping with the Ṣūfī Latinus tradition. Centaurus (Fig. 5.10) is partly a horse and partly a nude figure with curly hair on top. His left hand holds the right foreleg of Lupus, and his right hand touches the belly of Lupus. In MS 207, f. 134v Centaurus holds a branch with leaves in keeping with the Ṣūfī Latinus tradition. From this comparison it is clear that the constellation drawings on the globe have little in common with the Ṣūfī Latinus tradition seen in a number of manuscripts.Whatever the origin of the constellation drawings on Cusanus’s globe, it should not be sought among the Arabic influences dominating the mathematical tradition in the Latin West around 1300.The only remarkable agreements between the constellation drawings in Bernkastel-Kues MS 207 and on the globe are first of all the nudity of most human figures. In this respect the constellation drawings in MS 207 deviate from the norm of the Ṣūfī Latinus corpus. A second common feature is the wavylike borders of the river Eridanus. On the globe the same characteristic is used for the presentation of Aqua, but in MS 207 the borders of the stream of water are presented as straight lines. And third it is worth noting that the typical hat worn by Cepheus and Bootes on Cusanus’s globe is also seen on the left shoulder of Jupiter in MS 207, f. 115v.72 Interesting as this is, it is not

355

72 Krchňák 1964, p. 121, Fig. 1.

the mathematical tradition in medieval europe sufficient to establish a straightforward relation between the globe and the codex. Whereas the date of production of the globe seems fairly well established it is not clear where the globe was made. Around 1300 instrument making was not yet an established trade. Instruments were made through cooperation between scholars and artists, working in wood and metal. Such a grouping of people could be found in monasteries, at royal courts, and in commercial cities. Hartmann believed that one of Cusanus’s instruments, the torquetum, could be connected with Nuremberg. And since he could date this instrument to 1434 he thought that there might be a connection with a certain Nicholas of Heybech from Erfurt. Astronomical tables of this Nicolas were included in BernkastelKues MS 211, the same codex in which he had found the note by Cusanus on the acquisition of the instruments and sixteen codices.73 His next step was to suggest that this astronomer from Erfurt might have been identical with a certain Magister Nicolao orlogista, who was recorded in Nuremberg around 1431/4.74 Thus it seemed not unreasonable to presume that the codices and the other instruments were once the property of this Nicholas of Heybech from Erfurt.75 In 1963 Krchňák showed that Hartmann’s thesis was untenable because Nicholas of Heybech must have been older than 70 in 1431.76 Examining the codices connected with Cusanus, Krchňák developed a completely different thesis. The interpretation of the extant Cusanus codices is complex. Not all manuscripts can be supposed to have been part of the sixteen 73 On these tables see Goldstein and Chabás 2008. 74 Hartmann 1919, pp. 11–14. 75 Zinner 1967/1979, p. 383 has taken over this attribution to Nicolaus of Heybreck. 76 Krchňák 1964, pp. 165–6.

codices which Cusanus bought in 1444 together with three instruments. Some have been lost, others have been separated and bound differently and a few are now in other libraries.Among the extant codices Krchňák found four originating from Germany (MS 211, parts of MS 210 and of MS 212, MS Harley 3702), three from Paris (MS 209, part of MS 212, MS 213), one from Toulouse (MS 214), three from Prague (MS 207, MS 208, MS 210), one from Toledo (MS Harley 3734) and one from Italy (MS Harley 5402). These various backgrounds suggest strongly that many extant codices were not necessarily part of the acquisition made in 1444. Yet Krchňák believes that MS 207, MS 208, and MS 210 belong to those acquired in 1444. The connection of Bernkastel-Kues MS 207 and Cusanus’s globe is far from clear. Krchňák presumes a common origin of the codex and the globe because of the hunting hat occurring in MS 207 on f. 115v and on the globe. His other argument for connecting the codex and the globe is the agreement in artistic style. The line drawings, nakedness, and hair styles of the human figures would connect Bernkastel-Kues MS 207 with Prague, and in its trace also Cusanus’s globe.77 However, it has not been shown that the hunting hat and the style of drawings were localized to Prague. His analysis of MS 208 and MS 210 serves to add to his claim that Cusanus’s globe would have been made in Prague. Glosses in these manuscripts show that around 1300 connections existed between the court in Prague and two astronomers from Spain. Krchňák identified one of them as Alvaro de Oviedo, a translator from

77 Krchňák 1964, p. 135. He believes that the artistic style of the constellations cycle in this codex compares well with the Welislaw bible (Prague, Nationalbibliothek, MS XXIIIc 24).

356

5.3 MAPS IN THE MATHEMATICAL TRADITION Toledo, but this has been questioned.78 However that may be, Krchňák believes that these Spanish astronomers brought Cusanus’s astrolabe from Spain to Prague. He also believes that the presence of these Spanish astronomers in Prague indirectly confirms that Cusanus’s globe was made there around 1300. He presents, however, no evidence for either presumption. I do not question the presence of Spanish astronomers working at the Prague court around 1300, but I am not convinced that the globe was built there by them. One could reason that the location of the solstitial colure through pole C 15.7º west of the colure for Ptolemy’s epoch shows that the user was familiar with the Parisian Alfonsine Tables which were available from 1320 on, but this argument is not decisive if the maker and the user are not the same person. My main reason for doubting a Spanish maker is that the design of Cusanus’s globe is so very unlike a globe from Muslim Spain. Although all human constellations are presented in front view as they are on Islamic globes the constellation drawings on Cusanus’s globe recall the very opposite of Arabic traditions in constellation design. In fact the globe’s constellations are even unlike anything known from the Middle Ages and one would even be inclined to date them to the fifteenth century.79 However, Perseus’ helm contradicts such a hypothesis. As long as the origin of the constellation drawings remains the puzzle it is today, any guess on its place of origin is premature. All the same, this globe of the second quarter of the fourteenth century is closest to what I imagine a Greek model of Ptolemy’s precession globe would have looked like.

. MAPS IN THE MATHEMATICAL TRADITION In the fifteenth century a revival in map making in central Europe took place which, through the work of Dana Bennett Durand, became known as the Vienna-Klosterneuburg map corpus. The greater part of the material is centred on geographical problems, such as finding the correct coordinates of places, their latitudes and longitudes, and so on. Two sketches prepared by Conrad of Dyffenbach are based on a modified version of the list of coordinates included in the Toledan Tables.80 These early Dyffenbach terrestrial maps are preserved inVatican City, Biblioteca Apostolica Vaticana, MS Palat. lat. 1368, ff . 46v– 47v and ff. 65v–66r. Preceding the latter map are, on ff 63r–64v, four celestial maps. Already in 1915 Saxl had recorded in his description of Vatican City MS Palat. lat. 1368 the existence of four celestial maps on ff . 63r– 64v of an unusual design.81 They were first studied in 1937 by Uhden, but gained significance when Durand discussed them in the context of the Vienna map corpus.82 The part of the codex with the maps appears to have been written around 1426 by Conrad of Dyffenbach, witness of which is a remark made at the end of the astrological treatise (f. 45r): ‘Et sic finitur centiloquium Ptholomei scriptum per me Conradum de Dyffenbach anno domini 1426, festo epiphanie domini etc’.83 Conrad of Dyffenbach matriculated at Heidelberg University in 1399 and later became a

78 Krchňák 1964, pp. 136–44. For the rejection of Alvaro de Oviedo, see Yamamoto and Burnett 2000, p. xxvi. 79 Hartmann 1919, p. 36. For an example of a Spanish map, see Addendum.

357

80 81 82 83

Durand 1952, p. 107. Saxl 1915, pp. 10–15, esp. p. 15. Uhden 1937; Durand 1952, pp. 114–17. Saxl 1915, p. 10.

the mathematical tradition in medieval europe prebendary of the church of St Peter in Aschaffenburg. Conrad was probably either a student or a colleague of Johannes of Wachenheim, who matriculated in 1377 in Prague and then moved to Heidelberg University where he became Rector in 1387. Johannes later obtained a canonry in the church of St Cyriac at Neuhausen near Worms and was also known as Johannes de Wormacia. It is not known whether Conrad of Dyffenbach was the author of the celestial maps or only the copyist.The maps are preceded by an illustrated star catalogue on ff. 51r–56v said to have been verified by Johannes of Wachenheim for 1420, and on ff . 56v–58v there is a list of stars with their planetary natures and another listing their place in the zodiacal signs for 1400.84 On ff. 59r–62v there follows a series of drawings of the discs of an equatorium, a device for calculating the positions of the planets. The celestial maps on ff . 63r–64v are followed by a terrestrial map (ff. 65v–66r, labelled by Durand Dyffenbach II) which Durand suggests may have been inspired by the celestial maps. Before discussing the context of the celestial maps, something must be said about their projection.

5.3.1 The Dyffenbach projection There are four celestial maps divided over four pages (Figs 5.13–5.16), which are described in more detail in Appendix 5.1 as M1a–d. One of the maps, labelled here M1a, is circular and extends from the ecliptic north pole to the ecliptic. It is marked by a grid consisting of a series of equidistant circles centred around the ecliptic north pole, which represent parallels for every 5°, and a series of straight lines extending from the ecliptic north pole to the ecliptic,

which represent great circles for every 5°. In modern terms this map is a polar azimuthal equidistant projection of the northern celestial hemisphere. Examples of celestial maps with equidistant circles centred on the equatorial north pole were known in the Middle Ages (Section 3.2) and may indicate that such maps were known in Antiquity. The surviving medieval examples show however that the very notion of a projection does not yet underline the construction of these maps. A typical ‘error’ in these medieval maps is that oblique circles are presented as circles whereas in the polar azimuthal equidistant projection such circles are mapped onto higher order curves which are difficult to draw. The first thorough treatment of this projection is given by the ninth-century Arab astronomer and mathematician Ḥabash al-Ḥāsib.85 As discussed in Chapter 4, al-Bīrūnī mentioned and rejected this projection since one has to present the celestial sphere into two halves, with the result that the borders of each cut through the zodiacal constellations and would divide them over the two hemispheres ‘and that is far from what is sought’.86 The objection raised here is, however, not restricted to the polar azimuthal equidistant projection but applies to any presentation of the celestial sphere in two maps bounded by the ecliptic. The constellations located in the zodiac are, generally speaking, half north and half south of the ecliptic. Considering the importance attached to the zodiac such a division of the zodiacal constellations is not commendable. Extending the maps to include the zodiacal constellations completely, as was done with the Vienna maps discussed below, has the disadvantage that the 85 Kennedy et al. 1999. 86 Berggren 1982, p. 52.

84 Saxl 1915, pp. 14–15.

358

5.3 MAPS IN THE MATHEMATICAL TRADITION circles parallel but south to the ecliptic have a greater diameter than the ecliptic. The objection raised by al-Bīrūnī is certainly of interest in discussing the Dyffenbach maps because it may explain why next to the map of the northern hemisphere bounded by the ecliptic there are

also three maps (M1b–M1d) in another projection centred on the zodiac. Overstepping the boundaries was clearly no option for the author of the Dyffenbach maps. This alternative way to map the zodiac was investigated by Uhden and most of his

Fig. 5.13 Part of the Dyffenbach map M1a in Vatican City, MS Palat. lat. 1368, f. 63v. (Courtesy of the Biblioteca Apostolica Vaticana,Vatican City.)

359

the mathematical tradition in medieval europe conclusions were taken over by later authors. tion, which maintains the correct proportion of Uhden associated the zodiacal maps M1b–M1d the longitude intervals, such a ratio holds only for with the trapezoidal projection—calling it the a latitude of 48°.Thus Uhden concluded: oldest known example of it. Uhden noticed that the ratio of the longitude intervals at respectively ‘In determining the size of the latitudinal degree, the parallel for a latitude 30° and at the ecliptic then, the author of this map must have proceeded from a premise very different from that of Nicolaus (latitude 0°) is 2:3 whereas in the Donis projec-

Fig. 5.14 Part of the Dyffenbach map M1a and map M1c in Vatican City, MS Palat. lat. 1368, f. 64r. (Courtesy of the Biblioteca Apostolica Vaticana,Vatican City.)

360

5.3 MAPS IN THE MATHEMATICAL TRADITION

Fig. 5.15 The Dyffenbach map M1b in Vatican City, MS Palat. lat. 1368, f. 63r. (Courtesy of the Biblioteca Apostolica Vaticana,Vatican City.)

Donnus. The former’s [Dyffenbach] method becomes clear only when compared with the map described above. Measurement shows that the trapezoidal projection plan was derived directly from the equidistant planisphere.The distances between the meridians on the celestial equator and those on the parallels at 30° both follow the system of azimuthal projection and form the basis of the drawing of the second map.A most curious method, indeed, a second example of which can scarcely exist and which hardly deserves imitation.’87

This statement induced Durand to say that ‘in fact the network of the trapezoidal Dyffenbach

star maps appears to have been derived not by true projection from a globe, but rather by measurements from the azimuthal frame constructed on f. 63v’, that is the polar map.88 Uhden’s conclusion that the size of the latitudinal degree was determined by measuring ratios on the polar map is not convincing. Besides, the method used in constructing the three zodiacal Dyffenbach maps follows a simple mathematical principle and may therefore be marked as a proper projection. The Dyffenbach projection—as I propose to call it—consists of a series of equidistant straight lines, representing parallels to the ecliptic,

87 Uhden 1937, p. 8.

88 Durand 1952, p. 116.

361

the mathematical tradition in medieval europe

Fig. 5.16 The Dyffenbach map M1d in Vatican City, MS Palat. lat. 1368, f. 64v. (Courtesy of the Biblioteca Apostolica Vaticana,Vatican City.)

and a series of straight lines extending from the ecliptic north and south pole to the ecliptic, representing great circles. The basic structure is shown in Scheme 5.2. Simple geometry shows that in this Dyffenbach projection the ratio of the lengths of a degree at respectively latitudes 30° and 0° is proportional to CD:AB = PR:PS = 2:3. Generally, the ratio of the lengths of a degree at latitudes b and 0° is equal to EF:AB = PQ:PS = (90°-b): 90°. Note that the projection does not require a central meridian, the position of the poles P and T can be placed anywhere along the lines at a distance of 90° from the ecliptic. The Dyffenbach

projection differs thus in its defining characteristics from the Donis projection in which the ratio of the lengths of a degree at respectively latitudes b and 0° is proportional to cos b.89 In a way one could place the Dyffenbach projection between the polar azimuthal equidistant projection and the Donis projection but conceptually it is closer to the former.The Dyffenbach projection could have been developed from the polar azimuthal equidistant projection simply by

89 Durand 1952, p. 151, incorrectly claims that the author of the Dyffenbach maps used the trapezoidal projection for which Nicolaus Germanus is credited.

362

5.3 MAPS IN THE MATHEMATICAL TRADITION zodiac consisting of a band bounded by the circles parallel to the ecliptic 6° north and south of it. Each map extends in longitude by roughly four signs of the zodiac. It would have been astronomically perhaps more logical to make four zodiacal maps covering each three signs, corresponding to the four seasons.The choice to make three instead of four maps must have had a practical reason. If we look at the size of the maps in latitude the situation is less systematic.The map on f. 63r (Fig. 5.14/M1b), covering the first four signs of the zodiac (Aries, Taurus, Gemini, Cancer), extends from latitude 30° north to 55° south of the ecliptic to include such southern constellations as Eridanus and Canis Maior. The other two maps on respectively f. 64r (Fig. 5.15/M1c), covering the second set of four signs (Leo,Virgo, Libra, Scorpius) and on f. 64v (Fig. 5.16/M1d), covering the last set of four signs (Sagittarius, Capricornus,Aquarius, Pisces) extend both from latitude 30° north to 30° south of the ecliptic. Scheme 5.2 Construction underlying There are also a few non-zodiacal constellations the Dyffenbach projection. sometimes only presented by some of their stars but all have latitude less than 30° north or south. replacing the series of equidistant circles centred Taken together one gets the impression that the on the pole by a series of straight parallel lines. author of the maps was exploring the scope of The connection between the polar map M1b his projection and, after the trial seen in map and the zodiacal map M1c. on f. 64r might sug- M1b (Fig. 5.14) to extend further south, decided gest this since both maps are centred on the sum- that this did not deserve following up in the mer solstitial colure. However, this is misleading other maps, presumably because the ratio of the because the zodiacal map is drawn upside-down lengths of a degree at respectively latitudes 55° with respect to the north–south orientation of and 0° is equal to (90°-55°):90° = 0.39. This the polar map, and as such is not a continuation should be compared to the corresponding value of the polar map. cos 55 ° = 0.57 in the polar azimuthal equidistant Looking now at the details of the Dyffenbach projection and the Donis projection. maps we note that each map is based on a grid of 5.3.2 Astronomical significance 5° × 5° in longitude and latitude.The parallels 5° north and south of the ecliptic are not drawn but Looking at the astronomical features of the maps are replaced by lines 6° north and south of the it is clear that the polar and the zodiacal maps ecliptic, conforming to the antique concept of the share a few aspects in construction. In setting out 363

the mathematical tradition in medieval europe the scales in longitude the signs run from left to right on both the polar map and the zodiacal ones except in the zodiacal map M1c where the longitude runs from right to left because the map is upside-down. It is not clear how consciously this choice was made. In Western writing authors precede from left to right naturally. However, the result is that the east–west order of the stars is presented in the maps as these are seen on a globe and not as in the sky. Using the map’s grid the position of each star is indicated according to its longitude and latitude recorded in the Ptolemaic star catalogue but corrected for precession. The brightest stars are indicated by a starry symbol and nebulous stars by a dot surrounded by a small dotted circle. However, most stars are marked by a number, which indicates its brightness. In the Ptolemaic catalogue there are 15 stars of the first, 45 stars of the second, 208 stars of the third, 474 stars of the fourth, 217 stars of the fifth, and 49 stars of the sixth magnitude. In addition there are 9 faint stars, 5 nebulous, and 3 in Coma. It is clear that stars of the fourth magnitude are the most numerous and therefore the number 4 is found most frequently in the maps. Next to the magnitude the map maker also added short descriptions of the location of the stars within the constellation to which they belong. Astrological information is also added. Occasionally a proper name is added to wellknown stars. For example, the brightest star in Canis Minor (shown in the enlarged picture in Fig. 5.17) is marked by a starry symbol with its medieval name algomesa and the other star belonging to this constellation is indicated by the number 4, its magnitude, and described as the neck (collo) of algomesa. The name used for the constellation in medieval times stemming from the Arabic was also used for its brightest star.

Fig. 5.17 Detail of the Dyffenbach map M1b in Vatican City, MS Palat. lat. 1368, f. 63r. (Courtesy of the Biblioteca Apostolica Vaticana,Vatican City.)

In the area south of Canis Minor are two stars which attract attention because they should not be there. These stars belong to the constellation Navis (nos 44 and 45). According to the Greek and Arabic versions of the Ptolemaic star catalogue both stars should lie at southern latitude of respectively -75º and -71º 45´.90 In the Latin translation of Gerard of Cremona, star no. 44 of Navis, described as ‘in remo sequente et dicitur canopus et est suhel’, is of the first magnitude and its latitude is -29°. On the map this star is marked by an asterisk, labelled ‘canap[. . .] in navi/in remo/saturni [et] jouis’, and its position agrees with Gerard’s value -29°. Star no. 45 of Navis, described in the catalogue as ‘Reliqua sequens earum’, is of the third magnitude and its latitude is -21° 50´. On the map this star is marked by the number 3 and labelled ‘sequens canap[. . .]’, and its position agrees also with the erroneous latitude -21° 50´ recorded in the Latin translation of Gerard of Cremona.91 The erroneous positions of stars nos 44 and 45 of Navis tell us that Durand’s assumption that 90 Kunitzsch III 1991, p. 163. 91 Kunitzsch II 1990. Kunitzsch assures me that these erroneous latitudes occur exclusively in Gerard’s translation (Letter 3 July 2010). In the printed edition of the Almagest of 1515 and the Alfonsine catalogue of 1524 the latitudes of nos 44 and 45 are corrected to respectively -69° and -61° 50´.

364

5.3 MAPS IN THE MATHEMATICAL TRADITION the star catalogue preceding the maps on ff. 51r– 56v by Johannes of Wachenheim was used in constructing the maps is incorrect.92 The latitudes of stars nos 44 and 45 of Navis in this star catalogue are respectively -75° and -71° 50´. In related star catalogues, such as in Vatican City, Biblioteca ApostolicaVaticana, MS Palat. lat. 1377, ff. 183r–194v for the epoch ad 137, the latitude of star no. 44 is given as -29° but this is followed by a correction to -75° and the latitude of no. 45 is given as -71° 50´.93 And in Oxford, Bodleian Library, MS Rawl. C. 117, ff . 145r–157r for the Alfonsine epoch 1252 (17º 8´), the erroneous value of no. 44 (-29°) is changed to -69° and that of no. 5 (-21° 50´) is left unchanged. It seems that there was a certain awareness that the values of the latitudes of these stars in Gerard’s catalogue were wrong. The entries in these various catalogues show that the maker of the Dyffenbach maps used a copy not far removed from the Latin translation of Gerard of Cremona but of course corrected for precession. The erroneous positions of stars nos 44 and 45 in Navis also tell us that the star catalogue in Vienna MS 5415, corrected for precession by 18° 56´ for the epoch 1424,was not used in constructing the Dyffenbach maps because the latitudes of stars nos 44 and 45 are given there as -75° and -77° 45´ (instead of -71° 45´!). The reason to suppose a relation between the Dyffenbach maps and this Vienna star catalogue is that both sources represent Bootes with a stick in one hand and a bow in the other. This image of Bootes is very unusual and must stem from a common source, a thesis supported by the images of Cepheus in both the Vienna catalogue and the polar map M1a.

92 Durand 1952, p. 115. 93 See the Warburg Institute Iconographic Database http:// warburg.sas.ac.uk/photographic-collection/iconographic-database/.

In order to determine the epoch of a map or a globe it is usually best to select a number of stars close to the ecliptic and subsequently determine the differences between the longitudes of the stars on the map and those in the Ptolemaic catalogue for the epoch ad 137. The mean value of these differences generally speaking gives a fair estimate of the required precession correction for the map or globe. For the Dyffenbach maps I have limited the selection to those stars marked by an asterisk because only for these can a fairly good position be determined. The longitudes of these stars (MLon) and their latitudes (MLat) are shown in Table 5.1, together with the Ptolemaic values (PLon and PLat) and the differences in longitude (DLon) and latitude (DLat). If all 14 stars are included the precession correction is equal to 19.3º ± 0.17º, which in terms of the Alfonsine trepidation theory corresponds to the period between 1446 and 1482. Among these 14 stars there are 2 which have values of Dlon which differ 1.5 times the standard deviation from the mean value. If these stars are rejected a new mean value can be determined which, using the same criterion, allows one to reject one more star. This process converges after the rejection of four stars (nos 11–14 in Table 5.1).Three of the four stars are located on the zodiacal map M1b which extends far to the south. The location of the fourth star, α PsA, is hard to determine.Anyway, when these four stars are left out, the precession correction is equal to 18.93º ± 0.10º, which in terms of the Alfonsine trepidation theory corresponds to the period between 1415 and 1441 which agrees well with the date of the maps. If only the four stars of the polar map M1a are used (nos 1–4 in Table 5.1) the precession correction is equal to 18.96º ± 0.09ºm which is close to the values obtained for

365

the mathematical tradition in medieval europe Table 5.1 Stellar longitudes on Dyffenbach’s maps compared to Ptolemaic values No.

BPK

Modern

PLon

MLon

PLat

MLat

DLon

DLat

1 2 3 4 5 6 7 8 9 10 11 12 13 14

110 197 222 223 393 469 488 510 735 818 670 768 892 848

α α α β α α β α α α α β α α

177.0 34.8 55.0 62.8 42.7 122.5 144.5 176.7 62.0 77.7 300.0 49.8 77.2 89.2

196.0 54.0 74.0 81.5 62.0 141.0 163.0 195.5 81.5 96.5 320.0 70.0 97.5 109.5

31.5 30.0 22.5 20.0 -5.2 0.2 11.8 -2.0 -17.0 -39.2 -23.0 -31.5 -29.0 -16.2

31.0 30.0 23.0 20.0 -5.5 0.0 12.0 -2.0 -17.5 -39.0 -23.0 -32.0 -29.0 -16.0

19.0 19.2 19.0 18.7 19.3 18.5 18.5 18.8 19.5 18.8 20.0 20.2 20.3 20.3

-0.5 0.0 0.5 0.0 -0.3 -0.2 0.2 0.0 -0.5 0.2 0.0 -0.5 0.0 0.2

19.30 0.64 0.17 18.93 0.32 0.10

-0.07 0.29 0.08 -0.07 0.30 0.09

Boo Per Aur Aur Tau Leo Leo Vir Ori CMa PsA Ori Car CMi

Mean value of all 14 stars Standard deviation of all stars Error in the mean Mean value of all but stars nos 11–14 Standard deviation of all but stars nos 11-14 Error in the mean

all maps. This shows that the maker was capable of updating the catalogue he used. For unknown reasons the maps were not finished. On the polar map M1a only 7 of the 21 northern constellations in the Ptolemaic star catalogue have been completed (Ursa Minor, Ursa Maior, Draco, Cepheus, Bootes, Corona Borealis, and Auriga). In addition some of the stars belonging to the constellations Perseus and Ophiuchus have been plotted. On the zodiacal map M1b Aries, Taurus, Gemini, Cancer, and Leo (the western part) are presented. North of the ecliptic one finds Triangulum and south of it Cetus (the eastern part), Eridanus, Orion, Lepus, Canis Maior, and Canis Minor. Next to the erroneous stars nos 44 and 45 of Navis, discussed above, one finds east of Canis Maior a few more stars that belong to Navis, but the contour of the ship is not drawn.

On the zodiacal map M1c Leo (the eastern part),Virgo, Libra, and Scorpio are drawn. North of the ecliptic one finds the three stars of Coma Berenices (Leo 6e–8e), marked oc, oc, and ne, with a note saying that they lie between the tail of Leo and Ursa Maior. Another star plotted north of Virgo is probably the northernmost of the three stars in the leg of Bootes (Boo 20). South of the ecliptic one finds Crater and Corvus, but not Hydra and two stars that belong to Lupus (Lup 1–2). On the zodiacal map M1d Sagittarius, Capricornus, Aquarius, and Pisces are presented. North of the ecliptic are four stars of Pegasus, the identifications of which are troublesome.At first sight they seem to represent the bright stars of second magnitude in the square of Pegasus (Peg 1–4) but these stars ought to lie more to the east. South of the ecliptic one finds Piscis Austrinus

366

5.3 MAPS IN THE MATHEMATICAL TRADITION and Cetus. A few stars of Sagittarius are misplaced. Sgr 23 and 24 are off by 5°, and Sgr 25 in the front right hock of Sagittarius is off by 20°, thus creating the curious shape of this constellation. These incorrect positions may have been part of the star catalogue but could also have been introduced by the maker of the map. The constellations drawn on the zodiacal map raise many questions. One might think that the presentation of the constellation figures was not the first concern of the maker of the maps. As mentioned in Section 5.2 Ptolemy advises making the shapes of the individual constellations as simple as possible, surrounding the stars within the same figure only by lines. Yet, Ptolemy must have meant recognizable figures, not the vague forms drawn in the Dyffenbach maps. Some figures are worse than others. On map M1b (Fig. 5.14) Eridanus and Leo are more easily recognized than Taurus and the Gemini, whereas on map M1c (Fig. 5.15) Crater and Corvus are barely discernible as a bowl and a bird. It is not so difficult to identify Aquarius with his stream of water ending in Piscis Austrinus on map M1d (Fig. 5.16) but Cetus is presented as a curiously shaped animal.The often oddly shaped constellations in the zodiacal maps contrast with the figures drawn in the polar map. Especially the images of Bootes and Cepheus show that the map maker— although not a gifted artist—had access to a model for drawing the constellation figures.The best explanation for the clumsy figures in the zodiacal maps is, in my opinion, that the map maker consciously ignored existing iconographic traditions and tried to draw the constellations from the descriptions of the Ptolemaic star catalogue. His result shows that in the absence of a good model this is not at all easy. This does not change the fact that the maps are novel in a number of ways: the choice of the

projection; the choice of marking the stars by the number of their magnitude instead of by dots of different sizes; the choice of adding information of the location of the stars with respect to the constellation figure. All this seem to point to a search for a method of mapping the celestial sphere on a plane such that most of the information in the star catalogue was made available graphically.

5.3.3 The Vienna maps The next step in the development of mathematical celestial cartography in Europe is connected with the codex Vienna, Österreichische Nationalbibliothek, MS 5415, which contains a number of interesting astronomical texts. On ff. 161r–191r one finds the treatise on globe making, the Tractatus de sphaera solida, and on ff. 192r–210v there follows another one, the Tractatus de spera volubili of Qusṭā ibn Lūqā. After a number of empty pages (ff. 211r–216r) a short note follows on f. 216v about how to prepare the grid of maps representing the northern and southern hemispheres.This is in turn followed on ff. 217r–251v by a star catalogue for the epoch 1424 with stellar longitudes 18° 56´ in excess of the Ptolemaic longitudes. The Tractatus de sphaera solida in Vienna MS 5415 stands out for its graphic presentations. Next to the usual schematic drawings of the mounting in the shape of a hemispherical bowl an image of a celestial globe is included on f. 180v (see Fig. 5.26 below), which in all respects has the appearance of a real globe almost as we know it today. Preceding these various schemata are two celestial maps, on f. 168r and f. 170r (see Figs 5.18 and 5.19). These maps are described in more detail in Appendix 5.1 and shall here be referred to as the Vienna maps. According to Durand, Vienna MS 5415 was among the four manuscripts (the three others are

367

the mathematical tradition in medieval europe

Fig. 5.18 The northern celestial hemisphere in Vienna MS 5415, f. 168r. (Courtesy Österreichische Nationalbibliothek,Vienna, Picture Archive.) See also Plate VI.

368

5.3 MAPS IN THE MATHEMATICAL TRADITION

Fig. 5.19 The southern celestial hemisphere in Vienna MS 5415, f. 170r. (Courtesy Österreichische Nationalbibliothek,Vienna, Picture Archive.) See also Plate VII.

Vienna MS 5418, Munich Clm 56, Munich Clm 10662) written by Reinardus Gensfelder (ca. 1385–1457?).94 This ‘wandering scholar’ was born in Nuremberg. He received his university educa94 Durand 1952, pp. 44–8.

tion in Prague where he became magister artium in 1408. Thereafter he continued his studies in Padua. Between 1433 and 1436 Gensfelder seems to have spent some time in Salzburg, possibly in the monastery of St Peter. In 1436 he entered the monastery of Reichenbach but he continued to

369

the mathematical tradition in medieval europe travel. In 1439 he went to Vienna, in 1440 to Passau, and in 1441 he was in Klosterneuburg. In 1444 Gensfelder became a priest in the parish of Tegernheim close to Regensburg. He appears to have died before1457. When and where Gensfelder produced Vienna MS 5415 has been a topic of debate. Dates mentioned in the literature vary from 1435 to 1444. The former date 1435 is mentioned on f. 191r: ‘Explicit tractatus ...finitus anno 1435o currente’.95 The later date 1444 occurs on f. 159v: ‘Explicit tractatus Albionis finitus anno Christi 1444o currente etc.’, and on f. 180r:‘anno Domini 1444o’.96 It has been argued that the date on f. 159v is a writing error of 1434 and that the date on f. 180r might refer to an adjustment made on that page because on f. 191r it is clearly stated that the Tractatus de sphaera solida was finished in 1435.97 However that may be, for the maps a date of 1435 seems most probable because they are closely connected to the Tractatus de sphaera solida. The question of the place of production of Vienna MS 5415 must be left open since there is no consensus among scholars on where the manuscript was produced. Durand claims that it was copied in 1435 during Gensfelder’s visit to Salzburg and that he also prepared the maps included in the codex there.98 This visit to Salzburg is, according to Durand, attested ‘by the subscriptions of several of the sections in the two Vienna manuscripts (i.e., Codices 5415 and 5418), also in Palat. lat. 1374, f. 112v’.99

95 Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland). 96 Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland). 97 Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland). 98 Durand 1952, pp. 45 and 116. 99 Durand 1952, p. 45, note 1.

Unfortunately this cannot be confirmed.100 It has also been argued from the coats of arms of Vienna, Austria, and Klosterneuburg on f. 33v of the MS 5415 that Gensfelder was in or around Vienna in the years 1433–35.101 This is why Vienna and Klosterneuburg have also been proposed as the place where Gensfelder might have copied the manuscript. 102 Wherever the place of production ofVienna MS 5415 might have been, scholars agree that this important manuscript is closely connected with the activities of the Vienna astronomical school. Its most prominent member was John of Gmunden (ca. 1384–1442), an astronomer and mathematician, who lectured at Vienna University.103 John is famous for his educational texts on devices of all sorts. His collection of instruments, which included among others a celestial globe, an astrolabe, and an armillary sphere, was bequeathed to the University of Vienna.104 Georg Müstinger (born before 1400–42) was another important member of the Vienna school. Müstinger was prior of the Augustinian monastery of Klosterneuburg, and also vicar general of the archdiocese of Salzburg. The ties between Salzburg on the one hand and Vienna and Klosterneuburg on the other are, for example, expressed on the Klosterneuburg map, the centre of which is close to Salzburg while the basic radius line runs between Vienna and Klosterneuburg.105

100 I acknowledge with pleasure the information given by Martin Roland and Dieter Blume. 101 Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland). 102 Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland) proposes Vienna and Blume et al. in preparation, Klosterneuburg. 103 Uiblein 1988; Simek and Chlench 2006. 104 Uiblein 1988, p. 61. 105 Durand 1952, p. 232;Wawrik 2006, pp. 58 and 60–2.

370

5.3 MAPS IN THE MATHEMATICAL TRADITION

Scheme 5.3 The main grid of the northern and southern hemispheres in Vienna MS 5415, f. 168r and f. 170r.

There can hardly be a greater contrast than that existing between the Dyffenbach and the Vienna maps.While the Dyffenbach maps show the hesitant search for method in constructing celestial maps, the maker of the Vienna maps seems to have solved most problems associated with such an enterprise.The difference between the Dyffenbach and the Vienna maps is especially visible in the drawings of the constellations, but before discussing this a few remarks on the projection of the Vienna maps must be made. The Vienna maps serve in the first place as a model for drawing the constellations on a celestial globe, as described in the Tractatus de sphaera solida. This does explain why the maker chose the equidistant projection for his maps, as applied in Dyffenbach’s map M1a. However, when compared to this latter map, the number of great cir-

cles through the ecliptic pole in theVienna maps is greatly reduced. The stars and their constellations are outlined with respect to a grid that consists of an outer boundary circle and 12 straight lines representing respectively the ecliptic and 12 great circles through the ecliptic pole (see Scheme 5.3). Added to this basic grid are a number of circles centred on the equatorial pole (N and S in Scheme 5.3) which do not occur on the Dyffenbach map. One pair of circles represents the polar circles described in the Tractatus de sphaera solida. The other equatorial circle drawn on the Vienna maps passes through the first points of Aries and Libra and extends on one side beyond the ecliptic. It presumably represents the Equator. By definition the Equator should not only pass through the equinoxes but also through the points T located on the solstitial

371

the mathematical tradition in medieval europe colures through the first points of Cancer and Capricornus, at a distance equivalent to 90° from the equatorial poles (compare Scheme 5.3). However, since in the equidistant projection oblique circles like the Equator are projected as ovals instead of circles, the Equators drawn on both hemispheres do not pass through the points T in Scheme 5.3. In the northern hemisphere two more circles are drawn (dotted in Scheme 5.3). The smaller of these two circles is centred on the north equatorial pole N. It has been suggested that this smallest circle of a diameter equivalent to 4.7° traces the daily rotation of the star at the end of the tail of Ursa Minor (α UMi). The ecliptic coordinates of α UMi for 1424 using the Ptolemaic catalogue are longitude 79.1° (Gem 19° 6´) and latitude 66°. When converted to equatorial coordinates we obtain a right ascension of 358.5° and a declination of 85.6°.Thus α UMi would have been 4.4° from the north equatorial pole which is only slightly less than 4.7°. The smallest circle could therefore represent the daily rotation of the star at the end of the tail of Ursa Minor (compare Fig. 5.18). However, this explanation cannot be the whole story, if only because the northernmost intersection of the small circle with the solstitial colure (point P in the northern hemisphere in Scheme 5.3, where a dot is clearly visible) is the centre of another circle which passes through the equinoxes. How this greater circle should be understood is not evident. In the southern hemisphere this centre (point P in the southern hemisphere in Scheme 5.3) is also marked, although the corresponding circle through the equinoxes is not drawn.There is a trace of a small circle around point P instead of around the south equatorial pole S (see Fig. 5.19). The meaning of this small circle is also unclear. My

guess is that the map maker tried to compensate for the fact that the Equator did not pass through the solstices, but understandably did not succeed in finding an alternative solution. In that sense the additional circles in the maps are best seen as trials of drawing the Equator correctly. It shows that the polar equidistant projection was not yet fully understood by the map maker. As already mentioned above, there is no detailed grid to plot the stars on the Vienna maps.The most likely method used by the map maker for marking the stellar positions is by using a ruler with an equidistant scale in latitude in analogy to the use of a great circle centred on the ecliptic pole for indicating the stellar positions on the sphere as described in the Tractatus de sphaera solida. By using the scale along the ecliptic and that of the ruler the position of the star was marked by a point (or hole) in the parchment at the latitude of the star.The map maker next added a number to the point to identify the star with its position in the constellation figure as described in the star catalogue. Once the stars belonging to one and the same constellation were marked, the constellation itself could be drawn around the group of stars. An interesting aspect of the northern hemisphere of the Vienna maps is that the zodiacal constellations extend across the ecliptic. The reason for this is clearly to avoid the zodiacal constellations becoming divided between the two hemispheres which—as al-Bīrūnī had argued—is unacceptable. In plotting the stars the map maker or the maker of its model must have used a star catalogue which must account for the following characteristics: 1. The longitudes of its stars differ with respect to the corresponding Ptolemaic values by

372

5.3 MAPS IN THE MATHEMATICAL TRADITION

2.

3.

4.

5.

18° 53´ ± 21´, which mean value and standard deviation was obtained by measuring the ecliptic longitudes of 18 stars located close to the ecliptic. The numbering of the stars within the constellation Andromeda deviates from that in most medieval star catalogues. For example, the stars that are listed in modern editions as nos 11–14, 15, 16–23 in the description of Andromeda are in the map numbered 20–23, 19, and 11–18, respectively. The numbering of the stars within the constellation Auriga deviates from that in most medieval star catalogues.Two stars are missing: one is a star in the left arm, Aur 9, and the other is in the right knee, Aur 14. As a result the stars, that are listed in modern editions as nos 10–13 in the description of Auriga, are in the map numbered nos 9–12, respectively, and since Aur 14 is missing altogether, no. 12 is the last star in Auriga. There are a few positions that deviate from those common in most medieval star catalogues.The stars Ari 9 and Ari 10 in the tail of Aries are south of the ecliptic instead of north and the star Navis no. 45 lies south instead of north of Navis no. 44. The names of the stars presented on the Vienna maps, summarized in Table 5A.1 in Appendix 5.1, include quite a number of unusual Arabic star names that do not occur in most medieval star catalogues.

The features 1–5 define a catalogue tradition which is exemplified by Vienna star catalogue in Vienna MS 5415 on ff. 217r–251v.106 This catalogue is greatly inflated with star and constella-

tion names compiled from several sources including texts translated from the Arabic, which accounts for most of the star names on theVienna maps.107 The stellar longitudes in the Vienna star catalogue are adapted for precession for the epoch 1424 by adding 18° 56´ to the Ptolemaic longitudes consistent with the mean value 18° 53´ ±21´ quoted above.The numbers of the stars in Andromeda deviate from the more usual order. The entry of Auriga consists of 12 stars only. The latitudes of Ari 9–10 are south instead of north of the ecliptic and the latitudes of stars nos 44 and 45 of Navis are respectively given as -75° 0´ and -77° 45´. The latter value deviates from the latitude -71° 45´ given in most medieval star catalogues, with the result that the star Navis no. 45 is south instead of north of Navis no. 44.There is one inconsistency: in the Vienna catalogue the latitude of Arcturus (Boo 1e) is given as 25° instead of 31° 30´ but on the map the latter correct value is used. Clearly, a very close copy of this Vienna catalogue was used in the construction of the maps or its model. The most outstanding feature of the constellation designs of the Vienna maps is that all human figures are without exception seen from the rear.108 No example of this way of presentation from earlier times existed in the Middle Ages.The only other document that comes close to the Vienna maps in this respect, but not quite, is the Farnese globe discussed in Section 2.6. In medieval illustrated manuscripts the constellations are sometimes drawn face-on, sometimes as seen from behind. Arabic globes present the constellation figures consistently in front view as the mirror images of the figures as seen in the sky. In short, the constellation images on the Vienna

106 These features were found already by Rosenfeld 1980, pp. 151–72 in her study of Dürer’s maps of 1515. See also Warner 1979, pp. 74–5.

373

107 Kunitzsch 1986b. 108 Dekker 1992.

the mathematical tradition in medieval europe maps do not fit into a specific medieval tradition and as such represent a unique highlight in celestial cartography. In 1927 Saxl suggested that the Vienna maps are a precise copy of an oriental model.109 Saxl’s argument is based on certain Arabic elements in the presentations of some constellations. As mentioned before, Arabic pictorial traditions in celestial cartography were transmitted to the Latin West mostly by way of the Ṣūfī Latinus corpus.The illustrations in the constellation cycle of this corpus are all connected through typical features of al-Ṣūfī’s uranography as, for example, the sickle in Hercules’s raised hand, the head of Ghūl carried by Perseus, an extended sleeve of Orion and a bunch of branches in the hand of Centaurus. The characteristics of Hercules and Perseus are included on theVienna maps but those of Orion and Centaurus are not. To complicate matters I like to mention the image of Lyra which on the map is drawn as a bird.This image results from a translation of an old Arabic name of Lyra or a few stars thereof,‘an-nasr al-wāqic’, meaning ‘the Falling Eagle’.110 The Latin name vultur cadens was introduced in the Latin West through star tables used in constructing astrolabes and through Gerard of Cremona’s star catalogue and this is behind Lyra’s image of a bird occurring in Western iconographic traditions but not in constellation cycles belonging to the Ṣūfī Latinus corpus.111 The examples mentioned here show that the background of the iconography of the Vienna maps is complex and that the author/ artist of its model seems to have borrowed from 109 Saxl 1927, pp. 25 and 38: ‘ein genaues Abbild einer orientalischer Vorlage’. 110 Kunitzsch 1961, p. 87, no. 195a; Kunitzsch 1974, p. 177; Kunitzsch 1986c, pp. 45–50. 111 On vultur cadens in star tables, see Kunitzsch 1966, the Types mentioned in the index on p. 127 and the additional types VIII.35, XI.22, and XIII.10.

a variety of existing traditions. It also shows that Saxl’s thesis of an oriental exemplar for the Vienna maps cannot be maintained, the more so since an Arabic tradition can neither explain presentations of the constellations in rear view nor can it account for the representation of the Milky Way drawn on the Vienna maps. As an alternative for explaining the unusual style of the constellations Roland suggested that in addition to Arabic influences there may have been antique examples at hand in Vienna.112 It is hard to substantiate this possibility. Considering the close connection between the maps and Gerard of Cremona’s Latin translation from the Arabic of the Ptolemaic star catalogue, I doubt that in particular the rear-view presentations of constellations on the Vienna maps can be explained by antique examples. It may not be satisfying to conclude that the constellation designs of the Vienna maps are not connected with a specific constellation cycle, yet in the absence of a clear link to any such cycle the thesis that especially its rear-view iconography was newly created while making a celestial globe is worth considering. Indeed, in shaping the constellations into rear view the astronomer/artist may have adapted images from a variety of sources, and this may account for one aspect of the complex background of the Vienna maps. Since the presentations on theVienna maps are internally consistent, in the sense that all human constellation figures are seen in rear view, the maker of the exemplar (model globe) of the Vienna maps must have applied a specific rule. The rule could have been suggested by the descriptive part of the Ptolemaic star catalogue, explaining where, in which part of the body, left 112 Mitteleuropäische Schulen V 2012, Kat. Nr. 77 (M. Roland).

374

5.3 MAPS IN THE MATHEMATICAL TRADITION or right and so on, a star had to be located. By insisting that a star described by Ptolemy in the right hand or in the left foot ends up on the globe in the right hand or in the left foot of a constellation all human figures are automatically presented from the rear. At the same time the shapes and attitudes of the constellations would agree with the Ptolemaic iconography as discussed in Section 4.4. The awareness of the significance of these descriptions in drawing constellations is seen in the Dyffenbach maps M1b– M1d, although there the maker did not succeed in drawing recognizable figures. The images in the Vienna maps may well be the final result of a number of now lost trials in this respect.Anyhow, the demand for correspondence between text and images gained importance in the fifteenth century. On most fifteenth- and sixteenth century maps and globes the human constellation figures are without exception drawn in rear view. But let me return toVienna MS 5415.As mentioned before, the star catalogue in this codex must have been very close to the one used for the Vienna maps and the question arises of how in particular the constellation designs in the maps and the star catalogue are related.The styles of the drawings in theVienna catalogue and of those on the Vienna maps point to work by different artists.113 Also the iconography of a number of the constellation figures in the star catalogue clearly differs from that in the maps. In the catalogue Cepheus is drawn upright instead of kneeling and he carries a sceptre and a globus cruciger, Bootes is equipped with an additional bow, Hercules is drawn in the star catalogue face on and carries a lion’s skin in his extended left hand, Cassiopeia is dressed and sits with outstretched arms on a 113 Mitteleuropäische SchulenV 2012,Kat.Nr.77 (M.Roland). Saxl 1927, p. 30, believed that the drawings on the maps and in the catalogue were by the same hand.

throne holding a small sphere in her left hand, and Orion’s tunic is turned into a more military outfit with a helm and a horn. The images of these constellations are not comparable with those in the maps.Those of Bootes and Cepheus point to a constellation cycle in a star catalogue which left its trace on the Dyffenbach map M1a. Other constellations such as Hercules, Cassiopeia, and Orion may derive from the same cycle. But what can be said about the other constellations? Looking at the zodiacal constellations one finds that some (Aries, Cancer, Leo, Libra, Capricornus, and Pisces) are close to the images on the maps and others (Taurus, Virgo, Sagittarius, and Aquarius) are the reverse of those on the map. Indeed, on both the map and in the catalogue Taurus extends his left leg in front of him,Virgo points with her right finger to her head,Sagittarius holds the bow in his left hand, and Aquarius the urn under his right arm.Thus the catalogue images ofTaurus,Virgo, Sagittarius, and Aquarius have the same left and right characteristics as those on the Vienna maps. Provided that the artist knew how to reverse an image it is possible that a number of zodiacal constellations on the maps were copied from the catalogue or vice versa. Of special interest in this respect is the image of Gemini in the catalogue. In Scheme 5.4 the schematic images of Gemini on theVienna maps and in theVienna star catalogue are presented. I have also added the image of Gemini in the map in Munich, Clm 14583, discussed later.The image in Munich, Clm 14583 in Scheme 5.4 is slightly adapted to correct the deformations caused by the binding in the manuscript (see Figs 5.18 and 5.20). It is clear that all three images present the twins in rear view, showing their backs.The attitude of the Gemini, especially the western orientation of their legs on the Vienna map and on the maps in Munich Clm 14583, are consistent with the stellar

375

the mathematical tradition in medieval europe

Scheme 5.4 The images of Gemini in Vienna MS 5415 f. 168r, f. 233v, and in Munich Clm 14583, f. 70v.

configuration as seen on a globe as it is described in the Ptolemaic star catalogue.The image of the Gemini in theVienna star catalogue, on the other hand, is clearly the mirror image—not the reversed image—of the other two (ignoring the bunches of flowers)!This mirror image of Gemini is significant because it cannot be traced to an Islamic celestial globe. It could only be derived ultimately from a globe in the Western, mathematical tradition as presented on theVienna maps. The example of Gemini suggests strongly that a number of zodiacal constellations in the catalogue were copied from a globe or a map and not the other way round. The image on the map in Munich, Clm 14583 in Scheme 5.4 confirms this. It suggests a scenario in which the artist of the star catalogue used a source related to a globe or map as his model, and copied some constellation images without modification (Aries, Cancer, Leo, Libra, Capricornus, and Pisces), reversed a few others (Taurus, Virgo, Sagittarius, and Aquarius) from globe-view to sky-view and presented one by its mirror image (Gemini). Such a scenario is confirmed by a few non-zodiacal constellations in the star catalogue. Most human figures are

again presented face on, as seen in the sky. The catalogue images of Ophiuchus and Andromeda could easily have been obtained by reversing the images on a globe or map.And here too one finds an exception. Centaurus (f. 249r) is presented in rear view and he holds the lance with his left hand, whereas on the southern map in Vienna 5415 and on the map in Munich, Clm 14583 he holds it in his right hand. Thus the catalogue image of Centaurus is the mirror image of the figure depicted on the southern map in Vienna 5415 instead of the reversed image. Taken all together, the iconography of the constellations in the Vienna star catalogue seems the result of merging an existing constellation cycle with images borrowed from a source stemming from the Vienna maps or its model. A glimpse of this mix may be seen on f. 247v where Crater is drawn twice: as a wooden tub with two handles placed on Hydra, as on the Vienna maps, and independently as a vase. As an aside I note that this scenario for the origin of the constellation designs is not contradicted by the relation between the illustrations in the Vienna star catalogue and those in Klosterneuburg,

376

5.3 MAPS IN THE MATHEMATICAL TRADITION Augustiner-Chorherrenstift, MS 125, ff. 6r–16r.114 This latter codex includes a constellation cycle illustrating excerpts of a text of Michael Scot (fl. c.1235), court astrologer to Emperor Frederick II.115 At the request of Frederick II Scot composed a work on astronomy and astrology, which includes a descriptive star catalogue Liber de signis. This medieval text includes a number of constellations which do not occur in the mathematical tradition and vice versa omits a few that are part of it.116 When the images in Klosterneuburg MS 125 are compared to those in the star catalogue in Vienna MS 5415, one sees that the presentations of the zodiacal constellations, among which is that of Gemini, agree.This holds also for a number of non-zodiacal constellations among which are Ursa Maior, Ursa Minor, Draco, Corona Borealis, Ophiuchus, Bootes (with sword in MS 125 and with traces thereof in MS 5415), a slightly adapted Perseus, Orion (with an ox-hide in MS 125), Navis, Canis Minor, Canis Maior, and Lepus.The presentations of a number of constellations, for example Hercules, Auriga, Andromeda, Eridanus, Centaurus, and Ara, in Klosterneuburg MS 125 are on the other hand in keeping with the characteristic iconography associated with Scot’s text.117 These typical Scot-illustrations are not found in the Vienna catalogue. For example, the image of Auriga in Klosterneuburg MS 125 is a driver on a wagon, which fits Scot’s iconography well in contrast to that in MS 5415 which seems to be the reverse of an image defined by the stellar configuration as it is described in the Ptolemaic star cata114 Klosterneuburg, Augustiner Chorherrenstiftes MS 125, ff. 6r–16r, see Haidinger 1991, pp. 33–34. I thank Martin Roland for bringing this codex to my attention. 115 Bauer 1983; Burnett 1994; Ackermann 2009. 116 Ackermann 2009, pp. 146–251. 117 Bauer 1983, pp. 44–46, Hercules; pp. 49–50, Auriga; pp. 53–55, Andromeda; pp. 61–63, Eridanus; pp. 72–74, Ara; pp. 74–76, Centaurus.

logue and as it is depicted on the Vienna maps. And although traces in the image of Andromeda in the catalogue inVienna MS 5415 show that the artist intended originally an image of this chained woman with trees at her side in keeping with Scot’s iconography, the attitude of the final image of Andromeda agrees with the reverse of an image defined by the Ptolemaic stellar configuration as it is depicted on theVienna maps.These examples of Auriga and Andromeda suggest that the artists of both cycles had access to more than one source, one being closely connected to Michael Scot’s star catalogue, the other a globe-related one. Alois Haidinger proposed that the images in Klosterneuburg MS 125, which can be dated to 1440 by watermarks, were taken partly from Vienna MS 5415 and partly from a cycle in the Scot tradition.118 This would explain indeed the agreements and disagreements between the two constellation cycles,but does not help us to understand the designs of a number of constellations in the catalogue in Vienna MS 5415 and their relation to theVienna maps. The complex background of constellation designs of the Vienna maps and of cycles created in or around Vienna in the first half of the fifteenth century shows at any rate that the artist of the globe-related source had a clear understanding of the reversal of images. Drawing the constellations on a globe such that the left and right characteristics in the Ptolemaic catalogue descriptions are preserved was clearly an issue in Viennese scientific circles. Although this does not answer unambiguously the question of the origin of the iconography of the Vienna maps, a globe-making thesis would allow an astronomer/artist to create his own rear-view

377

118 Haidinger 1980, pp. 101–9.

the mathematical tradition in medieval europe

Fig. 5.20 Map of the zodiac and UMi, UMa, and Dra in Munich, Munich Clm 14583, ff. 70v–71r. (Courtesy of the Bayerische Staatsbiliothek, München.)

designs from a variety of sources that must have been available to him in or around Vienna.

5.3.4 Other fifteenth-century maps The 1512 inventory of Regiomontanus’s estate mentions Imagines celj et alia.119 According to Zinner this refers to a now lost pair of maps like that in Vienna MS 5415, which supposedly were accompanied by a star catalogue for the epoch 1424 but which by 1512 would have become separated from that catalogue.120 The same maps may have been recorded in the 1522 catalogue of Bernard Walther who acquired a substantial part of the instruments and books of Regiomontanus:’ Facies stellarum fixarum. In pergameno depictae in 119 Zinner 1990, p. 250, no. 257. 120 Zinner 1990, p. 202, lists two copies of the 1424 catalogue in Nuremberg MS Cent.V 53 und V 61.

duabus tabellis’.121 Celestial maps are also listed in inventory of the Wiener Hofbiblothek made by Conrad Celtis, and a letter of 1512 by Johannes Cuspinianus, a member of the Vienna humanist circle, mentions another pair entitled: ‘imagines coeli australes et boreales in planum proiectas et artificiose formatas’.122 All these maps may have been modelled on the Vienna copies.Today two sets of manuscript maps remain, which are described in more detail in Appendix 5.1.123 One set survives in Munich Clm 14583,ff.70v–73r (Figs 5.20–5.22), 121 Zinner 1990, p. 252, no. 291a. 122 Voss 1943, pp. 90–1. 123 Grössing 1983, p. 150, mentions a pair of maps in Vienna MS 5268 f. 30v, a codex in the hand of Johannes von Gmunden. This turns out to be a ghost map.According to Kunitzsch (private communication), there is on f. 30v a star table of 44 stars computed for the year 1436, not a star map. On the next page, f. 31r, is another star table of 41 stars computed for the year 1432 with the remark ‘Et recepta ex Spera solida’.

378

5.3 MAPS IN THE MATHEMATICAL TRADITION

Fig. 5.21 Map of the constellations north of the ecliptic in Munich, Munich Clm 14583, ff. 71v–72r. (Courtesy of the Bayerische Staatsbiliothek, München.)

the other set is known as the Nuremberg maps of 1503. The codex Munich Clm 14583 was copied between 1447 and 1455 by Fredericus(Friedrich Gerhart), an industrious monk of St. Emmeram in Regensburg.124 In the period from 1436 to 1464 he transcribed in all eight codices on scientific topics. It is not clear what education Frederick received. According to Zinner he measured the altitude of the Sun with the help

of a globe but could not design the face of a sundial.125 In 1453 Fredericus was in Salzburg where he calculated a solar eclipse for 30 November of that year. He may have visited Vienna in 1456 but he was again in St. Emmeram in 1459, where he stayed until he died in 1463.126 The maps are in the first part of the codex with astronomical texts (ff. 1–76). The first 43 pages contain astronomical tables which are

124 Durand 1952, pp. 71–6. See also Meurer 2007, pp. 1177–8.

379

125 Zinner 1990, p. 44. 126 Meurer 2007, p. 1178.

the mathematical tradition in medieval europe

Fig. 5.22 Map of the constellations south of the ecliptic in Munich Clm 14583, ff. 72v–73r. (Courtesy of the Bayerische Staatsbiliothek, München.)

followed by a star catalogue with the title Composicio spere solide (ff. 44r–62v). At the end of the catalogue it says that it was written in Reichenbach in 1451. The star catalogue in Munich Clm 14583 is not illustrated and the longitudes of its stars are adapted to the epoch 1444 by a precession correction of 19° 6´. The stars are not numbered but those in Andromeda follow the same deviant order as in the catalogue in Vienna MS 5415. The latitudes of Navis nos 44 and 45 are respectively -75° 0´ and -21° 45´.The latter value should be -71° 45´.The catalogue in

Munich Clm 14583 is no doubt part of the complicated transmission pattern behind the Vienna catalogue, but it is not a direct copy of it. The catalogue is followed by a number of empty pages (ff. 63r–69v). On f. 70r, the page preceding the maps on ff. 70v–73r, is a list of the Ptolemaic constellations with the incipit: ‘Rota 48 ymagines celi’, dated 1454. On the pages following the maps, ff. 73v–76v, is a list of constellation names and the number of their stars stemming from the descriptive tradition and simple drawings of the constellations without text. These drawings

380

5.3 MAPS IN THE MATHEMATICAL TRADITION belong to a fifteenth-century tradition associated with Book III of Hyginus, De Astronomia. The maps are but poor copies astronomically speaking. One map, on ff. 70v–71r, presents the zodiacal constellations and Ursa Minor, Ursa Maior, and Draco (see Fig. 5.20). The zodiacal constellations are drawn north of the ecliptic instead of extending beyond it as they should. Another map on ff . 71v–72r presents all the nonzodiacal constellations north of the ecliptic (see Fig. 5.21).The third map on ff. 72v–73r shows all the non-zodiacal constellations south of the ecliptic (see Fig. 5.22).There are no stars marked in the maps nor are the constellations labelled. Only the names of the zodiacal signs are added in the maps. The style and shape of all figures agrees with those on the Vienna maps. The bunches of flowers in the hands of Gemini is the only feature that does not occur on the Vienna maps. How did this small difference between the maps in Munich Clm 14583 and theVienna maps come about? Either Gemini’s bunches of flowers were part of the exemplar used for copying the maps or they were not.The latter possibility can be dismissed because it would require a specific initiative from a rather careless copyist. Gemini’s bunches of flowers would thus have been on the exemplar, which implies that the Munich and the Vienna maps derive from a common exemplar rather than the one being a slightly adapted copy of the other. One can therefore reject Durand’s suggestion that Gensfelder had taken his celestial maps (that is to say, presumably those in Vienna MS 5415) to Reichenbach where they supposedly could have served as the example for Fredericus.127

127 Durand 1952, p. 116.

5.3.5 The Nuremberg maps In 1943 Voss published a study of a pair of manuscript maps, here referred to as the Nuremberg maps (Figs 5.23–5.24), which appeared to be closely related to the better known pair produced by Albrecht Dürer (1471–1528), Conrad Heinfogel (1470–1530), and Johannes Stabius (d. 1522), and published in 1515.128 These latter maps, usually referred to as Dürer’s maps because it was he who cut the wood blocks, proved extremely successful throughout the sixteenth century. Their iconography served as the model for the planisphere published by Peter Apian (1495–1552) in 1536 and reprinted with a different typeset in his Astronomicum Caesarum in 1540.129 Dürer’s figures were also used on the manuscript celestial globe of 1532 and the printed globe of 1536 by Caspar Vopel (1511–61), on that of 1537 produced by Gemma Frisius (1508–55) together with Gaspar van der Heyden (c.1496–after 1549) and Gerard Mercator (1512–95), and, for example, on the manuscript celestial globe made under the supervision of Johannes Praetorius (1537–1616) in 1566.130 Like Dürer’s maps of 1515 the production of the Nuremberg maps of 1503 was a cooperative undertaking, the participants of which are associated with poems in the corners of the southern hemisphere. In the right top corner is a poem paying tribute to Konrad Heinfogel (d. 1517) and Nuremberg. Below the poem is

128 Voss 1943.The relation with Dürer’s maps is discussed on pp. 119–22. 129 Apian’s planisphere of 1536 is described in Warner 1979, p. 10, and reproduced in Kunitzsch 1986c. 130 For Vopel’s globe, see Dekker 2010a; Gemma Frisius’s globe is described in Dekker 1999, pp. 87–91 and 341–2. For Praetorius’s globe, see my description in Bott 1992, vol. 2, pp. 637–8.

381

the mathematical tradition in medieval europe

Fig. 5.23 The northern hemisphere of 1503 (Courtesy Germanisches Nationalmuseum, Nuremberg, Inv. Nr. Hz 5576.)

Heinfogel’s coat of arms. Heinfogel entered the University of Erfurt in 1471 but spent most of his creative life in Nuremberg. He is especially remembered for his German translation of the Sphere of Sacrobosco and for his contribution to the production of Dürer’s maps of 1515.131 He seems to have worked with Bernard Walther (1430–1504), a wealthy Nuremberg merchant with a passion for astronomy who collaborated with Regiomontanus in making astronomical observations.132

In the bottom left corner is a poem on winds by the Dutch physician Theodorius Ulsenius (c.1460–1508) who spent much time abroad, especially in Germany (Nuremberg, Augsburg, Mainz, Freiburg, and Cologne).133 Ulsenius was not only a physician but also a poet and a close friend of Conrad Celtis.134 He published in 1496 in Nuremberg an astronomical-medical poem on syphilis which was illustrated by Dürer. Ulsenius left Nuremberg in 1501 when he moved to Mainz. He returned to his native country in 1507.

131 Heinfogel (Brévart 1981), p. II. 132 On Walther, see Zinner 1990, pp. 138–42, 144–7, and 157–61. Kremer 1980; Kremer 1981.

382

133 Santing 1992. 134 Santing 1992, pp. 130–5.

5.3 MAPS IN THE MATHEMATICAL TRADITION

Fig. 5.24 The southern hemisphere of 1503 (Courtesy Germanisches Nationalmuseum, Nuremberg, Inv. Nr. Hz 5577.)

Perhaps the most prominent person connected with the maps is Sebastianus Sperancius (d. 1525) presented in the bottom right corner as the man holding an armillary sphere as is explained in the text below him. He was a student of Celtis at the University of Ingolstadt. From 1499 until 1503 Sperancius lectured in Nuremberg and there made a sundial outlined by the mathematician Johannes Stabius (d. 1522) that still exists.135 In the following three years (1503–1506) he taught at the University of 135 Zinner 1967/1979, p. 539.

Ingolstadt but then moved to Brixen where he became secretary of Bishop Mattäus Lang. In 1521 Sperancius became Bishop of Brixen in which capacity a pair of globes was dedicated to him in 1522.136 The core of the Nuremberg maps, the stars and their constellations, recalls in many respects the Vienna maps. It is easy to see that the 1503 maps are based on a star catalogue belonging to 136 Oberhummer 1926. Chet Van Duzer informed me (February 2009) that the Brixen pair of globes is now at the Department of Rare Books and Manuscripts,Yale Center for British Art.

383

the mathematical tradition in medieval europe the Vienna tradition. For example, the numbers of the stars in the constellation Andromeda follow the deviant order occurring in theVienna star catalogue.The dependence of the Nuremberg maps on the Vienna catalogue is confirmed by the fact that on the northern hemisphere the stars Ari 9 and Ari 10 in the tail of Aries are south of the ecliptic instead of north, and on the southern hemisphere the star Navis no. 44 lies north of Navis no. 45. Also the precession correction applied to the stellar longitudes in the Nuremberg maps recalls the Vienna star catalogue. Voss has shown that the map’s stellar longitudes exceed the corresponding Ptolemaic ones for the epoch AD 137 by 18° 58´ ± 11´, which is close to the value of 18° 56´ used inVienna star catalogue and the Vienna maps.137 However, the two stars missing in Auriga in the Vienna star catalogue are included in the Nuremberg maps with the result that the stars are listed as nos 1–14. The Nuremberg maps are thus not straightforward copies of the Vienna maps. The most significant deviation from the Vienna maps is that the 1503 maps present the northern and southern hemisphere in stereographic projection. This means that the stars were plotted by using a latitude scale designed for stereographic projection using techniques known from the construction of astrolabes.This technique was known to Heinfogel, who used it on a parchment astrolabe preserved in his copy of Johannes Stöffler’s Almanac of 1499.138 It is not clear why stereographic projection was preferred above equidistant projection. Perhaps this choice was induced by the fact that the maps did not serve as a model for globe making, or because by this choice the problems of drawing oblique 137 Voss 1943, p. 113. 138 Voss 1943, p. 128.

circles in the equidistant projection are avoided since in stereographic projection all circles, inclusive of oblique ones, are presented as circles (or straight lines). It is worth noting that next to the polar circles small circles have been drawn around the north and south equatorial pole of the Nuremberg maps, as on the Vienna maps. The presence of these incomprehensible small circles suggests that a copy of the Vienna maps was at hand while the Nuremberg maps were constructed. Zinner has suggested that this copy may well be the lost maps of Regiomontanus.139 If these lost maps were faithful copies of the Vienna maps, quite a number of changes have been introduced on the 1503 maps in addition to the change in projection. For example, the Milky Way is left out of the Nuremberg maps and no star names have been added. The names of the constellations are written in capital letters and some names on the Nuremberg maps (OPHIVLCVS (sic), SAGITTA, EQVVS PEGASVS, ERIDANVS, ARA, and PISCIS NOTVS) replace the corresponding names on the Vienna maps (Serpentarius, ystius, equus volans, fluuius, sacrum thuribulum, and piscis meridionalis). The constellation designs on the Nuremberg maps follow closely those on theVienna maps in the sense that all are drawn from behind, although the artist of the Nuremberg maps has made a greater effort to turn the heads to show their faces. But there are also a number of iconographic differences. On the Vienna maps Cepheus, Bootes, Hercules, and Orion are dressed but on the Nuremberg maps they are nude. On the Vienna maps the constellations Hercules and Perseus show the Arabic impact on constellation design but on the Nuremberg 139 Zinner 1990, p. 252, no. 291a.Voss 1943, p. 116. See also Exhibition catalogue 1973, p. 21, Kat. 71.

384

5.3 MAPS IN THE MATHEMATICAL TRADITION maps this has vanished: Hercules hold a lion’s skin and a club while Perseus holds a proper Medusa head and has wings on his feet, in agreement with Greek-Roman mythology. Other iconographic adaptations are the ox head of Orion’s pelt and the presentation of Navis as only half a ship. The ox hide is mentioned by Michael Scot when he let Jupiter say: ‘excoria vitulum saginatum et pellem pone in urina tua et viri tui septem diebus, et nascetur tibi filius cui nomen erit Orion’.140 The image of Orion holding an ox hide is not exceptional in the fifteenth century. It occurs, for example, in Klosterneuburg, MS 125, f. 13v, a constellation cycle related to the cycle in Vienna MS 5415, and on Stöffler’s globe as discussed below.141 Although the artist of the Nuremberg maps is unknown he left his personal stamp on the maps through his style of drawing the constellations and the decorative elements in the corners of the maps. In the northern hemisphere are the images and the names of the four elements and the gods associated with them. On the southern hemisphere four compass directions are added across the celestial map and at the border of the map are sixteen wind heads and their names. Heinfogel’s preoccupation with winds is manifest from a manuscript drawing in his copy of Johannes Stöffler’s Almanac of 1499, with a compass rose and the names of 16 compass directions entitled: ‘Sunt in summa 64 ventorum species secundum Ulsenium frisium’.142 The addition of compass directions and wind heads in a celestial chart centred on the ecliptic is not functional since the relation between the horizon and the celestial sky is not fixed. Compass directions and wind

heads are more often added to maps of the world, depicting the lands and seas on earth where east and west have a permanent meaning.These and other decorative elements in the Nuremberg maps should be understood as an expression of an idea of the universe which extends beyond celestial charts such as theVienna maps. By introducing images of the planets, the four elements, and the winds around the celestial maps the designers of the Nuremberg maps have conceptually added a cosmographic dimension to celestial cartography.AsVoss has shown, this approach fitted well into the humanist outlook on the world in which celestial cartography was just a lesser aspect.This may explain why no effort was made to number the scale along the ecliptic or to adapt the stellar positions to 1500, a time close to the date of construction. From the point of view of celestial cartography the most conspicuous aspects of the Nuremberg maps are its use of stereographic projection and the introduction of the new humanist approach in constellation design based on classical form.143

5.3.6 A planisphere by an anonymous maker The oldest extant celestial map with constellations images in stereographic projection made in the Latin West (that is, not counting the retes of astrolabes which show only a selection of 20–50 stars) is a planisphere drawn on the back of a brass instrument known as the albion. Maps of this type are extremely rare.The only comparable map is John Blagrave’s Astrolabium uranicum of 1596.144 For a long time the present albion in the collection of the Museo Astronomico e

140 Ackermann 2009, pp. 218–19 and 390–1. 141 Haidinger 1991, pp. 33–4. 142 Voss 1943, p. 128.

143 Saxl 1927, p. 35; Panofsky and Saxl 1933, pp. 240–1. 144 Warner 1979, pp. 32–3.

385

the mathematical tradition in medieval europe

Fig. 5.25 Planisphere on the back of an albion. (Reproduced from Turner (G) 1991, p. 70.)

Copernicano in Rome was listed among the objects stolen from the museum in 1984.145 Recently it became clear that it was mistakenly placed on that list.The present discussion is based on a picture of the map (Fig. 5.25) which allows only a few superficial remarks.146 The map in the stereographic projection extends from the north equatorial pole to a declination of around 35° south. The planisphere thus differs from the Nuremberg maps which are drawn in stereographic projection centred on the ecliptic poles. Since positions in star catalogues are usually available in ecliptic coordinates only, the maker of the present planisphere has inaccurately engraved a grid consisting of great circles through the ecliptic pole and parallels to the ecliptic. How to draw such a grid was 145 ‘Theft of Instruments in Rome’, Bulletin of the Scientific Instrument Society, no. 4, 1984, p. 18. 146 The picture is from Turner (G) 1991, p. 70.

well known from the construction of astrolabes since it coincides with a grid of lines of constant altitude and azimuth for a plate for (geographical) latitude equal to 90°-ε, where ε is the obliquity of the ecliptic. In a range extending 6° north and south of the ecliptic the parallels to the ecliptic have been engraved for every 1° to mark the zodiacal band. In addition the Equator and the tropics are engraved.A scale for declination numbering every 6° is added along the solstitial colure and a scale for ecliptic latitude numbering every 6° along the great circle passing through the ecliptic pole and the equinoxes. The stars are marked by small crosses of different sizes. Not all constellations engraved on the plate are drawn as seen on a globe and not all of the 48 Ptolemaic constellations are presented. Since the map is cut-off at a southern declination of 35°, a number of constellations are incomplete. The tip of the tail of Scorpius and the legs of Sagittarius are absent and only the westernmost part of Navis,the head of Centaurus, and the legs of Lupus are seen. Completely absent are Ara and Corona Australis. The design of the constellations has a number of conspicuous features. Cetus is drawn in an attitude that makes him stand more or less face on. Hydra is presented with dragon’s wings. Aquarius is naked apart from a piece of cloth drawn around his body and he holds an urn in his right hand.Virgo is drawn face on, with wings and her northern hand pointing upwards where it is cut by the Tropic of Cancer.The branch held in her northern hand recalls the image of the ivy leaf on some Islamic globes (see for example Fig. 4.17).Yet, the present map does not exhibit many Arabic features. Hercules is presented with a club and a lion’s skin, Perseus has wings around his feet, Lyra is drawn as a lyre, and Orion has a piece of cloth or skin in his left hand, not an extended

386

5.3 MAPS IN THE MATHEMATICAL TRADITION sleeve. Neither does the iconography of the planisphere fit into the Vienna map tradition. This raises the question of where and when the map was made. The albion was invented in 1326 by Richard of Wallingford (1292?–1336), abbot of St. Albans.147 It is part of a class of instruments designed for calculating the positions of the Sun, the Moon, and the planets. Usually these instruments consist of a series of plates but the albion, meaning ‘all-by-one’, combines the various discs into one plate. North, who studied the treatise written by Wallingford in great detail, proposed a date for the present albion/ planisphere in the fourteenth or early fifteenth century.148 The Viennese astronomer John of Gmunden revised and expanded the treatise by Richard of Wallingford in the first quarter of the fifteenth century.149 The albion was among the collection of instruments bequeathed by John of Gmunden to the university of Vienna and the albion is also mentioned among a series of instruments in the abbey of Reichenbach.150 According to Poulle it is not possible to decide from what is left of the present albion whether its construction follows the description of Richard of Wallingford or that of John of Gmunden.151 Stellar positions are sometimes helpful in establishing a date. Although it is not possible to measure the stellar positions accurately from the picture in Fig. 5.25, one can say that the map is compatible with an Alfonsine epoch of 1252. For example, with an Alfonsine precession correction of 17º 8’ , the star on the end of the 147 148 149 150 151

North 1976. North 1976, p. 274. Hadrava and Hadravová 2006. Uiblein 1988, p. 61; Durand 1952, p. 334. Poulle 1980, p. 406.

front leg of Canis Maior (CMa 9) is west of the solstitial colure and the more advanced of the stars in the left knee (CMa 10) is east of it.152 The positions of the stars in the legs of Canis Maior on the planisphere agree with these positions. If correct, the epoch of the planisphere (1252) is not indicative for the date of production of the planisphere. Although the use of an Alfonsine epoch is not inconceivable, a more detailed study of the star positions on the instrument is needed to confirm this hypothesis. A date can also be surmised from the style of some the constellations drawings.The image of a dragon with wings, used on the planisphere for Hydra, occurs in a cycle of constellation drawings stemming from Michael Scott in Oxford, Bodleian Library, MS Can. Misc. 554 (north Italy, second quarter of the fifteenth century).153 In the illustrated manuscript of the fifteenth century with Germanicus’s Aratea, Florence, Biblioteca Laurenziana, Plut 89, sup 43 (Florence, 1470), Cetus is a presented on f. 43r as a winged dragon.154 The iconographical characteristics of the images of Draco, Serpens, Cetus, and Hydra are easily transferred from one constellation to another. The wings of Hydra on the present planisphere fit into this and are compatible with a date in the fifteenth century and possibly Italy as the place of production. Hopefully a detailed study of the instrument is feasible in the near future and a better assessment of its date and place of production can be made. 152 The positions of CMa 9 and CMa 10 in the Alfonsine star catalogue for the epoch 1252 are respectively 88º 8’ and 91º 48’. 153 Saxl and Meier 1953, pp. 341–4. Image available in Iconographic Database of The Warburg Institute, see the drawing in MS Can. Misc. 554, f. 161v of Serpens. 154 McGurk 1966, pp. 26–7. Image available in Iconographic Database of The Warburg Institute, see the drawing in Biblioteca Laurenziana, Plut 89, sup 43, f. 43r of Cetus.

387

the mathematical tradition in medieval europe

. GLOBES IN THE SERVICE OF ASTROLOGY

of the north equatorial pole on the altitude scale in the globe drawing shows that a latitude of around 48º for Vienna is used, suggesting that The first Western globe maker known by name the drawing represents a real globe. A noticeable is Jean Fusoris (ca. 1365–1436) who studied feature on the horizon ring is its combination medicine at the University of Paris.155 He of scales of the zodiac and the calendar. This obtained his bachelor’s degree in 1379 and his combination serves to find the place of the Sun master’s in 1391. He had a workshop in Paris, in the zodiac at a certain day of the year and, as the first of its kind, where he made all sorts of mentioned in the Tractatus de sphaera solida, was instruments, especially astrolabes. After a visit commonly engraved on the back of astrolabes.157 to England he was accused of espionage and In addition to the scales of the zodiac and the exiled to Mezieres-sur-Meuze and later to calendar, there is a scale for the azimuth. On the Reims. He continued to make instruments outer border of the horizon ring the names of while in exile. Before he left for England Fusoris the points of the compass are added. In this pichad written a text on globes, compositio revolu- ture the celestial sphere itself is marked by a tionum spere solide, presumably to accompany number of circles: the Equator graduated four the globe he made for King Henry V. Another times 0º–90º, the ecliptic graduated twelve times globe was made in 1410 for Pope John XXIII. 0º–30º, the circles of constant longitude for Unfortunately nothing more is known about every 30º, the tropics and the north polar circle, these Fusoris globes. as described in the Tractatus de sphaera solida. More can be said of the sphaera solida men- How the constellations would have been drawn tioned in the will of Johannes of Gmunden.156 on the sphere of John’s globe is shown by the This globe was almost certainly made after the Vienna maps discussed above. instructions in the treatise Tractatus de sphaera John’s globe was probably one of a series made solida in Vienna MS 5415 (f. 161r–191r) men- by members of the Vienna astronomical school. tioned above.The detailed drawing of a globe in In his Viri Mathematici the Viennese mathematithis treatise on f. 180v (Fig. 5.26) may give a fairly cian and astronomer Georg Tannstetter (1480/ good idea of John’s globe. 82–1530/35) described short biographical notes The sphere is mounted at the equatorial poles on fourteenth and fifteenth century astronomers. in a meridian ring which is placed in a stand Of Georg Peurbach (1423–61), the Viennese with four legs (only three are seen in the draw- astronomer and inventor of instruments, it says ing) supporting the horizon ring.The meridian that he made several ‘spaeras solidas’.158 These ring has three graduated scales: one scale for globes would in all probability also be designed declination and another for its complement.The after the Vienna pattern. outermost scale for altitude is not described in In the second half of the fifteenth century the treatise Tractatus de sphaera solida. This scale globes were also made in Rome. Bills dated depends on geographical latitude. The location 1477 mention globes by Nicolaus Germanus 155 Poulle 1963, pp. 86–8. 156 Uiblein 1988, p. 61.

157 Chlench 2007, p. 98. King 1995a, p. 376. 158 Graf-Stuhlhofer 1996, p. 158.

388

5.4 GLOBES IN THE SERVICE OF ASTROLOGY

Fig. 5.26 Drawing of a celestial globe in Vienna MS 5415, f.180v. (Courtesy Österreichische Nationalbibliothek, Vienna, Picture Archive.)

389

the mathematical tradition in medieval europe (ca. 1420–ca. 90).159 Germanus started his scientific career in the monastery of Reichenbach, where successive abbots fostered his interest in astronomy.160 His skill in globe making may well be connected with the Viennese tradition. His globes are listed in an inventory of 1481 of the Vatican Library: an Octava Sphera (a celestial globe), and a Cosmographia (a terrestrial globe) exhibited in the Pontificia (the Library), and again in an inventory of 1487 where it is said: ‘Spera in qua et terrae et maria ex Ptolemaeo cum orizonte. Spera in qua signa caelestia cum suis polis et elevationibus’.161 Today only two celestial globes of the fifteenth century remain, which are described in more detail in Appendix 5.2.162 One of the extant globes was owned by Martin Bylica (1433/4?–93?), a famous astrologer.163 Bylica entered the University of Cracow in 1452, where a chair in astrology was held by Andreas Grzymalas. In 1456 Bylica received his bachelor’s degree and three years later his master’s. He lectured at Cracow University from 1459–1463. In 1463 he continued his studies in Italy, at the universities of Padua and Bologna, and lectured there on various astrological issues in 1463/64. As court astrologer of Cardinal Rodericus Borgia he visited Rome in 1464 and there met Johannes Regiomontanus, who had come to Rome at the invitation of Cardinal Bessarion. The dialogue written by Regiomontanus, ‘Dialogus inter Viennensem et Cracoviensem adversus Gerardum Cremonensem in planetarum theoricas deliramenta’,

with a discussion between Johannes fromVienna and Martin from Cracow, immortalizes the meeting between these two astronomers.164 Regiomontanus and Bylica were invited to Hungary to take up posts at the newly founded University of Poszony, for which foundation Matthias Corvinus, King of Hungary from 1458–90, had received a papal charter on 19 May 1465 through the kind offices of Janus Pannonius, a nephew of archbishop of Gran, and Chancellor of Hungary János Vitéz (1408–72).165 Before moving to Poszony, Regiomontanus and Bylica stayed at the archbishop’s palace at Esztergom where Regiomontanus produced with Bylica’s help his Tabulae directionem profectionumque with tables for calculating the boundaries of the mundane houses and directions for their use.166 In July 1465 the two astronomers moved to Poszony. While in Hungary, Regiomontanus worked on the construction of instruments. He wrote a treatise on the torquetum, dedicated toVitéz and a treatise on the regula ptolemaei (also called triquetum) which he dedicated to King Matthias.167 Regiomontanus left Hungary in 1471 when he went to Nuremberg to carry out his ideas to reform astronomy. Bylica’s astrological commitment is evident from the horoscope cast for the opening of the university of Poszony on 5 June 1467, his lectures on astrology, and, for example, from a dispute with Jan Stercze, court astrologer to János Rozgon, held in 1468 before the Hungarian Diet in Poszony.168 Bylica seems to have had the upper hand in the debate and was awarded 100 florins.After the decline of the University, Bylica

159 The Latin text of these bills is in Ruysschaert 1985, p. 95. For a translation in English, see Babicz 1987, pp. 161–2. 160 Durand 1952, pp. 80–3. 161 Ruysschaert 1985, pp. 97–8. 162 I do not count here the unfinished globe described by Hartmann 1919, pp. 42–50. 163 Birkenmajer 1972; Vargha and Both 1987; Hayton 2007.

390

164 165 166 167 168

Hayton 2007, pp. 187–8. Gabriel 1969, pp. 38–9. Zinner 1990, p. 92. Zinner 1990, pp. 98–100. Zinner 1990, pp. 91–2; Hayton 2007, pp. 185–6.

5.4 GLOBES IN THE SERVICE OF ASTROLOGY spent the best part of his life as an astrologer at the court of King Matthias who died on 6 April 1490. Thereafter Bylica remained in Hungary and died a few years later in 1493. He donated his instruments—a celestial globe, an astrolabe, and a torquetum—to his home town university in Cracow where they have been since 1494.169 For centuries these instruments were in the library of the Collegium Maius but in 1953 they were transferred to the Jagiellonian University Museum. The celestial globe of 1480 and the astrolabe of 1486 carry the coat of arms of Bylica showing Sagittarius above a rose with five petals in the centre of the field, with sunrays emanating from a starry symbol in the top right corner. On top of the field is a hat with double tasselled ropes characterizing the title of Protonotary Apostolic held by Bylica.170 All three instruments donated by Bylica to his alma mater have been attributed to Hans Dorn.171 This instrument maker was born in Austria between 1430 and 1440 and studied astronomy in Vienna between 1450 and 1461, first under Georg Peurbach and then under Regiomontanus. Dorn learned his skills in instrument making from Peurbach. According to Tanstetter Dorn was a capable instrument maker who made three globes:

The precise whereabouts of Dorn in the 1560s are not known. It seems that he arrived in Buda before 1478 because from a record in the Nuremberg archives it follows that King Matthias sent him in that year to Nuremberg to buy the instruments and books of Regiomontanus. Dorn’s efforts were in vain and he returned empty-handed to Buda.173 Back in Hungary Dorn made a number of instruments for Bylica. After King Matthias had died Dorn returned to his monastery in Vienna where he continued to make instruments, witness of which is a horizontal sundial in the British Museum, signed ‘DAS CHOMPAS IS GERECHT AVF ALLE LAND VND HAT GEMACHT PRVDER HANNS DORN PREDIGER ORDEN VON WIEN ANNO DOMINI 1491’.174 Letters of 1501 by Thomas Dainerius, a secretary of the nuncio in Buda, confirm that Hans Dorn also made instruments for King Laudislaus II, the successor of Hungarian King Matthias, in particular an astrolabe and a sundial.175 He died in 1493. Let me now turn to Dorn’s globe shown in Fig. 5.27. In basic outline it resembles the type of globe shown in the drawing in MS 5415 in Fig. 5.26 but it has a number of features that set it a apart from the Vienna globe. It consists of a sphere mounted in an adjustable meridian ring supported by a ‘Joannem Doren eorundem instrumentorum elaborastand with a horizon plate (Fig. 5.28) but there the torem artificiosissimum. Hic postea ordinem fratrum predicatorum ingressus, ibidem varia instrumenta ex aere: agreement stops as far as the construction is connoviter vero sphaeras solidas tres mirae magnitudinis cerned. Conspicuous for the time of production diligenter elaboravit.Vixit hic frater Joannes in monaste- is the hour circle (Fig. 5.29) which must be a later rio fratrum predicatorum usque in annum christi 1509 addition to judge by its modern lettering. The ubi magno confectus senio quievit in pace.’172 sundial in the south corner of the horizon plate is conspicuous for better reasons (Fig. 5.30). Its novel

169 All three instruments are shown in Levenson 1991, pp. 221–4, nos 120–22. 170 Ameisenowa 1959, Fig. 2. 171 Zinner 1967/1979, pp. 292–7. 172 Graf-Stuhlhofer 1996, p. 164.

173 Zinner 1990, p. 157. 174 Details can be found on www.mhs.ox.ac.uk/epact/ [accessed 21 March 2012]. 175 Zinner 1967/1979, p. 293 and Ameisenowa 1959, p. 46.

391

the mathematical tradition in medieval europe

Fig. 5.27 The celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

392

5.4 GLOBES IN THE SERVICE OF ASTROLOGY

Fig. 5.28 Horizon of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

Fig. 5.29 Hour circle of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

design with a magnetic compass with the needle showing a variation of 10° is the invention of Peurbach, Dorn’sViennese teacher.176 In order to use the globe it has to be adjusted to local conditions.This involves three steps. First the meridian ring (Fig. 5.31) has to be aligned with the local meridian plane. This could have been done using the compass on the horizon ring. Other methods were known to find the local meridian line but the use of a compass for this is novel. When the meridian ring is in the local meridian plane the wind directions engraved on the horizon plate agree with the real directions of a place. Next one has to adjust the globe to the proper geographical latitude by turning the mobile meridian ring in its own plane until the elevation of the pole above the horizon ring agrees with the latitude of the place. The last step is to rotate the sphere around its own axis to make the stars on the sphere correspond to those in the sky overhead. In daytime this can be done with the help of the Sun, whereas at night the stars can be used. In globe treatises it is recommended to place a peg on the place of the Sun in the zodiac, and then turn the sphere until no shadow is seen. This method works of course only in daytime. With Dorn’s globe the problem is easily solved for day and night with the astrolabe disc placed on top of the meridian ring. The mobile support of the disc consists of two quadrants which extend to the horizon plate and can rotate with the support in azimuthal direction. By turning the quadrants round the zenith and using the alidade of the astrolabe disc on top (Fig. 5.32) one can sight the Sun or a star and fix the azimuth of the celestial object. Next the celestial sphere is turned until

393

176 Zinner 1967/1979, p. 464.

the mathematical tradition in medieval europe

Fig. 5.30 a–b Sundial on the horizon of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

Fig. 5.31 Meridian ring of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

394

5.4 GLOBES IN THE SERVICE OF ASTROLOGY

Fig. 5.32 The orthographic grid at the back of the astrolabe disc at on top of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

Fig. 5.33 Mundane house on the astrolabe disc on top of the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

the Sun (whose position on the zodiac for a specific time of the year can be found on the horizon ring) or the star concerned is under the appropriate quadrant.Then the celestial configuration on the globe corresponds with that in the sky. This method, using the azimuth direction of the celestial object, cannot be applied with a common astrolabe because with this latter instrument only altitudes can be measured. If the altitude of the Sun is measured using the umbra recta and versa scales on the astrolabe disc on top of the globe, one can determine simultaneously what time it is by using the zodiacal ring in combination with the equal and unequal hour lines on the one side (Fig. 5.33) or with the orthographic grid on the other side of the astrolabe disc (Fig. 5.32).To find the time at night, one can after having sighted a star read off where the ecliptic is intersected by the horizon plate and enter this

into the side of the astrolabe disc with the zodiac ring. The zodiacal ring and the unequal hour lines are traditional features of the common astrolabe.177 The grid in the orthographic projection is a later development. It is engraved on the back of an astrolabe made by Regiomontanus in 1462 and other astrolabes belonging to the same tradition.178 As an aside I note that in the fifteenth and sixteenth century the grid in the orthographic projection is sometimes labelled organum ptolemei.179 This label refers to the method of constructing a specific set of declination lines in the orthographic projection corresponding to certain moments that the Sun is in the zodiacal signs

395

177 Proctor 2005. 178 King and Turner 1994. 179 Zinner 1967/1979, pp. 130–4.

the mathematical tradition in medieval europe are fixed by the intersections between the ecliptic and the ‘circles of positions’, passing through 30º divisions of the Equator (see Scheme 5.5). Fixed boundary methods have the advantage that they can be marked graphically, and thus greatly simplify the determination of the houses. The astrolabe disc on top of Dorn’s celestial globe is engraved with a grid of lines of the boundaries of the mundane houses fixed by the equatorial method for a latitude of 47.5º (Fig. 5.33).The main boundaries of the 12 houses are marked by dots. Each house is subdivided by curves into 10 subsections. A series of construction dots on a straight line Scheme 5.5 The boundaries of the mundane houses mark the centres of the circles of the mundane after the equatorial method are fixed by the intersections between the ecliptic and the circles of houses. On top of this pattern of boundaries is the positions passing through 30º divisions of the Equator. already mentioned zodiacal ring with a ruler. To make a horoscope an astrologer would have in the course of a year. In earlier medieval litera- to know the time of birth.This is used to set the ture the label organum ptolemei was used for recti- ecliptic on the astrological plate (Fig. 5.33) in the linear dials, as for example the navicula and right position.Then the points of intersection of Regiomontanus’s dial with straight parallel lines the ecliptic and the lines of the mundane houses marking the hour lines.180 The grid in the ortho- can be determined. By using the point of intergraphic projection differs conceptually from section of the ecliptic and the horizon the celestial rectilinear dials, if only because the hour lines are sphere can also be set to correspond to the celestial sky at the moment of birth. The astrological sections of ellipses, not straight lines. The main function of the astrolabe disc on top function of Dorn’s globe is further emphasized by of the globe is, however, to find the mundane the planetary natures of the stars marked on it.The houses for making horoscopes. Various methods astrological characteristics of the fixed stars are were available to determine the boundaries of the expressed by means of the influences thought to mundane houses. One, known as the prime verti- be exerted by the planets. All this makes Dorn’s cal method, is commonly ascribed to Campanus, globe a suitable aid for an astrologer. Let us now consider in more detail the stars another was known as the equatorial method and the credit for it is often given to Regiomontanus.181 and the constellations engraved on the sphere. As north has shown, these two fixed methods The longitudes of the stars on Dorn’s globe difwere known long before in Arabic literature and fer with respect to the corresponding Ptolemaic used on Eastern astrolabes. In the equatorial values by 19° 56´ ± 12´, which averaged value method, the boundaries of the mundane houses and standard deviation were obtained by measuring the ecliptic longitudes of 24 stars located close to the ecliptic. How to interpret this value 180 Eagleton 2010, pp. 93–119. 181 North 1986, pp. 27–30. is not clear. Ameisenowa states that—following 396

5.4 GLOBES IN THE SERVICE OF ASTROLOGY the calculations of Birkenmajer—the stellar positions correspond to their actual positions in the sky in 1586, which is 106 years after the date of production of the globe. Even more mysterious is her remark that ‘from this result Birkenmajer concluded that the position of the stars on the globe was set for 1424 according to the AlfonsianTables’.182 The Alfonsine precession correction for 1424 used in the Vienna catalogue is 18° 56’, which is 1° less than the precession correction of Dorn’s globe. There are in principle two ways to determine the precession correction: by calculation or by observation. If the stellar positions on Dorn’s globe were corrected by calculation we may assume that the Alfonsine trepidation theory was used.Then the value of 19° 56´ would correspond to an epoch of about 1532.183 At face value there seems to be no good reason to calculate the precession correction for a date about 50 years ahead. However, it would be a feasible choice if the maker wanted to ensure the validity of his globe for the next 100 years.Thus this interpretation cannot be ruled out. If the precession correction was determined by observation one can predict what value applies for the year 1480. Since there is a systematic error in the Ptolemaic star catalogue of around 1° it is best to calculate the stellar positions in 1480 by precessing the accurate stellar longitudes in the star catalogue of Tycho Brahe (for the epoch 1601). Using an averaged modern rate of 1° in 72 years one arrives at a precession correction of 19° 40´ for 1480, which is 16´ less than the value 19° 56´ ± 12´obtained here. Since errors can easily

amount to 10´ we cannot rule out this way of explaining the globe’s precession correction either. In the absence of a definite explanation I am inclined to think that the globe maker found it convenient to adapt all 1025 stellar longitudes in a 1424 catalogue simply by increasing the longitudes by 1°, and thus validate his globe for the period of 1480–1580. Whatever the precise interpretation of the globe’s precession correction may be, it is certain that the catalogue used by Dorn belonged to the Vienna tradition. Since the stars on the globe are not numbered, it is not possible to compare the ordering of the stars in Andromeda and in Auriga with that in the star catalogue inVienna MS 5415. However, the star in the right knee of Auriga (Aur 14) is missing on the globe as in the Vienna map and catalogue. Further, the stars in the tail of Aries (Ari 9 and Ari 10) are south of the ecliptic (Fig. 5.34) and star no. 45 in the rudder of Navis is south of star no. 44 (Fig. 5.35), as in the Vienna map and catalogue. The nomenclature on Dorn’s globe does not follow in all respects theVienna tradition.All the names are engraved in capital letters. Some constellation names on Dorn’s globe (AVRIGA,

182 Ameisenowa 1959, p. 15. I cannot verify her statement because the paper she refers to is written in Polish and not accessible to me. 183 As an aside I note that the precession correction of the stars on Dorn’s astrolabe of 1486 is 19° 23’ ± 8’. In terms of the Alfonsine trepidation theory this would correspond to an epoch of 1472, which is not bad at all for an astrolabe made in 1486.

397

Fig. 5.34 Aries on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

the mathematical tradition in medieval europe 1486 astrolabe. These are two names in Orion, IVGVLA A OR (α Ori) and IVGVLA B OR (γ Ori), and one name in Cetus, MENTVM (α Cet). Iugula and Jugulae are names used in Roman sources for Orion or his belt.184 On Dorn’s globe IVGLA A OR and IVGVLA B OR are used for the stars on the shoulders of Orion (Fig. 5.36).The label MENTVM is on the globe in the same location as the name Menkar on the Vienna map. Menkar is a medieval Arabic name used for the first star in Cetus (α Cet). On Dorn’s astrolabe of 1486 the position of the star labelled MENTVM agrees with the position of α Cet.

Fig. 5.35 Argo on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

SAGITTA, AQVLA, EQVVS PEGASVS, ERIDANVS, ARA, and PISCIS MERIDIANVS) replace the corresponding names on the Vienna maps (Agitator, ystius, vvlt(vr) volans, equus volans, fluuius, sacrum thuribulum, and piscis meridionalis). Most of these alternative names occur in the Vienna star catalogue.Whereas star names in the middle of the fifteen century are still determined by transliterations from the Arabic, Dorn’s globe exhibits the trend for marking the stars by Roman or Latin labels, see Table 5A1 (p. 412). The stars which on the Vienna map are called alhayoth and denebkaytoz, are labelled on the globe respectively HEDVS and CAVDA. Indeed,of the 17 names there are six (ACARNAR (θ Eri), ALDEBORA (α Tau), DVBHE (α UMa), MARKEB (τ Pup), RIGEL (β Ori), and SVEL (α Car)) which still reflect the medieval Arabic nomenclature. A few names are unusual but typical for Dorn, since they occur also on his 398

Fig. 5.36 Orion on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.) 184 Le Boeuffle 1977, pp. 129–33.

5.4 GLOBES IN THE SERVICE OF ASTROLOGY Latin. In 1467 a copy was made for the library of King Matthias. 186 It may be taken for granted that Trezibond’s translation was known in Buda. Yet, there is no good reason why a label for the fourth, insignificant star should be transferred to the first star of Cetus (α Cet). Finally a few words should be said about the iconography of the constellation images of Dorn’s globe. Considering his Viennese background it is no surprise that the designs follow in the main the Vienna tradition as exemplified by the maps in Vienna MS 5415 discussed above. Yet there are a few significant deviations from the maps. For example, Bootes is engraved as a nude figure instead of being dressed. Cassiopeia is no longer nude but wears a long dress and a kerchief over her head which covers her face and extends to her shoulders and she holds no

Fig. 5.37 Cassiopeia on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.)

It seems therefore that MENTVM was meant as a replacement for Menkar, but according to Kunitzsch the name cannot have been derived from Menkar. A reference to mentum is used for the fourth star in the entry of Cetus, ‘Praecedens de tribus & est in mento’, in the Latin translation of Ptolemy’s Almagest made about 1451, at the request of Pope Nicholas V, directly from the Greek by the humanist George of Trezibond, or Trapezuntius (1395–1484).185 This humanist version of the star catalogue differs from Gerard of Cremona’s Latin translation from the Arabic by the use of what humanists considered ‘good’

185 The first printed edition of Trapezuntius’s translation appeared in 1528, see Trapezuntius 1528.

399

Fig. 5.38 Hercules on the celestial globe attributed to Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.) 186 Monfasani 1976, p. 194.

the mathematical tradition in medieval europe Compared to the maps the most striking change on Dorn’s globe for me is the image of Cassiopeia (Fig. 5.37). Can one see in it the woman who boasted that her beauty surpasses that of the Nereids? In the star catalogue Vienna MS 5415, f. 224v Cassiopeia is presented with certain elegance, which cannot be said of Dorn’s image. Dorn’s Cassiopeia with her awkward hands contrasts strongly with the other well engraved constellations. These latter images could have been inspired by the constellation cycle of the star catalogue Vienna MS 5415, the Vienna maps, or copies thereof. The lion’s skin in the image of Hercules seems to be a new element compared to the Vienna maps but this attribute is already part of the image of Hercules in the star catalogue inVienna MS 5415, f. 222v. It is a central theme in the discussion of Ameisenowa who interprets it as a correction of ‘the change introduced by the Arabs’.188 The mythological Hercules is not part of the Ptolemaic iconography proper.The theme Fig. 5.39 Perseus on the celestial globe attributed to of the reintegration of classical form developed Hans Dorn. (Courtesy of the Jagiellonian University Museum, Cracow, Inventory no. 4039–37/V.) by Saxl is, within the context of the present study, one of introducing myths in the mathematical attribute in her excessively large hands (Fig. 5.37). tradition in map and globe making.This process Hercules still holds a curved sword in his raised may have been helped by the fact that the artists right hand but is now presented more explicitly of constellation cycles in illustrated Ptolemaic as a warrior in a suit of armour and a lion’s skin star catalogues seem to have borrowed, among is added to his left hand (Fig. 5.38). Orion still has others, from those belonging to the descriptive a club in his raised right hand and a sword in a tradition. On Dorn’s globe Hercules does not scabbard but he too is dressed in a suit of armour. yet have the classical shape with which he is He has been given a Phrygian hat to wear and presented in the early fourteenth century on holds a cloth in his raised left hand instead of an Cusanus’s globe (Fig. 5.9) discussed above in animal skin (Fig. 5.36).187 Crater is a kettle with Section 5.1 and on the Nuremberg maps one handle instead of a wooden tub with two (Fig. 5.23). The constellations Perseus and Lyra are more telling about the trend to rectify Arabic handles as on the Vienna maps. iconography: Perseus still carries the head of 187 Ameisenowa 1959, p. 27 sees this as ‘a torch flame downwards’.

400

188 Ameisenowa 1959, p. 39.

5.4 GLOBES IN THE SERVICE OF ASTROLOGY Ghūl, the desert demon, in keeping with the Ṣūfī Latinus tradition (Fig. 5.39) and Lyra is still drawn as Vultur volans.189 A prominent element in the iconography of Dorn’s globe seems to be that Hercules and Orion are dressed in suits of armour. Their armour may have been borrowed from the images in the star catalogue in Vienna MS 5415, f. 222v and f. 243r, respectively. However, on the globe Orion wears a Phrygian hat, not a proper helm. In the illustrated manuscript in Florence, Biblioteca Nazionale Centrale Angeli MS 1147 A.6, dating from the second half of the fifteenth century, four constellations are dressed in armour and all wear a helmet: Hercules (without a lion’s head), Perseus (without sword but with a proper Medusa head), Auriga (with goat and harness), and Orion (with club, sword and a pelt). This cycle must stem from a globe because the east– west orientations of the constellations are as seen on a globe and all human figures are in rear view.190 In this connection it is also worth mentioning the celestial hemisphere of the Old Sacristy in Florence. This fresco presents half of the celestial sky, which at a certain time, July 1442, was above the horizon in Florence, and all constellations are consistently facing the viewer in keeping with Hipparchus’s rule. 191 Two of the visible figures on the fresco, Perseus and Orion, are also dressed in armour. The trend to present constellation figures as warriors, as seen in the Vienna maps and star catalogue and on Dorn’s globe, seems to be a characteristic trend in constellation design in the second half of the fifteenth century which does not yet foreshadow a

return to classical form seen on the later Nuremberg maps. The second extant fifteenth-century globe, now in the Landesmuseum Württemberg Stuttgart, was made by the astronomer Johann Stöffler (1452–1531) in 1493 for Bishop Daniel Zehender of Konstanz. Stöffler is said to have made another globe in 1499 for Bishop Johann Dalberg of Worms but this one is now lost. Stöffler was born in Justingen, a small town near Blaubeuren. On 21 April 1472 he entered the University of Ingolstadt, where he obtained his bachelor’s degree in September 1473 and his master’s in January 1476. After completing his studies he obtained the parish of Justingen where next to his duties as a priest he worked on astronomical and astrological issues. His most important publication during this stay in Justingen was the Almanach nova plurimis annis venturis inserentia published in 1499 in collaboration with the astronomer Jakob Pflaum of Ulm for the years 1499–1531.192 This almanac was a continuation of the Ephemerides astronomicae ab anno 1475 ad annum 1506, published by Regiomontanus in 1474.193 Stöffler’s Almanach reproduces Regiomontanus’s instruction for the use of the tables and includes additional material. Among the additions is a list of the names, the ecliptic and equatorial coordinates for the epoch 1499, the magnitudes and the astrological natures of 52 stars (Tabula Stellarum fixarum Insigniorum).194 Next is a list of the locations of the 28 lunar mansions, their names, and their astrological significance. Other astrological topics follow, such as the best time for bloodletting, and so on and tables for determining the

189 Ameisenowa 1959, Fig. 13. 190 McGurk 1966, p. 33 and Plate IVd; Lippincott 1985, p. 70. 191 Forti et al.1987; Lapi Ballerini 1987.

192 Oestmann 1993, pp. 8–9 and cat. 24, pp. 55–6. Stöffler 1499. 193 Zinner 1990, pp. 117–30, esp. p. 124. 194 Stöffler 1499, pp. 9v–10v.

401

the mathematical tradition in medieval europe boundaries of the mundane houses for latitudes 42º, 45º, 48º, 51º, and 54º using the equatorial method, then known as that of Regiomontanus. In the period 1499–1551 13 editions were published of Stöffler’s Almanach. The publication of the Almanach created a great deal of sensation. Stöffler had predicted for the year 1524 20 planetary conjunctions of which 16 would take place in a watery sign (such as Pisces). Such a configuration was doomed to bring about great changes. Stöffler’s prognostication was linked to others that predicted a deluge, a popular theme throughout the Middle Ages. In Europe, more than 100 different pamphlets were published on the 1524 prognostication.195 In response to a publication by Tanstetter, who argued against a great flood, Stöffler justified himself by saying that he never predicted a deluge, only great changes, and moreover that he believed that only God himself could cause the end of the world.196 In 1507 Stöffler became professor of mathematics at the University of Tübingen, where he lectured on various topics such as Ptolemy’s Geography. In 1522 he became rector there. In Tübingen Stöffler continued to produce important astronomical works. In 1512 he published a book on the construction and use of the astrolabe, Elucidatio fabricae ususque astrolabii, which appeared in 16 editions. In this manual his astrological interests are expressed again by his description of the construction of the boundaries of the mundane houses after the equatorial or Regiomontanus’s method. How to draw a horoscope is extensively discussed in the second part of the treatise on the use of the astrolabe. A work on astronomical tables, his Tabulae astro-

nomicae, followed in 1514. Not long thereafter his Calendarium romanum magnum (Oppenheim: Jakob Koebel, 24 March 1518) appeared, which in addition to extensive astronomical information contains proposals for calendar reform. Astrology also left its trace in this work. There is, for example, a section on blood-letting accompanied by a full-page woodcut of an anatomical man showing the points for bloodletting for the various circumstances described in the text. Stöffler’s most famous pupil was Philipp Melanchthon (1497–1560).197 Under Stöffler’s influence Melanchthon acquired,next to knowledge of astronomy, mathematics, and geography, a strong belief in astrology—as he acknowledged on several occasions. Between 1535 and 1545 Melanchthon lectured about the Tetrabiblos, and he prepared a Latin translation of it which was published in 1553 alongside the second Greek edition by Joachim Camerarius. Against this backdrop it does not come as a surprise that Stöffler’s celestial globe for Bishop Daniel of Konstanz, described in detail in Appendix 5.2 (WG3) and shown in Fig. 5.40, also bears the mark of his astrological interests. The design of the globe made in Justingen follows in most respects theVienna model shown in Fig. 5.26. Stöffler added, however, two new construction features.The first is a set of semicircles which serve to determine the boundaries of the 12 mundane houses by the equatorial or Regiomontanus’s method.The same astrological structure for determining the mundane houses is seen on top of a planetary clock made in 1555 by Philipp Immser (1500–70), another pupil of Stöffler, in cooperation with Emmoser.198 Another unique feature of his globe is the hour

195 Oestmann 1993, p. 9. 196 Graf-Stuhlhofer 1996, pp.135–40.

197 On Melanchthon, see Stupperich 1990. 198 Oestmann 1993, pp. 31–4.

402

5.4 GLOBES IN THE SERVICE OF ASTROLOGY

Fig. 5.40 The celestial globe of Johannes Stöffler. (Landesmuseum Württemberg, Stuttgart; Photo: Peter Frankenstein, Hendrik Zwietachs.)

403

the mathematical tradition in medieval europe circle on top of the meridian ring. Stöffler’s celestial globe is the oldest surviving globe with this accessory. The hour circle serves as an easy mechanical way to find the time of certain events, such as the rising and setting of the Sun and the stars.When correctly adjusted it can also be used for easily finding the configuration in the sky at the moment of birth, and so on. Earlier Arabic treatises on the use of globes provided trigonometric methods for solving time-related problems. Since calculations are usually cumbersome, astrolabes were often used for solving these problems graphically. Stöffler’s hour circle still shows the influence of the astrolabe, since its dial plate is engraved with the same set of unequal hours lines commonly found on an astrolabe such as that shown in Stöffler’s Elucidatio (Fig. 5.41). It has the advantage that equal and unequal hours can be used simultaneously for expressing the time. Stöffler’s hour circle and the set of semicircles make it easy to solve astrological problems, such as casting a horoscope for a particular moment and place. Additional astrological information, such as the planetary natures of the stars, which Dorn engraved on his globe, could be found in Stöffler’s Almanach. The longitudes of the stars on Stöffler’s globe differ with respect to the corresponding Ptolemaic values on average by 19° 38´ ± 11´, which value was determined by measuring the ecliptic longitude of 16 stars located close to the ecliptic. Stöffler also used this value of 19° 38´ in his star tables for the epochs 1499 and 1500, in respectively his Almanac and Elucidatio, consistent with the prediction of the Alfonsine trepidation theory. The epoch of Stöffler’s globe may therefore be reliably set to 1500. The nomenclature on Stöffler’s globe follows in the main that on the Vienna maps. Often Stöffler gives additional names for the constella-

Fig. 5.41 The unequal hour lines on an astrolabe plate from Johannes Stöffler’s Elucidatio. (Photo: Elly Dekker.)

tions. For example, the names OLOR and ANGVITENENS are added to the corresponding names on the Vienna maps (Gallina and Serpentarius). The star names marked on Stöffler’s globe are listed in Table 5A.1 (p. 412) in Appendix 5.1 together with those on theVienna maps and Dorn’s globe. Most but not all of the names on Stöffler’s globe occur in the Vienna star catalogue. Stöffler’s star names are also found in the star catalogue in the second edition of the Alfonsine Tables of 1492, the history of which has been discussed extensively by Kunitzsch.199 It is plausible that Stöffler used for his 1493 globe this particular 1492 star catalogue, properly adapted for precession, because two labels occurring on Stöffler’s globe: Icalurus and Suhel ponderosus Canopius occur exclusively in the editions of the Alfonsine Tables of 1492 and 1518 (1521). Icalurus is 199 Kunitzsch 1986b. Kunitzsch’s study is based on the catalogues in the editions of Venice 1483, 1492, 1518 (dated 1521 at the end of the book), 1524; Paris 1545,1553; and Madrid 1641.

404

5.4 GLOBES IN THE SERVICE OF ASTROLOGY a misreading or miswriting of the Latin ‘et est incalurus’. Stöffler may also have used this 1492 catalogue of the Alfonsine Tables for the star tables published in his Almanac of 1499 and in his treatise of the astrolabe Elucidatio fabricae ususque astrolabii of 1512.200 The constellation designs on Stöffler’s globe recall only in some respects the Vienna tradition. For example, all constellations are drawn in rear view as on the Vienna maps and on Dorn’s globe. On Stöffler’s globe, Crater is represented by the typical wooden tub seen on the Vienna maps but apart from this one finds quite a number of iconographic differences. Important changes are seen in the way some constellations are dressed. Auriga and Ophiuchus, who are nude on the Vienna maps, have been painted in nicely coloured suits, narrowed at their middle. In addition to changes in dress, other deviant characteristics—some substantial and others minor—are introduced with respect to the iconography of theVienna maps. A number of conspicuous attributes of especially Bootes, Cassiopeia, Andromeda, and Virgo recall the aforementioned medieval constellation cycle connected with Michael Scot whose descriptive star catalogue Liber de signis includes many astrological predictions. Scot’s iconography was used in the editio princeps of Germanicus’s Latin translation of Aratus’s poem The Phaenomena published in Bologna in 1474.201 The woodcuts of the Scot illustrations were also used in the 1482 and 1485 editions of Hyginus’s De Astronomia, published by Erhard Ratdolt in Venice, and in many other astronomical works printed during the Renaissance.202 Erhard Ratdolt used the woodcuts again with a few

additional images when he published a German translation of Scot’s Liber de signis in 1491 with the confusing title Hyginus von den XII zaichen und XXXVI pilden des hymels mit yedes stern.203 Scot’s iconography was readily available at the end of the fifteenth century. Scot describes Bootes as a farmer wearing a hat with long hair, and holding a sickle in his right and a lance in the left hand, attributes that are easily recognized in the picture of Bootes on Stöffler’s globe, albeit that the left and right hand are exchanged.204 The sheaf of corn on his left side underlines his role as a farmer. It is not explicitly mentioned in Scot’s text but it is certainly part of Scot’s iconography and occurs in the constellation cycle in Vienna MS 2352, f. 13v and in the woodcuts of the Scot illustrations. The impact of Scot’s iconography is also seen in Virgo who holds a sceptre in her right hand (Fig. 5.42). Scot says that Virgo is in the house of Mercury,who gave her the sceptre.205Ackermann suggests that this attribute may derive from the image of Virgo in Madrid, Biblioteca Nacional MS 19, ff . 57v. Andromeda and Cassiopeia on Stöffler’s globe partly recall Scot’s iconography. The myth around Andromeda, the daughter of Cepheus and Cassiopeia, is well known. It starts with the impiety of Cassiopeia challenging the beauty of the Nereids, the daughters of Poseidon. For this act Andromeda is punished and exposed to the sea monster Cetus. Just in time Perseus rescues her and presumably marries her.To commemorate this story all five participants in the drama were placed among the stars. On Stöffler’s globe, Andromeda is chained at her wrists to the

200 Stöffler 1512, f. XX. 201 Bauer 1983, p. 12. 202 The Scot illustrations have been reprinted in Condos 1997.

203 Blume et al. in preparation. I thank Dieter Blume for this information. 204 Ackermann 2009, pp. 182–3 and 362–3. 205 Ackermann 2009, pp. 158–9 and 347.

405

the mathematical tradition in medieval europe her throne although it is not clear why this is so. Scot describes Cassiopeia as a beautiful well dressed woman with outstretched arms, as was common in the descriptive tradition, but this attitude does not fit the Ptolemaic stellar configuration.207 On Stöffler’s globe bothAndromeda and her mother are presented as nude figures as on the Vienna maps. Perseus wears a loincloth and holds a slightly curved sword in his right hand above his head. In his lowered left hand he carries a cut-off head from which blood spatters which pictures vividly the beheading of Medusa as described by Scot and other authors. The wings at his feet are mentioned by Hyginus in Book II.12. As discussed above in connection with the later Nuremberg maps (see Fig. 5.24) the ox hide held by its head in Orion’s raised left hand (Fig. 5.44) may come from Scot. There is an interesting difference though, because whereas in the Nuremberg maps the ox hide is held by the tail and the head hangs down, on Stöffler’s globe the head is held in Orion’s hand.This same Fig. 5.42 Virgo on the celestial globe of Johannes orientation is seen in a constellation cycle Stöffler. (Landesmuseum Württemberg, Stuttgart; connected with Michael Scot’s treatise in Vienna Photo: Peter Frankenstein, Hendrik Zwietachs.) MS 3394, f. 227 where Scot’s text is missing and the name Hyginus is mentioned instead at the branches of two trees at her sides and Cassiopeia end of the text preceding the image.208 This looks in a mirror held in her left hand and her manuscript is dated around 1470 and was writother hand is tied to the ornament at the back of ten in a north Italian scriptorium, possibly in the throne (Fig. 5.43). Scot describes Andromeda, Padua.The myth explaining the ox hide is given tied to trees between mountain rocks, as being in Hyginus Book II.34: above her middle a woman and below it a man, ‘Aristomachus, however, says there was at Thebes a partly dressed and partly nude.206 The manner in certain Hyrieus (Pindar says he lived on the island which Andromeda is tied to the trees agrees with of Chios), who received Jupiter and Mercury as his Scot’s description but she is not the hermaphroguests, and sought from them the gift of becoming dite that Scot outlines. In the printed version of a father. Further, in order to obtain his request Scot’s iconography Cassiopeia is also fastened to 207 Ackermann 2009, pp. 187–8 and 366. 208 Ackermann 2009, pp. 546–9, esp. p. 549.

206 Ackermann 2009, pp. 190–1 and 368.

406

5.4 GLOBES IN THE SERVICE OF ASTROLOGY

Fig. 5.43 Andromeda and Cassiopeia on the celestial globe of Johannes Stöffler. (Landesmuseum Württemberg, Stuttgart; Photo: Peter Frankenstein, Hendrik Zwietachs.)

more easily, he sacrificed an ox and placed it before them at a banquet. When Hyrieus had done this, Jupiter and Mercury ordered that the hide of the ox be removed and that the oxhide, into which they urinated, should be buried. From the oxhide was later born a lad whom Hyrieus called Urion [“urine born”], because of his origin, but longstanding custom calls him Orion’.209

Other iconographic adaptations are seen in the image of Cepheus, who on Stöffler’s globe is painted like a king, with a crown on his head, a sceptre in his right hand, and a sword attached to a belt around his middle. Scot mentions only the sword.The crown and sceptre do occur in some constellation cycles, for example in Munich Clm 595, f. 40r and on the Dyffenbach map M1a (Fig. 5.13) although less convincingly than on the globe. Auriga’s role as a charioteer is underlined by the harness in his right hand and, less commonly, a wheel at his side. 209 The translation is from Condos 1997, p. 148.

Fig. 5.44 Orion on the celestial globe of Johannes Stöffler. (Landesmuseum Württemberg, Stuttgart; Photo: Peter Frankenstein, Hendrik Zwietachs.)

407

the mathematical tradition in medieval europe The most interesting feature of Hercules’s outfit is not his colourful attire or the lion’s skin but the branch with fruits in front of his right lower leg which may represent the golden apples of the Hesperides. The golden apples are not exclusively mentioned by Scot and since Scot described Hercules as a naked man with sword, it may well be that the inspiration for this image did not come from Scot. A last feature that certainly does not originate from Scot’s iconography is that of two dogs connected by leads to the wrist of the same hand that holds the lance (see the dogs in the right lower corner of Fig. 5.42). Bootes’s dogs are part of the image of Bootes as a young man in the fifteenth-century illustrated manuscript in Florence, Biblioteca Nazionale Centrale Angeli MS 1147 A.6, f. 7v.210 This image is part of a cycle that, as mentioned above, must stem from a globe. This may support the suggestion that Bootes’s two dogs emerged from an attempt to make sense of a difficult phrase in Gerard of Cremona’s Ptolemaic star catalogue of Boo 8 (μ Boo).211 There can be no doubt that the globe’s artist borrowed from Scot’s iconography, but he also borrowed from other sources and seems to have combined a good knowledge of mythology with great imagination.The colourful way in which many figures are dressed, including even Ophiuchus who as a rule is nude, may point to an artist from northern Italy. This anonymous designer left his monogram, a sword with a letter N, on the constellation Centaurus.212 His cooperation with Stöffler resulted in a globe that combines elements of a

210 McGurk 1966, p. 33 and Plate IVd. 211 Dekker 2010a, p. 173. 212 Oestmann 1995/6, p. 64.

medieval descriptive iconographic tradition and the Western mathematical tradition, and in this way highlights the astronomical, astrological and mythological interests in Renaissance celestial cartography.

appendix 5.1 European celestial maps made before 1500 M1. VATICAN CITY, BIBLIOTECA APOSTOLICA VATICANA, MS Plate. lat. 1368, ff. 63r–64v Heidelberg or vicinity, first half of the fifteenth century. folio size: 29.3 × 39.4 cm. author : Conrad of Dyffenbach. f. 45r: ‘Et sic finitur centilogium Ptolomei scriptum per me Conradum/de Dyffenbach Anno domini 1426 festo epiphanie domini etc’. There are four celestial maps divided over four pages which are ordered after their projection.

M1a. ff. 63V–64r: Map of the northern hemisphere (Figs 5.13–5.14). cartography: Language Latin. Polar equidistant projection from the north ecliptic pole to the ecliptic. Great circles through the ecliptic pole are drawn every 5º; circles parallel to the ecliptic are drawn every 5º. The ecliptic is graduated (12 times 0º–30º; numbered every 5º, division 1º); the (sometimes abbreviated) names of the 12 zodiacal signs are placed at the beginning of each sign and their symbols in the middle of it. (The symbols of Aries and Taurus have been exchanged.) The great circles through the beginning of Aries, Gemini, and Libra are numbered every 5º. At the end of the great circle through the beginning of Cancer is the label: colurus.

408

Appendix 5.1 European celestial maps made before 1500 astronomical notes: A few northern Ptolemaic constellations are drawn and labelled: ursa minor, ursa maior, draco, cepheus, boetes/teguius/lanceator, corona, agitator [?].The stars within a constellation are marked by the numbers of their magnitudes, presumably from the Ptolemaic star catalogue. Some stars of Perseus and Ophiuchus are marked but these constellations are neither finished nor drawn. A few stars are labelled: alfeta (α CrB), alhaiot (α Aur), alramech/ artophilax (α Boo), cauda (α UMi), alioze (ε UMa), and edub (α UMa). The constellations are drawn in a primitive way. Ursa Minor is hardly recognizable as a bear. Bootes is presented with a lance in his right hand and a bow in his raised left hand. Cepheus wears a crown and carries in his left hand a sceptre and in his right hand a globus cruciger, an orb with a cross.

M1b: f. 63r: Map of the zodiac (Fig. 5.15), [lon 25º–150º, lat N 30º–S 55º] cartography: Language Latin. Dyffenbach projection from the north and south ecliptic poles to the ecliptic. Great circles through the ecliptic pole are drawn as straight lines for latitudes N 10°–30° and S 10°– 55° for every 5°, and for latitudes 6° N and S, marking the boundaries of the ecliptic. The ecliptic is labelled eclipticus; it is graduated (from Ari 25° to Leo 30°; numbered every 5°, division 5°); the beginning of the scale at Ari 25° is labelled arietis and the names of next four zodiacal signs are placed at the beginning of each sign: Thaurus, Gemini, Cancer, and Leo. The great circles at the boundaries through Ari 25° and Leo 30° are numbered every 5° for latitudes N 10°–30° and S 10°– 55° and at 6° N and 6° S of the ecliptic. The northern and southern part of the map are labelled: septentrio and meridies. astronomical notes: The stars are marked on the map by the numbers of their magnitudes (2–6), presumably taken from the Ptolemaic star catalogue. The brightest stars of the first magnitude are indicated

by a starry symbol (*). Nebulous object are sometimes presented by a point in a dotted circle, or by labels oc and ne. The texts around stars indicate their position within the constellation.The stellar configurations have been surrounded by the contours of the constellations. External stars, often labelled ‘ex [. . .]’, are also in most cases enclosed by a line.The astrological natures are added to some of the brighter stars.The following zodiacal constellations are drawn: Aries, Taurus, Gemini, Cancer, and the western part of Leo. North of the zodiac one finds Triangulum and south of it the eastern part of Cetus, Eridanus, Orion, Lepus, Canis Maior, and Canis Minor.There are a number of stars east of Canis Maior that belong to Navis but the contours of the ship are not drawn.Two stars that belong to the constellation Navis (nos 44 and 45) and which should actually lie below Canis Maior, lie north of Canis Maior. One is labelled: ‘canap[. . .] in navi/in remo/saturni [et] jouis’ and the other, below Canis Minor: ‘sequens canap[. . .]’. Their positions in the present map are based on erroneous latitudes (respectively -29° and -21° 50´) recorded in some star catalogues. The constellations are labelled (in red?): ymago arietis, y[ma]go thauri, gem ante[. .]s, gem seq[. .]s, y[ma]go cancri, y[ma]go ceti, and Cetus, ymago orionis and Orion, y[ma]go leporis, y[ma]go canis, twice y[ma]go flu[. . .]s. There are names for the brighter stars: aldabaram (α Tau), alfeta (α CrB), rigil (β Ori), algomesa (α CMi), alhabor (α CMa), canap[. . .] (α Car), cor leonis (α Leo), and for some nebula: P[re]sepe and Pleyades.

Mlc. f. 64r: Map of the zodiac ( Fig. 5.14 ), [lon 150º–270º, lat N 30º–S 30º]. cartog raphy: Language Latin. Dyffenbach projection from the north and south ecliptic poles to the ecliptic. Great circles through the ecliptic pole are drawn as straight lines for the range of longitudes 150º–270º for every 5º; parallels to the ecliptic are drawn as straight lines for latitudes N 10°–30° and S 10°–30° for every 5°, and for latitudes 6° N and S,

409

the mathematical tradition in medieval europe marking the boundaries of the ecliptic.The ecliptic is graduated (fromVir 0° to Sgr 30°; numbered every 5°, division 5°); the names of four zodiacal signs are at the beginning of each sign: virgo, libra, Scorpio, and Sagit[arius]. The great circles at the boundaries through Vir 0° and Sgr 30° are numbered every 5° for latitudes N 10°–30° and S 10°–55° and at 6° N and 6° S of the ecliptic astronomical notes: The stars are marked as on M1b.The following zodiacal constellations are drawn: the eastern part of Leo, Virgo, Libra, and Scorpio. North of the zodiac one finds the three stars of Coma Berenices (Leo 6e–8e), marked oc, oc, and ne, with a note saying that they lie between the tail of Leo and Ursa Maior. One more star plotted north of Virgo is probably the northernmost of the three stars in the leg of Bootes (Boo 20). South of the zodiac one finds Crater, Corvus, and two stars that belong to Lupus (Lup1–2). The constellations are labelled (in red?): ymago leonis, y[ma]go virginis, y[ma] go librae, y[ma]go scorpionis, y[ma]go vasis, and corui. There are names for the brighter stars: cauda (β Leo), Praevindemiatorem? (ε Vir), Spica (α Vir), and cor scorpionis (α Sco).

M1d. f. 64v: Map of the zodiac ( Figs 5.16 ). [lon 270º–30º, lat N 30º–S 30º] cartography: Language Latin. Dyffenbach projection from the north and south ecliptic poles to the ecliptic. Great circles through the ecliptic pole are drawn as straight lines for the range of longitudes 270º–30º for every 5º; circles parallel to the ecliptic drawn as straight lines for latitudes N 10°–30° and S 10°–30° for every 5°, and for latitudes 6° N and S, marking the boundaries of the ecliptic.The ecliptic is graduated (from Cap 0° to Ari 30°; numbered every 5°, division 5°); the names of four zodiacal signs are at the beginning of each sign: Capricornus, Aqua[rius], pisces, and Aries. The great circle at The great circle the boundary through Cap 0° is numbered every 5° for

latitudes N 10°–30° and S 10°–55° and at 6° N and 6° S of the ecliptic. astronomical notes: The stars are marked as on M1b.The following zodiacal constellations are drawn: Sagittarius, Capricornus, Aquarius, and Pisces. North of the zodiac are four stars of Pegasus, the identification of which is troublesome. At first sight they seem to represent the bright stars of magnitude 2 in the square of Pegasus (Peg 1–4) but these stars ought to lie more to the east. South of the zodiac one finds Piscis Austrinus and Cetus.The star Sgr 25 in the front right hock of Sagittarius is off by 20°, thus creating the curious shape of the constellation.The constellations are labelled (in red?): ymago sagitarii,y[ma]go capricorni, y[ma]go aquarii, y[ma]go piscum, y[ma]go ceti [. . .]. There are no stars named. comments: The projection referred to here as the Dyffenbach projection is described in detail in Section 5.3. It has commonly been described as trapezoidal and for that reason has been confused with the Donis projection.The bow held by Bootes is also part of the drawing of this constellation inVienna MS 5415 (f. 221r). In this constellation cycle Cepheus also holds a globus cruciger, an orb with a cross (f. 220r). Literature: Durand 1952, pp. 114–17; Saxl I 1915, pp. 10–15,Tafel XI, Fig. 24; for the inscription on f. 45r see p. 13. See also Saxl II 1927, pp. 22–5 and Uhden 1937.

M2. VIENNA, ÖSTERREICHISCHE NATIONALBIBLIOTHEK, MS 5415, f. 168r and f. 170r Vienna or 1434/1435.

Klosterneuburg

or

Salzburg, ca.

folio size: 29.0 ×21.6 cm/ folded parchment. author : Reinhardus Gensfelder. The codex was acquired in 1780 by the Österreichische Nationalbibliothek as part of the old municipal library in Vienna.

410

Appendix 5.1 European celestial maps made before 1500 M2a. f. 168r: Map of the northern hemisphere, from the north ecliptic pole to south of the ecliptic to include the zodiacal constellations ( Fig. 5.18 ). cartog raphy: Language Latin. Great circles presented as straight lines through the ecliptic pole have been drawn in black ink for every 30°, marking the boundaries of the zodiacal signs. The ecliptic has a radius of 13.5 cm; it is graduated (12 times 0°–30°; each sign is divided into five parts of 6°, which are in turn subdivided into parts of 1°; each sign is numbered at 12°, 18°, 24°, and 30°). The numbers of the signs themselves (1, . . . ,12) are added in the first section of 6° of each sign; these numbers are drawn in black ink.The degrees/numbers of the zodiacal scale are drawn alternatively in red and black ink (sign 1: black/red, sign 2: red/black, . . . , 11 black/red, sign 12: red/black). In addition four other circles have been drawn. Two of these are drawn in black ink and are centred on the north equatorial pole which is located on the solstitial colure, at a distance of 3.6 cm from the north ecliptic pole. The largest of these two circles passes though the north ecliptic pole and presumably is meant to represent the north polar circle.The smallest circle has a radius of 0.7 cm.Two other circles are drawn in red ink; both pass through the first points of Aries and Libra and extend beyond the ecliptic circle. One of them is centred on the north equatorial pole and has a radius of 14.0 cm and presumably is meant to represent the part of the Equator north of the ecliptic. The centre of the other circle is also located on the solstitial colure, but at a distance of 2.9 cm from the ecliptic pole; it has radius of 13.8 cm. Its centre coincides with the northernmost intersection of the small circle (of 1.4 cm in diameter centred on the north equatorial pole) with the solstitial colure, where a dot is clearly visible.When expressed as fractions of the radius of the ecliptic, the distance of the north equatorial pole from the centre of the northern map amounts to 0.267 and the radius of the small circle inside the north polar circle is 0.052. The radii of the two large circles amount to 1.022 and 1.037.

When assuming that the equidistant projection was used in constructing the map, the distance of the north equatorial pole from the centre of the map amounts to 24°, and the radius of the small circle inside the south polar circle is to 4.7°.The radii of the other two circles would correspond to 92° and 93.3°, respectively. astronomical notes: Epoch 1424 (α Leo in Leo 21° 20´). All stars are marked by a hole in the parchment. Stars located within a constellation figure are marked in red ink and numbered in black ink. The brightest stars are marked by a starry symbol, the others by dots of varying sizes. Unformed or external stars, located outside constellation figures, are marked in black ink; they are not numbered. One unformed star below the tail of the great Bear has been crossed over by red ink.The Milky Way is drawn, but it is not labelled. The names of the stars, listed in Table 5A.1 below, are in red ink. constellations: Of the 48 Ptolemaic constellations 33 are presented.These include all the constellations of the zodiac and north of it.Three constellations are not named: Ursa Maior, Serpens, and Triangulum. All constellation names are written in red ink. descriptions : Ursa Minor, labelled Ursa minor, is a small bear with a long tail. His back is turned to Ursa Maior. Ursa Maior, not labelled, is a great bear with a long tail. Draco, labelled draco, is a snake with four curls; his tongue sticks out his mouth. Draco’s head is below the left foot of Hercules. Cepheus, labelled Cepheus, is seen from the rear, dressed in a tunic, has curly hair and wears a Phrygian hat. He is kneeling on his right leg and his arms are stretched out. Bootes, labelled Bootes, is seen from the rear; he is dressed in a tunic and has curly hair. His left arm is raised and in his right hand is a straight stick which touches the right foot of Hercules. Corona Borealis, labelled Corona, is an open crown with petals. Hercules, labelled hercules vel saltator, is seen from the rear; he has curly hair and he is dressed in some kind of armour with gloves covered by a tunic. His head is

411

the mathematical tradition in medieval europe Table 5A.1 A Star names on the Vienna maps, and the globes of Hans Dorn and Johannes Stöffler BPK 1 24 33 35 48 78 92 95 110 111 119 149 163 179 197 202 222 234 240 271 288 317 318 331 346 393 424 469 488 510 553 565 624 646 670 713 725 733 735 736 768 790 805 818 848

Identification

α α ε η γ α γ μ

α α α α α α α β α α δ α α β α ε β α α α β α α λ δ δ α α ζ β α γ β τ2 θ α α

UMi UMa UMa UMa Dra Cep Boo Boo Boo CrB Her Lyr Cyg Cas Per Per Aur Oph Oph Ser Aql Peg Peg Peg And Tau Gem Leo Leo Vir Sco Sco Cap Aqr PsA Cet Cet Cet Ori Ori Ori Eri Eri CMa CMi

Vienna maps

Dorn’s globe

Stöffler’s globe

alrucaba dubhe

CAVDA DVBHE

Alrucaba Stella polaris dubhe Alioth bennenatz Rasaben Alderaimim Teginus Icalurus Ascimech Arramech Alpheta Rasalheti Wega Deneb adigege [vel] Arided Scheder Algenib Caput Algol Hircus

razdaben Teginus alramech alfeta vvega addigege ariof Scheder algenib razd algola alhayoth razdalhaue yed razdalagueb alkair scheat mankar Enifalferaz mirach

HEDVS

yed Alkaÿr Scheat Markab

ALDEBORA razdalgeuze cor leonis cauda leonis Spica azime[ch] cor scorpionis cauda scorpionis algedi Scheat

COR LEONIS CAVDA LEONES[!] SPICA

menkar pentakaiton denebkaytoz bedelgeuze bellatrix rigil augetenar acarnar alhabor algomeisa

MENTVM VENTER CAVDA IVGLA(!) A OR IVGVLA B OR RIGEL ACARNAR SIRIVS

Mirach Aldebran Rasalgenze Cor Cauda Spica Cor Cauda Cauda Sceath Fomahaut Menckar Venter ceti Denebcaÿton

Angetenar Acarnar Alhabor Sirius Algomeÿsa continued

412

Appendix 5.1 European celestial maps made before 1500 Table 5A.1 Continued BPK 855 892 905 921 931

Identification p

α α α γ

Pup Car Hya Crt Crv

Vienna maps

Dorn’s globe

Stöffler’s globe

markeb Suel alphart

MARKEB SVEL

Markeb Suhel ponderosus Canopius Alphart Serpente idra Alhes Algorab

algorab et coruus

a On the Vienna map there is in addition a label ‘caput algol’ which I presume is not a star name but a label for the head of Medusa. b For this name, see Kunitzsch 1986b, p. 97, note 22.

west of that of Ophiuchus. He is kneeling on his right knee and his left foot is above the head of Draco. His left arm is stretched out in the direction of Lyra and he holds a curved sword in his raised right hand. Lyra, labelled vvltvr cade(n)s, is presented as a bird, with a crooked beak. Cygnus, labelled gallina, is a bird with an outstretched neck and outstretched wings, as if flying. Cassiopeia, labelled Cassiepea, is turned in her chair and thus seen from the rear. She is nude and her right arm is stretched. In her left hand she holds a long feather. perseus, labelled P[e]rseus, is a naked figure with curly hair, seen from the rear. He holds a curved sword in his right hand above his head and he carries a head with devil’s ears in his lowered left hand. The four stars in the head of Medusa are labelled: caput algol. Auriga, labelled Agitator, is a nude figure with curly hair, seen from the rear. His head is turned west and his knees are slightly bent but he is not kneeling. Both arms are lowered. On his left shoulder stands a goat and around his right wrist is a harness. His right foot touches the northern horn of Taurus. Ophiuchus, labelled Serpentarius, is a naked figure with curly hair, seen from the rear. His head is turned east away from the nearby head of Hercules. He holds the body of Serpens in his hands. One of his feet rests on the body of Scorpius. Serpens, not labelled, is a snake with an open mouth. Its body, which encircles the wrists and middle of Ophiuchus, has four coils. Sagitta, labelled ystius?, is a simple arrow north of Aquila. Aquila, labelled vvlt(vr) volans, is drawn as a bird with outstretched wings, flying in a south-eastern

direction. Delphinus, labelled delphin, is drawn as a dolphin. Equuleus, labelled Equus p(ri)or, is drawn as the head of a horse. pegasus, labelled Equus volans, is drawn as half a horse with wings. Andromeda, labelled Andromeda, is a nude female figure with her hair in tresses around her head, seen from the rear. She holds a band or cord in her hand which encircles her middle. Her body is more or less parallel to the ecliptic, and the top of her head touches the belly of Pegasus. Her left arm is raised above the northern one of the Pisces. The other, right arm is stretched towards the north.Triangulum, not labelled, is drawn as a triangle. Aries, labelled Aries, is drawn as a ram with two horns and a curly fleece. He lies with his forefeet bent. He is looking backwards to Taurus.The ecliptic cuts through his body and passes above his tail.Taurus, labelled thaurus, is a half bull with a bent head, two front legs, and two horns. The ecliptic passes through his body and his head. The northern horn extends to the left foot of Auriga.The Pleiades are labelled: Pliades. Gemini, labelled Gemini, consist of two nude figures with curly hair, both seen from the rear. Their heads are turned to each other and their legs stretch westwards. They are without attributes.The right arm of the western twin rests on the shoulder of the eastern twin. Cancer, labelled Cancer, is a crawfish with two claws facing Leo and three legs on either side. The ecliptic passes through the main body. Leo, labelled leo, is a lion is standing on its hindlegs with his forefeet as if jumping. He has his mouth open and is looking forward to Cancer.

413

the mathematical tradition in medieval europe The lion’s tail makes a loop. The ecliptic passes through the chest and the hindlegs. Virgo, labelled virgo, is a female figure with curly hair and with wings, seen from the rear. She wears a long dress with a belt. Her head is turned in profile to the north.The body aligns more or less with the ecliptic. The ecliptic passes through her southern wing. She points with her right hand to her head. On her lowered left hand is a bright star, presumably Spica, close to the ecliptic. Libra, labelled libra, is presented by a pair of scales. Scorpius, labelled Scorpio, is drawn as a scorpion with two short claws, three legs on both sides, and a segmented tail. Sagittarius, labelled Sagittarius, is a horse with a nude figure on top, seen from the rear. The male figure has curly hair and a head band with bands of cloth fluttering behind him. He looks forward in the direction of Scorpius. In his left hand he carries a bow and in his (invisible) right hand he holds the arrow. The ecliptic intersects his head. capricornus, labelled Capricornus, has two short horns and a fish tail. The ecliptic intersects him just below the neck and through the tail. Aquarius, labelled Aquarius , is a nude figure with curly hair, seen from the rear. His slightly bent left arm is stretched westwards and holds a folded piece of cloth. The ecliptic intersects his body at the hips. His right arm rests on an urn from which water streams. The stream is cut-off by the ecliptic. Pisce s, labelled pisces , consists of two fishes. The southern of the two is located below the wing of Pegasus. The other, northern fish is located below the raised arm of Andromeda. There is band with a knot which connects the tails of the fishes.

M2b. f. 170r: Map of the southern hemisphere, from the south ecliptic pole to the ecliptic ( Fig. 5.19 ). cartog raphy: Same as map M2a, but here the ecliptic is slightly differently graduated: (12 times 0°–30°; each sign is divided into five parts of 6°; only the first of these five parts is subdivided in

parts of 1°; each sign is numbered at 12°, 18°, 24°, and 30°). The numbers of the zodiacal scale are drawn alternately in red and black ink starting with black in the first sign. The signs themselves are not numbered on this map. In addition two other circles have been drawn. One of these is drawn in black ink; it is centred on the south equatorial pole which is located on the solstitial colure, at a distance of 3.6 cm from the south ecliptic pole. This circle passes though the ecliptic pole and presumably is meant to represent the south polar circle.The other circle is drawn in red ink and passes through the first points of Aries and Libra; it is centred on the south equatorial pole; it has a radius of 14.0 cm and presumably represents the part of the Equator south of the ecliptic. There is another point indicated on the solstitial colure at a distance of 2.9 cm from the south ecliptic pole around which a small circle has been traced, presumably with a pair of dividers, because this circle is not drawn in ink; it does not pass through the south equatorial pole and it has diameter of about 1 cm. When expressed as fractions of the radius of the ecliptic, the distance of the equatorial pole from the centre of the southern map amounts to 0.267 and the radius of the vague compass tracing inside the south polar circle is 0.037.The radius of the largest circle centred on the south equatorial pole is 1.037. When it is assumed that the equidistant projection was used in constructing the map, the distance of the north equatorial pole from the centre of the map amounts to 24°, and the radius of the vague compass tracing inside the south polar circle 3.3°. The radius of the largest circle would correspond 93.3°. astronomical notes: All stars are marked by a hole in the parchment. Stars located within a constellation figure are marked in red ink and numbered in black ink. The brightest stars are marked by a starry symbol, the others by dots of varying sizes. Most of the unformed or field stars, located outside constellation figures, are marked in black ink and a few in red ink; they are not numbered.Two unformed

414

Appendix 5.1 European celestial maps made before 1500 stars below Lepus have been crossed over by red ink. The Milky Way is drawn, but it is not labelled. The names of the stars, listed in Table 5A.1 below, are in black. constellations: Of the 48 Ptolemaic constellations 15 are presented.These include all the constellations south of the zodiac. One constellation, Canis Minor, is not named.All names are all written in red ink. descriptions: Cetus, labelled Cetus, is presented as a whale. Orion, labelled Orion, is seen from the rear. He has curly hair and he is dressed in some kind of armour with gloves covered by a tunic. He holds his head backwards to show his face. He holds an animal skin in his raised left hand and carries a club in his raised right hand. He kneels on his left knee and his right leg is slightly bent. He has a belt around his middle to which a sword in a scabbard is attached. Eridanus, labelled fluuius, is a river presented by a band which starts at the left foot of Orion, and streams first west to Cetus. It continues in the opposite, eastern direction until it makes another turn and ends at the last star of the river (θ Eri). Lepus, labelled lepus, is a hare with long ears south of Orion. Canis maior, labelled canicula, is a dog with an open mouth. Canis Minor, not labelled, is a walking dog with a collar. Navis, labelled navis ut archa noe, is a ship with a mast, a crow’s nest, and three ropes, but no sails. There are two steering oars which seem to emerge from behind the ship.At the western end of the ship is a balustrade and at the eastern end a dog’s head. Hydra, labelled ydra, is a snake with two coils.The mouth is open and his tongue is shown. The end of the tail is above the head of Centaurus. Crater, labelled vas ut c(ra)t(er), is a tub with two handles, standing behind on the body of Hydra. Corvus, labelled coruus, is a bird standing with its feet on the body of Hydra. It is picking the snake. Centaurus, labelled Ce(n)taurus, is a horse with a nude figure with curly hair on top, seen from the rear. On his right arm rests a shield and in his right hand he holds a lance which pierces the head of Lupus. Lupus, labelled lupus, is an animal with its

mouth open, held by Centaurus.Ara, labelled Sacrum thuribulu(m) vel lar, is a square altar with flames on top. It is upside-down. Corona Australis, labelled corona, is an open crown with petals. Piscis Austrinus, labelled piscis meridio(na)lis, is a fish with its head turned towards its tail, mouth open showing its teeth. comments: The maps are part of the treatise on the construction and use of a celestial globe, Vienna MS 5415, ff. 161r–191r, Tractatus de sphaera solida, the explicit of which gives the date of the copy: ‘Explicit tractatus ...finitus anno 1435 currente’.This is presumably also the date of the maps.The codex has on f. 33v the coats of arms of Vienna, Austria, and Klosterneuburg. Literature: Saxl II 1927, pp. 24–31, pp. 34–38, and pp. 150–55; Roland 2012, Kat. no. 77, pp. 19–28; Blume et al. to be published.

M3. MUNICH, BAYERISCHE STAATSBIBLIOTHEK, Clm 14583, ff . 70v–73r St Emmeran, between 1447–55. Author : Fredericus (Friedrich Gerhart). There are three celestial maps divided over six pages.

M3a: ff. 70v–71r: Map of the zodiacal and three northern constellations Ursa Minor, Ursa Maior, and Draco ( Fig. 5.20 ). cartog raphy: Language Latin.The map is bounded by the zodiac presented by three concentric circles. Great circles presented as straight lines have been drawn (in red ink) through the ecliptic north pole. The signs (not to be confused with the zodiacal constellations) are labelled in red ink: Aries; Thaurus; Gemini; Cancer; Leo; Virgo; Libra; Scorpio; [Sag]ittarius; Capricornus; Aquarius; Pisces. astronomical notes: Neither stars nor the Milky Way are marked.The zodiacal constellations and three

415

the mathematical tradition in medieval europe northern ones, Ursa Minor, Ursa Maior, and Draco, are drawn but not labelled.

comments: Although primitively drawn, the present maps shares most iconographic characteristics with those described above (M2). Literature: Durand 1952, p. 174.

M3b: ff. 71v–72r: Map of the constellations north of the zodiac (Fig. 5.21). cartog raphy: Language Latin.The map is bounded by the zodiac presented by three concentric circles. Great circles presented as straight lines have been drawn (in red ink) through the ecliptic north pole. The signs are labelled in red ink: Aries; Thaurus; Gemini; Cancer; Leo; Virgo; Libra; Scorpio; Sagittarius; Capricornus; Aquarius; Pisces. astronomical note s: Neither stars nor the Milky Way are marked. All 21 Ptolemaic constellations north of the zodiac are drawn but none labelled: Ursa Minor, Ursa Maior, Draco, Cepheus, Bootes, Corona Borealis, Hercules, Lyra, Cygnus, Cassiopeia, Perseus, Auriga, Ophiuchus, Serpens, Sagitta, Aquila, Delphinus, Equuleus, Pegasus, Andromeda, and Triangulum.

M3c: ff. 72v–73r: Map of the constellations south of the zodiac (Fig. 5.22). cartog raphy: Language Latin. The map is bounded by the zodiac presented by three concentric circles. Great circles presented as straight lines have been drawn (in red ink) through the ecliptic south pole. The signs are labelled in black and red ink: Aries; Thaurus; Gemini; Cancer; Leo; Virgo; Libra; Scorpio; Sagittarius; Capricornus; Aquarius; Pisces. Names in black seem to be a correction of other names in red which have been wiped out (though not completely). There are also names below the zodiac in another hand. astronomical notes: Neither stars nor the Milky Way are marked.All 15 Ptolemaic constellations south of the zodiac are drawn but not labelled: Cetus, Orion, Eridanus, Lepus, Canis Maior, Canis Minor, Navis, Hydra, Crater, Corvus, Centaurus, Lupus, Ara, Corona Australis, Piscis Austrinus.

M4. NUREMBERG, GERMANISCHES NATIONALMUSEUM, Inv. Nr. Hz 5576/5577. Nuremberg, 1503. Folio size: 66.5 × 66.5 cm. Authors/contributors: Konrad Heinfogel, Theodericus Ulsenius, Sebastian Sperancius

M4a. Inv. Nr. Hz 5576: Map of the northern hemisphere ( Fig. 5.23 ). In the corners of the map are the images and the names (in red ink) of the four elements and the gods associated with them. In the top left corner one finds images and names of IGNIS, APOLLO, and MARS; in the top right corner are images and names of AER, SATVRNVS, and VENVS; in the bottom left corner are images and names of TERRA, IVPPITER [sic],the goddesses of vengeance ALLECTO, MEGAERA, TESIPHONE, as well of PLVTO and CERBERVS; in the bottom right corner one finds images and names of AQVA, MERCVRIVS, and LVNA. cartog raphy: Language Latin.The map is in stereographic projection from the north ecliptic pole to south of the ecliptic to include the zodiacal constellations. Great circles presented as straight lines through the ecliptic pole have been drawn for every 30°, marking the boundaries of the zodiacal signs. The ecliptic has a radius of 24 cm; it is graduated (12 times 0°–30°; each sign is divided into parts of 1°, a division marked by dots); the signs are neither labelled nor numbered. In addition to the ecliptic five other circles have been drawn.Three of these with a radius of 21.7, 26.4, and 32.4 cm respectively, are centred on the north ecliptic pole and mark the boundaries of the

416

Appendix 5.1 European celestial maps made before 1500 zodiacal band and the boundary of the map.Two others are centred on the north equatorial pole, labelled POLVS ARCTIKVS, which is located on the solstitial colure, at a distance of 5.0 cm from the north ecliptic pole. The largest of these two circles passes though the north ecliptic pole and represent the north polar circle. The smallest circle has a radius of 0.9 cm. When expressed as fractions of the radius of the ecliptic, the distance of the north equatorial pole from the centre of the northern map amounts to 0.267, and the radii of the three circles centred on the ecliptic pole amount to 0.9, 1.1, and 1.35. Assuming that the stereographic projection was used in constructing the map, the distance of the north equatorial pole from the centre of the map amounts to 23.4°, and the radii of the three circles parallel to the ecliptic would correspond to 84°, 95.5°, and 107°, respectively. The radius of the small circle around the north polar pole is then 4.3°. astronomical notes: Stars inside constellation figures are numbered in black and many of the external stars are numbered in red ink, following the order of the Ptolemaic star catalogue. The brightest stars are marked in gold by starry symbols, the weaker ones by a dot surrounded by a circle filled with gold. Unformed or external stars, located outside constellation figures, are marked by black dots of varying sizes. Only one star name in Ursa Maior, possibly dubhe, is vaguely visible. constellations: Of the 48 Ptolemaic constellations 33 are presented.These include all the constellations of the zodiac and north of it. One constellation is drawn but not named: Serpens.The other constellations are labelled in red ink. descriptions: Ursa Minor, labelled VRSA MINOR, is a small bear with a long tail. His back is turned to Ursa Maior. Ursa Maior, labelled VRSA MAIOR, is a great bear with a long tail. Draco, labelled DRACO, is a snake with four curls; his tongue sticks out his mouth. Cepheus, labelled CEPHEVS, is a nude figure seen from the rear, with curly hair and a beard. His head is turned east. He

wears a Phrygian hat. He is standing with his arms stretched out. Bootes, labelled BOOTES, is a nude figure seen from the rear, with curly hair and a beard. His head is turned east. His left arm is raised and in his right hand is a lance which ends above the right foot of Hercules. Corona Borealis, labelled CORONA, is an open crown with petals. Hercules, labelled HERCVLES, is a nude figure seen from the rear, with curly hair and a beard. His head, which is turned east, is west of that of Ophiuchus. He is kneeling on his right knee and his left foot is above the head of Draco. His left arm is stretched out in the direction of Lyra and his wrist is covered by a lion’s skin. He holds a club in his raised right hand. Lyra, labelled VVLTVR CADE(N)S, is presented as a bird. Cygnus, labelled GALLINA, is a bird with outstretched wings, as if flying. The bird has a long outstretched neck. cassiopeia, labelled CASSIOPEIA, is turned in her chair and seen from the rear. She is nude but wears a crown and her right arm is stretched. In her left hand she holds a long feather. Perseus, labelled PERSEVS, is a naked figure seen from the rear, with curly hair, a beard, and wings on his feet. He looks upwards and holds a curved sword in his right hand above his head and he carries the head of Medusa, labelled: CAPVT ALGOL, in his lowered left hand. Auriga, labelled AGITATOR, is a nude figure seen from the rear, with curly hair and a beard. His head is turned west and his knees are slightly bent but he is not kneeling. Both arms are lowered. On his left shoulder stands a goat and around his right wrist is a harness. His right foot touches the northern horn of Taurus. Ophiuchus, labelled OPHIVLCVS [sic], is a naked figure seen from the rear, with curly hair and a beard. His head is turned east away from the nearby head of Hercules. He holds the body of Serpens in his hands. One of his feet rests on the body of Scorpius. Serpens, not labelled, is a snake with an open mouth. Its body, which encircles the wrists and middle of Ophiuchus, has two coils. Sagitta, labelled SAGITTA, is drawn as a simple arrow north of Aquila. Aquila, labelled VVLTVR VOLA(N)S, is drawn as a bird with out-

417

the mathematical tradition in medieval europe stretched wings, flying in a southeastern direction. Delphinus, labelled DELPHIN, is drawn as a dolphin. Equuleus, labelled EQVVS PRIOR, is drawn as the head of a horse. Pegasus, labelled EQVVS PEGASVS, is drawn as half a horse with wings. Andromeda, labelled ANDROMEDA, is a nude female figure seen from the rear with her head facing north. Her hair is laid in tresses around her head. She holds a chain in her hand which passes behind her. Her body is more or less parallel to the ecliptic, and the top of her head touches the belly of Pegasus. Her left arm is raised above the northern one of the Pisces. The other right arm is stretched towards the north.Triangulum, labelled DELTON, is drawn as a triangle. Aries, labelled ARIES, is drawn as a ram with two horns. He lies with his forefeet bent. He is looking backwards to Taurus. The ecliptic cuts through his body and passes above his tail. Taurus, labelled TAURVS, is a half bull with a bent head, two front legs, and two horns.The ecliptic passes through his body and his head.The northern horn extends to the left foot of Auriga. Gemini, labelled GEMINI, consist of two nude figures with curly hair, both seen from the rear. Their heads are turned to each other and their legs stretch westwards. They are without attributes.The right arm of the western twin rests on the shoulder of the eastern twin. cancer, labelled CANCER, is a crawfish with two claws facing Leo and four legs on either side. The ecliptic passes through the main body. Leo, labelled LEO, is a lion standing on its hindlegs with his forefeet as if jumping. He has his mouth open and is looking forward to Cancer. The lion’s tail makes a loop. The ecliptic passes through the chest and the hindlegs. Virgo, labelled VIRGO, is a female figure seen from the rear, with wings and with her hair laid in tresses around her head. She wears a long dress with a belt. Her head is turned in profile to the north.The body aligns more or less with the ecliptic. The ecliptic passes through her southern wing. She points with her right hand to her head. In her lowered left hand she holds an ear of wheat with the bright star Spica.

Libra, labelled LIBRA, is presented by a pair of scales. Scorpius, labelled SCORPIO, is drawn as a scorpion with two short claws, four legs on either side, and a segmented tail. Sagittarius, labelled SAGITTARIVS, is a horse with a nude figure on top, seen from the rear. The bearded male figure seems bold. He has a head band with garments attached to it which flutter behind him. In his left hand he carries a bow and in his (invisible) right hand he holds the arrow. The ecliptic intersects his head. Capricornus, labelled CAPRICORNVS, has two short horns and a fish tail. The ecliptic intersects him just below the neck and through the tail. Aquarius, labelled AQVARIVS, is a nude figure with curly hair, seen from the rear. His head is turned west and his slightly bent left arm is stretched westwards and holds a folded piece of cloth. The ecliptic intersects his body at the hips. His right arm rests on an urn from which water streams all the way below his feet. Pisces, labelled PISCES, consists of two fishes.The southern of the two is located below the wing of Pegasus.The other, northern fish is located below the raised arm of Andromeda. There is band with a knot which connects the tails of the fishes.

M4b. Inv. Nr. Hz 5377: Map of the southern hemisphere (Fig. 5.24). On top of the name is the date: ANNO DO MDIII. In the top left corner one finds images and names of the three fates: CLOTHO, LACHESIS, and ATROPOS.To the right is a figure carrying the coat of arms of Nuremberg. In the right top corner: ‘CLARA TVIS RVTILANT ARMIS CEV LVMINABINA/SEC DECVS EXIMIAE FVLGES VIRTVTIS HONOSQVE/ TOCIVS GENERIS HEIMFOGEL MORIBVS APTVM/NOMEN HABENS CVNCTIS GRATVS BONVSQVE BENIGNVS’. Below this text is the coat of arms of Heinfogel and the figure and name of VANITAS.The female figure

418

Appendix 5.1 European celestial maps made before 1500 has a text in a band around her body: ‘MECVM SVNT FORTITVDO ET AGILITAS/MECVM EST IVVENTVS ET SPECIOSITAS/MECVM SVNT DIVICIE ET GLORIA/MECVM SVNT LETICIE ET DELICIE’and below it:‘HEC OMNIA VANITAS’. In the bottom left corner is the figure and name of BACHVS. Below him is a poem by Theodorius Ulsenius: (in red) ‘VENTORVM DESCRIPCIO/ THEORICI VLSENII’(in black, except the first letters): ‘VENTORVM BOREAS PRINCEPS ZEPHIR EVRVS ET AVSTER/EX ISTIS MEDII CONSTITVVNTVR ITEM/COLLATERANT EVRVM VVLTVRNVS SVBQVE SOLANVS/ SVNT NOTVS AVSTRALIS AFFRICVS ET SOCII/CIRCIVS VT ZEPHIRVM SEMPERQVE FAVONIVS ORNANT/VVLTAQVILO BOREE CHORVS ET ESSE COMES/PRIMVS ERIT DEXTER QVOCIENS HUNC EVRE VEL AVSTER/PRAESTITERIS. RELIQVIS PRIME SINISTER ERIS’. In the bottom right corner are two figures. One sits on a celestial sphere and represents Urania. The other figure is a man holding an armillary sphere and represents Sebastianus Sperancius, as explained in the text below him: (in red): ‘SEBASTIANVS SPERANCIVS’ (in black, except the first letters): ‘QVAE REGIS IGNIVOMOS O DIVA VRANIA COELOS/LEGIBVS AETERNIS VASTVM QVI ORBEM MODERANTVR/CALLEAT ILLORVM SPERANCIVS ABDITA QVAEQVE/DA PRECOR ET FAVSTVM TRIBVASPER TE[M] PORAFATV[M]’. Cartog raphy: Language Latin.The map is in stereographic projection from the south ecliptic pole to the ecliptic. Great circles are presented as straight lines through the ecliptic pole, labelled POLVS ZODIACI, have been drawn for every 30°, marking the boundaries of the zodiacal signs. The ecliptic has a radius of 24 cm; it is graduated (12 times 0°–30°; each sign is divided into parts of 1°, a divi-

sion marked by dots); the signs are neither labelled nor numbered. In addition to the ecliptic three other circles have been drawn. One of these with a radius of 27 cm is centred on the south ecliptic pole and marks the boundary of the map.Two others are centred on the south equatorial pole, labelled POLVS ANTARTIKVS, which is located on the solstitial colure, at a distance of 4.9 cm from the north ecliptic pole.The largest circle passes though the north ecliptic pole and represents the south polar circle. The smallest circle has a radius of 0.9 cm.When expressed as fractions of the radius of the ecliptic, the distance of the north equatorial pole from the centre of the northern map amounts to 0.267, and the radius of the boundary circle centred on the ecliptic pole amounts to 1.13. Assuming that stereographic projection was used in constructing the map, the distance of the north equatorial pole from the centre of the map amounts to 23.4°, and the radius of the boundary circle corresponds to 97°.The radius of the small circle around the north polar pole is then 4.3°. Across the map are four compass directions in red ink: MERIDIES, OCCIDENS, SEPTENTRIO, ORIENS. At the border of the map are wind heads and the corresponding names of the winds: AVSTER, AFFRICVS, ZEPHIROAVSTER, PAVONIVS, ZEPHIRVS, CIRCIVS, ZEPHIROBOREAS, CHORVS, BOREAS, AQVILO, EVROBOREAS, VVLTVRNVS, EVRVS, SVBSOLANVS, EVROAVSTER, NOTVS. astronomical notes: Stars inside constellation figures are numbered in black and external stars are numbered in red ink, following the order of the Ptolemaic star catalogue. The brightest stars are marked in gold by starry symbols, the weaker ones by a dot surrounded by a circle filled with gold. Unformed or external stars, located outside constellation figures, are marked by black dots of varying sizes. constellations: Of the 48 Ptolemaic constellations 15 are presented.These include all the constel-

419

the mathematical tradition in medieval europe

APPENDIX 5.2 European celestial globes made before 1500

lations south of the zodiac. All names are written in red ink. descriptions: cetus, labelled CETVS, is presented as a whale. Orion, labelled ORION, is a nude figure seen from the rear, with curly hair and a beard. His head is backwards to show his face. He holds an ox hide in his raised left hand and carries a club in his raised right hand. He kneels on his left knee and his right leg is slightly bent. He has a belt around his middle to which a sword in a scabbard is attached. Eridanus, labelled ERIDANVS, is a river presented by a band with a wavy pattern which starts at the left foot of Orion, and streams first west to Cetus. It continues in the opposite, eastern direction until it makes another turn and ends at the last star of the river (θ Eri). Lepus, labelled LEPVS, is a hare with long ears south of Orion. Canis Maior, labelled CANIS MAIOR, is a dog with a collar. Canis Minor, labelled CANIS MINOR, is a walking dog with a collar. Navis, labelled ARGONAVIS, is half a ship with a mast but no sails.There are two steering oars on one side of the ship. Hydra, labelled HIDRA, is a snake with two coils. The mouth is open and his tongue is shown. The end of the tail is in front of the head of Centaurus. Crater, labelled VAS, is a tub with two handles standing on the body of Hydra. Corvus, labelled CORVVS, is a bird standing on the body of Hydra. It is picking the snake. Centaurus, labelled CENTAURVS, is a horse with a nude figure with a bold head and a beard on top, seen from the rear. He holds a lance in his hands which pierces the head of Lupus. A shield is attached to a belt around his shoulder. Lupus, labelled LVPVS, is an animal with its mouth is open, held by Centaurus. Ara, labelled ARA, is a square altar with flames on top. It is upsidedown. Corona Australis, labelled CORONA MERI:, is an open crown with petals. Piscis Austrinus, labelled PISCIS NOTVS, is a fish with its head turned towards its tail, mouth open showing its teeth. comments: The artist of these maps is unknown. Literature: Voss 1943.

WG1. BERNKASTEL-KUES, ST. NIKOLAUS HOSPITAL (CUSANUSSTIFT) Ø sphere 27.2 cm. Date: 1320–40. Acquired in 1444 in Nuremberg by Cardinal Nicolaus Cusanus. construction: The hollow sphere of birch wood is 20 mm thick, and 27.2 cm in diameter. The sphere is closed by a circular disc of 11.8 cm in diameter and covered with plaster and cloth. Next layers of white oil paint have been added to smooth the surface. At the north and south ecliptic poles a messing circular disc (diameter 3.1 cm) is fixed by four nails.A messing ring is attached to these discs such that it can rotate around the sphere. Half of the ring is 8 mm thick, but the size of the other half is cut out such that one side of the ring coincides precisely with a great circle through the poles (see Fig. 5.6). This part of the ring through the ecliptic poles is divided into units of 5° and subdivided into 1°, but not numbered. At a distance of around 23.5° is a provision to attach a meridian ring. cartog raphy: The ecliptic is graduated (not numbered, division into 1° by dots). Perpendicular to the ecliptic is a circle (not graduated) passing through the ecliptic poles and the star Sirius (α CMa). Along a circle at a distance of about 24° from the north and south ecliptic poles one finds several holes, presumably indicating the equatorial poles for a number of epochs. Following Hartmann 1919, p. 30, the positions of these holes, labelled A, B, and C, are schematically summarized in Scheme 5.1. One of the holes (A in Scheme 5.1) lies 12.4° east (i.e. in advance) of the great circle through Sirius. Two other holes (B and C in Scheme 5.1.) are shifted with respect to the great circle through Sirius 20.5° east and 3.3° west, respectively.Around the points A and C are traces of a

420

Appendix 5.2 European celestial globes made before 1500 small circle and a series of points which were caused by the nails with which a circular disc was fixed to the sphere at the equatorial poles at A and C. Hartmann 1919, p. 32 also recorded a number of circles specific to each of the equatorial poles A, B, and C: the Equator corresponding to pole A; a part of the Equator corresponding to pole C; the tropics corresponding to pole B; two parallel circles around the north and south pole at a distance of 35º from pole B; a circle of 36º around the star α UMi (Hartmann 1919, p. 32 says ‘α Ursae majoris, unsern jetzigen Polarstern’ which shows that α UMi is intended here). astronomical notes: The stellar positions are marked by small holes drilled into the sphere and filled with red wax. The sizes of the holes vary with the brightness of the star from ½ to 2 mm. All 48 Ptolemaic constellations have been drawn in brownish ink. In Taurus is a group of seven stars representing the Pleiades. constellations: All 48 Ptolemaic constellations are drawn and none are labelled. descriptions: Ursa Minor is a small bear with a short tail. His belly is turned to Ursa Major. Ursa Maior is drawn as a great bear with a long tail. Draco is a snake with two bends; his tongue sticks out his mouth. Cepheus is a naked figure with curly hair and a hunter’s hat. He is kneeling on his left leg and his arms are stretched. The right hand points to Cassiopeia. Bootes is a naked figure with curly hair and a hunter’s hat, walking westwards. He has a girdle on his waist. His right arm is raised and intersects at his elbow with a specific ever-visible circle. In his left (eastern) hand is a straight stick which ends on the left foot of Hercules. Corona Borealis is a crown with six petals, three of which are drawn on the outside and the other three inside the ring. Hercules is a naked figure with curly hair, a moustache, and a beard. His slightly bent head is west of that of Ophiuchus. He is kneeling on his left leg and his right leg is above the head of Draco. His right arm is stretched out in the direction of Lyra and his left arm is raised. He holds a lion’s skin with a long tail in his

right hand, and he carries a club in his left hand. Lyra is presented as a lyre. Cygnus is a bird with outstretched wings, as if flying. The bird has a long beak at the end of an outstretched neck. Cassiopeia is drawn in profile as a naked figure, presumably female, sitting in a simple square chair. Her left arm is stretched out in the direction of Perseus and her bent right arm is raised. Her legs seem to be drawn between the legs of her chair but her feet are in front of it. Perseus is a naked figure with a warrior’s helm on his head. His right arm is lowered and he carries a female head with long hair in his right hand. In his left hand raised above his head he holds a sickle with teeth. Auriga is a naked figure with curly hair. His head is turned west and his knees are slightly bent but he is not kneeling. Both arms are lowered. On his right shoulder sits the head of a goat and on his right wrist is a smaller goat. His left foot touches the northern horn of Taurus. Ophiuchus is a naked figure with curly hair. His head is turned west to face the nearby head of Hercules. He holds Serpens in his hands. One of his legs is on the body of Scorpius. Serpens is a snake with a two-forked tongue, passing in front of the thighs of Ophiuchus. Sagitta is drawn as a simple arrow north of Aquila.Aquila is drawn as a bird with outstretched wings, flying in a southeastern direction. Delphinus is drawn as a dolphin with a beard and a fin, showing his teeth. Equuleus is drawn as the head of a horse. Pegasus is drawn as half a horse with wings. Andromeda is a female figure with long hair. She wears a long dress with a belt around her middle. Her body is more or less parallel to the ecliptic, and the top of her head touches the belly of Pegasus. Her right arm is raised above the northern one of the Pisces. The other left arm is stretched towards the north.Triangulum is drawn as a triangle. Aries is drawn as a ram with two horns and a curly fleece. He is standing on his hindlegs with forefeet as if jumping. He is looking backwards to Taurus.The ecliptic cuts through his right foreleg and passes under his tail. Taurus is a half bull with a bent head, two front legs, and two horns.The ecliptic passes through his body and neck. The northern

421

the mathematical tradition in medieval europe horn extends to the left foot of Auriga. Gemini consists of two nude figures with curly hair.Their heads are turned to each other. They are without attributes. The right arm of the western twin is stretched towards Auriga; the right arm of the eastern twin rests on the shoulder of the western twin. The left arms of both twins are bent. Cancer is a crab with two claws facing Leo and three legs on either side. The ecliptic intersects the body lengthways. Leo is a lion is standing on its hindlegs with his forefeet as if jumping. He has his mouth open and shows his tongue. The lion’s tail makes a loop. The ecliptic passes through the chest and the hindlegs.Virgo is a female figure with long hair and with wings, and wears a long dress with a girded top. Her head is turned in profile to the north.The body aligns more or less with the ecliptic. The ecliptic passes through her southern wing. The left hand is on her breast. Her lowered right hand with a bright star, presumably Spica, is close to the ecliptic. Libra is presented by the segmented claws of Scorpius. Scorpius is drawn as a scorpion with two claws, three legs, and a segmented tail of seven parts. Sagittarius is a horse with a nude figure on top.The male figure has curly hair. In his right hand he carries a bow and in his left hand he holds the arrow.The ecliptic intersects him in the neck, just below his head. Capricornus has two horns and a fish tail.The ecliptic intersects him just below the neck and through the tail. Aquarius is a nude figure with curly hair. His slightly bent left arm is stretched westwards. The ecliptic intersects his body at the middle. His left arm holds an urn from which water streams. The stream runs down but does not connect to the flow of water that streams south from the ecliptic and below the feet of Aquarius to the mouth of Piscis Austrinus. Pisces consists of two fishes.The southern of the two fishes is located below the wing of Pegasus. The other, northern fish is located below the raised arm of Andromeda. There is a barely visible ‘cord’ which connects the tails of the fishes. Cetus is presented as a whale, the head of which is south of Aries. The

mouth is wide open and the teeth are shown. Orion is a naked figure with curly hair. His head is turned towards Taurus. He holds a shield in his raised right arm. He carries a club in his raised left hand. He kneels on his left knee and his right leg is bent. He has a belt around his middle to which a sword in a scabbard is attached. Eridanus is a river presented by a band with wave-like borders. It starts at the western lower leg of Orion and streams first west to Cetus. It continues in the opposite, eastern direction until it makes another turn and ends at the last star of the river (θ Eri). Lepus is a hare with long ears. Canis Maior is a dog with a collar around his neck. Canis Minor is a walking dog. Navis is the rear part of a sailing ship with a mast and a triangular sail. There are two steering oars, the southern one of which emerges from behind the ship. Hydra is a snake with a head that is drawn twice.The mouth is wide open and his teeth are shown. The head is below the southern claw of Cancer.The end of the tail is above the head of Centaurus. Crater is a cup with handles standing on the body of Hydra. Corvus is a bird standing on the body of Hydra. It is picking the snake. Centaurus is a horse with a nude figure with curly hair on top. His arms are stretched out in front of him. His left hand holds the right foreleg of Lupus, his right hand touches the belly of Lupus. Lupus is an animal with its mouth is open, held by Centaurus. His teeth and tongue are shown. Ara is a square altar with flames on top. It is upside-down. Corona Australis is, like the northern crown, a crown with six petals, three of which are drawn on the outside and the other three on the inside the ring. It is located in front of the left leg of Sagittarius. Piscis Austrinus is a fish with an open mouth, with its head turned east. comments: For illustrations, see Figs 5.2–5.12. This globe is unfortunately not in good condition. Although I examined the globe personally in 1992, my description depends greatly on Hartmann’s excellent study of it. Literature: Hartmann 1919 and my description in Bott 1992, pp. 508–9, no. 1.8.

422

Appendix 5.2 European celestial globes made before 1500 WG2. CRACOW, JAGIELLONIAN UNIVERSITY MUSEUM , Inv. no. 4039–37/V Ø sphere 40 cm, height 132 cm; made in Hungary, Buda. Date: 1480. Maker : Attributed to Hans Dorn. Made for Martin Bylica who donated the globe after his death in 1493 to the University of Cracow. construction: The brass sphere consists of two hemispheres fixed to each other at the Equator.There are holes at the north and south ecliptic poles. The sphere is mounted at the north and south equatorial pole in a graduated brass meridian ring (clockwise from N: 0°–90°; 90°–0°; S: 90°–0°; 0°–90°; numbered every 5°, division 1°). On top of the meridian ring is an hour circle (twice 0–12 hours; marked every hour, divided into ¼ hours) and a pointer, which is firmly attached to a handle that helps to rotate and tilt the sphere. All numbers are gothic except those on the hour circle. The meridian ring fits into a brass stand consisting of four quarter-circles, which rise to support a square horizon plate (51.5 × 51.5 cm). The quarter circles are joined around the support for the meridian ring. From the support curved legs divert downwards and end in feet made of claws around balls. Around the circular cut in the horizon plate are a number of scales (from inside to outside):for the ecliptic (12 times 0°–30°; numbered every 5°, division 1°) with the Latin names of the zodiacal signs: ARIES, THAVRVS, GEMINI, CANCER, LEO, VIRGO, LIBRA, SCORPIO, SAGITARIVS (sic), CAPRICORNVS, AQVARIVS, PISCES; for the Julian calendar (numbered every five days from 5–25, and the last day of month (for July, August, September, and October this last day (30/31) is missing), division 1 day) with the Latin names of the months: IANVARIVS, FEBRVARIVS, MARCIVS, APRILIS, MAIVS, IVNIVS, IVLIVS, AVGVSTVS, SEPTEBER (sic), OCTOBER, NOVEMBER, DECEMBER. The

zodiac is aligned with respect to the calendar such that the first point of Aries is at 11 March, that of Cancer at 13 June, that of Libra at 14 September, and that of Capricorn at 12 December. In the outermost ring is a wind rose, starting from north anti-clockwise: (no name for north), CHORVS, CIRCIVS, ƷEPHIRVS, FAVONVIS, AFRISVS, (no name for south), NOTHVS, EVRVS, SVBSOLĀN(VS), VVLT(VR) NVS, BOREAS. The name at the south is possibly hidden under the accessory to fix the meridian ring. On the horizon plate the last capital letter S is often, but not always, elongated. In the south corner of the horizon plate is a sundial with string-gnomon and a compass having a magnetic variation of around 10°. In the northern corner is the coat of arms of Martin Bylica, showing Sagittarius with sunrays in the top behind him around a starry symbol and a rose with five petals below the centaur. On top of the field is a hat with double tasselled ropes characterizing the title of Protonotary Apostolic held by Martin Bylica. astrolabe disc: On top of the meridian ring is a vertical rod attached to a mobile support for a disc with a diameter of 28 cm. From this support two quadrants extend to the horizon plate which can rotate with the support in azimuthal direction. The limb of the mater of the astrolabe disc is graduated for degrees (0°–360°; numbered every 5°, division 1°). The inside of the mater is engraved just below the rim with a scale for equal hours (numbered every hour: 1–24) and two sets of curves in stereographic projection: the twelve unequal hour lines (numbered every hour: 1–12) and a grid of lines marking the boundaries of mundane houses and their divisions for latitude 47.5º.The twelve houses are labelled in Latin: PRIMA,SECVNDA,TERTIA,QVARTA,QVINTA, SEXTA, SEPTIMA, OCTAVA, NONA, DECIMA, VNDECIMA, DVODECIMA.The main boundaries are marked by dots. Each house is subdivided by curves into 10 subsections. A series of dots on a straight line marks the centres of the circles of the mundane houses. On top of this is a zodiacal ring sustained by

423

the mathematical tradition in medieval europe bars in the north–south and east–west directions with a ruler on top, attached by way of a 6-petal rose such that both ring and ruler can rotate independently around the north pole. The ecliptic is graduated (12 times 0°–30°; numbered every 5°, division 5°) with the Latin names of the zodiacal signs: ARIFS [sic], THAVRVS, GEMINI, CANCER, LEO, VIRGO, LIBRA, SCORPIO, SAGITARIVS [sic], CAPRICORNVS, AQVARIVS, PISCES. On the back of the astrolabe disc the limb is graduated for degrees (clockwise from the zenith: 90°–0°; 0°–90°; 90°–0°; 0°–90°; numbered every 5°, division 1°). In the lower half are two quadrants each with scales for the VMBRA VERSA (0–12; numbered every unit, divided into 24 units) and the VMBRA RECTA (12– 0; numbered every unit, divided into 24 units). Inside these graduated scales is a grid (sometimes labelled organum ptolemei) consisting of two sets of lines in the orthographic projection: the parallels between the tropics corresponding to specific positions of the Sun in the ecliptic and 12 equal hour lines (numbered 1–11 along the tropics). North and south of the Equator, along the hour lines 1 and 11, is a scale (numbered 10, 20, 30) expressing which parallels correspond to locations 10, 20, 30 degrees in the zodiacal signs indicated at the sides. The signs are labelled: from the Tropic of Cancer to that of Capricorn around the autumnal equinox: CA, LEO, VIRGO, LIBRA, SCORP, SA; from the Tropic of Capricorn to that of Cancer around the vernal equinox: CA, AQVA, PISCES, ARIES, TAVRVS, GE. Along a semicircle north of the Equator is a graduated scale for declination (clockwise and anti-clockwise from the Equator: 0°–90°; numbered every 5°, division 1°). An alidade with sights is attached to the centre of the astrolabe disc such that the alhidade can rotate around the north pole. The empty area north of the Tropic of Cancer is filled with a band with the following text: ‘HORA(M)·SOLE·LVCENTE·VIDEBIS·SI·AB· ELEVACIONE·SOLIS·REGVLA· CVM·FILO· SECVNDVM · NVMERVM · RESIDVI · LATITVDINIS·REGIONIS· DEMISSA· FILVM· SVPER· COLLECTVM.’

The empty area south of the Tropic of Capricorn is filled with a band with the following text: ‘ EX · ELEVATIONE·SOLIS·ET·IPSO·RESIDVO ·IN·INTERIORI·CIRCVLO* PROTRAXERIS· Q V O D · PA R A L E LV M · S O L I S · I N T E R · SECANDO·HORAM·OSTENDET 1480.’ cartog raphy: Language Latin. There are great circles through the ecliptic pole and the boundaries of the zodiacal signs.The Equator is graduated (0º–360º; numbered every 5º, division 1º).The ecliptic is graduated (12 times 0º–30º; numbered every 5º from 5º–25º, division 1º).The numbers of the zodiacal signs (1, . . . , 12) are added in the last section of 5º.The polar circles, the tropics, and the colures are drawn but not labelled. astronomical notes: (α Leo is in Leo 22.5°).The longitudes of the stars plotted on the globe exceed on the average the Ptolemaic longitudes by 19° 56´±12´. The brightness is indicated by four different symbols (starry symbols with respectively 8, 7, 6, 5, and 4 rays). For some but not all stars,the planetary symbols are engraved. The MilkyWay is drawn but not labelled.The star names are listed in Table 5A.1 in Appendix 5.1 above. constellations: All 48 Ptolemaic constellations are engraved and most are labelled. descriptions: Ursa Minor, labelled VRSA MINOR, is a small bear with a long tail. His back is turned to Ursa Maior. Ursa maior, labelled VRSA MAIOR, is a great bear with a long tail. Draco, labelled DRACO, is a snake with four curls; his tongue sticks out his mouth. Cepheus, labelled CEPHEVS, is seen from the rear, dressed in a tunic, with hair emerging from a Phrygian hat. He is kneeling on his right leg and his arms are stretched out. Bootes, labelled BOETES, is a naked figure with curly hair, seen from the rear. His left arm is raised and in his right hand is a straight stick which ends on the right foot of Hercules. Corona Borealis, labelled CORANA (sic), is an open crown with petals. Hercules, labelled HERCVLES, is seen from the rear; he is dressed in a suit of armour and has mid-length curly hair. His head is west of that of Ophiuchus. He is kneeling on his right knee and his left foot is above the head of Draco. His left

424

Appendix 5.2 European celestial globes made before 1500 arm is stretched out in the direction of Lyra. He holds a lion’s skin by his left hand and a curved sword in his raised right hand.Lyra, labelled VVLTVR CADENS, is presented as a bird with a short crooked beak. Cygnus, labelled GALINA, is a bird with outstretched wings, as if flying.The bird has a short beak. Cassiopeia, labelled CASSFPIA (sic), is turned in a simple square chair and thus seen from the rear. She wears a long dress and a long kerchief over her head which covers her face and extends to her shoulders. Her right arm is stretched out. She has no attributes. Perseus, labelled PERSEVS, is a naked figure with mid-length curly hair, seen from the rear. He holds a curved sword in his right hand above his head and he carries a head with devil’s ears in his lowered left hand. Auriga, labelled AVRIGA, is a nude figure seen from the rear, with a long pointed cap extending in a kind of short cape over his shoulders. His left knee is bent. Both arms are lowered. On his left shoulder stands a goat and in his right hand is a harness. His right foot touches the northern horn of Taurus. Ophiuchus, labelled SERPNTARIVS (sic), is a naked figure with curly hair seen from the rear. His head is turned west towards the nearby head of Hercules. He holds Serpens in his hands. One of his feet rests on the body of Scorpius. Serpens is a snake with an open mouth. Its body, which encircles the lower arms and middle of Ophiuchus, has four coils. Sagitta, labelled SAGITTA, is drawn as a simple arrow.Aquila, labelled AQVILA, is drawn as a bird with outstretched wings, flying in a southeastern direction. Delphinus, labelled DELPHINVS, is drawn as a dolphin with sharp teeth. Equuleus, labelled EQVVS PRIOR, is drawn as the head of a horse.Pegasus, labelled EQVVS PEGASVS, is drawn as half a horse with wings. Andromeda, labelled ANDROMADA (sic), is a nude female figure with her hair in tresses around her head, seen from the rear. She holds a chain in her hands which encircles her middle. Her body is more or less parallel to the ecliptic, and the top of her head touches the belly of Pegasus. Her left arm is raised above the northern one of the Pisces.The other right arm is stretched towards the north. Triangulum, labelled TRIANGVLVS, is

drawn as a triangle.Aries, labelled ARIES, is drawn as a ram with two horns and a curly fleece. He lies with his forefeet bent. He is looking backwards to Taurus. The ecliptic cuts through his body and passes above his tail.Taurus, labelled TAVRVS, is a half bull with a bent head, two front legs, and two horns.The ecliptic passes through his body and his head. The northern horn extends to the left foot of Auriga. Gemini, labelled GEMINI, consist of two nude figures with curly hair, both seen from the rear. Their heads are turned to each other and their legs stretch westwards. They are without attributes. The right arm of the western twin rests on the shoulder of the eastern twin. Cancer, labelled CANCER, is a crawfish with two claws facing Leo and three legs on either side. The ecliptic passes through the main body. Leo, labelled LEO, is a lion standing on its hindlegs with his forefeet as if jumping. He has his mouth open. The lion’s tail makes a loop.The ecliptic passes through the chest and the hindlegs.Virgo, labelled VIRGO, is a female figure with her hair in tresses around her head and with wings, seen from the rear. She wears a long dress with a belt. Her head is turned in profile to the north.The body aligns more or less with the ecliptic.The ecliptic passes through her southern wing. She points with her right hand to her head. In her lowered left hand she holds an ear of wheat with the bright star Spica. Libra, labelled LIBRA, is presented by a pair of scales. Scorpius, labelled SCORPIVS, is drawn as a scorpion with short claws, five northern and four southern legs, and a segmented tail. Sagittarius, labelled SAGITARIVS (sic), is a horse with a nude figure on top, seen from the rear.The male figure has a cloak attachments and an ornamental belt. In his left hand he carries a bow and in his (invisible) right hand he holds the arrow. The ecliptic intersects his head. Capricornus, labelled CAPRICOR(NVS), has two long horns and a fish tail. The ecliptic intersects him through the mouth, just below the neck and through the tail. Aquarius, labelled AQVARIVS, is a nude figure with curly hair, seen from the rear. His slightly bent left arm is stretched westwards and holds a folded piece of cloth. The ecliptic intersects his body at the hips. His

425

the mathematical tradition in medieval europe right arm passes through the handle of an urn from which water runs, which streams to the mouth of Piscis Austrinus. Pisces, labelled PISCES, consists of two fishes. The southern of the two is located below the wing of Pegasus. The other northern fish is located below the raised arm of Andromeda. There is band with a knot which connects the tails of the fishes. Cetus, labelled CETVS,is presented as a whale.Orion, labelled ORION, is dressed in a suit of armour, with hair emerging from a Phrygian hat. He has curly hair and is seen from the rear. He holds a cloth in his raised left hand and carries a club in his raised right hand. He kneels on his left knee and his right leg is slightly bent. He carries a sword in a scabbard. Eridanus, labelled ERIDANVS, is a river presented by a band which starts at the left foot of Orion, and streams first west to Cetus. It continues in the opposite, eastern direction until it makes another turn and ends at the last star of the river (θ Eri). Lepus, labelled LEPVS, is a hare with long ears. Canis Maior, labelled CANIS MAIOR, is a wolf-like animal with wide open mouth, erect ears, and hair in its neck. Canis Minor, labelled PROCHION, is a running dog with a collar. Navis, labelled NAVIS, is a galleon with a mast, a crow’s nest, and a sail.There are two steering oars which emerge from both sides of the ship. At the western end of the ship is a chair with a shield attached to it. Hydra, labelled IDRA, is a snake with long ears. Its open mouth shows his teeth and tongue. The end of the tail is above the head of Centaurus. Crater, labelled CRATER, is a kettle with one handle standing on the body of Hydra. Corvus, labelled CORVVS, is a bird standing on the body of Hydra. It is picking the snake. Centaurus, labelled CENTAVRVS, is a horse with a nude figure on top, seen from the rear. He has long curly hair held together by a band. On his middle is an ornamental belt. On his right arm rests a shield which is attached to a strap around his neck.With his right hand he holds the left legs of Lupus. In his (invisible) left hand he holds a stick which ends at the head of Lupus. Lupus, labelled LVPVS, is an animal with its mouth is open, held by Centaurus.Ara, labelled ARA, is a square pedestal with flames on top. It is upside-down. Corona Australis,

labelled CORONA AVSTIALIS (sic), is a domed crown with petals on the border and one on top. Piscis Austrinus, labelled PISCIS MERIDIANVS, is a fish with mouth open, showing its teeth. comments: I acknowledge with pleasure the assistance of Marcin Banas of the Jagiellonian University Museum in making the description of this globe. The precessions correction of 19° 56´ ± 12´ was determined by measuring the ecliptic longitudes of 24 stars.The data on sizes are from Ameisenowa 1959, p. 12 who also mentions the circumference of the sphere as 125.4 cm. Zinner 1967, reprint 1979, mentions a circumference of 124 cm, that is a diameter of 39.5 cm. Pilz 1977, p. 63 quotes a height of 1.32 m and a diameter of 1.24 m, confusing the diameter with the circumference of the globe. Chlench 2007, p. 76, mentions a diameter of 1.32 m, confusing the diameter with the height of the globe. Zinner 1967, reprint 1979, p. 295 mentions the diameter of the astrolabe disc of 28 cm and the size of the horizon plate. Ameisenowa 1959, p. 12 says that the sphere is made out of one piece of brass. Excess material was removed from a hole in the south polar area by a tightly fitting plate. Her source is Birkenmajer whose text I have not been able to consult. King and Turner 1994, p. 194, say that the elongated last capital letter S in some names of the months on the horizon plate is typical for Dorn. Bartha 1990/1991 p. 39, and Bartha 2000, p. 49, mentions a scale for azimuth on the horizon plate from 0°–360° with a division into 1° which is not there. Literature: Ameisenowa 1959; Zinner 1967/1979, pp. 292–7.

WG3. STUTTGART, WURTTEMBERGISCHES LANDESMUSEUM , Inv. no.WLM 2000–120 Ø sphere 49 cm, height 107 cm; made in Justingen. Date: 1493. Author : Johannes Stöffler; an artist’s monogram consisting of a sword with the letter N is marked on the hindquarters of the constellation Centaurus.

426

Appendix 5.2 European celestial globes made before 1500 In the seventeenth century the globe was the property of the Dom School in Konstanz; in 1825 it is mentioned in a description of the Dom; thereafter the globe was placed in the library of the Gymnasium in Konstanz. In 1895 it was given on loan to the Germanisches Nationalmuseum, GNM Inv. Nr. WI 1261 and it is now in the Wurttembergisches Landesmuseum. There are two inscriptions on the stand (Figs 5.45a–b). On the left side is the image of a man pointing to the sphere. Below him is the inscription from Ovid, Metamorphoses, I. lines 78–79, 84–86:‘NAT(VS) HOMO EST QVEM DIVINO SEMINE FECIT/ILLE

OPIFEX RERVM MVNDI MELIORIS ORIGO/ PRONAQ(VE) QVOM SPECTENT ANIMALIA CETERA/TERRAM OS HOMINI SVBLINE DEDIT CAELVMQ(VE) VI-/DERE IVSSIT ET ERECTOS AD SYDERA TOLLERE VVLT(VS)’. On the right side is a coat of arms with a lion on a white field. Left of it is the other inscription: ‘SPHAERAM HANC SOLIDAM/IOANNES STÖFFLER IVSTING-/ENSIS ANNO CHRISTI MAXIMI/1493 FOELICISSIMO SYDERE FA-/ BREFECIT’. construction: The sphere is made of wood and around 5 cm thick. It is mounted on an axis through

Figs 5.45 a–b Inscriptions on the stand of the celestial globe of Johannes Stöffler. (Photo: Elly Dekker.)

427

the mathematical tradition in medieval europe the north and south equatorial poles in a metal meridian ring, 10 mm thick and 39 mm wide.The meridian ring is graduated for declination (clockwise and anticlockwise from N: 90°–0; 0°–90°; numbered every 5°, division 1°) and its complement (clockwise and anti-clockwise from N: 0°–90°; 90°–0°; numbered every 5°, division 1°) and fits into a wooden stand on four legs, which are connected to each other by wooden strengthening. On top of the meridian ring is a brass hour circle with pointer by which the sphere can be set to equal or unequal time with the help of a handle connected to the polar axis. The stand supports a wooden horizon ring. On its outer boundary is a series of nails and the four main compass directions: ‘ORIENS, MERIDIES, OCCIDENS, SEP-

TENTRIO’. On top of the horizon ring are a number of scales (from inside to outside): for azimuth (clockwise and anti-clockwise from N: 90°–0°; 0°–90°; numbered every 5°, division 1°); for the ecliptic (12 times 0°–30°; numbered every 5°, division 1°) with the Latin names of the zodiacal signs; for a calendar with the names of the saints, dominical letters and the Latin names of the months.The zodiac is aligned with respect to the calendar such that the first point of Aries is between 10 and 11 March. In the outermost ring are compass directions marked by 12 wind heads (Fig. 5.47). At the month October is the coat of arms of Daniel of Konstanz, his mitre and crosier (Fig. 5.46). Above the coat of arms is the inscription:‘Danielis Dei gratia Pontificis Bellinensis foelicia hec sunt Arma’. Around

Fig. 5.46 Coat of arms on the horizon ring of the celestial globe of Johannes Stöffler. (Photo: Elly Dekker.)

Fig. 5.47 Wind head on the horizon ring of the celestial globe of Johannes Stöffler. (Photo: Elly Dekker.)

428

Appendix 5.2 European celestial globes made before 1500 the sphere, close to its surface, are two sets of four brass semicircles passing through the north and south points of the horizon. These semicircles are connected in the middle by a brass arc. The points of intersection of these semicircles with the ecliptic on the sphere determine the boundaries of the mundane houses. cartog raphy: Language Latin.There are great circles through the ecliptic poles and the boundaries of the zodiacal signs. The ecliptic is labelled ZODIAC(VS); it is graduated (12 times 0º–30º; numbered every 5º, division 1º). The zodiacal band is defined by two parallels 12º north and south of the ecliptic. The ecliptic poles are labelled ‘P:Z:S:’ and ‘POL(VS) ZODIACI MERI:’. The Equator is labelled EQVINOCCIALIS; it is graduated (0º–360º; numbered every 5º, division 1º).The equatorial poles are labelled:‘POLVS SEPTENTRIO/NALIS ARCTICVS VEL/BOREALIS and [POLVS] ANTARCTICVS’.The polar circles are labelled ‘CIRCVL(VS) ARCTICVS’ and ‘CIRCVLVS ANTARCTICVS’. The tropics are labelled ‘TROPIC(VS) CANCRI VEL ESTIVALIS’ and ‘TROPICVS’ HVEMALIS/ CAPRICORNI’. The colures are drawn and labelled: ‘COLVRVS EQVINOCIALIS and COLVR(VS) SOLSTI[. . .]’.The solstitial colures are graduated (N and S from the Equator 0°–90°; numbered every 5°, division 5°). astronomical notes: (α Leo is in Leo 22°). The longitudes of the stars plotted on the globe exceed on the average the Ptolemaic longitudes by 19° 38’ ± 11’. The stars are marked by brass nails with a starry head consisting of six rays. Different brightnesses are indicated by different sizes.The Milky Way is drawn and labelled: GALAXIA.The star names are listed in Table 5A.1 in Appendix 5.1 above. constellations: All 48 Ptolemaic constellations are drawn and most are labelled. descriptions: Ursa Minor, labelled VRSA MINOR AVT CINOSVRA, is a small bear with a long tail. Ursa Maior, labelled ARCTOS M[. . .] VRSA MAIOR [VE]L ARCTVR, is a great bear

with a long tail. Draco, labelled DRACO, is a snake with his tongue sticking out his mouth. Cepheus, labelled CEPHEVS, is seen from the rear. He is dressed in a tunic, wears a crown, holds a sceptre in his right hand and has a sword attached to a belt around his middle. Bootes, labelled ARCTOPHILAX [VE]L BOETES, is seen from the rear. He wears a hat, a tunic and boots, and holds in his right hand a lance which ends on the right foot of Hercules. In his raised left hand he has a sickle. On his left side is a sheaf of corn. In his right side are two dogs connected by leads to the wrist of the same hand that holds the lance. Corona Borealis, labelled CORONA BOREALIS, is an open crown with petals. Hercules, labelled HERCVLES AVT GENVFLEXVS, is seen from the rear; he is dressed in a colourful garment. He is kneeling on his right knee and his left foot is above the head of Draco. His left arm is stretched out in the direction of Lyra. He holds a lion’s skin in his left hand and a stick or club in his raised right hand. In front of his right lower leg is a bunch of branches, possibly the golden apples of the Hesperides. Lyra, labelled VVLTVR CADENS, is presented as a bird with a short crooked beak. Cygnus, labelled OLOR AVT GALLINA, is a bird with outstretched wings. The bird has a winding neck. Cassiopeia, labelled CASSIOPEIA, is turned in a throne with a high square back and an ornament on top and thus seen from the rear. She is nude and looks in a mirror held in her left hand. Her raised right hand is tied to the ornament at the back of the throne. Perseus, labelled PERSEVS, is seen from the rear. He has long curly hair, wears a loincloth and has wings at his feet. He holds a slightly curved sword in his right hand above his head. In his lowered left hand he carries a cut-off head from which blood spatters. Auriga, labelled AVRIGA AVT AGITATOR, is seen from the rear. He wears a hat, a tunic, and boots. On his left shoulder stands a goat. His head is turned west and he is on his knees. Both arms are lowered. In his right hand is a harness and his left hand seems to rest on a carriage wheel. His right foot touches the northern horn of Taurus. Ophiuchus, labelled SERPENTARIVS [VE]L

429

the mathematical tradition in medieval europe ANGVITENENS, is seen from the rear; he is dressed in a colourful garment. His head is turned west towards the nearby head of Hercules. He holds the body of Serpens in his hands. One of his feet rests on the body of Scorpius. Serpens, labelled SERPENS is a snake with an open mouth. Its body, which encircles the lower arms and middle of Ophiuchus, has four coils. Sagitta, labelled SAGICTA (sic), is drawn as a simple arrow. Aquila, labelled AQVILA, is a bird but it is hardly visible. Delphinus, labelled DELPHIN, is drawn as a dolphin with sharp teeth. Equuleus, labelled EQVVS PRIOR, is drawn as the head of a horse. Pegasus, labelled EQV(VS) Z[. . .] ALAT(VS), is drawn as half a horse with wings. Andromeda, labelled ANDROMADA (sic), is a nude female figure with her hair held together by a tress around her head, and seen from the rear. She is chained at her wrists to the branches of two trees at her sides.The chain passes behind her back. Her body is more or less parallel to the ecliptic, and the top of her head touches the belly of Pegasus. Her left arm is raised above the northern one of the Pisces. The other right arm is stretched towards the north.Triangulum, labelled TRIANGVLVS, is drawn as a triangle. Aries, labelled ARIES, is drawn as a ram with two horns and a curly fleece. He lies with his forefeet bent. He is looking backwards to Taurus.The ecliptic cuts through his body and passes above his tail. Taurus, labelled THAVRVS, is half a bull with a bent head, two front legs, and two horns. The ecliptic passes through his body and his head. The northern horn extends to the right foot of Auriga.The Pleiades are marked by seven stars which are labelled: Plijades. Gemini, labelled GEMINI, consist of two nude figures, both seen from the rear.Their heads are turned to each other and their legs stretch westwards.They are without attributes.The right arm of the western twin rests on the shoulder of the eastern twin and the left arm of the eastern twin is around the middle of the western twin. Cancer, labelled CANCER, is a crawfish with two claws facing Leo and three legs on either side. The ecliptic passes through the main body. The two Asses are labelled: Due asini. Leo, labelled LEO, is a lion standing on its

hindlegs with his forefeet as if jumping. His mouth is slightly open.The lion’s tail makes a loop.The ecliptic passes through his forefeet.Virgo, labelled VIRGO, is a female figure seen from the rear with her hair held together by a tress around her head and with wings. She wears a long dress with a belt loosely around her middle. Her head is turned in profile to the north. The body aligns more or less with the ecliptic. The ecliptic passes through her southern wing. She points with her right hand to her head. In her lowered left hand she holds an ear of wheat with the bright star Spica. In her other right hand she holds a sceptre. A banner with the text ‘Justitia terras reliquit, quia victa jacet pietas’, is connected to the hand holding the sceptre. Libra, labelled LIBRA, is presented by a pair of scales. Scorpius, labelled SCORPIO, is drawn as a scorpion with short claws and a segmented tail. Sagittarius, labelled SAGICTARI(VS) (sic), is a horse with a nude figure on top, seen from the rear. The male figure wears a hat and from it emerges very long hair that flies behind him. In his left hand he carries a bow and in his (invisible) right hand he holds the arrow.The ecliptic intersects his head. Capricornus, labelled CAP[RI]CORN(VS), has two long horns and a fish tail. The ecliptic intersects him through the mouth, below the neck and through the tail. Aquarius, labelled AQRI(VS), is seen from the rear. All he wears is a loincloth. His slightly bent left arm is stretched westwards and holds a folded piece of cloth.The ecliptic intersects his body at the hips. His right lower arm is on top of an urn from which water runs, which streams to the mouth of Piscis Austrinus. Pisces, labelled PISCES, consists of two fishes. The southern of the two is located below the wing of Pegasus.The other, northern fish is located below the raised arm of Andromeda. There is band with a knot which connects the tails of the fishes. Cetus, labelled CETVS MAGNVS AVT PISTRIX, is presented as a whale. Orion, labelled ORION, is dressed as a knight, seen from the rear. His head is backwards to show his face. He holds an ox hide by its head in his raised left hand and carries a club in his raised right hand. He kneels on his left knee and his right leg is slightly bent.

430

Appendix 5.2 European celestial globes made before 1500 He carries a sword in a scabbard. Eridanus, labelled FLVVIVS GYON SIVE NILVS, is a river presented by a band with a wavy pattern which starts at the left foot of Orion, and streams first west to Cetus. It continues in the opposite, eastern direction until it makes another turn and ends at the last star of the river (θ Eri). Lepus, labelled LEPVS, is a hare with erect ears. Canis Maior, labelled CANIS MAIOR, is a dog with a collar, as if jumping. Canis Minor, labelled CANIS MINOR PROCION, is a walking dog with a collar. Navis, labelled NAVIS [VE]L ARGVS, is half a ship with a mast, a crow’s nest, and a lowered sail.There are two steering oars which emerge from both sides of the ship.At the western end of the ship is a small building and at the cut-off side there is a cloud. Hydra, labelled HYDRA, is a snake with its mouth open, showing its teeth. The end of the tail is above the head of Centaurus. Crater, labelled VAS [VE]L CRATER, is a tub with two handles standing on the body of Hydra. Corvus, labelled CORV(VS) APPOLLINE(VS), is a bird standing on the body of Hydra. It is picking the snake.

Centaurus, labelled CENTAVRVS AVT CHYRON, is a horse with a figure on top, seen from the rear. He has long curly hair and his middle is marked by a hairy belt. Above his right arm is a hard to identify object which is attached to a belt around his shoulder. He holds with both hands a lance which pierces the head of Lupus. Lupus, labelled LVPVS, is an animal with its mouth is open, held by Centaurus. Ara, labelled ARA, is a square pedestal with flames on top. It is upside-down. Corona Australis, labelled CORONA MERIDIONALIS [VE]L AVSTRALE SERVM, is an open crown with petals. Piscis Austrinus, labelled PISCIS MERIDIONALIS, is a fish with its head turned towards its tail, mouth open showing its teeth. comments: The precessions correction of 19° 38’ ± 11’ was determined by measuring the ecliptic longitude of 16 stars located close to the ecliptic. Literature: Moll 1877; Zinner 1967/1979, pp. 543–5; my description in Bott 1992, Kat. 1.16, pp. 516–18; Oestmann 1993; Oestmann 1995/6.

431

epilogue

E

arly attempts to describe the stars and to bring order to their distribution over the sky indicate the start of scientific enquiry in astronomy. The introduction of the moving sphere as a model for understanding the celestial phenomena caused a great breakthrough in scientific thinking about the structure of the world. It provided the momentum for making celestial globes and mapping the stars. All extant globes contain a celestial grid consisting of the main celestial circles defined by the daily and annual motions of the Sun and the stars. Descriptions of the locations of constellations with respect to this grid by, for example, the Greek astronomer Eudoxus provided the necessary information for drawing constellations on a globe. These building blocks for making globes in the descriptive tradition, the oldest branch of celestial cartography, were available from the fourth century bc onwards. The first generation of globes must have been characterized by Eudoxan colures passing through the middle of the respective zodiacal constellations and by an ecliptic not yet divided into signs. No globes from this early stage of mapping have survived but two unusual medieval hemispheres testify their existence, Next to being instrumental to further the understanding of the cosmos without knowledge of the ins and outs of spherical trigonometry, globes were greatly appreciated in Antiquity as decorative objects.All three still extant antique globes belong to this class. On all three globes the colures pass just west of the respective zodiacal constellations (Aries, Cancer, Libra or the

Claws, and Capricorn), but in other respects they differ greatly. A number of characteristics of Kugel’s globe, as, for example, an ecliptic not divided into signs and the unusual course of the river Eridanus, are reminiscent of the older Eudoxan tradition. The presentation of its constellations by the mirror images of those as seen in sky adds significantly to our ideas on how constellations were drawn on globes in Antiquity. The Mainz globe stands out in particular for its detailed presentation of the Milky Way that follows closely the description in Ptolemy’s Almagest, the main extant source of the mathematical branch in globe making. Yet in other respects this Mainz globe still belongs to the descriptive tradition as is testified by the presentation of anonymous star groups which occur on Kugel’s and the Mainz globe, but which have disappeared from later cartographic traditions. The locations of the colures on the Farnese globe have given rise to controversies about its date and origin. Some scholars have taken for granted that this globe was copied from a globe in the mathematical tradition, the other main branch of celestial cartography. If so, the Farnese globe shows what remains of the precision of a mathematical globe when it (perhaps after repeated copying) is converted into a work of art. From an artistic point of view the presentations of the constellations on the Farnese globe are without parallel in celestial cartography. It would be an error of judgement to think that the constellations on early mathematical globes would have been comparable in design to those

Epilogue on the Farnese globe. While all three extant antique globes have their own individual history they support together the overall picture that astronomers and artists together have left their mark in the development of models of the celestial sky. The cultural impact of globes and more generally of astronomy is also echoed in the oldest known ceiling painting of the celestial sky in the bath house of Quṣayr cAmra, believed to have been built in the first half of the eighth century, which was modelled on a Greek celestial globe in the descriptive tradition. Contrary to what have been claimed in the literature, the ceiling painting does not reflect any detail that would require knowledge of Ptolemy’s Almagest. Although no antique celestial maps from the descriptive tradition have survived, their existence in Antiquity may be deduced from still extant maps in illustrated manuscripts dating from Carolingian and later times. Medieval maps can be divided into three distinct types:

• pairs of summer and winter hemispheres • planispheres • pairs of hemispheres separated by the Equator. All pairs of summer and winter hemispheres have their origin in globes. On one pair (in Aberystwyth MS 735C) and on a winter hemisphere (in Monza MS B 24/163 (228)) the colures pass through the middle of the respective zodiacal constellations. These maps were apparently copied from an early Eudoxan globe and –as mentioned above—provide indirect proof of the existence of such globes. On the remaining pairs of hemispheres the colures pass just west of the respective zodiacal constellations, as on the three extant antique globes. The majority, in all eight including two Byzantine pairs, are part of a tradi-

tion that is characterized by an image of the ivy leaf, the origin of which asterism is rather obscure. This ivy leaf must also have been depicted on the Greek globe used as the model for the ceiling painting in the bath house of Quṣayr cAmra.The parallel circles and the locations of the constellations on this group of maps are completely spoilt by corruption through repeated copying. Six of the maps in this group appear with the text of the Revised Aratus latinus and all emanate from one rather corrupt exemplar. One pair of summer and winter hemispheres in Aberystwyth MS 735C is of an independent type and presents the most complete image of the sky as far as the number of constellations is concerned. However, the grids in these maps are limited to the boundaries of the maps and the zodiac. Planispheres present the celestial sphere in one piece from the north pole to the ever-invisible circle. Perhaps it was because of this format that for a long time it was taken for granted that these medieval planispheres are based on stereographic projection. Examination of the construction details of the ten extant medieval planispheres show that this is not the case. Instead the maps are based on an equidistant model in which the parallel circles are drawn proportional to their distance from the north pole. This is a rather natural choice for maps copied from a celestial globe and does not imply that map makers had a well developed notion of equidistant projection. The medieval planispheres can be divided into two groups: one ordering the constellations as they are depicted on a globe and another as in the sky. Four planispheres in globe-view belong to an older tradition in which Libra is presented by the Claws of Scorpius. The planispheres in sky view belong all to a later (Roman) tradition in which Libra is presented by (a figure holding)

433

Epilogue a pair of scales.These sky-view maps were probably obtained by the mirror image of a planisphere in globe-view. Finally, there are a number of closely-related planispheres occurring in manuscripts stemming from a now lost codex with Germanicus’s Aratea made for the Florence humanist Agnolo Manetti during his stay at Naples in 1466–68.This group of planispheres is more an expression of antiquarian interest than of astronomical learning.This series fostered the first printed celestial map in 1488. The third group of medieval maps comprises two pairs of hemispheres separated by the Equator. The colures on these maps pass on the average through the eighth degree of the respective zodiacal constellations as described by Martianus Capella.This may point to an antique background. A few of the constellations on the pair of maps in Bernkastel MS 212 recall a constellation cycle belonging to the star catalogue De ordine ac positione stellarum in signis which originates from Carolingian times. The other pair of maps in Darmstadt MS 1020 occurs in the middle of an astronomical poem. The northern Darmstadt map shows the ordering of the constellations as depicted on a globe but the southern map shows them as seen in the sky. This inconsistency may have come about while copying these maps from the halves of a globe. The Darmstadt pair could be connected with the globe making ventures of Gerbert of Aurillac which—contrary to the opinion of some scholars—is shown here to be unrelated to Arabic examples or sources. The Darmstadt maps provide by far the best clue of how Gerbert’s celestial globe may have looked like. Extant globes and maps in the mathematical tradition are all relatively late although the necessary ingredients for making them were available from the second century bc when

Hipparchus discovered the phenomenon of precession, compiled a now lost star catalogue, and made a now lost celestial globe. Thus until 1500 all extant globes and maps in the mathematical tradition were based on the star catalogue in Ptolemy’s Almagest. The precession globe described in it may be Ptolemy’s own invention. Unfortunately no antique copy of it has survived. Greek mathematical astronomy spread in the eighth century from Alexandria to the Islamic world where the Almagest was translated into Arabic. In the ninth century Arabic astronomers wrote the first treatises on the use of globes. In these treatises the celestial globe is predominantly presented as an analogue computer for solving problems in spherical trigonometry, although its function as an observational instrument is also sometimes discussed. The earliest extant mathematical celestial globes were made in Muslim Spain in ca. 1080 which although made in the West show glimpses of an early Eastern tradition in globe making. In addition to a few Greek features and typical Islamic elements these globes have characteristics that are seen neither in early Greek sources nor on later Islamic globes. An unmistakable highlight in celestial cartography is the Book on the Constellations of the Fixed Stars which the Persian astronomer al-Ṣūfī wrote for his patron cAḍud al-Dawla. This work includes a star catalogue adapted to the epoch 964 by adding 12° 42´ to the corresponding Ptolemaic longitudes valid for the epoch ad 137. The illustrations of this treatise in Oxford, MS Marsh 144 may—as suggested by al-Bīrūnī— have been copied from a globe, possibly one designed by al-Sūfi himself.The stellar configurations presented in the drawings in MS Marsh 144 include a number of al-Ṣūfī’s own

434

Epilogue observations which are not part of the star catalogue included in his book. Al-Ṣūfī’s conspicuous uranography has been very influential in the Arabic world and later in the Latin West through the Ṣūfī Latinus corpus. All extant eastern Islamic globes adorned with constellation figures and made before 1500 show the impact of al-Ṣūfī’s uranography. All these globes are designed for a fixed epoch. This means that globe makers had to calculate the longitudes of the stars for the required time. The data on the globes made before 1500 show that the precession corrections are consistent with al- Ṣūfī’s constant rate of precession of 1º in 66 years. Arabic astronomy spread from the Middle East to Muslim Spain where the Almagest was translated from Arabic into Latin (1175). From the beginning of the fourteenth century Latin treatises on the construction and use of globes also became available. One Latin text is a translation of the Arabic treatise written by Qusṭā ibn Lūqā, of which a Castilian version had already been made in the thirteenth century. Another Latin text, Tractatus de sphaera solida written in 1303, may have been newly written by using an as yet unidentified Arabic text. The earliest still extant globe made in the Latin West, Cusanus’s globe, dates from about 1320–40. It is a precession globe, the construction of which is described in the Almagest. Such a globe can be adjusted to an arbitrary epoch. There are several holes marked on Cusanus’s globe for different epochs. One hole corresponds to the Ptolemaic epoch ad 137. The interpretation of the other holes in terms of dates is difficult because it is not clear which theory was used to adapt the longitudes of the stars for the epoch concerned. The globe’s iconography is unlike anything known from the Middle Ages or from the Arabic tradition in globe making. Surely this

globe raises more questions than can be answered and any guess on its place of origin is therefore premature. Next in chronological order come the now lost globes made by Jean Fusoris in France in the fourteenth century. Other now lost globes were made before 1435 by members of the Vienna astronomical school. Today only two fifteenthcentury globes survive: the globe made by Hans Dorn in 1480 for Martin Bylica, the court astrologer of King Matthias of Hungary, and another made by the astronomer Johannes Stöffler in 1493 for Bishop Daniel Zehender of Konstanz. Both globes underline the use of celestial globes for finding the right information to act or decide according to astrological doctrines.This application had already been advertised in the prologue to the globe treatise Tractatus de spera solida. It criticized Ptolemy’s description of the celestial globe in the Almagest because it had not been intimated ‘how this instrument might be brought to perfection so that it could be put to everyday uses, i.e. [finding] ascendants, equations of the houses, and other things necessary in this application [i.e. astrology]’.1 The designs of the globes made by Dorn and Stöffler to help the astrologer in his task would have been satisfactory in this respect. In the first half of the fifteenth century the first extant celestial maps in the mathematical tradition emerged.This is not to say that maps in the mathematical tradition were not made in Antiquity but again no maps have survived.The constellations engraved on the well-known Salzburg fragment from the second century ad are not representative for the mathematic tradition although the grid itself is. The complete absence of celestial maps other than the retes of

435

1 Lorch 1980b, p. 156.

Epilogue astrolabes in the Islamic tradition is a puzzle that needs further study because it cannot be explained by a lack of interest in techniques and methods to map the surface of a sphere onto flat planes. Knowledge of stereographic projection came to the Latin West from Muslim Spain through the introduction of the astrolabe around 1000. Leaving such astrolabes aside, the first celestial map engraved with constellation images in stereographic projection made in Europe dates in all probability from the fifteenth century. By that time other maps in the mathematical tradition had been produced in Europe. Around 1425 Conrad of Dyffenbach made the earliest still extant set of maps based on the Ptolemaic star catalogue. Conrad used two projections for constructing his maps. His trapezoidal projection appears to be completely new and not related to the better known Donis projection. The novel features of these trapezoidal maps point to a search for a method on how to map the celestial sphere on a plane. Unfortunately these trapezoidal maps were not a great success and the projection is not seen again in celestial cartography. Another map in the polar azimuthal equidistant projection made by Dyffenbach was not finished.A more successful use of the polar equidistant projection was made in ca. 1435 for a pair of maps which is closely connected to the Vienna globe making enterprise. Construction details of these Vienna maps show that this projection was not yet fully understood. An outstanding feature of theseVienna maps is that all human figures are without exception seen from the rear.This rearview iconography may have been generated while making a celestial globe. By insisting that a star described by Ptolemy in the right hand or in the left foot of a constellation ends up on the

globe also in the right hand or in the left foot all human figures are automatically presented from the rear. The correspondence between the Ptolemaic descriptions and images gained in importance in the fifteenth century. In the sixteenth century all maps and globes present the human constellation figures in rear-view. In the Middle Ages mythology had been a standard ingredient of descriptive star catalogues. Map makers in the mathematical tradition worked with the Ptolemaic star catalogue which incorporates only a few mythological features. In the last quarter of the fifteenth century classical mythology became however more widely known through the (printed) texts of Hyginus and Michael Scot. The impact is especially evident on Stöffler’s globe of 1493: Engonasis (Ptolemy’s figure on its knees) is represented by the mythological Hercules, Perseus has wings on his feet, the head of Ghūl is exchanged for that of Medusa, and Orion’s pelt is turned into an ox hide. The same myth-inspired designs are seen on the Nuremberg maps of 1503, the forerunners of Dürer’s maps of 1515, the first printed maps in the mathematical tradition. This story outlined by the artefacts described in this work is bound to be incomplete. Yet, it has shown that globe making was for a long time the most significant stimulus in the development of celestial cartography in both the descriptive and mathematical traditions. Medieval maps were convenient replacements for globes, serving to illustrate books such as Aratus’s Phaenomena describing the constellations and their myths. Only in the fifteenth century were celestial maps created in their own right independently of globes, foreshadowing the modern period in celestial cartography in the Western world.

436

BIBLIOGRAPHY Abattouy 2007 Mohammed Abattouy, ‘Khāzinī: Abū al-Fatḥ c Abd al-Raḥmān al-Khāzinī (Abū Manṣūr cAbd al-Raḥmān, cAbd al-Raḥmān Manṣūr)’, in BES (Hockey 2007), pp. 629–30. Ackermann 2009 Silke Ackermann, Sternstunden am Kaiserhof. Michael Scotus und sein Buch von den Bildern und Zeichen des Himmels, Frankfurt am Main 2009. Allen 1963 Richard Hinckley Allen, Star names. Their Lore and Meaning, New York 1963 (first published as ‘Starnames and Their meanings’ in 1899). Ameisenowa 1959 Zofia Ameisenowa, The globe of Martin Bylica of Olkusz and Celestial Maps in the East and in the West, Warschau 1959. Aratus (Mair 1921) Aratus, Phaenomena (edition and English translation by G. R. Mair), Cambridge Massachusetts/London 1921. Aratus (Erren 1971) Aratos Phainomena. Sternbilder und Wetterzeichen (edition and German translation by Manfred Erren), Munich 1971. Aratus (Kidd 1997) Aratus, Phaenomena (edition and English translation by Douglas Kidd), Cambridge 1997. Aratus (Martin 1998) Aratos, Phénomènes (edition with French translation by Jean Martin), 2 vols, Paris 1998. Aristotle (Lee 1978) Aristotle, Meteorologica (edition and English translation by H. D. P. Lee), Cambridge Massachusetts/London 1978.

Assemani 1790 Simone Assemani, Globus Caelestis Cufico Arabicus Veliterni Musei Borgiani, Padua 1790. Autolycos (Aujac 1979) Autolycos de Pitane, La sphère en mouvement; Levers et couchers héliaques. Testimonia (edition with French translation by Germaine Aujac with collaboration of Jean-Pierre Brunet et Robert Nadal), Paris 1979. Avienus (Soubiran 1981) Avienus, Les Phénomènes d’Aratos (edition with French translation by Jean Soubiran), Paris 1981. Avilés 2001 Alejandro García Avilés, El Tiempo y los Astros. Arte, Ciencia y Religíon en la Alta Edad Media, Murcia 2001. Babicz 1987 Józef Babicz, ‘The Celestial and Terrestrial Globes of the Vatican Library, dating from 1477, and their maker Donnus Nicolaus Germanus (ca 1420–ca 1490),’ Der Globusfreund 35–37 (1987), pp. 155–68. Baehrens 1879 E. Baehrens, Germanici Arateorum quae supersunt: Poetae latini minores, I, Leipzig 1879. Baehrens 1883 E. Baehrens, Poetae latini minores, V, Leipzig 1883. Baily 1843 Francis Baily, ‘The catalogues of Ptolemy, Ulugh Beigh, Tycho Brahe, Halley, Hevelius [...]’, Memoirs of the Royal Astronomical Society XIII (1843). Barney et al. 2006 Stephen A. Barney, W. J. Lewis, J. A. Beach, Oliver Beghof, The Etymologies of Isidore of Seville, Cambridge 2006. Bartha 1990/1991 Lajos Bartha, ‘Ein Renaissance-Himmelsglobus als astronomisches Instrument: Der Dorn-Bylica-Globus

Bibliography aus dem Jahr 1480’,Der Globusfreund 38/39 (1990/1991), pp. 37–44. Bartha 2000 Lajos Bartha, ‘A Renaissance celestial globe as an analogue computer’, in Klaus Hentschel and Axel D. Wittmann, The role of visual Representation in Astronomy: History and Research Practrice, Acta Historica Astronomiae 9 (2000), pp. 44–52. Bauer 1983 Ulrike Bauer, Der Liber Introductorius des Michael Scotus in der Abschrift Clm 10268 der Bayerischen Staatsbibliothek München:Ein illustrierter astronomisch-astrologischer Codex aus Padua, 14. Jahrhundert, Munich 1983. Bayer 1603 Johannes Bayer, Uranometria, Augsburg 1603. Beer 1932 Arthur Beer, ‘The astronomical significance of the Zodiac of Quṣayr cAmra’, in Creswell 1932, pp. 296–303. Beer 1967 Arthur Beer, ‘Astronomical Dating of Works of Art’, Vistas in Astronomy 9 (1967), pp. 177–223. Benndorf, Weiss and Rehm 1903 O. Benndorf, E. Weiss and A. Rehm, ‘Zur Salzburger Bronzescheibe mit Sternbildern’, Jahreshefte des Österreichischen Archeologischen Institutes in Wien 6 (1903), pp. 32–49; O. Benndorf wrote Part I (pp. 32–35); E.Weiss contributed part II (pp. 35–41) and A. Rehm part III (pp. 41–49). Berggren 1982 J. L. Berggren, ‘Al-Bīrūnī on Plane Maps of the Sphere’, Journal for the History of Arabic Science 6 (1982), pp. 47–81.

Bergmann 1985 W. Bergman, Innovationen des 10. und 11. Jahrhunderts: Studien zur Einführung von Astrolab und Abakus im lateinischen Mittelalter, Stuttgart 1985. BES (Hockey 2007) Thomas Hockey et al. (eds), The Biographical Encyclopedia of Astronomers, New York 2007. Bianchini 1697 Francesco Bianchini, La Istoria Universale provata con monumenti, e figurate con simboli degli antichi, Rome 1697. Birkenmajer 1972 Aleksander Birkenmajer, ‘Marcin Bylica’, in M. Biskup et al., Etudes d’Histoire des Sciences en Pologne, Krakow 1972, pp. 533–6. Bischoff 2004 Bernhard Bischoff, Katalog der festländischen Handschriften des neunten Jahrhunderts (mit Ausnahme der wisigotischen) II: Laon-Paderborn. Wiesbaden 2004. Blume 2007 D. Blume, ‘Sternbilder und Himmelswesen. Zum Bildgebrauch des Mittelalters’, in Bildwelten des Wissens. Kunsthistorisches Jahrbuch für Bildkritik. Imagination des Himmels, Berlin 2007, pp. 73–85. Blume et al. in preparation Dieter Blume, Katharina Glanz, Mechthild Haffner, Wolfgang Metzger, Sternbilder des Mittelalters und der Renaissance, Der gemalte Himmel zwischen Wissenschaft und Phantasie Teil II 1200–1500. In preparation. Boeme 2001 H. Boeme, ‘Oinopides Astronomie und Geometrie’, in M. Toepell (ed.), Mathematik im Wandel, Berlin 2001, pp. 40–53.

Berggren and Jones 2000 J. Lennart Berggren and Alexander Jones, Ptolemy’s Geography: An Annotated Translation of the Theoretical Chapters, Princeton and Oxford 2000.

Boll 1899 F. Boll, ‘Beiträge zur Überlieferungsgeschichte der griechischen Astrologie und Astronomie’, Sitzungsberichte Bayerische Akad. Phil-Hist. Klasse (1899), pp. 77–141.

Berggren and Thomas 1996 J. L. Berggren and R.S.D. Thomas, Euclid’s Phaenomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy, New York 1996.

Boll 1901 F. Boll, ‘Die Sternkataloge des Hipparch und des Ptolemaios’, Bibliotheca Mathematica 3 (1901), pp. 185–95.

438

Bibliography Boll 1903 F. Boll, Sphaera. Neue Griechische Texte und Untersuchungen zur Geschichte der Sternbilder, Leipzig 1903.

Bubnov 1899 Nicolai Mikhailovich Bubnov, Gerberti opera mathematica, Berlin 1899.

Borrelli 2008 Arianna Borrelli, Aspects of the Astrolabe: ‘architectonica ratio’ in tenth- and eleventh-century Europe, [Sudhoffs Archiv 57], Stuttgart 2008.

Burnett 1994 Charles Burnett, ‘Michael Scot and the Transmission of Scientific Culture from Toledo to Bologna via the Court of Frederick II Hohenstaufen’, Micrologus 2 (1994), pp. 101–26.

Borst 1995 A. Borst, Das Buch der Naturgeschichte. Plinius und seine Leser im Zeitalter des Pergaments [Abhandlungen der Heidelberger Akademie der Wissenschaften, Philosophisch-historisch Klasse], Heidelberg 1994, 2nd improved edition, Heidelberg 1995. Borst 1998 Arno Borst, Die karolingische Kalenderreform [Monumenta Germania Historica. Schriften 46], Hannover 1998.

Butzer and Lohrmann 1993 P. L. Butzer and D. Lohrmann, Science in Western and Eastern Civilizations in Carolingiuan Times, Basel 1993. Carruthers 2006 Mary Carruthers, The Craft of Thought: Meditation, Rhetoric, and the Making of Images, 400–1200, Cambridge 1998. I used the third edition printed in 2006.

Boschen 1972 Lothar Boschen, Die Annales Prumiensis. Ihre nähere und ihre weitere Verwandtschaft, Düsseldorf 1972.

Casulleras and Samsό 1996 Josep Casulleras and Julio Samsό, From Bagdad to Barcelona. Studies in the Islamic Exact Sciences in Honour of Prof. Juan Vernet, Barcelona 1996.

Bott 1992 Gerhard Bott (ed.), Focus Behaim Globus: 1. Aufsätze; 2. Katalog, Nuremberg 1992.

Chabás and Goldstein 2003 José Chabás and Bernard R. Goldstein, The Alfonsine Tables of Toledo, Dordrecht 2003.

Bowen and Goldstein 1983 Alan C. Bowen and B. R. Goldstein, ‘A new View of Early Greek Astronomy’, Isis 74 (1983), pp. 330–40.

Charbonnel and Iung 1997 Nicole Charbonnel and Jean-Eric Iung (eds), Gerbert L’Européen, Actes du colloque d’Aurillac 4–7 juin 1996, Société des lettres, sciences et arts ‘La HauteAuvergne’, Mémoires 3 (1997).

Bowen and Goldstein 1991 A.C. Bowen and B.R. Goldstein,‘Hipparchus’ Treatment of early Greek Astronomy: The case of Eudoxus and the Length of Daytime’, Proceedings of the American Philosophical Society 135 (1991), pp. 233–54. Bowen and Todd 2004 Alan C. Bowen and Robert B. Todd, Cleomedes’ Lectures on Astronomy, Berkeley CA 2004. Brieux and Maddison 1974 A. Brieux and F.R. Maddison, ‘Bastulus or Nastulus? A Note on the Name of an Early IslamicAstrolabist’,Archives Internationales d’Histoire des Sciences 24 (1974), pp. 157–60. Brunet et al. 1998 J.-P. Brunet, R. Nadal and Cl. Vibert-Guigue, ‘The Fresco of the Cupola of Qusayr cAmra’, Centaurus 40 (1998), pp. 97–123.

Charette 2003 François Charette, Mathematical Instrumentation in Fourteenth-Century Egypt and Syria: The Illustrated Treatise of Najm al-Dīn al-Miṣrī, Leiden 2003. Charette 2007 François Charette, ‘Ḥabash al-Ḥāsib: Abū Jaʿfar Aḥmad ibn ʿAbd Allāh al-Marwazī’, in BES (Hockey 2007), pp. 455–7. Charette and Schmidl 2004 François Charette and Petra G.Schmidl,‘Al-Khwārizmī and Practical Astronomy in Ninth-Century Baghdad. The Earliest Extant Corpus of Texts in Arabic on the Astrolabe and Other Portable Instruments’, SCIAMVS 5 (2004), pp. 101–98.

439

Bibliography Charvet and Zucker 1998 P. Charvet and A. Zucker, Le Ciel. Mythes et histoire de constellations. Les Catastérismes d’Ératosthène, with astronomical comments by Jean-Pierre Brunet and Robert Nadal, Paris 1998. Chlench 2007 Kathrin Chlench, Johannes von Gmunden deutsch. Der Wiener Codex 3055. Deutsche Texte des Corpus astronomicum aus dem Umkreis von Johannes von Gmunden, Vienna 2007. Cicero (Buescu 1966) Cicéron, Les Aratea (edition with French translation by Victor Buescu), Hildesheim 1966.

Creswell 1932 K. A. Creswell, Early Muslim Architecture, Tome I, Oxford 1932. Cumont 1916 Franz Cumont, ‘Astrologica’, in Revue Archéologique 5e serie III (1916), pp. 1–22. Cuvigny 2004 Hélène Cuvigny, ‘Une sphère céleste antique en argent ciselé’, in Hermann Harrauer and Rosario Pintaudi (eds), Gedenkschrift Ulrike Horak (P. Horak), Florence 2004, pp. 345–80. Damsté 1974 Onno Damsté, Herodotos Historiën, Bussum 1974.

Cicero (Soubiran 1972) Cicéron, Aratea fragments poétiques (edition with French translation by Jean Soubiran), Paris 1972.

Day Lewis 1983 C. Day Lewis, Virgil. The EcloguesThe Georgics, Oxford 1983.

Collinder 1931 Per Collinder, ‘On structured properties of open galactic clusters and their spatial distribution’, Annals of the Observatory of Lund 2 (1931).

Dekker 1990 Elly Dekker, ‘The Light and the Dark: A Reassessment of the Discovery of the Coalsack Nebula, the Magellanic Clouds and the Southern Cross’, Annals of Science 47 (1990), pp. 529–60.

Comes 1996 Mercè Comes, ‘The accession and recession theory in al-Andalus and the North of Africa’, in Casulleras and Samsό 1996, pp. 349–64.

Dekker 1992 Elly Dekker, ‘Der Himmelsglobus—Eine Welt für sich’, in Bott 1992, vol. 1. pp. 89–100.

Comes 2001 Mercè Comes, ‘Ibn al-Hā’im’s trepidation model, Suhayl 2 (2001), pp. 291–408. Condos 1997 Theony Condos, Star Myths of the Greeks and Romans: A Sourcebook containing The Constellations of Pseudo-Eratosthenes and the Poetic Astronomy of Hyginus, Grand Rapids 1997. Contreni 1978 John J. Contreni, The Cathedral School of Laon from 850 to 950, (Münchener Beiträge zur Mediävistik und Renaissance-Forschung 29), Munich 1978. Corsepius 1996 Katharina Corsepius (ed.), Antiquarische Gelehrsamkeit und bildende Kunst. Die Gegenwart der Antike in der Renaissance, (Bonner Beitrage zur Renaissanceforschung, Band 1), Cologne 1996.

Dekker 1999 Elly Dekker (with contributions from Silke Ackermann, Jonathan Betts, Maria Blyzinsky, Gloria Clifton, Ann Leane, and Kristen Lipincott), Globes At Greenwich: A Catalogue of Globes and Armillary Spheres in the National Maritime Museum,Greenwich, Oxford and Greenwich 1999. Dekker 2000 Elly Dekker,‘A Close Look at two Astrolabes and their Star Tables’, in Folkerts and Lorch 2000, pp. 177–215. Dekker 2003 Elly Dekker, ‘Precession globes’, in Marco Beretta, Paolo Galluzzi and Carlo Triarico (eds), Musa Musaei. Studies on Scientific Instruments and Collections in Honour of Mara Miniati, Florence 2003, pp. 219–35. Dekker 2004 Elly Dekker, Catalogue of Orbs, Spheres and Globes, Istituto e Museo di Storia della Scienza, Florence 2004.

440

Bibliography Dekker 2008a Elly Dekker,‘Carolingian Planetary Observations: the Case of the Leiden Planetary Configuration’, Journal for the History of Astronomy 39 (2008), pp. 77–90.

De Meyier 1977 K. A. de Meyier, Codices manuscripti Bibliotheca Universitatis. Codices Vossiani Latini, pars III: Codices in octavo, Leiden 1977.

Dekker 2008b Elly Dekker, ‘A “Watermark” of Eudoxan Astronomy’, Journal for the History of Astronomy 39 (2008), pp. 213–28.

De Smet 1968 A. de Smet, Les sphères terrestre & céleste de Gérard Mercator, 1541 et 1551: Reproductions anastatiques des fuseaux originaux gravés par Mercator et conservés à la Bibliothèque Royale à Bruxelles, Brussels 1968.

Dekker 2009 Elly Dekker, ‘Featuring the First Greek Celestial Globe’, in Globe Studies (English version of Der Globusfreund), 55/56 (2009), pp. 133–52. Dekker 2010a Elly Dekker, ‘Caspar Vopel’s Ventures in SixteenthCentury Celestial Cartography’, Imago Mundi, 62: 2 (2010), pp. 161–90. Dekker 2010b Elly Dekker,‘The Provenance of the Stars in the Leiden Aratea Picture Book’, Journal of the Warburg and Courtauld Institutes LXXIII (2010), pp. 1–37. Dekker and Kunitzsch 2008/9 Elly Dekker and Paul Kunitzsch, ‘An Early Islamic Tradition in Globe Making’, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 18 (2008/9), pp. 155–211. Dell’ Era 1974 Antonio dell’ Era, Una ‘caeli descriptio’ d’eta carolingia, Palermo 1974. Dell’ Era 1979a Antonio dell’ Era,‘Una rielaborazione dell’Arato latino’, in Studi Medievali XX (1979), pp. 268–301. Dell’ Era 1979b Antonio dell’ Era, ‘Una miscellanea astronomica medievale: gli “Scholia Strozziana” a Germanico’, in Atti della Accademia Nazionale dei Lincei. Memorie, Classe die Scienze morali, storiche e filologiche. ser. VIII, vol. XXIII, fasc. 2, Rome 1979, pp. 147–267. Dell’ Era 1979c Antonio dell’ Era, ‘Gli “Scholia Basileensia” a Germanico’, in Atti della Accademia Nazionale dei Lincei. Memorie, Classe die Scienze morali, storiche e filologiche. ser. VIII, vol. XXIII, fasc. 4, Rome 1979, pp. 301–79.

Destombes 1956 Marcel Destombes,‘Globes célestes et catalogues d’étoiles orientaux du Moyen-Age’, Actes du VIIIe Congrès International d’Histoire des Sciences, Firenze 1956, vol. 1 (1956), pp. 313–24. Reprinted in Destombes 1987, pp. 79–89. Destombes 1958 Marcel Destombes, ‘Un globe céleste arabe du XII siècle’, Comptes rendus de l’Académie des Inscriptions et Belles Lettres, Paris 1958, pp. 300–13. Reprinted in Destombes 1987, pp. 91–104. Destombes 1960 Marcel Destombes, ‘Un globe céleste inédit de l’époque Seljoukide (539 de l’Hégire)’, Actes du IXe Congès International d’Histoire des Sciences, Barcelona Madrid 1959 (1960) vol. 1, pp. 447–52. Reprinted in Destombes 1987, pp. 121–6. Destombes 1987 G. Schilder, P. van der Krogt, and S. de Clercq (eds), Marcel Destombes (1905–1983). Selected Contributions to the History of Cartography and Scientific Instruments, Utrecht 1987. Dibon-Smith 1992 Richard Dibon-Smith, Starlist 2000:A Quick Reference Star Catalog for Astronomers, New York 1992. Dicks 1985 D. R. Dicks, Early Greek Astronomy to Aristotle, New York 1970. Printed in paperback 1985. Dietrich 1999 A. Dietrich,‘Ibn al-Qifṭī’, in Encyclopedia of Islam, Leiden 1999, vol. 3, p. 840. Dilke 1987 O. A.W. Dilke, ‘Itineraries and Geographical Maps in the Early and Late Roman Empires’, in Harley and Woodward 1987, pp. 234–57.

441

Bibliography Dizer and Meyer 1979 M. Dizer and W. Meyer, ‘The celestial globe of the Kandili made by Jacfar ibn cUmar ibn Dawlatshāh al-Kirmānī’, in Hakim Mohammed Said (ed.), History and Philosophy of Science. Proceedings of the International Congress of the History and Philosophy of Science, Islamabad, 8–13 December, 1979, Karachi 1979, pp. 14–19.

Dunbabin 1999 Katherine M.D. Dunbabin, Mosaics of the Greek and Roman World, Cambridge 1999.

Domenicucci 1996 P. Domenicucci, Astra Caesarum: Astronomia, astrologia e catasterismo da Cesare a Domiziano, Pisa 1996.

Eagleton 2010 Catherine Eagleton, Monks, Manuscripts and Sundials: The Navicula in Medieval England, Leiden 2010.

Dorn 1830 Bernhard Dorn, ‘Description of the Celestial Globe belonging to Major-General Sir John Malcolm, G.C.B, K.L.S, etc., etc., deposited in the Museum of the Royal Asiatic Society of Great Britain and Ireland’, Transactions of the Royal Asiatic Society 2 (1830), pp. 371–92.

Eastwood 2007 Bruce E. Eastwood, Ordering the Heavens: Roman Astronomy and Cosmology in the Carolingian Renaissance, Leiden 2007.

Drechsler 1873 Adolph Drechsler, Der arabische Himmels-Globus angefertigt 1279 zu Maragha von Muhammed bin Muwajid Elardhi zugehörig dem Königl. mathematisch-physikalischen Salon zu Dresden, Dresden 1873. Drecker 1927 J. Drecker, ‘Das Planisphaerium des Claudius Ptolomaeus’, Isis 9 (1927), pp. 255–78.

Durand 1952 Dana Bennett Durand, The Vienna-Klosterneuburg Map Corpus of the Fifteenth Century.A study in the transition from medieval to modern science, Leiden 1952.

Elkhadem 1992 Hossam Elkhadem, ‘Le traité de l’emploi du globe céleste d’al-’Urḍī (XIIIe siècle)’, Scientarium Historia 18 (1992), pp. 25–42. Eratosthenes (Robert 1878) Eratosthenis Catasterismorum Reliquiae (edition by C. Robert), Berlin 1878. Eratosthenes (Olivieri 1897) Pseudo-Eratosthenis Catasterismi (edition by A. Olivieri), Leipzig 1897.

DSB (Gillispie 1981) Charles Coulston Gillispie (ed.), Dictionary of Scientific Biography, New York 1981.

Eratosthenes (Pàmias and Geus 2007) Eratosthenes Sternsagen (edition and German translation by Jordi Pàmias and Klaus Geus), Oberhaid 2007.

Duits 2005 Rembrandt Duits, ‘Celestial transmissions. An iconographical classification of constellation cycles in manuscripts (8th-15th centuries)’, Scriptorium LIX (2005), pp. 147–202, and plates 26–49.

Evans 1998 James Evans, The History and Practice of Ancient Astronomy, Oxford 1998.

Duke 2002 Dennis W. Duke, ‘Hipparchus’ Coordinate System’, Archive for History of Exact Sciences, 56 (2002), pp. 427–33. Duke 2006 Dennis W.Duke,‘Analysis of the Farnese Globe’, Journal for the History of Astronomy 37 (2006), pp. 87–100. Duke 2008 Dennis Duke,‘Statistical dating of the Phenomena of Eudoxus’, DIO 15 (2008), pp. 7–23.

Evans 2004 James Evans, ‘The Astrologer’s Apparatus: A picture of Professional Practice in Greco-Roman Egypt’, Journal for the History of Astronomy 35 (2004), pp. 1–44. Evans and Berggren 2006 James Evans and J. Lennart Berggren, Geminos’s Introduction to the Phenomena: A Translation and Study of a Hellenistic Survey of Astronomy, Princeton, NJ 2006. Exhibition catalogue 1973 Das Werden eines neuen astronomischen Weltbildes im Spiegel alter Handschriften und Druckwerke. Ausstellung ÖNB,Wien 1973.

442

Bibliography Exhibition catalogue 1999 Hoch Renaissance im Vatikan: Kunst und Kultur im Rom der Päpste I 1503–1534, Germany 1999. Al-Farghānī (Lorch 2005) Al-Farghānī, On the Astrolabe (edition and English translation by Richard Lorch), Stuttgart 2005. Fauser 1973 Alois Fauser, Kulturgeschichte des Globus, Munich 1973. Feraboli 1994 Simonetta Feraboli, Hermetis Trismegisti De triginta sex decanis, Turnhout 1994. Field 1996 J. V. Field, ‘European Astronomy in the First Millennium: the Archaeological Record’, in Walker 1996, pp. 110–22. Folkerts and Lorch 2000 Menso Folkerts and Richard Lorch (eds), Sic itur ad astra. Studien zur Geschichte der Mathematik und Naturwissenschaften. Festschrift für den Arabisten Paul Kunitzsch zum 70. Geburtstag,Wiesbaden 2000. Forti et al. 1987 Guiseppe Forti, Isabella Lapi Ballerini, Brunella Monsignori Fossi, Piero Ranfagni,‘Un planetario del XV secolo’, L’astronomia 62 (1987), pp. 5–14. Fowden 2004 Garth Fowden, Quṣayr cAmra: Art and the Umayyad Elite in Late Antique Syria, London 2004. Gaborit-Chopin 1967 Danielle Gaborit-Chopin, ‘Les dessins d’Adémar de Chabannes’, Bulletin Archéologique du Comité des Travaux Historiques et Scientifiques (1967), pp. 183–225. Gabriel 1969 Astrik L. Gabriel, The Mediaeval Universities of Pécs and Pozsony, Frankfurt am Main 1969. Gee 2000 Emma Gee, Ovid, Aratus and Augustus: Astronomy in Ovid’s Fasti, Cambridge 2000. Geminus (Aujac 1975) Géminos, Introduction aux phénomènes (edition and French translation by Germaine Aujac), Paris 1975.

Gerbert d’Aurillac (Riché and Callu 1993) Gerbert d’Aurillac, Correspondence, 2 vols (edition and French translation by P. Riché and J. P. Callu), Paris 1993. Germanicus (Breysig 1867) Germanici Caesaris Aratea cum Scholiis, (edition by A. Breysig), Berlin 1867. Reprinted in Berlin 1969. Germanicus (Le Boeuffle 1975) Germanicus, Les Phénomènes d’Aratos (edition with French translation by André Le Boeuffle), Paris 1975. Germanicus (Gain 1976) The Aratus Ascribed to Germanicus Caesar (edition with English translation by D. B. Gain), London 1976. Gibbs 1984 Sharon Gibbs with George Saliba, Planispheric Astrolabes from the National Museum of American History, Washington 1984. Gingerich 2002 Owen Gingerich,‘The trouble with Ptolemy’, Isis 93 (2002), pp. 70–4. Goldstein 1983 B. R. Goldstein, ‘The obliquity of the Ecliptic in Ancient Greek Astronomy’, Archives Internationales d’Histoire des Sciences, XXXIII (1983), pp. 3–14. Goldstein and Bowen 1991 B. R. Goldstein and A.C. Bowen, ‘The Introduction of Dated Observations and Precise Measurement in Greek Astronomy’, Archive for History of Exact Sciences 43 (1991), pp. 93–132. Goldstein and Chabás 2008 Bernard R. Goldstein and José Chabás,‘Transmission of Computational Methods within the Alfonsine Corpus: The Case of Nicholaus de Heybech’, Journal for the History of Astronomy, 39 (2008), pp. 345–55. Goldstein and Hon 2007 Bernard R. Goldstein and Giora Hon,‘Celestal charts and spherical triangles: the unifying power of symmetry’, Journal for the History of Astronomy 38 (2007), pp. 1–14. Graf-Stuhlhofer 1996 Franz Graf-Stuhlhofer, Humanismus zwischen Hof und Universität. Georg Tannstetter (Collimitius) und sein

443

Bibliography wissenschaftliches Umfeld im Wien des frühen 16. Jahrhunderts,Vienna 1996. Grasshoff 1990 G. Grasshoff, The History of Ptolemy’s Star Catalogue, New York, Berlin 1990. Graves 1957/1977 Robert Graves, Suetonius. The Twelve Caesars, Aylesbury Bucks 1977, first printed in 1957. Grössing 1983 Helmuth Grössing,‘Fifteenth- and sixteenth-century astronomical and mathematical manuscripts in the Austrian National Library, Journal for the History of Astronomy 14 (1983), pp. 149–51. Gundel 1936 W. Gundel, ‘Neue astrologische Texte des Hermes Trismegistos’, Abhandlungen der Bayersichen Akad. der Wissenschaften, Phil.-hist. Abteilung. Neue Folge, Heft 12, Munich 1936. Gunther 1923 R. T. Gunther, Early Science in Oxford, Vol. 2: Astronomy, Oxford 1923. Gunther 1931/1976 R. T. Gunther, The Astrolabes of the World, London 1931, reprinted in 1976. Guye and Michel 1970 Samuel Guye and Henri Michel, Mesures du Temps et de l’Espace. Horloges, montres et instruments anciens, Fribourg 1970. Hadrava and Hadravová 2006 Petr Hadrava and Alena Hadravová, ‘Das Albion des Richard von Wallingford und seine Spuren bei Johannes von Gmunden und Johannes Schindel’, in Simek and Chlench 2006, pp. 161–7. Haffner 1997 Mechthild Haffner, Ein antiker Sternbilderzyklus und seine Tradierung in Handschriften vom frühen Mittelalter bis zum Humanismus. Untersuchungen zu den Illustrationen der «Aratea» des Germanicus, Hildesheim 1997. Haidinger 1980 Alois Haidinger, Studien zur Buchmalerei in Klosterneuburg und Wien vom späten 14. Jahrhundert bis um

1450, unpublished dissertation. Since 2003 available on http://www.ksbm.oeaw.ac.at/dissha/ [accessed 21 March 2012]. Haidinger 1991 Alois Haidinger, Katalog der Handschriften des Augustiner Chorherrenstiftes Klosterneuburg. Cod. 101–200 (Veröffentlichungen der Kommission für Schrift- und Buchwesen des Mittelalters, Reihe II, Band 2/2),Wien 1991. Halleux 1998 Robert Halleux, ‘De Lotharingse wiskundeschool en de opkomst van de Arabisch-Latijnse wetenschap in de 11de en de 12de eeuw’, in ‘Robert Halleux, Camélia Opsomer, and Jan Vandersmissen, Geschiedenis van de wetenschappen in België van de Oudheid tot 1815, Brussel 1998, pp. 27–40. Halma 1821 N. Halma, Les Phénomènes d’Aratus de Soles, et de Germanicus César, avec les scholies de Théon, les Catastérismes d’Eratosthène, et la Sphère de Leontius, Paris 1821. Harley and Woodward 1987 J. B. Harley and David Woodward (eds), The History of Cartography, Vol I: Cartography in Prehistoric, Ancient, and Medieval Europe and the Mediterranean, Chicago 1987. Harley and Woodward 1992 J. B. Harley and David Woodward (eds), The History of Cartography,Vol. II, Book one: Cartography in the Traditional Islamic and South Asian Societies, Chicago 1992. Hartmann 1919 J. Hartmann, ‘Die astronomischen Instrumente des Kardinals Nikolaus Cusanus’, Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematich-Physikalysche. Klasse, Neue Folge no. 10, Berlin 1919. Hartner DSB vol. 1 Willy Hartner, ‘al-Battānī’, DSB (Gillispie 1981), vol. 1, pp. 507–16. al-Hassan et al. 2002 A. Y. al-Hassan, Maqbuk Ahmed, and Albert Zaki Iskander (eds), Science and Technology in Islam: The Exact Sciences, Unesco Publishing 2002.

444

Bibliography Haye 2007 Thomas Haye, ‘Die Astronomie des Hyginus als Objekt hochmittelalterlicher Lehrdichtung’, Sudhoffs Archiv 91 (2007), pp. 99–117. Hayton 2007 Darin Hayton, ‘Martin Bylica at the Court of Matthias Corvinus: Astrology and Politics in Renaissance Hungary’, Centaurus 49 (2007), pp. 185–98. Heath 1981/1913 Thomas Heath, Aristarchos of Samos. The Ancient Copernicus, NewYork 1981, first published 1913. Heath 1981/1921 T. Heath, A History of Greek Mathematics, 2 vols. New York 1981, first published 1921. Heilen 2000 Stephan Heilen,‘Eudoxus von Knidos und Pytheas von Massalia’, in Wolfgang Hübner (ed.), Geographie und verwandte Wissenschaften, Stuttgart 2000, pp. 55–73. Heinfogel (Brévart 1981) Konrad Heinfogel, Sphaera materialis (edition by Francis B. Brévart), Göppingen 1981. Hevelius 1690 Johannes Hevelius, Prodromus Astronomiae, Danzig 1690. Hipparchus (Manitius 1894) Hipparchi in Arati et Eudoxi Phaenomena commentariorum libri tres (edition and German translation by Karl Manitius), Leipzig 1894. Homburger 1962 Otto Homburger, Die illustrierten Handschriften der Burgerbibliothek Bern: die vorkarolingischen und karolingischen Handschriften, Bern 1962. Honigmann 1950 Ernest Honigmann, ‘The Arabic Translation of Aratus’ Phaenomena, Isis 41 (1950), pp. 30–1. Huber 1958 Peter Huber, ‘Ueber den Nullpunkt der babylonischen Ekliptik’, Centaurus V (1958), pp. 192–208. Hübner 2009 Wolfgand Hübner, ‘Ein Sternbild zuviel. Zu einem neuentdeckten Lehrgedicht aus dem 13. Jahrhundert’, Sudhoffs Archiv 93 (2009), pp. 83–6.

Hyginus (Le Boeuffle 1983) Hygin. Astronomie (edition and French translation by A. Le Boeuffle), Paris 1983. Hyginus (Viré 1992) Hygini De Astronomia (edited by Ghislaine Viré), Stuttgart and Leipzig 1992. Jomard 1854 Edmé François Jomard, Les Monuments de la géographie, ou Recueil d’anciennes cartes européennes et orientales [...], Paris 1854. Jones (C) 1939 Charles W. Jones, Bedae Pseudepigrapha: Scientific Writings Falsely Attributed to Bede, New York 1939. Reproduced in Charles W. Jones, Bede, the Schools and the Computus, and Ashgate 1994. Jones (K) 1975 Kenneth Glyn Jones, The Search for the Nebulae, Cambridge 1975. Jones (A) 2002 Alexander Jones, ‘Eratosthenes, Hipparchus and the Obliquity of the Ecliptic’, Journal for the History of Astronomy 33 (2002), pp. 15–19. Jones (A) 2006 Alexander Jones, ‘The Keskintos astronomical inscription: text and interpretations’, SCIAMVS 7 (2006), pp. 3–41. Kaibel 1894 J. Kaibel,‘Aratea’, Hermes 29 (1894), pp. 82–123. Kennedy 1990 E. S. Kennedy, ‘Al-Ṣūfī on the Celestial Globe’, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 5 (1990), pp. 48–93. Reprinted in Kennedy 1998, chapter III. Kennedy 1998 E. S. Kennedy, Astronomy and Astrology in the Medieval Islamic World, Aldershot 1998. Kennedy DSB vol. 2 E. S. Kennedy, Abū’l -Rayḥān al-Bīrūnī, DSB (Gillispie 1981), vol. 2, pp. 147–58. Kennedy and Debarnot 1990 E. S. Kennedy and M.-Th. Debarnot, ‘The mappings proposed by Bīrūnī’, Zeitschrift für Geschichte der

445

Bibliography Arabisch-Islamischen Wissenschaften 5 (1990), pp. 145–7. Reprinted in Kennedy 1998, chapter V. Kennedy et al. 1999 E. S. Kennedy, P. Kunitzsch, and R.P. Lorch, The Melon-Shaped Astrolabe in Arabic Astronomy, Stuttgart 1999. Ker 1957 N. R. Ker, Catalogue of Manuscripts containing AngloSaxon, Oxford 1957. Kerscher 1988 Gottfried Kerscher, ‘Qvadriga temporvm. Zur SolIkonographie in Mittelalterlichen Handschriften und in der Architekturdekoration (Mit einen Exkurs zum Codex 146 der Stiftsbibliothek in Göttweig)’, in Mitteilungen des Kunsthistorischen Institutes in Florenz xxx (1988) Heft 1/2. King 1978 David King, ‘Notes on the Astrolabist Nastulus/ Bastulus’, Archives Internationales d’Histoire des Sciences 28 (1978), pp. 115–18. King 1995a D. A. King, ‘The earliest known European astrolabe in the Light of other early astrolabes’, in Stevens et al. 1995, pp. 359–404. King 1995b David King,‘Early Islamic Astronomical Instruments in Kuwaiti Collections’, in Arlene Fullerton and Géza Fehérvári, Kuwait Arts and Architecture: A Collection of Essays. Kuwait 1995, pp. 76–96. King 1996 David King, ‘Islamic Astronomy’, in Walker 1996, pp. 143–74. King 2005 David A. King, In Synchrony with the Heavens: Studies in Astronomical Timekeeping and Instrumentation in Medieval Islamic Civilization, Vol. 2. Instruments of Mass Calculation, Leiden 2005. King 2007 David King, ‘Ibn Yūnus: Abū al-Ḥasan cAlī ibn cAbd al-Raḥmān ibn Aḥmad ibn Yūnus al-Ṣadafī, in BES (Hockey 2007), pp. 573–74.

King DSB vol. 14 David A. King,‘Ibn Yūnus’, DSB (Gillispie 1981), vol. 14, pp. 574–80. King and Kunitzsch 1983 David King and P. Kunitzsch, ‘Nasṭūlus the Astrolabist Once Again’, Archives Internationales d’Histoire des Sciences 33 (1983), pp. 342–3. King and Saliba 1987 David A. King and George Saliba (eds), From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E. S. Kennedy, Annals of the New York Academy of Sciences, Vol. 500, New York 1987. King and Turner 1994 David A. King and Gerard L’E.Turner,‘The astrolabe presented by Regiomontanus to Cardinal Bessarion in 1462’, Nuncius.Annali di Storia della Scienza 9 (1994), pp. 165–205. Kirchner 1926 Joachim Kirchner, Beschreibendes Verzeichnis der Miniaturen und des Initialschmuckes in den Phillipps-Handschriften, Leipzig 1926. Knorr 1991 Wilbur R. Knorr, ‘Another look at Ptolemy’s Ivy Leaf ’, Journal for the History of Astronomy 22 (1991), pp. 180–83. Korn 1996 Ursula Korn,‘Der Atlas Farnese. Eine archäologische Betrachtung’, in Corsepius 1996, pp. 25–44. Krchňák 1964 Alois Krchňák, ‘Die Herkunft der astronomischen Handschriften und Instrumente des Nikolaus von Kues’, Mitteilungen und Forschungsbeiträge der CusanusGesellschaft 3 (1964), pp. 109–80. Kremer 1980 Richard L. Kremer, ‘Bernard Walther’s Astronomical Observations’, Journal for the History of Astronomy 11 (1980), pp. 174–91. Kremer 1981 Richard L. Kremer, ‘The Use of Bernard Walther’s Astronomical Observations: Theory and Observation

446

Bibliography in Early Modern Astronomy’, Journal for the History of Astronomy 12 (1981), pp. 124–32.

tory of Astronomy 17 (1986), pp. 89–98. Reprinted in Kunitzsch 1989, chapter XXII.

Kugel 2002 Alexis Kugel with contributions by Koenraad Van Kleempoel and Jean Claude Sabrier, Spheres. The Art of the Celestial Mechanic, Paris 2002, pp. 22–26.

Kunitzsch 1986c Paul Kunitzsch, Peter Apian und Azophi: Arabische Sternbilder in Ingolstadt im frühen 16. Jahrhundert, München 1986.

Kunitzsch 1961 Paul Kunitzsch, Untersuchungen zur Sternnomenklatur der Araber. Wiesbaden 1961.

Kunitzsch I 1986 Paul Kunitzsch, Claudius Ptolemäus: Der Sternkatalog des Almagest. Die arabisch-mittelalterliche Tradition. I: Die arabischen Übersetzungen,Wiesbaden 1986.

Kunitzsch 1965 Paul Kunitzsch,‘Ṣūfī Latinus’, Zeitschrift der Deutschen Morgenländischen Gesellschaft 115 (1965), pp. 65–74. Kunitzsch 1966 Paul Kunitzsch, Typen von Sternverzeichnissen in astronomischen Handschriften des zehnten bis vierzehnten Jahrhunderts, Wiesbaden 1966. Kunitzsch 1974 Paul Kunitzsch, Der Almagest. Die Syntaxis Mathematica des Claudius Ptolemäus in arabisch-lateinischer Überlieferung,Wiesbaden 1974. Kunitzsch 1974b Paul Kunitzsch, ‘Die arabischen Sternbilder des Südhimmels (I)’, Der Islam 51 (1974), pp. 37–54. Kunitzsch 1980 Paul Kunitzsch,‘Two Star Tables from Muslim Spain’, Journal for the History of Astronomy 11 (1980), pp. 192– 201. Reprinted in Kunitzsch 1989, chapter IV. Kunitzsch 1983 Paul Kunitzsch, Über eine anwā’-Tradition mit bisher unbekannten Sternnamen, (Bayerische Akademie der Wissenschaften, Philosophisch-Historische Klasse, Heft 5) Munich 1983. Kunitzsch 1986a Paul Kunitzsch, ‘The astronomer Abu ’l-Ḥusayn al-Ṣūfī and his Book on the Constellations’, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften, 3 (1986), pp. 56–81. Reprinted in Kunitzsch 1989, chapter XI. Kunitzsch 1986b Paul Kunitzsch, ‘The Star catalogue commonly appended to the Alfonsine Tables’, Journal for the His-

Kunitzsch 1987a Paul Kunitzsch,‘Al-Khwārizmī as a Source for the Sententie astrolabii’, in King and Saliba 1987, pp. 227–36. Kunitzsch 1987b Paul Kunitzsch, ‘A medieval reference to the Andromeda Nebula’, The Messenger (ESO) 49 (1987), pp. 42–3. Kunitzsch 1989 Paul Kunitzsch, The Arabs and the Stars, Variorum reprints, Northampton 1989. Kunitzsch 1990 Paul Kunitzsch, ‘Al-Ṣūfī and the astrolabe stars’, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 6 (1990), pp. 151–66. Kunitzsch II 1990 Paul Kunitzsch, Claudius Ptolemäus: Der Sternkatalog des Almagest. Die arabisch-mittelalterliche Tradition. II: Die lateinische Übersetzung Gerhards von Cremona, Wiesbaden 1990. Kunitzsch III 1991 Paul Kunitzsch, Claudius Ptolemäus: Der Sternkatalog des Almagest. Die arabisch-mittelalterliche Tradition. III: Gesamtkonkordanz der Sternkoordinaten, Wiesbaden 1991. Kunitzsch 1992/93 Paul Kunitzsch, ‘An Arabic celestial globe from the Schmidt Collection,Vienna’ in Der Globusfreund, 40/41 (1992/93), pp. 77–88. Reprinted in Kunitzsch 2004. Kunitzsch 1997 Paul Kunitzsch, ‘Les relations scientifiques entre l’Occident et le monde arabe a l’ époque de Gerbert’,

447

Bibliography in Charbonnel and Iung 1997, pp. 193–203. Reprinted in Kunitzsch 2004. Kunitzsch 1998 Paul Kunitzsch, ‘The astronomer al-Ṣūfī as a source for Uluġ Beg’s star catalogue (1437)’, in La science dans le monde iranien à l’époque islamique. Actes du colloque tenu à l’Université des Sciences Humaines de Strasbourg (6–8 juin 1995).Téhéran 1998 (Bibliothèque Iranienne, 50), pp. 41–7. Kunitzsch 2004 Paul Kunitzsch, Astronomy and Mathematics in the Medieval Arab and Western Worlds,Variorum Collected Studies Series, CS791 Ashgate 2004. Kunitzsch 2005 Paul Kunitzsch, ‘Scientific contacts and influences between the Islamic world and Europe: the case of Astronomy’, in Ekmeleddin İhsanoğlu (ed.), Cultural Contacts in Building a Universal Civilisation: Islamic Contributions. Istanbul 2005, pp. 123–38. Kunitzsch DSB vol. 13 Paul Kunitzsch, Al-Ṣūfī, DSB (Gillispie 1981), vol. 13, pp. 149–50. Künzl 2000 Ernst Künzl with contributions of Maiken Fecht and Susanne Greiff , ‘Ein römischer Himmelsglobus der mittleren Kaiserzeit. Studien zur römischen Astralikonograpfie’, Jahrbuch des Römisch-Germanischen Zentralmuseums Mainz 47 (2000), pp. 495–594. Künzl 2005 Ernst Künzl, Himmelsgloben und Sternkarten. Astronomie und Astrologie in Vorzeit und Altertum, Stuttgart 2005. Lapi Ballerini 1987 Isabella Lapi Ballerini, ‘The celestial hemisphere of the Old Sacristy and its restoration’, The Burlington Magazine 129 (1987), pp. 51–2. Lattin 1961 Harriet Pratt Lattin, The Letters of Gerbert with his Papal Privileges as Sylvester II, New York 1961. Le Boeuffle 1977 André Le Boeuffle, Les noms latins d’astres et de constellations, Paris 1977.

Le Bourdellès 1985 Hubert Le Bourdellès, L’Aratus Latinus. Etude sur la culture et la langue latines dans le Nord de la France au VIIIe siècle, Lille 1985. Lehmann 1953 Paul Lehmann, ‘Adelman von Lüttich’, in Neue Deutsche Biographie 1 (1953), p. 60 [Onlinefassung]; URL: http://www.deutsche-biographie.de/ pnd104275413.html [accessed 21 March 2012]. Leiden Aratea 1989 B. Bischoff, B. Eastwood,T. A.-P. Klein, F. Mütherich, and P. J. Obbema, Aratea. Kommentar zum Aratus des Germanicus MS.Voss. Lat. Q.79. Bibliotheek der Rijksuniversiteit Leiden, Luzern 1989. Lesne 1938 E. Lesne, Histoire de la propriété ecclésiastique en France, IV, Lille 1938, pp. 236–41. Levenson 1991 Jay A. Levenson (ed.), Circa 1492: Art in the Age of Exploration, Catalogue for an Exhibition held at the National Gallery of Art,Washington. Yale University Press, New Haven and London 1991. Lindgren 1976 Uta Lindgren, Gerbert von Aurillac und das Quadrivium: Untersuchungen zur Bildung im Zeitalter der Ottonen, Wiesbaden 1976. Lippincott 1985 Kristen Lippincott, ‘The astrological vault of the Camera di Griselda from Roccabianca’, Journal of the Warburg and Courtauld Institutes 48 (1985), pp. 43–70. Lippincott 1990 Kristen Lippincott, ‘Two astrological ceilings reconsidered: the Sala di Galatea in the Villa Farnesina and the Sala del Mappamondo at Caprarola’, Journal of the Warburg and Courtauld Institutes 53 (1990), pp. 185–207. Lippincott 2006 Kristen Lippincott, ‘Between text and Image: Incident and accident in the history of astronomical and astrological illustration’ in P. Morel (ed.), L’art de la Renaissance entre science et magie, Paris and Rome 2006, pp. 3–34.

448

Bibliography Lippincott 2011 Kristen Lippincott,‘A chapter in the Nachleben of the Farnese Atlas: Martin Folkes’s globe’, Journal of the Warburg and Courtauld Institutes 74 (2011), pp. 281-99.

Maass 1902 E. Maass, ‘Salzburger Bronzetafel mit Sternbildern’, Jahreshefte des Österreichischen Archeologischen Institutes in Wien 5 (1902), p. 196.

Locher 1984 Kurt Locher, ‘Ptolemy’s Ivy Leaf ’, Journal for the History of Astronomy 15 (1984), pp. 32–34.

Makariou 1998 Sophie Makariou, L’apparence des cieux: astronomie et astrologie en terre d’Islam, Paris 1998.

Lorch 1980a Richard Lorch,‘Al-Khāzinī’s “Sphere that Rotates by Itself ” ’, Journal for the History of Arabic Science 4 (1980), pp. 287–329, reprinted in Lorch 1995, chapter XI.

Makariou and Caiozzo 1998 Sophie Makariou and Anna Caiozzo, ‘La tradition des Étoiles fixes sur les globes célestes et dans les manuscripts illustrés d’al Sufi’, in Makariou 1998, pp. 97–119.

Lorch 1980b Richard Lorch,‘The sphaera solida and related instruments’, Centaurus 24 (1980), pp. 153–61, reprinted in Lorch 1995, chapter XII.

Manilius (Goold 1977) Manilius, Astronomica (edition and English translation by G. P. Goold), Cambridge MA and London 1977.

Lorch 1994 Richard Lorch. ‘Mischastrolabien im arabisch-islamischen Kulturgebiet’, in Anton Gotstedter (ed.), Ad radices. Festband zum fünfzigjährigen Bestehen des Instituts für Geschichte der Naturwissenschaften der Johann-Wolfgang-Goethe-Universität Frankfurt am Main, Stuttgart 1994, pp. 231–6. Lorch 1995 Richard Lorch, Arabic Mathematical Sciences: Instruments,Texts,Transmission, Aldershot 1995. Lorch and Kunitzsch 1985 Richard Lorch and Paul Kunitzsch, ‘Ḥabash al Ḥāsib’s Book on the Sphere and its Use’, Zeitschrift für Geschichte der Arabisch-Islamischen Wissenschaften 2 (1985), pp. 68–98; reprinted in Lorch 1995, chapter XIII. Lorch and Martínez Gázquez 2005 Richard Lorch and José Martínez Gázquez, ‘Qusta ben Luca, De sphera uolubili’, Suhayl 5 (2005), pp. 9–62.

Manitius 1963 K. Manitius, Ptolemäus, Handbuch der Astronomie, 2 vols, Leipzig 1963. Martianus Capella (Dick 1925) Martianus Capella, De nuptiis Philologiae et Mercurii, Liber VIII (edition by A. Dick), Leipzig 1925. Martin 1956 J. Martin, Histoire du texte des Phénomènes d’Aratos, Paris 1956. Marx 1905 J. Marx, Verzeichnis der Handschriften-Sammlung des Hospitals zu Cues bei Bernkastel a./Mosel,Trier 1905. Mayer 1956 L. A. Mayer, Islamic astrolabist and their works, Genève 1956. McGurk 1966 P. McGurk, Catalogue of Astrological and Mythological Illuminated Manuscripts of the Latin Middle Ages IV: Astrological Manuscripts in Italian Libraries (other than Rome), London 1966.

Lowney 2006 Chris Lowney, A vanished World: Muslims, Christians and Jews in Medieval Spain, Oxford 2006.

McGurk 1973 P. McGurk,‘Germanici Caesaris Aratea cum Scholiis: A new illustrated witness from Wales’, The National Library of Wales Journal XVIII (1973), pp. 197–216.

Maass 1898 E. Maass, Commentariorum in Aratum Reliquiae, Berlin 1898 (repr. 1958).

McGurk 1981 P. McGurk, ‘Carolingian astrological manuscripts’, in Margeret Gibson and Janet Nelsom, Charles the Bald:

449

Bibliography Court and Kingdom. Papers Based on a Colloquium held in London in April 1979, London 1981, pp. 317–32. McGurk et al. 1983 P. McGurk, D.N. Dumville, M.R. Godden, and A. Knock, Early English Manuscripts in facsimile. XXI.An Eleventh-century Anglo-Saxon Illustrated Miscellany (British Library Cotton Tiberius.V. Part I), Copenhagen 1983. Mercier 1976 Raymond Mercier, ‘Studies in the medieval conception of precession I’, Archives Internationales d’Histoire des Sciences 25 (1976), pp. 197–220. Mercier 1977 Raymond Mercier, ‘Studies in the medieval conception of precession II’, Archives Internationales d’Histoire des Sciences 26 (1977), pp. 33–71. Mercier 1996 Raymond Mercier, ‘Accession and Recession: Reconstruction of the Parameters’, in Casulleras and Samsό 1996, pp. 299–347. Meucci 1878 F. Meucci, Il globo celeste arabico del secolo XI, Florence 1878. Michel 1954 Henri Michel,‘Les tubes optiques avant le télescope’, Ciel et terre. Bulletin de la Société belge d’astronomie, de méteorologie et de physique du globe 70 (1954), pp. 175– 84. Migne PL Jacques Paul Migne, Patrologia Latina database, Cambridge 2000. Millás Vallicrosa 1931 J. M. Millás Vallicrosa, Assaig d’història de les idees físiques i matemàtiques a la Catalunya medieval, Barcelona 1931. Millás Vallicrosa 1947 J. M. Millás Vallicrosa, El libro de los fundamentos de las Tablas astronómicas de R. Abraham ibn cEzra, Madrid and Barcelona 1947. Mitteleuropäische Schulen V 2012 Mitteleuropäische Schulen V (ca.1410–1450), Wien und Niederösterreich, ca. 1410–1450. Edited by Katharina

Hranitzky, Veronika Pirker-Aurenhammer, Susanne Rischpler, Martin Roland, Michaela Schuller-Juckes, Christine Beier, Andreas Fingernagel, Alois Haidinger (Die illuminierten Handschriften und Inkunabeln der Österreichischen Nationalbibliothek 14),Wien 2012. Moll 1877 Albert Moll, Johannes Stöffler von Justingen. Ein Characterbild aus dem ersten halbjahrhundert der Universität Tübingen, Linday 1877. Monfasani 1976 John Monfasani, George of Trebizond:A Biography and a Study of his Rhetoric and Logic, Leiden 1976. Mostert 1997 Marco Mostert,‘Les traditions manuscrites des oeuvres de Gerbert’, in Charbonnel and Iung 1997, pp. 307–346. Munk Olsen 1982 B. Munk Olsen, L’Étude des auteurs classiques latins aux XIe et XIIe siècles, Paris 1982. Muris and Saarmann 1961 Oswald Muris und Gert Saarmann, Der Globus im Wandel der Zeiten. Eine Geschichte der Globen, Berlin and Stuttgart 1961. Musil et al. 1907 Alois Musil et al., Kusejr ‘Amra, Kaiserliche Akademie der Wissenschaften,Wien 1907. Mütherich 1990 Mütherich,‘Book Illumination at the Court of Louis the Pious’, in P. Godman and R. Collins, Charlemagne’s Heir. New Perspectives on the Reign of Louis the Pious (814–840), Oxford 1990, pp. 593–604. Mütherich 1989 Florentine Mütherich, ‘Die Bilder’, in Leiden Aratea 1989, pp. 31–58. Nadal and Brunet 1983/1984 R. Nadal and J.-P. Brunet, ‘Le ‘Commentaire’ d’Hipparcque. I. La sphère mobile’, Archives for History of Exact Sciences 29 (1983/1984), pp. 210–36. Nadal and Brunet 1984 R. Nadal and J.-P. Brunet, ‘Le ‘Commentaire’ d’Hipparcque. II. Positions de 78 étoiles’, Archives for History of Exact Sciences 40 (1984), pp. 306–54.

450

Bibliography Nagle 1995 Betty Rose Nagle, Ovid’s Fasti, Indianapolis 1995.

Wissenschaften in Wien, Philosophisch-historische Klasse, Denkschriften 67 (1926), no. 3, pp. 1–15.

Nallino 1903 C. A. Nallino, Al-Battānī sive Albatenii Opus Astronomicorum, Vol. I, Milan 1903.

Obrist 2004 Barbara Obrist, La cosmologie médiévale.Textes et images I. Les fondements antique, Florence 2004.

Nasr 1976 Seyyed Hossein Nasr, Islamic Science: An Illustrated Study, London 1976.

Oestmann 1993 Günther Oestmann (with a contribution from Elly Dekker and Peter Schiller), Schicksalsdeutung und Astronomie. Der Himmelsglobus des Johannes Stoeffler von 1493, Stuttgart 1993.

Nasr DSB vol. 13 Seyyed Hossein Nasr, Naṣīr al-Dīn al-Ṭūsī, DSB (Gillispie, 1981), vol.13, p. 514. Neugebauer 1975 O. Neugebauer, A History of Ancient Mathematical Astronomy, 3 vols, Berlin and New York 1975. Neuss 1941 Wilhelm Neuss, ‘Eine karolingische Kopie antiker Sternzeichen-Bilder im Codex 3307 der Biblioteca Nacional zu Madrid’, Zeitschrift des Deutschen Vereins für Kunstwissenschaft 8 (1941), pp. 113–40. Newton 1977 R. R. Newton, The Crime of Claudius Ptolemy, Baltimore 1977. North 1975 John North, ‘Monasticism and the first mechanical clocks’, in J.T. Fraser and N. Lawrence (eds), The Study of Time, New York 1975, pp. 381–93. Reprinted in John North, Stars, Minds and Fate: Essays in Ancient and Medieval Cosmology, London 1989, pp. 171–86. North 1976 John North, Richard of Wallingford: An Edition of his Writings with Introductions, English Translation and Commentary, 3 vols, Oxford 1976. North 1986 John North, Horoscopes and History, London 1986. Obbema 1989 Pieter F. J. Obbema, ‘Die Handschrift’, in Leiden Aratea 1989, pp. 9–29. Oberhummer 1926 Eugen Oberhummer,‘Die Brixener Globen von 1522 der Sammlung Hauslab-Liechtenstein’, Akademie der

Oestmann 1995/96 Günther Oestmann, ‘Johannes Stoeffler’s Celestial Globe’, with a report by Thomas Grunert, ‘The digital three-dimensional reconstruction of Stoeffler’s Globe’, Der Globusfreund 43/44 (1995/96), pp. 59–76. Oestmann 2002 Günther Oestmann, ‘Measuring and dating the Arabic celestial globe at Dresden’, in Maurice Dorikens (ed.), Scientific Instruments and Museums. Proceedings of the XXth International Congress of History of Science (Liège, 20–26 July 1997), Turnhout 2002, pp. 291–8. Panofsky and Saxl 1933 E. Panofsky and Fritz Saxl, ‘Classical Mythology in Mediaeval Art’, Metropolitan Museum Studies, IV (1933), pp. 228–79. Pedersen 2002 F. S. Pedersen, The Toledan Tables:A Review of the Manuscripts and the Textual Versions with an Edition, Copenhagen 2002. Pellegrin I 1975 Elisabeth Pellegrin et al., Les manuscrits classiques latins de la Bibliothèque Vaticane: Tome I, Paris 1975. Pellegrin II.1 1978 Elisabeth Pellegrin et al., Les manuscrits classiques latins de la Bibliothèque Vaticane: Tome II.1, Paris 1978. Pellegrin II.2 1982 Elisabeth Pellegrin et al., Les manuscrits classiques latins de la Bibliothèque Vaticane, Tome II.2, Paris 1982.

451

Bibliography Pellegrin 1982 Elisabeth Pellegrin, Manuscrits latins de la Bodmeriana, Cologny-Genève 1982.

atti del Gerberti symposium, Bobbio 25–27 Juglio 1983, Bobbio, Archivum Bobiense. Studia II, 1985. Reproduced in Poulle 1996, chapter XI.

Peters and Knobel 1915 C. H. F. Peters and E.B. Knobel, Ptolemy’s Catalogue of Stars (Carnegie Institution, Publication no. 86), Washington 1915.

Poulle 1988 Emmanuel Poulle, ‘The Alfonsine tables and Alfonso X of Castille’, Journal for the History of Astronomy 19 (1988), pp. 97–113. Reproduced in Poulle 1996, chapter V.

Philips 1968 Kyle M. Philips, ‘Perseus and Andromeda’, American Journal of Archaeology 72 (1968), pp. 1–23. Pighius 1587 Stephanus Vinandus Pighius, Hercules Prodicius, seu principiis Iuventutis vita et peregrination, Antwerp 1587. Pilz 1977 Kurt Pilz, 600 Jahre Astronomie in Nürnberg, Nuremberg 1977. Pinder-Wilson 1976 R. H. Pinder-Wilson, ‘The Malcolm celestial globe’, The Classical Tradition, The British Yearbook 1 (1976), pp. 83–101. Pingree 1970 David Pingree, ‘The Fragments of the Works of al-Fazārī,’ in Journal of Near Eastern Studies 29 (1970), pp. 103–23. Pingree 2009 David Pingree, Eastern Astrolabes, Adler Planetarium & Astronomy Museum, Chicago 2009. Pliny (Rackham 1938/1979) Pliny, Historia naturalis (edition and English translation by H. Rackham), Cambridge MA and London (first printed 1938) 1979. Poulle 1963 Emmanuel Poulle, Un constructeur d’instruments astronomiques au XVe siècle, Jean Fusoris, Paris 1963. Poulle 1980 Emmanuel Poulle, Les instruments de la théorie des planètes selon Ptolémée: Équatoires et Horlogerie planétaire du XIIIe au XVIe sciècle, 2 vols, Paris 1980. Poulle 1985 Emmanuel Poulle, ‘L’Astronomie de Gerbert’, in Giacomo Barabino (ed.), Gerberto: scienza, storia e mito:

Poulle 1996 Emmanuel Poulle, Astronomie plaétaire au Moyen Âge latin,Variorum reprints, Northampton 1996. Poulle 2009 Emmanuel Poulle,‘Review of Arianna Borelli, Aspects of the Astrolabe’, Journal for the History of Astronomy 40 (2009), pp. 240–2. Proctor 2005 David Proctor, ‘The Construction and use of the astrolabe’, in Van Cleempoel 2005, pp. 15–22. Ptolemy (Heiberg 1898–1903) Claudii Ptolemaei Syntaxis Mathematica, 2 vols, edited by J. L. Heiberg, Leipzig 1898–1903. Puig 1987 Roser Puig, Los tratados de constructiόn y uso de la azafea de Azarquiel, Madrid 1987. Puig 1996 Roser Puig, ‘On the eastern sources of Ibn al-Zarqālluh’s orthographic projection’, in Casulleras and Samsό 1996, pp. 737–53. Puig 2007 Roser Puig, ‘Zarqālī: Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Tujībī al-Zarqālī ‘, in BES (Hockey 2007), pp. 1258–60. Ragep 1996 F. Jamil Ragep, ‘Al-Battānī, Cosmology and the History of Trepidation in Islam’, in Casulleras and Samsό 1996, pp. 267–98. Ramsey and Licht 1997 John. T. Ramsey and A. Lewis Licht, The Comet of 44 BC and Caesar’s Funeral Games [American Philological Association American classical studies 39], Atlanta 1997.

452

Bibliography Rawlins 1982 Dennis Rawlins, ‘An investigation of the ancient star catalogue’, Publications of the Astronomical Society of the Pacific 94 (1982), pp. 359–73. Reeve 1980 M. D. Reeve,‘Some astronomical manuscripts’, Classical Quarterly XXX, 2 (1980), pp. 508–22. Reeve 1983 M. D. Reeve,‘Aratea’, in Reynolds 1983, pp. 18–24. Rehm 1899a A. Rehm, Eratosthenis Catasterismorum Fragmenta Vaticana, Ansbach 1899. Rehm 1899b A. Rehm, ‘Zu Hipparch und Eratosthenes’, Hermes 34 (1899), pp. 251–79.

Rico y Sinobas 1863 Manuel Rico y Sinobas, Libros del saber de astronomía del rey D. Alfonso X de Castilla, I-V, Madrid 1863–1867. Riese 1869 Alexander Riese (ed.) Anthologia latina sive Poesis latinae supplementum, 2 vols, Leipzig 1869. Rodney DSB vol. 5 Joel. M. Rodney, Martin Folkes’, DSB (Gillispie, 1981), vol. 5, pp. 53–4. Rojo Orcajo 1929 T. Rojo Orcajo, ‘Catálogo descriptivo de los códices que se conservan en la Santa Iglesia Catedral de Burgo de Osma’, Boletín de la Real Academia de Historia 94 (1929), pp. 706–10.

Rehm 1941 Albert Rehm, Parapegmastudien. Mit einem Anhang Euktemon und das Buch De signis, Munich 1941.

Roscher 1884–1937 W. H. Roscher (ed.), Ausführliches Lexicon der griechischen und römischen Mythologie, 6 vols and 4 supplements, Leipzig 1884–1937.

Renardy 1979 C. Renardy, ‘Les écoles liégeoises du IXe au XIIe siècle: grandes lignes de leur évolution’, Belgisch Tijdschrift voor Filologie en Geschiedenis LVII (1979), pp. 309–28.

Rosenfeld 1980 Rochelle S. Rosenfeld, Celestial maps and globes and star catalogues of the sixteenth and early seventeenth centuries, unpublished PhD New York University, 1980.

Reynolds 1983 L. D. Reynolds, Texts and Transmission: A Survey of the Latin Classics, Oxford 1983.

Rück 1888 Karl Rück, Auszüge aus der Naturgeschichte des C. Plinius Secundus in einem astronomisch-komputistischen Sammelwerke des achten Jahrhunderts, Munich 1888.

Riché 1987/2006 Pierre Riché, Gerbert d’Aurillac: Le pape de l’an mil, Paris 1987. Reprinted in 2006. Richer (Latouche 1937) Richer, Histoire de France (888–995) (edition and French translation by Robert Latouche), Paris 1937. Richter-Bernburg 1982 Lutz Richter-Bernburg, ‘Al-Bīrūnī’s Magal fi tasṭīḥ al-ṣuwar wa-tabṭīkh al-kuwar: a translation of the preface with notes and commentary’, Journal for the History of Arabic Science 6 (1982), pp. 113–22. Richter-Bernburg 1987 Lutz Richter-Bernburg, ‘Ṣāʿid, the Toledan Tables, and Andalusī Science’, in King and Saliba 1987, pp. 373–401.

Ruysschaert 1985 José Ruysschaert, ‘Du globe terrestre attribué à Giulio Romano aux globes et au planisphère oubliés de Nicolaus Germanus’, Bolletino dei Monumenti Musei e Gallerie Pontifice 6 (1985), pp. 93–104. Sācid al-Andalusī 1985 Sācid al-Andalusī, Tabaqāt al-umam (edition by H. BūcAlwān), Beirut 1985. Ibn aṣ-Ṣalāḥ (Kunitzsch 1975) Ibn aṣ-Ṣalāḥ, Zur Kritik der Koordinatenüberlieferung im Sternkatalog des Almagest (edition and German translation by Paul Kunitzsch), Abhandlungen der Akademie der Wissenschaften in Göttingen, Philologisch-Historische Klasse, Dritte Folge, Nr. 94, Göttingen 1975.

453

Bibliography Samhaber 2000 Friedrich Samhaber, Die Zeitzither. Georg von Peuerbach und das Helle Mittelalter, Raab 2000. Samsó 1977 Julio Samsó,‘A Homocentric solar model by Abū Jacfar al-Khāzin’, Journal of the History of Arabic Science 1 (1977), pp. 268–75. Reprinted in Samsó 1994, chapter XI. Samsó 1987 Julio Samsó, ‘Alfonso X and Arabic Astronomy’, in Mercè Comes, Roser Puig and Julio Samsó (eds), De Astronomia Alphonsi Regis, Proceedings of the Symposium on Alfonsine Astronomy held at Berkely (Barcelona 1987), pp. 23–38. Reprinted in Samsó 1994. Samsó 1990/1994 Julio Samsó, ‘Trepidation in al-Andalus in the 11th Century’, Revised version of a paper delivered at a symposium on ‘New perspectives on Early Science’ in honour of Olaf Pederson, Aarhus Denmark 1990. Printed in Samsó 1994, chapter VIII. Samsó 1994 Julio Samsó, Islamic Astronomy and Medieval Spain, Aldershot 1994. Samsó 1996 Julio Samsó, ‘Al-Bīrūnī in al-Andalus’, in Casulleras and Samsό 1996, pp. 583–612. Samsó 2005 Julio Samsó, ‘Qusṭā ibn Lūqā and Alfonso X on the celestial globe’, Suhayl 5 (2005), pp. 63–79. Samsó 2007 Julio Samsó, ‘Alfonso X’, in BES (Hockey 2007), pp. 29–31. Samsó and Castelló 1988 Julio Samsó and Francisco Castelló, ‘An hypothesis on the Epoch of Ptolemy’s Star Catalogue According to the Authors of the Alfonsine Tables’, Journal for the History of Astronomy 19 (1988), pp. 115–20. Reprinted in Samsó 1994, chapter XX. Samsó and Comes 1988 Julio Samsó and Mercè Comes,‘Al-Ṣūfī and Alfonso X’, Archives Internationales d’Histoire des Sciences 38 (1988), pp. 67–76. Reprinted in Samsó 1994, chapter XVII.

Santing 1992 C. G. Santing, Geneeskunde en humanisme. Een intellectuele biografie van Theodericus Ulsenius (c. 1460–1508), Rotterdam 1992. Savage-Smith 1985 E. Savage-Smith, Islamicate Celestial Globes:Their History, Construction, and Use, with a chapter on iconography by Andrea P. A. Belloli,Washington 1985. Savage-Smith 1990/91 E. Savage-Smith, The classification of Islamic celestial globes in the light of recent evidence’, Der Globusfreund 38–39 (1990/91), pp. 23–9. Savage-Smith 1992 E. Savage Smith, ‘Celestial mapping’, in Harley and Woodward 1992, pp. 12–70. Savage-Smith 1997 Emilie Savage-Smith, ‘Islamic celestial globes and related instruments’, in Francis Maddison and Emilie Savage-Smith, Science, Tools and Magic, Part One: Body and Spirit, Mapping the Universe, Oxford 1997, pp. 168–84. Saxl 1915 Fritz Saxl, Verzeichnis astrologischer und mythologischer illustrierter Handschriften des lateinischen Mittelalters in römischen Bibliotheken, Heidelberg 1915. Saxl 1927 Fritz Saxl, Verzeichnis astrologischer und mythologischer illustrierter Handschriften des lateinischen Mittelalters: II. Die Handschriften in der National-Biblothek in Wien. Heidelberg 1927. Saxl 1932 Fritz Saxl,The Zodiac of Qusayr cAmra’, in Creswell 1932, pp. 289–95. Saxl and Meier 1953 Fritz Saxl and Hans Meier, Verzeichnis astrologischer und mythologischer illustrierter Handschriften des lateinischen Mittelalters: III. Handschriften in Englischen Biblotheken. London 1953. Schaefer 2002 B. E. Schaefer, ‘The great Ptolemy-Hipparchus Dispute’, Sky and Telescope 103 (2002), pp. 38–44.

454

Bibliography Schaefer 2004 B. E. Schaefer, ‘The latitude and epoch for the origin of the astronomical lore of Eudoxus’, Journal for the History of Astronomy 35 (2004), pp. 161–223. Schaefer 2005 B. E. Schaefer, ‘The epoch of the constellations on the Farnese atlas and their origin in Hipparchus’s lost catalogue’, Journal for the History of Astronomy 36 (2005), pp. 167–96. Schaldach 2004 K. Schaldach, ‘The Arachne of the Amphiareion and the Origin of Gnomonics in Greece’, Journal for the History of Astronomy 35 (2004), pp. 435–45.

Sphere: Text, Translation and Commentary, Sciamvs 8 (2007), pp. 37–139. Simek and Chlench 2006 Rudolf Simek and Katrin Chlench, Johannes von Gmunden (ca. 1384–1442). Astronom und Mathematiker, Vienna 2006. Ibn Sinān (Saidan 1983) Ibrāhīm ibn Sinān ibn Thābit ibn Qurra, Kitāb Ḥarakāt al-Shams, edited by A. S. Saidan in Rasāʾil Ibn Sinān, Kuwait 1983, pp. 274–304. Sourdel 1979 D. Sourdel,‘Ibn Mādjid’, The Encyclopaedia of Islam, New Edition, Leiden and London 1971, vol. III, pp. 856–9.

Schaldach 2006 K. Schaldach, Die antiken Sonnenuhren Griechenlands: Festland und Peloponnes, Frankfurt am Main 2006.

Southwick 2006 Leslie Southwick, ‘The Great Helm in England’, Arms and Armour 3 (2006), pp. 5–77.

Schlachter 1927 A. Schlachter, Der Globus: Seine Entstehung und Verwendung in der Antike. Nach den literarischen Quellen und den Darstellung in der Kunst [Stoicheia. Studien zur Geschichte des antiken Weltbildes und der griechischen Wissenschaft, VIII], Leipzig 1927.

Stahl 1952 W. H. Stahl, Commentary on the Dream of Scipio by Macrobius, New York 1952.

Schnorr von Carolsfield 1882 Franz Schnorr von Carolsfield (ed.), Katalog der Handschriften königlichen öffentlichen Bibliothek zu Dresden, Dresden 1882. Sédillot 1844 Louis-Amélie Sédillot, Mémoire sur les instruments astronomiques des Arabes, Paris 1844. Sesti 1991 Giuseppe Maria Sesti, The Glorious Constellations: History and Mythology, Translated from the Italian by Karin H. Ford, New York 1991.

Stahl et al. 1977 William Harris Stahl, Richard Johnson, and E. L. Burge, Martianus Capella and the Seven Liberal Arts, Volume I. ‘The quadrivium of Martianus Capella’;Volume II. ‘The Marriage of Philology and Mercury’, NewYork 1977. Stautz 1999 Burkhard Stautz, Die Astrolabiensammlungen des Deutschen Museums und des Bayerischen Nationalmuseum, Munich 1999. Steele 2008 John M. Steele, A Brief Introduction to Astronomy in the Middle East, London, Berkeley, and Beirut 2008.

Sezgin 1997 Fuat Sezgin, Texts and Studies, Islamic Mathematics and Astronomy, vol. 26, cAbdarraḥmān aṣ-Ṣūf ī Abu L-Ḥusain ibn cUmar (d. 376/986), Frankfurt am Main 1997.

Stevens 1997 Wesley M. Stevens, ‘Astronomy in Carolingian schools’, in P. Butzer, M. Kerner, and W. Oberschelp, Karl der Grosse und sein Nachwirken: 1200 Jahre Kultur und Wissenschaft. Charlemagne and his Heritage: 1200 Years of Civilisation and Science in Europe. Turnhout 1997, pp. 417–87.

Sidoli and Berggren 2007 Nathan Sidoli and J. L. Berggren,‘The Arabic version of Ptolemy’s Planisphere or Flattening the Surface of the

Stevens et al. 1995 W. M. Stevens, G. Beaujouan, and A. J. Turner (eds), The Oldest Latin Astrolabe, Physis 32 (1995).

455

Bibliography Stöffler 1499 Johannes Stöffler, Almanach nova plurimis annis venturis inseruientia, Ulm 1499.

Richard Lorch, Bayerische Akademie der Wissenschaften Philosopisch-Histiorische Klasse Sitzungsberichte 2011, Heft 1.

Stöffler 1512 Johannes Stöffler, Elucidatio fabricae ususque astrolabii, Oppenheym 1512.

Thiele 1898 Georg Thiele, Antike Himmelsbilder: Mit Forschungen zu Hipparchos, Aratos und seinen Fortsetzern und Beiträgen zur Kunstgeschichte des Sternhimmels, Berlin 1898.

Strabo (Jones 1917/1997) Strabo, Geography Books 1–2, (edition and English translation by Horace Leonard Jones), Cambridge MA and London (first printed in 1917), reprint 1997. Strohmaier 1984 Gotthard Strohmaier, Die Sterne des Abd ar-Rahman as-Sufi, Hanau/Main 1984. Stückelberger 1990 A. Stückelberger, ‘Sterngloben und Sternkarten. Zur wissenschaftlichen Bedeutung der Leidener Aratus’, Museum Helveticum 47 (1990), pp. 70–81. Stückelberger 1994 A. Stückelberger, Bild und Wort: Das illustrierte Fachbuch in der antiken Naturwissenschaft, Medizin und Technik, Mainz am Rhein 1994. Stupperich 1990 Robert Stupperich, ‘Philipp Melanchthon‘, in: Neue Deutsche Biographie, Band 16, Berlin 1990, pp. 741–5. Al-Ṣūfı ̄ (Schjellerup 1874) H. C. F. C. Schjellerup, Description des étoiles fixes, translation of the Suwar al kawākib by cAbdarrahmān al-Sūfī, Petersburg 1874. Reprinted in Sezgin 1997, pp. 5–282. Suter 1922 Heinrich Suter,‘Über die Projektion der Sternbilder und der Länder von Al-Bîrûnî’, in Abhandlungen zur Geschichte der Naturwissenschaften und der Medizin, Erlangen 4 (1922), pp. 80–93. Theodosius (Kunitzsch and Lorch 2010) Theodosius, Sphaerica: Arabic and Medieval Latin Translations edited by Paul Kunitzsch and Richard Lorch, Stuttgart 2010. Theodosius (Kunitzsch and Lorch 2011) Theodosius, De habitationibus: Arabic and Medieval Latin Translations edited by Paul Kunitzsch and

Thurston 2002 Hugh Thurston, ‘Greek Mathematical Astronomy Reconsidered, Isis 93 (2002), pp. 58–69. Tibbetts 1997 G. R. Tibbetts, ‘Sulaymān al-Mahrī’, The Encyclopaedia of Islam, New Edition, Leiden and London 1997, Vol. IX, pp. 827–28. Tihon 1993 Anne Tihon, ‘L’astronomie à Byzance à l’Epoque Iconoclaste (VIII–Xe Siècles)’, in Butzer and Lohrmann 1993. Toomer 1968 G. J. Toomer, ‘A Survey of the Toledan Tables’, Osiris 15 (1968), pp. 5–174. Toomer 1984 G. J.Toomer, Ptolemy’s Almagest, London 1984. Toomer DSB vol. 7 G. J. Toomer, ‘al-Khwārizmī’, DSB (Gillispie, 1981), vol. 7, pp. 358–65. Toomer DSB vol. 15 G. J. Toomer, ‘Hipparchus’, DSB (Gillispie, 1981), vol. 15, pp. 207–24. Trapezuntius 1528 Claudii Ptolemaei Pheludiensis Alexandrini Almagestum seu magnae constructionis mathematicae opus plane divinum latina donatum lingua ab Georgio Trapezuntio usquequaq. doctissimo. per Lucam Gauricum Neapolit. divinae matheseos professorem egregium in alma urbe Veneta orbis regina recognitum anno salutis MDXXVIII labente, Venice 1528. Turner (A) 1985 A. J. Turner, The Time Museum.Time Measuring Instruments. Astrolabes and Astrolabe Related Instruments, Rockford 1985.

456

Bibliography Turner (A) 2000 A. J. Turner, The anaphoric Clock in the Light of Recent Research’, in Folkerts and Lorch 2000, pp. 536–47.

Vargha and Both 1987 MagdaVargha and Elöd Both,‘Astronomy in Renaissance Hungary’, Journal for the History of Astronomy 18 (1987), pp. 279–83.

Turner (G) 1991 Gerard L’E. Turner (ed.), Storia delle scienze: Gli strumenti, Torino 1991.

Vibert-Guigue and Bisheh 2007 ClaudeVibert-Guigue and Ghazi Bisheh, with a contribution by Frédér ic Imbert, Les peintures de Qusayr ʿAmra: Un bain omeyyade dans la bâdiya jordanienne, Beyrouth 2007.

Uhden 1937 R. Uhden,‘An equidistant and trapezoidal projection of the early fifteenth century’, Imago Mundi II (1937), pp. 8–9. Uiblein 1988 Paul Uiblein, ‘Johannes von Gmunden. Seine Tätigkeit an der Wiener Universität’, in Günther Hamann and Helmuth Grössing, Der Weg der Naturwissenschaft von Johannes von Gmunden zu Johannes Kepler,Vienna 1988, pp. 11–64. Upton 1932/33 Joseph M. Upton, ‘A manuscript of “the Book of the fixed stars” by cAbd ar-Raḥmān aṣ-Ṣūfī’, Metropolitan Studies 4 (1932/33), pp. 179–97. Reprinted in Sezgin 1997, pp. 355–73. Valerio 1987 Vladimiro Valerio, ‘Historiographic and Numerical Notes on the Atlante Farnese and its Celestial Sphere’, Der Globusfreund 35/37 (1987), pp. 97–124. Van Brummelen 2009 Glen Van Brummelen, The Mathematics of the Heavens and Earth.The Early History of Trigonometry, Princeton and Oxford 2009. Van Cleempoel 2005 Koenraad Van Cleempoel (with contributions from Silke Ackermann, François Charette, Elly Dekker, Paul Kunitzsch, Richard Lorch, David Proctor, and A.J.Turner), Astrolabes at Greenwich. A Catalogue of the Astrolabes in the National Maritime Museum, Greenwich, Oxford 2005. Van der Waerden 1952–53 B. L. van der Waerden,‘History of the Zodiac’, Archiv für Orientforschung 15 (1952–1953), pp. 216–30. Varenbergh 1888/1889 E. Varenbergh.‘Jean de Harlebeke’, Biografie Nationale de Belgique,Tome 10, 1888–1889, column 408.

Vieillard-Troiekouroff 1967 M. Vieillard-Troiekouroff, ‘Art carolingien et art roman parisiens. Les illustrations astrologiques jointes aux chroniques de Saint-Denis et de Saint-Germandes-Prés (IX-XIe siècles), Bulletin monumental 125 (1967), pp. 77–105. Viré 1981 Ghislaine Viré, ‘La transmission du De Astronomia d’Hygin jusqu’au XIII siècle’, Revue d’Histoire des textes 11 (1981), pp. 158–276. Virgil (Rushton Fairclough 1916) Virgil, Eclogues, Georgics, Aeneid I-VI (edition and English translation by H. Rushton Fairclough), London and Cambridge MA 1916. Vitruvius (Soubiran 1969) Vitruve, De l’Architecture Livre IX (edition with French translation by J. Soubiran), Paris 1969. Von Euw 2008 Anton Von Euw, Die St. Galler Buchkunst vom 8. bis zum Ende des 11.Jahthunderts, 2 vols, St Gallen 2008. Voss 1943 W. Voss,‘Eine Himmelskarte vom Jahre 1503 mit den Wahrzeichen des Wiener Poetenkollegiums als Vorlage Albrecht Dürers’, Jahrbuch der Preussischen Kunstsammlungen 64 (1943), pp. 89–150. Walker 1996 Christopher Walker (ed.) Astronomy before the Telescope, London 1996. Wanley 1705 Humfrey Wanley, Antiquae Literaturae Septentrionalis Liber Alter, seu Humphredi Wanleii Librorum Vett. Septentrionalium, qui in Angliae Bibliothecis extant, nec non multorum Vett. Codd. Septentrionalium alibi extantium

457

Bibliography Catalogus Historico-Criticus, cum totius Thesauri Linguarum Septentrionalium sex Indicibus, Oxford 1705 (reprint Hildesheim 1970).

Worrell 1944 W. H. Worrell ‘Qusta ibn Luqa on the Use of the Celestial Globe’, Isis 35 (1944), pp. 285–93.

Warner 1979 Deborah J.Warner, The Sky Explored. Celestial Cartography 1500–1800, New York and Amsterdam 1979.

Wrede 1982 Henning Wrede, Der Antikengarten der Del Bufalo bei der Fontana di Trevi, Trierer Winckelmannsprogramme 4, Trier 1982.

Wawrik 2006 Franz Wawrik, ‘Die Beeinflussung der frühen Kartografie durch Johannes von Gmunden und seinen Kreis’, in Simek and Chlench 2006, pp. 45–62. Wellesz 1959 Emmy Wellesz, An early al-Sūfī manuscript in the Bodleian Library in Oxford: A Study in Islamic Constellation Images, Ars Orientalis 3 (1959), pp. 1–26. Reprinted in Sezgin 1997, pp. 383–408. Wiesenbach 1991 Joachim Wiesenbach, ‘Wilhelm von Hirsau: Astrolab und Astronomie im 11. Jahrhundert’, Forschungen und Berichte der Archäologie des Mittelalters in Baden-Wurttemberg, Band 10/2 (Stuttgart 1991), pp. 109–56.

Wrede 1996 Henning Wrede, ‘Die Bürde der verpflichtende Macht Octavian und der Ausklang der hellinistischen Kunst’, in Corsepius 1996, pp. 45–50. Wrede and Harprath 1986 H. Wrede and R. Harprath, Der Codex Coburgensis. Das erste systematische Archäologiebuch. Römische Antiken-Nachzeichungen aus der Mitte des 16. Jahrhunderts. Kunstsammlungen der Veste Coburg 1986. Yamamoto and Burnett 2000 Jeiji Yamamoto and Charles Burnett, Abū Macšar on Historical Astrology. The book of Religions and Dynasties, Leiden 2000.

Wiesenbach 1993 Joachim Wiesenbach, ‘Pacificus von Verona als Erfinder einer Sternenuhr’, in Butzer and Lohrmann 1993, pp. 229–50.

Zinner 1967/1979 E. Zinner, Deutsche und niederländische astronomische Instrumente des 11.-18. Jahrhunderts. First edition 1956; second enlarged edition, 1967. Reprint of the second edition Munich 1979.

Wiesenbach 1994 Joachim Wiesenbach, ‘Der Mönch mit dem Sehrohr, Schweizerische Zeitschrift für Geschichte/Revue Suisse d’Histoire/Rivista Storica Svizzera 44 (1994), pp. 367–88.

Zinner 1990 E. Zinner, Regiomontanus: His Life and Work, Amsterdam 1990.This is a translation of Ernst Zinner. Leben und Wirken des Joh. Müller von Köningsberg genannt Regiomontanus, Munich 1938; second edition Osnabrück 1968.

Wilmart 1924 A. Wilmart, ‘Note sur l’abbiat d’Odbert’, Bulletin de la Société des antiquaries de la Morine XIV (1924), pp. 166–86.

Zuccato 2005 Marco Zuccato,‘Gerbert of Aurillac and a Tenth-Century Jewish Channel for the Transmission of Arabic Science to the West’, Speculum 80 (2005), pp. 742–63.

458

ADDENDUM: THE PAIR OF MAPS in MS Schoenberg jsl 057

hile the proofs of this book were being prepared, Giancarlo Truff a drew my attention to a pair of maps in MS Schoenberg jsl 057,from the Lawrence J.Schoenberg Collection. This Hebrew astronomical codex was written in Spain at the end of the fourteenth century.1 Among the various treatises included in this manuscript is a Hebrew translation of the Ptolemaic star catalogue on ff . 116–144, adapted for precession to the year 1391.This catalogue is richly illuminated by images of the 48 Ptolemaic constellations. Preceding the catalogue are two hemispherical maps (ff . 112–113) which extend from the north and south ecliptic poles to beyond the ecliptic, respectively (see Figs S1-S2). These two maps are the oldest extant pair in this particular format and in this sense can be seen as the forerunners of the Vienna maps discussed in Section 5.3.3. The location of the pair of maps in the codex would lead us to believe that they belong to the mathematical, Ptolemaic tradition. However, a close look shows that they are at best a copy of a mathematical example.There are no stars marked on the maps and the locations of the constellations are not all accurate. For example, on the

W

northern hemisphere the ecliptic intersects the shoulders of Sagittarius and on the southern map it passes through his head; in the northern hemisphere the solstitial colure passes through the legs of Gemini and on the southern hemisphere it passes between Gemini and Cancer. There are other confusing features in the design of the maps which need further study. The semicircle drawn inside the ecliptic representing the Equator can in principle help to decide whether the maps are based on an equidistant or a stereographic projection but the circle is not drawn very accurately. The ratio between the distance of the point of intersection of the Equator with the solstitial colure from the ecliptic pole and the radius of the ecliptic is about 0.80. This value is closer to the ratio predicted by the equidistant (0.74) than by the stereographic projection (0.66). The design of the constellations on the present pair of maps differs significantly from that on the Vienna map. In that sense the present pair of hemispheres cannot be seen as the forerunners of the Vienna maps. On Schoenberg’s maps the bears are not back to back; all human constellations are presented in front view and, with the

1 A facsimile of the codex has been made available on line by the University of Pennsylvania [http://hdl.library.upenn. edu/1017/d/medren/4852174]. A description of the codex is in Karl A. F. Fischer, Paul Kunitzsch, and Y. Tzvi Langermann,

‘The Hebrew Astronomical Codex MS. Sassoon 823’, The Jewish Quarterly Review N. S., vol. 78 (1988), pp. 253–92; reprinted in Y. T. Langermann, The Jews and the Sciences in the Middle Ages, Aldershot 1999, chapter X.

ADDENDUM: the pair of maps in ms schoenberg jsl 057

Fig. S1 The northern celestial hemisphere in MS Schoenberg jsl 057, f. 112. (Courtesy of Lawrence J. Schoenberg and Barbara Brizdle, Longboat Key.) See also Plate VIII.

exception of Gemini, all are dressed. Aquila is presented as an upside-down bird standing on Sagitta and the pans of the pair of scales representing Libra are placed towards the feet of Virgo. Above Leo is an image consisting of four leaves (?), presumably representing the

asterism later known as Coma Berenices, which is not depicted on the Vienna maps. These features are reminiscent of the Arabic tradition in globe making. However, a few others do not fit into this tradition. For example, on Islamic globes Orion is presented with an extended sleeve

460

ADDENDUM: the pair of maps in ms schoenberg jsl 057

Fig. S2 The southern celestial hemisphere in MS Schoenberg jsl 057, f. 113. (Courtesy of Lawrence J. Schoenberg and Barbara Brizdle, Longboat Key.) See also Plate VIII.

whereas on Schoenberg’s southern hemisphere Orion has a piece of cloth or animal skin in his hand. Also the presentation of other human constellations on the maps has been adapted to a more western medieval style (or perhaps already on its model map or globe). It has been suggested that the maps were copied from some European Latin text since

drawings like these are not known in the Islamic tradition. However, the use of the equidistant projection does not necessarily point to a map tradition. Its use is a rather natural choice for making a copy from a celestial globe. In short, this rare pair of maps gives us a glimpse of the otherwise unknown cartographic activities in Jewish circles in fourteenth-century Spain.

461

This page intentionally left blank

MANUSCRIPT INDE X A

E

Aberystwyth, The National Library of Wales MS 735C: 118–20, 127, 132, 138, 139, 142, 143, 159, 163, 168, 171, 172, 227, 228, 433

El Burgo de Osma, Archivo de la Catedral MS 7: 149, 154, 159, 163, 168, 171, 173, 237

F B Basle, Universitätsbibliothek MS AN. IV. 18: 116, 142, 144, 163, 168, 228 Berlin, Staatsbiblothek zu Berlin-Preussischer Kulturbesitz MS lat. 129 (formerly Phill. 1830): 146, 147, 154, 163, 168, 171, 175, 230, 233 MS lat. 130 (Phill. 1832): 154, 233 Bernkastel-Kues, Cusanusstift MS 207: 353–6 MS 208: 356 MS 209: 356 MS 210: 356 MS 211: 344, 356 MS 212: 181, 184, 187, 188, 191, 249, 356, 434 MS 213: 356 MS 214: 356 Boulogne-sur-Mer, Bibliothèque municipale MS 188: 117, 145, 148, 159, 160, 163, 167, 168, 173–5, 235, Plate III Bern, Burgerbibliothek MS 88: 145, 148, 159, 160, 163, 167, 168, 173, 174, 233, Plate III

C Cologny, Biblioteca Bodmeriana MS lat. 7: 177, 178

D Darmstadt, Landesbibliothek MS 1020: 182, 184, 187, 189–91, 205, 251, 434 Dresden, Sächsische Landesbibliothek - Staats- und Universitätsbibliothek MS Dc. 183: 120, 210, 255

Florence, Bibliotheca Laurenziana MS Plut 29.46: 341 MS Plut 40. 53: 179 MS Plut 89. sup 43: 179, 387 Florence, Biblioteca Nazionale Centrale Angeli MS 1147 A.6: 401, 408

G Gottweig, Stiftsbibliothek MS 7 (146): 256

I Istanbul, Ahmet III Library MS 3493: 299 MS 3505: 284

L Leiden, Universiteitsbibliotheek MS Voss. lat. 4° 79: 117, 145

Monza, Biblioteca capitolare MS B 24/163 (228): 120, 121, 138, 212, 433 MS F.9/176: 188, 189 Munich, Bayerische Staatsbibliothek Clm 210: 151, 154, 156, 157, 159, 163, 167, 168, 171, 175, 242, 247, 261 Clm 14583: 375, 376, 378, 379–81, 415 Clm 14689: 199, 200

O Oxford, Bodleian Library MS Can. Misc. 554: 387 MS Marsh 144: 67, 290–301, 303–06, 312–18, 320–2, 434, Plate V MS Rawl. C. 117: 365

N Naples, Biblioteca Nazionale MS XIV.D 37: 177 New York, Pierpont Morgan Library MS M. 389: 177

P K Klosterneuburg, AugustinerChorherrenstift MS 125: 377, 385 London, British Library MS Add. 15819: 177 MS Arundel 268: 341 MS Cotton Tib B.V, pars 1: 146, 148 MS Harley 647: 145, 146, 148, 150, 159, 163, 167, 168, 173, 175, 239 MS Harley 2506: 146 MS Harley 3734: 356 MS Harley 5402: 356 MS Old royal 15.B.IX: 196

M Madrid, Biblioteca Nacional MS 19 (16): 142, 177 MS 3307: 188, 189 MS 8282: 177

Paris, Bibliothèque nationale de France MS lat. 7412: 196, 197 MS lat. 12117: 189, 190 MS lat. 12957: 190, 213, 255 MS Arsenal 1036: 339

S St Gall, Stiftsbibliothek MS 902: 124, 219, 255 MS 250: 124, 193, 217, 255

V Vatican City, Biblioteca Apostolica Vaticana MS lat. 645: 188, 189 MS Barb. lat. 76: 177, 179 MS Barb. lat. 77: 177 MS Palat. lat. 1368: 357, 359, 360–2, 364, 408 MS Palat. lat. 1377: 365

Manuscript Index Vatican City, Biblioteca Apostolica Vaticana (cont.) MS Reg. lat. 123: 152, 154, 159, 163, 167, 168, 171, 175, 190, 245 MS Reg. lat. 309: 189 MS Reg. lat. 1324: 125, 221, 222, 256 MS Urb. lat. 1358: 179 MS gr. 1087: 120, 126,132, 141, 142,

153, 155, 159, 163, 168, 169, 171, 223, 228, 247, 264, 276 MS gr. 1291: 75, 120, 127, 131, 132, 141, 225, 264, 176, Plate II Vienna, Österreichische Nationalbibliothek MS 5415: 340, 365, 367–71, 373, 375–8, 380, 381, 385, 388, 391, 397, 399–401,

464

410, 415, Plates VI, VII MS 2352: 405 MS 3394: 406

Z Zurich, Zentralbibliothek MS Car C. 176: 206, 207

AUTHOR INDE X A c

Abd al-Raḥmān ibn Burhān 307 Abū ’l-Ḥasan cAbd Allāh ibn Yaḥyā 282 Abū l-Qāsim Ṣācid al-Andalusī 281 Abu’ṭ-Ṭaiyib Ṭāhir ibn al-Ḥusain 279 Abū cUthmān Sahl b. Bishr b. Ḥabīb b. Hāni’ 279 Accursius of Parma 341 Achilles 17 Adalhard of Corbie 151 Adelman 205 Ademar de Chabannes 190 c Aḍud al-Dawla 286, 287, 306, 434 Albacini, Carlo 87 Aldrovandi, Ulisse 87 Alfonso X of Castile 338, 340 c Alī ibn cĪsā 278 Alvaro de Oviedo 356, 357 Andronikos of Kyrros 28 Antoninus (Roman emperor) 13, 14, 348 Apian, Peter 160, 381 Aratus of Soli 1–5, 7–9, 11, 12, 14, 15, 17, 19, 20, 29–32, 34, 38–43, 49, 53, 55, 60–5, 67–8, 74, 76, 80–4, 95–101, 116–18, 120, 128–30, 132, 134–8, 140, 142, 145, 148, 151, 154, 155, 171–3, 181, 190–2, 199, 201, 211, 214, 215, 217,219, 221, 228, 240, 245, 255, 277–9, 313, 315, 405, 433, 436 Aristomachus 406 Aristotle 5, 6, 28 Aristyllus 10 Arzarquiel, see al-Zarqālluh Attalus of Rhodes 9 Augustus (Roman emperor) 71, 89, 90 Autolycus of Pitane 5, 14 Avienus, Rufius Festus 4, 117, 180, 233, 235 Ayyubid al-Malik al-Muẓaffar Maḥmūd of Ḥamāh 328 Azophi, see al-Ṣūfī

B al-Battānī 278–80, 283, 287, 288, 322, 340 Bayer, Johann 288 Bede, the Venerable 154, 155, 182, 206, 230, 233, 237, 245 Bentley, Richard 87, 88

Bessarion, Iohannes 390 Bianchini, Francesco 93, 94, 115 al-Bīrūnī 257–60, 280, 281, 291, 294, 296, 302, 309, 315, 358, 359, 372, 434 Blagrave, John 385 Boethius, Anicius Manlius Severinus 120, 198, 212, 235 Borgia, Rodericus 390 Bösch, Andreas 202, 203 Brahe, Tycho 68, 96, 288, 397 Burkart II (abbot of St Gall) 207 Bylica, Martin 390, 391, 423, 435

C Callippus 15 Camerarius, Joachim 402 Campanus of Novara 396 Cassini, Gian Domenico 93, 115 Celtis, Conrad (Konrad Celtes) 378, 382, 383 Cicero, Marcus Tullius 4, 62, 120, 145, 146, 207, 209, 212, 239 Cleomedes 10, 30 Columella 26 Conon of Samos 76, 141 Conrad of Dyffenbach 357, 358, 40–78, 436 Constantine of Fleury 191, 194, 201 Corvinus, Matthias (king of Hungary) 390 Cusa, Nicolas 343, 344, 350, 356, 420 Cusanus, see Cusa, Nicolas Cuspinianus, Johannes 378

D Dainerius, Thomas 391 Dalberg, Johann (bishop of Worms) 401 Demongenet, François 264 Dionysius 230 Dorn, Hans 391–401, 404, 405, 413, 423, 426, 435 Dunas ibn Tamīn al-Qarawī 205 Dürer, Albrecht 373, 381, 382, 436

E Emmoser, Gerhard 402 Eratosthenes 2–4, 29, 33, 37, 38, 64, 65, 76, 80, 82, 83, 120, 139, 140, 142, 198, 319

Euclid 5, 28, 29, 198 Euctemon 15 Eudemus of Rhodes 28 Eudoxus of Cnidos 1–3, 5,7, 9, 11, 14, 15, 17–20, 22, 24, 26–32, 38, 41–5, 48, 59–63, 65, 67, 68, 81–3, 91, 99, 100, 167, 201, 313, 432 Eutropius 49

F al-Farghānī 257, 259 Farnese, Alessandro (Cardinal) 87 al-Fazārī 259 Folkes, Martin 87, 88 Franco of Liege 205 Frederick II of Hohenstaufen 377 Fredericus (Friedrich Gerhart) Fusoris, Jean 388, 435

G Geminus 8–10, 15–18, 31–4, 39–41, 53, 57, 61, 76, 77, 97, 133, 198, 200, 201, 206, 274–76 Gemma Frisius, Reiner 381 Gensfelder, Reinardus 369, 370, 381, 410 George of Trezibond 399 Gerbert of Aurillac (later Pope Sylvester) 118, 189, 191, 192, 194–6, 198–202, 204–7, 251, 434 Germanicus, Julius Caesar 4, 17, 83, 97, 99–101, 116, 117, 120, 142, 145, 171, 177, 179, 192, 227, 228, 233, 235, 387, 405, 434 Gervvigus 174, 240 Grzymalas, Andreas 390

H Ḥabash al-Ḥāsib 160, 258, 259, 282, 283, 358 al-Ḥajjāj ibn Yūsuf ibn Maṭar 278, 279, 309, 315–22, 325 Hadrian (Roman emperor) 88 al-Ḥasan ibn Quraysh 279, 320 Heinfogel, Conrad 381, 382, 384, 385, 416, 418 Henry V (king of England) 388 Herodotus of Halicarnassus 27 Hevelius, Johannes 198

author index Heyden, Gaspar van der 381 Hipparchus ix, 1, 2, 9–20, 23, 26, 29–32, 34–42, 44, 45, 47, 60–3, 65, 67, 68, 74, 77, 79–82, 88, 91, 93–102, 252, 345, 434 Hyginus ix, 4, 17, 29, 32, 33, 38–40, 61, 62, 64–7, 69, 75, 78–84, 116, 141, 145, 154, 180, 190, 191, 198, 199, 201, 204, 206, 207, 240, 245, 247, 381, 405, 406, 436 Hypsicles of Alexandria 10

I Ibrāhīm ibn Sacīd al-Sahlī al-Wazzān 323, 325 Ibrāhīm ibn Sinān ibn Thābit ibn Qurra 279–81, 287, 313, 315, 316, 318–20 Isḥāq ibn Ḥunayn 279, 280, 282, 287, 313, 315, 316, 318–20 Ismācīl ibn Bulbul 282 Immser, Philipp 402 Isḥāq ibn Sīd 340 Isidore of Seville 154, 198, 206, 245

J Jābir ibn Sinān al-Ḥarrānī 278 Johan Daspa 340 Johannes von Wachenheim 358, 365 Johannes de Wormacia, see Johannes von Wachenheim John XXIII (Pope) 388 John of Gmunden 370, 378, 387, 388 John of Harlebeke 341–3 Julius Caesar 88–90

K Khālid ibn Yazīd ibn Mucāwiyah’ (Umayyad prince) 278 al-Khāzin 281 al-Khāzinī 284 al-Khwārizmī 257, 281 al-Kirmānī, Jacfar ibn cUmar ibn Dawlatshāh 309, 334, 335

ibn Mādjid, Aḥmad 291 al-Malik al-Kāmil 328 al-Ma’mūn (Abbasid caliph) 257, 279, 320 Manilius, Marcus 5, 8, 17–19, 22, 23, 26, 32, 33, 44, 46, 48, 61, 77–80, 87, 88, 97, 99, 100, 131, 134, 162, 167, 168, 198, 204 al-Marrākushī, Abū cAlī al-Ḥasan 260, 286 Martianus Capella 9, 10, 19, 23, 24, 29, 33, 34, 44, 47, 48, 78, 82, 83, 116, 131, 141, 167, 185, 186, 198, 199, 204, 434 Maslama al-Majrīṭī 322 Manetti, Agnolo 177, 434 Melanchthon, Philipp 402 Mercator, Gerard 296–9, 381 Michael Scot 377, 385, 387, 405, 406, 436 Muḥammad ibn Abū Bakr Ayyūb 328 Muḥammad ibn Hilāl 330 Müstinger, Georg 370 al-Muctamid (Abbasid caliph) 282

N ibn al-Nadīm 257, 258 Nasṭūlus 258 Nicephoros Gregoras 224, 249 Nicholas V (Pope) 399 Nicholas of Heybech 356 Nicolao orlogista 356 Nicolaus Germanus 361, 362, 388 Nicolaus Donnus, see Nicolaus Germanus Notker Labeo 207

M Macrobius, Ambrosius Theodosius 33, 116, 120, 154, 190, 198, 207, 209

Q Qayṣar ibn Abī al-Qāsim ibn Musāfir al-Abraqī al-Ḥanafī 328 ibn al-Qifṭī 278 Qusṭā ibn Lūqā 282, 283, 286, 308, 340, 341, 367, 435

R Regiomontanus, Johannes 340, 378, 382, 384, 390, 391, 395, 396, 401, 402 Remi of Trier 201 Richard of Wallingford 387 Richer of Saint-Remy 194, 195, 201, 202, 205 Rozgon, János 390

S O Odbert of Saint Omer 145, 233, 235 Oenopides of Chios 28 Oliva (abbot of Santa Maria de Ripoll) 154, 247 Otto III (Holy Roman emperor) 196

L Lang, Mattäus 383 Laudislaus II (king of Hungary) 391 Leontius 30, 32, 194 Ligorio, Pirro 87 Louis the Pious (Holy Roman emperor) 117

Plato 5 Plato of Tivoli 280 Pliny (Gaius Plinius Secundus) 17, 32, 78, 79, 89, 90, 153, 186 Porta, Guglielmo della 87 Praetorius, Johannes 381 Priscianus Grammaticus 154, 190, 191, 247 Profatius, see ibn Tibbon, Jacob ben Makhir 341 Ptolemy (Claudius Ptolemaeus) x, 6, 9, 12–14, 16, 18, 19, 36–41, 44, 45, 47, 52, 61, 63, 65, 67, 74, 77–9, 91, 93, 94, 96–101, 120, 140, 157, 160, 169, 224, 225, 249, 259, 270–2, 276, 278–81, 284, 286–91, 293, 294, 299, 305, 309, 310, 312, 313, 317, 319, 321, 327, 330, 331, 334, 339, 342–49, 351, 353, 355, 357, 367, 375, 399, 402, 432–36

P Pacificus of Verona 157, 160, 196 Paeonius 52 Pannonius, Janus 390 Peurbach, Georg 388, 391, 393 Pflaum, Jakob 401 Philip of Opus 27, 30 Pighius, Stephanus 84, 86, 87, 115 Pindar 406 Plancius, Petrus 63

466

Sabinus, Petrus 86, 87 ibn al-Ṣalāḥ 278–80, 287, 302, 320 Ṣamṣām al-Dawla 283 Sanjar ibn Malik-Shāh (Saljūq ruler) 284 Sarjūn ibn Hilīyā al-Rūmī 279 al-Sijzī 294 Sperancius (Sprenz), Sebastian (bishop of Brixen) 383, 416, 419 Stabius, Johannes 381, 383 Stephano del Bufalo 87 Stephanus Arlandi 341 Stercze, Jan 390 Stöffler, Johann 384, 385, 401–8, 412, 413, 426, 427, 428, 435, 436 Strabo 32, 33 Strata, Antonius de 180 Suetonius 90

author index al-Ṣūfī 67, 96, 259, 264, 276–81, 283, 284, 286–8, 290, 291, 293, 294, 296, 297, 299, 300, 302, 303, 305–7, 309–20, 322, 331, 332, 335, 336, 338, 339, 344, 349, 354, 355, 374, 434, 435 Sulaymān al-Mahrī 291 Synesius of Cyrene 52

Thietmar of Merseburg 196 ibn Tibbon, Jacob ben Makhir 341 Timocharis 10 Trapezuntius, see George of Trezibond al-Ṭūsī, Naṣīr al-Dīn 280, 281, 284, 312, 330

U T al-Ṭabarī, Muḥammad ibn Maḥmūd ibn c Alī 331 Tannstetter, Georg 388 Thābit ibn Qurra 279–81, 287, 313, 315, 316, 318–20 Theodoros Metochites 224, 249 Theodosius of Bithynia 5, 282 Theon the grammarian (first century BC) 3 Theon of Smyrna 28, 224, 249

Ulsenius, Theodorius 382, 416, 419 Ulugh Bēg 280, 299, 309 al-cUrḍī, Mu’ayyid al-Dīn 284, 330 al-cUrḍī, Muḥammad ibn Mu’ayyad 330, 331 c Utārid ibn Muhammad al-Hāsib 264, 322

Vitéz, János 390 Virgil 61, 141, 176, 230, 231, 242 Vitruvius, Pollio 17, 27–9, 43, 50, 156, 194 Vopel, Caspar 76, 296–300, 302, 381

W Walther, Bernard 378, 382 Werinhars I of Strasbourg 235 William of Hirsau 200, 204, 207

Y Yehūdah ibn Mosheh ha-Kohen 340 ibn Yūnus 279 Yūnus ibn al-Ḥusayn al-Aṣṭurlābī 309, 327

V

Z

Valens,Vettius 42 Varro, Narcus Terentius 17, 24, 26 Vespucci, Amerigo 291

al-Zarqālluh 260, 281, 311 Zehender, Daniel (bishop of Konstanz) 401, 435

467

This page intentionally left blank

Plate I

2.5 side east of the vernal equinoctial colure

2.6 side east of the summer solstitial colure

2.7 side east of the autumnal equinoctial colure

2.8 side east of the winter solstitial colure

2.9 region around the North Pole Figs 2.5-2.9 Kugel’s globe. (Courtesy of Galerie J. Kugel, Paris.) See also pages 58–59.

Plate II Fig. 3.11 a-b The pair of summer and winter hemispheres in Vatican City, MS gr. 1291, f. 2v, f. 4v. (Courtesy of the Biblioteca Apostolica Vaticana, Vatican City.) See also page 127.

Plate III

Fig. 3.15 Planisphere in Bern, MS 88, f. 11v. (Courtesy of the Burgerbibliothek, Bern.) See also page 148.

Fig. 3.16 Planisphere in Boulogne-sur-Mer, MS 188, f. 20r. (Courtesy of the Bibliothèque Municipale, Boulogne-sur-Mer.) See also page 148.

Plate IV

Fig. 4.3 The ceiling painting of the bath house (calidarium) in Quṣayr cAmra. (Photo: Claude Vibert-Guigue.) See also page 262.

Fig. 4.4 Sagittarius on the ceiling painting in Quṣayr cAmra, with on the left the tail of Scorpius and on the right, in front of Sagittarius’s feet, Corona Australis. (Photo from Vibert-Guigue and Bisheh 2007, Plate 137a. Courtesy of the Institut Français du Proche-Orient, Amman.) See also page 265.

Plate V

Fig. 4.7a Perseus as seen in the sky in the Bodleian Library, University of Oxford, MS Marsh 144, p. 111. (Courtesy of the Bodleian Library, Oxford.) See also page 292.

Fig. 4.11a Ursa Maior as seen on the sphere in the Bodleian Library, University of Oxford, MS Marsh 144, p. 43. (Courtesy of the Bodleian Library, Oxford.) See also page 304.

Plate VI

Fig. 5.18 The northern celestial hemisphere in Vienna MS 5415, f. 168r. (Courtesy Österreichische Nationalbibliothek,Vienna, Picture Archive.) See also page 368.

Plate VII

Fig. 5.19 The southern celestial hemisphere in Vienna MS 5415, f. 170r. (Courtesy Österreichische Nationalbibliothek,Vienna, Picture Archive.) See also page 369.

Plate VIII

Fig. S1 The northern celestial hemisphere in MS Schoenberg jsl 057, f. 112. (Courtesy of Lawrence J. Schoenberg and Barbara Brizdle, Longboat Key.) See also page 460.

Fig. S2 The southern celestial hemisphere in MS Schoenberg jsl 057, f. 113. (Courtesy of Lawrence J. Schoenberg and Barbara Brizdle, Longboat Key.) See also page 461.