New Perspectives on the History of Islamic Science Volume 3 9780754629146, 9781315248011

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New Perspectives on the History of Islamic Science

Islam and Science: Historic and Contemporary Perspectives Titles in the Series: Studies in the Islam and Science Nexus Volume 1 Muzaffar Iqbal Contemporary Issues in Islam and Science Volume 2 Muzaffar Iqbal New Perspectives on the History of Islamic Science Volume 3 Muzaffar Iqbal Studies in the Making of Islamic Science: Knowledge in Motion Volume 4 Muzaffar Iqbal

New Perspectives on the History of Islamic Science Volume 3

Edited by

Muzaffar Iqbal Center for Islam and Science, Canada

Routledge

Taylor & Francis Group LONDON AND NEW YORK

First published 2012 by Ashgate Publishing Published 2016 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN 711 Third Avenue, New York, NY 10017, USA Routledge is an imprint of the Taylor & Francis Group, an informa business Copyright © Muzaffar Iqbal 2012. For copyright of individual articles please refer to the Acknowledgements. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Notice : Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Wherever possible, these reprints are made from a copy of the original printing, but these can themselves be of very variable quality. Whilst the publisher has made every effort to ensure the quality of the reprint, some variability may inevitably remain. British Library Cataloguing in Publication Data New perspectives on the history of Islamic science. (Islam and science ; v. 3) 1. Islam and science. I. Series II. Iqbal, Muzaffar, 1954297.2'65-dc23 Library of Congress Control Number: 2011935823 ISBN 9780754629146 (hbk)

Contents Acknowledgements Editor's Acknowledgements Introduction PART I

THEORETICAL UNDERPINNINGS

1 David A. King (2004), 'Reflections on Some New Studies on Applied Science in Islamic Societies (8th-19th Centuries)', Islam & Science, 2, pp. 43-56. 2 Roshdi Rashed (1989), 'Problems of the Transmission of Greek Scientific Thought into Arabic: Examples from Mathematics and Optics', History of Science, 27, pp. 199-209. 3 Mohamad Abdalla (2007) 'Ibn Khaldün on the Fate of Islamic Science after the 11th Century', Islam & Science, 5, pp. 61-70 4 Roshdi Rashed (2005), 'Between Philosophy and Mathematics: Examples of Interactions in Classical Islam', Islam & Science, 3, pp. 153-65. Translated by RehdaAmeur. 5 Syamsuddin Arif (2009), 'The Universe as a System: Ibn Sïnâ's Cosmology Revisited', Islam & Science, 7, pp. 127—45. 6 Roshdi Rashed (2001), 'Al-Quhï: From Meteorology to Astronomy', Arabic Sciences and Philosophy, 11, pp. 157-204. PART II

vii ix xi

3

17 29

39 53 73

BUILDING BLOCKS OF THE REVISIONIST HISTORY

7 Roshdi Rashed (1999), 'Al-Quhï vs. Aristotle: On Motion', Arabic Sciences and Philosophy, 9, pp. 7-24. 8 Christian Houzel (2009), 'The New Astronomy of Ibn al-Haytham', Arabic Sciences and Philosophy, 19, pp. 1—41. 9 Roshdi Rashed (2007), 'The Configuration of the Universe: A Book by al-Hasan ibn al-Haytham?', Revue d'Histoire des Sciences, 60, pp. 47-63. 10 Julio Samsó (2008), 'Lunar Mansions and Timekeeping in Western Islam', Suhayl, 8, pp. 121-61. 11 David A. King (2008), An Instrument of Mass Calculation made by Nastülus in Baghdad ca. 900', Suhayl, 8, pp. 93-119. 12 Roshdi Rashed (1990), 'A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses', Ms, 81, pp. 464-91. 13 Syamsuddin Arif (2009), 'Causality in Islamic Philosophy: The Arguments of Ibn Sïnâ', Islam & Science, 1, pp. 51-68. 14 David A. King (1983), 'The Astronomy of the Mamluks', Ms, 74, pp. 531-55.

123 141 183 201 243 271 299 317

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15 Roshdi Rashed (2007) 'Arabic Versions and Reediting Apollonius' Conies', Study of the History of Mathematics, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, pp. 128-39. 16 Nathan Sidoli and Takanori Kusuba (2008), 'Nasïr al-Dïn al-Tüsfs Revision of Theodosius's Spherics', Suhayl, 8, pp. 9–46. 17 'Adi Setia (2008), 'Time, Motion, Distance, and Change in the Kalâm of Fakhr al-Dïn al-Râzï: A Preliminary Survey with Special Reference to the Matâlib 'Aliyah', Islam & Science, 6, pp. 13-29. 18 Emilia Calvo and Roser Puig (2006), 'The Universal Plate Revisited', Suhqyl, 6, pp. 113-57. 19 E.S. Kennedy and Nazim Paris (1970), 'The Solar Eclipse Technique of Yahyâ b. Abï Mansür', Journal for the History of Astronomy, 1, pp. 20-38. 20 George Saliba (2007), 'Arabic Science in Sixteenth-Century Europe: Guillaume Postel (1510-1581) and Arabic Astronomy', Suhayl, 7, pp. 115-64. PART III

343 355 393 411 457 477

LOOKING FORWARD

21 Roshdi Rashed (2001), 'History of Science at the Beginning of the 21st Century', in Juan José Saldaña (éd.), Science and Cultural Diversity, Proceedings of the XXI st International Congress of History of Science, vol.1, pp. 15-29 [pp. 1-11].

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Name Index

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Acknowledgements The editor and publishers wish to thank the following for permission to use copyright material. Armand Colin for the essay: Roshdi Rashed (2007), 'The Configuration of the Universe: A Book by al-Hasan ibn al-Haytham?', Revue d'Histoire des Sciences, 60, pp. 47-63. Barcelona University Arabic Department for the essays: Julio Samsó (2008), 'Lunar Mansions and Timekeeping in Western Islam', Suhayl, 8, pp. 121-61. Copyright © 2008 Publicacions I Edicions, Universitat de Barcelona; David A. King (2008), An Instrument of Mass Calculation made by Nastülus in Baghdad ca. 900', Suhayl, 8, pp. 93-119. Copyright © 2008 Publicacions I Edicions, Universitat de Barcelona; Nathan Sidoli and Takanori Kusuba (2008), 'Nasïr al-Dïn al-Tusï's Revision of Theodosius's Spherics', Suhayl, 8, pp. 9—46. Copyright © 2008 Publicacions I Edicions, Universitat de Barcelona; Emilia Calvo and Roser Puig (2006), 'The Universal Plate Revisited', Suhqyl, 6, pp. 113-57. Copyright © 2006 Publicacions I Edicions, Universitat de Barcelona; George Saliba (2007), 'Arabic Science in Sixteenth-Century Europe: Guillaume Postel (1510-1581) and Arabic Astronomy', Suhayl, 7, pp. 115-64. Copyright © 2007 Publicacions I Edicions, Universitat de Barcelona. Cambridge University Press for the essays: Roshdi Rashed (2001), 'Al-Quhï: From Meteorology to Astronomy', Arabic Sciences and Philosophy, 11, pp. 157-204. Copyright © 2001 Cambridge University Press; Roshdi Rashed (1999), 'Al-Quhïvs. Aristotle: On Motion', Arabic Sciences and Philosophy, 9, pp. 7-24. Copyright © 1999 Cambridge University Press; Christian Houzel (2009), 'The New Astronomy of Ibn al-Haytham', Arabic Sciences and Philosophy, 19, pp. 1-41. Copyright © 2009 Cambridge University Press. The Center for Islam and Science for the essays: David A. King (2004), 'Reflections on Some New Studies on Applied Science in Islamic Societies (8th-19th Centuries)', Islam & Science, 2, pp. 43-56. Copyright © 2004 the Center for Islam and Science; Mohamad Abdalla (2007) 'Ibn Khaldün on the Fate of Islamic Science after the llth Century', Islam & Science, 5, pp. 61-70. Copyright © 2007 the Center for Islam and Science; Roshdi Rashed (2005), 'Between Philosophy and Mathematics: Examples of Interactions in Classical Islam', Islam & Science, 3, pp. 153-65. Translated by Rehda Ameur. Copyright © 2005 the Center for Islam and Science; Syamsuddin Arif (2009), 'The Universe as a System: Ibn Sïnâ's Cosmology Revisited', Islam & Science, 1, pp. 127^5. Copyright © 2009 the Center for Islam and Science; Syamsuddin Arif (2009), 'Causality in Islamic Philosophy: The Arguments of Ibn Sïnâ', Islam & Science, 7, pp. 51-68. Copyright © 2009 the Center for Islam and Science; 'Adi Setia (2008), 'Time, Motion, Distance, and Change in the Kalâm of Fakhr al-Dïn al-Râzï: A Preliminary Survey with Special Reference to the Matâlib 'AliyaW, Islam & Science, 6, pp. 13-29. Copyright © 2008 the Center for Islam and Science.

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Science History Publications for the essays: Roshdi Rashed (1989), 'Problems of the Transmission of Greek Scientific Thought into Arabic: Examples from Mathematics and Optics', History of Science, 27, pp. 199-209. Copyright © 1989 Science History Publications Ltd; E.S. Kennedy and Nazim Paris (1970), 'The Solar Eclipse Technique of Yahyâ b. Abï Mansür', Journal for the History of Astronomy, 1, pp. 20-38. Copyright © 1970 Science History Publications Ltd. University of Chicago Press for the essays: Roshdi Rashed (1990), 'A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses', Isis, 81, pp. 464-91. Copyright © 1990 University of Chicago Press; David A. King (1983), 'The Astronomy of the Mamluks', Is is, 74, pp. 531-55. Copyright © 1983 University of Chicago Press. Every effort has been made to trace all the copyright holders, but if any have been inadvertently overlooked the publishers will be pleased to make the necessary arrangement at the first opportunity.

Editor's Acknowledgements The four volumes in this series owe a great deal to the painstaking work of a small group of historians of science who have studied numerous manuscripts, treatises, and instruments over the last four decades and whose work has been instrumental in revising our understanding of the Islamic scientific tradition. This series was made possible by their vigor and insights. It provides new perspectives on Islamic scientific tradition by presenting their work in a certain thematic order. I am grateful to all the authors and researchers whose work is included in this series. I wish to express my love and thanks to my son, Basit Kareem Iqbal, whose thoughtful critique of the four introductions has been helpful in reformulating certain arguments. His interest in various academic debates on themes related to Islamic scientific tradition and attention to detail and academic rigor has been inspiring. Needless to say that only I am responsible for the shortcomings in selection or presentation. A work of this nature cannot be free of editorial biases, even though one tries to present a balanced view of the fields. One hopes, nevertheless, that this series provides a broad spectrum of views on various aspects of Islamic scientific tradition and contributes to a richer understanding of the field in some small way. Wuddistân 9 Dhül-hijja, 1432/5 November 2011

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Introduction During the last four decades major advances have been made in our understanding of the history of Islamic scientific tradition, through the work of a few historians who were not satisfied with the standard narrative that had been constructed on the basis of very limited data as refracted through the ideological commitments of nineteenth-century Orientalists. Such new studies have not only seriously challenged the standard narrative on the basis of solid material evidence, they have also altered the theoretical framework for the study of the history of science in Islamic civilization. One of the more important corollaries of these studies is the emergence - in the wake of the hasty and inaccurate verdicts passed by the previous generation of historians and ideologues - of a more cautious attitude toward the subject. This awareness has been modulated by the sobering realization that what has been discovered, translated, and brought into perspective is only the tip of the iceberg, and that thousands of manuscripts and instruments remain in various libraries and private collections which have not even been cataloged, let alone closely studied. These developments have been the result of a complex process. At the beginning of the twentieth century it was assumed that we know all that there is to be known about the enterprise of science in the Islamic civilization: it was said with confidence that it was a shortlived and limited activity, induced by the translation movement which brought Greek science into Arabic, and that it was strangled by Islamic orthodoxy. (For more on this judgment, see the introduction to Volume I of this series.) To be sure, this verdict was ideologically influenced, but later historians of science were more interested in finding textual evidence for this verdict than examining its presuppositions. When they started to discover new texts and instruments, they were at first not inclined to revise the standard narrative; but eventually the combined weight of new discoveries led to the formulation of a narrative that is still in the making. This volume presents the broad outlines of the new narrative through representative works that challenge the previous understanding and expand the parameters of the inquiry. In general, new studies have changed our understanding of four key areas: (i) (ii) (iii) (iv)

The alleged dichotomy and opposition between religious and natural sciences; The dating and other questions related to the decline of science in Islamic civilization; The nature and extent of Muslim contributions to scientific knowledge; and The relationship between Islamic scientific tradition and the emergence of modern science.

Although the first of these four key subdomains has not been the main concern of historians of science, the new studies in the history of Islam nevertheless suggest that (contrary to what was alleged in the nineteenth century, and what has remained a constant theme in the discourse since then), Islam has never been inhospitable to science in any simple sense; in fact, David King has aptly suggested the reverse: 'science in the service of Islam' (see Chapter 1). In the realms of astronomical and geographical calculation, for instance, the

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fact remains that there was a religious obligation for Muslims to ascertain the exact dates of certain religious rites which follow the lunar calendar, to organize the times of prayer, and to determine the sacred direction (qibld) towards the Ka c ba in Makka. Initially it was mostly non-scientists who undertook such tasks, relying on folk astronomy. Their results were often rough approximations, and they often erred in determining the direction of the Ka c ba for areas far from Makka. This historical fact, which can still be attested by the many misaligned mosques in Morocco and other localities, is nevertheless not a case of Islam somehow being 'against' science; rather, it is a direct outcome of different methods used in determining the direction of prayer (qibld). The questions Islam posed, including those having to do with the times of prayer, can be described as acting as an incitement to discourse - hence the over 500 manuscripts unstudied in modern times, for instance, that David King draws on in his The Call of the Muezzin (2004, vol. 1), which deals with astronomical timekeeping and the determination of the times of prayer. In King's Instruments of Mass Calculation (2004, vol. 2), which deals with astronomical instruments, he found enough evidence to demonstrate that Muslim astronomers had serious programmes of instrumentation from the eighth through the nineteenth centuries. Some of these new perspectives on the Islam and science nexus were explored in Volume 1 of this series and, while not the main concern of the present volume, some articles - especially those in Part I - indirectly relate to this aspect of the discourse on Islamic scientific tradition, as they explore relationships between the natural sciences, philosophy, and Islamic intellectual thought. The standard narrative, which remained fully entrenched from the nineteenth century until the advent of the recent revisionist accounts, construed science and natural philosophy as isolated activities having little to do with other aspects of Islamic civilization. As Roshdi Rashed asks in Chapter 4, however: while scientific and mathematical research of the most advanced standards had been developed and worked out in Arabic in the urban centers of the Islamicate for a period of seven centuries, is it at all conceivable that philosophers, who were often themselves mathematicians, doctors, and so forth, would have remained recluse in their philosophical activity, totally oblivious to the mutations taking place under their eyes, and completely blind to the successive scientific results that were then being achieved? (p. 41 below)

Moreover, he continues, when faced with 'such an outburst of new disciplines and also success', can it be 'imagined that philosophers remained unperturbed by these developments, as to deduce that they were strictly confined to the relatively narrow frame of the Aristotelian tradition of neo-Platonism?' (ibid.). II

One of the key areas of interest for historians of science has been the dating of the so-called decline of science in Islamic tradition. New studies have seriously challenged the standard narrative by asking fundamental questions about this decline, whose date had been variously set as early as the eleventh, twelfth, and thirteenth centuries. While it is obvious that the Islamic scientific tradition in the nineteenth century was no longer as robust as it had been earlier, new perspectives on this aspect of Islamic science have emerged as a result of asking

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new questions: What do we mean by the 'decline' of a scientific tradition that was spread over a very large geographical area? Was the decline of the Islamic scientific tradition an isolated phenomenon, or was it part of a more general trend in the intellectual tradition to which it belonged? If the latter, then how did this broader process occur, and at what stage did this affect the scientific tradition? What were the social, political, and economic circumstances that were responsible for this general intellectual decline, which must have spread across the Muslim world with tremendous force? Were there any early signs of this trend? What corrective measures were attempted by authorities in the intellectual tradition? As a result of new studies, such familiar categorizations as the 'Golden Age of Islamic Science' turn out to be devoid of substantive content. Likewise, the oft-repeated notion of the end of the thirteenth century being the beginning of the decline of the Islamic science has also been shown to contradict historical data. New studies on the history of science have found major original works produced by thirteenth- and fourteenth-century astronomers and mathematicians, such as Athïr al-Dïn al-Abharï (d. c.638/1240), Mu'ayyad al-Dïn al-cUrdí (d. 665/1266), Nasfr al-Dïn al-Tusï (d. 673/1274), Qutb al-Dïn al-Shirâzï (d. 711/1311), and Ibn al-Shatir (d. 777/1375). Their contributions are so important that they cannot be discounted as isolated incidents of brilliance. Likewise, the work of scientists such as al-Jazârï (d. c.602/1205) in mechanics and Ibn al-Nafïs (607-87/1210-88) in medicine show that the vigour of scientific research had not dissipated by their time. In 1994, when George Saliba published his A History of Arabic Astronomy: Planetary Theories during the Golden Age of Islam, he intentionally phrased his subtitle to problematize the older periodization: the subtitle of the book intentionally designates this period [of so-called decline] as the Golden Age of Islam. This may be disturbing to students of Islamic intellectual history who are used to dismissing the works produced during this period as insignificant. What the evidence presented here now suggests is that if we can find such original work in astronomical planetary theories, and such mathematical sophistication and maturity in the presentations of these results, shouldn't we consider other disciplines as well, and try to find out if such vigorous scientific activity can be substantiated in other fields? In fact, at various points in these articles [of the book] I suggest that such research would promise to be extremely rewarding. (1994, p. 8)

Likewise, according to Kevin Krisciunas, 'at the time Ulugh Beg's observatory flourished it was carrying out the most advanced observations and analysis being done anywhere. In the 1420s and 1430s Samarqand was the astronomical and mathematical "capital of the world'" (1993, p. 11). And the discovery of two scientific instruments of a kind previously unknown to the historians of science prompted David King to remark: If one finds a microchip in a tomb in a pyramid then either some modern put it there or we should revise our opinions of the technological achievements of the ancient Egyptians. If the chip is essentially made of stone and bears inscriptions in hieroglyphics, then either the person who put it there was an Egyptologist with a somewhat perverse sense of humour, or we historians really do have a problem. (1999, p. xiii)

The discovery of these instruments also opened another neglected aspect of the question of decline:

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Western historians have been pre-occupied with the scientific heritage that was transmitted to the West. We are dealing here with materials that were not transmitted to the West, indeed - at least for the time when the two world-maps were made - we are dealing with the time when European science and technology had surpassed Islamic science and technology. This actually happened no earlier than the 16th century, (ibid., p. xiii)

The conclusions drawn from the discovery of new manuscripts and instruments have also been augmented by other studies which deal with social networks and contacts. For instance, in a significant contribution to the question of decline, Sonja Brentjes has focused on sixteenthand seventeenth-century travellers from Europe in the Ottoman and Safavid empires. Many of her articles are inspired by her 'dissatisfaction with current portrayals of the place and the fate of the so-called rational sciences in Muslim societies' (2010, p. 435): I came to recognize, she writes, that 'our previous meta-narrative of the intellectual relationships between the "West" and the "East", in particular between "Europe" and "Islam", was flawed on several levels' - not least in the presuppositions that guide intellectual inquiry, the criteria and methods involved in analysing historical evidence, and the questions foreclosed and presumed. Categories like inferiority and superiority or the mostly implicit beliefs that progress is the only 'natural' trajectory for science and that societies to which this 'axiom' does not apply are intrinsically flawed were part of the criteria upon which we built answers and evaluations. The search for the 'primeval locus or form' of a method, a subject matter, an institution or an observation or the reduction of the matter of inquiry to scientific content and usually only one of the cultures and its representatives involved in producing such kinds of knowledge dominate our repertoire of questions ... (Ibid., xiv-xv)

III

The third and fourth interrelated subdomains of the history of Islamic science, which have received considerable attention in recent decades, deal with the nature and extent of Muslim contributions to scientific knowledge and the relationship between the Islamic scientific tradition and the emergence of modern science. The old narrative had reduced Islamic scientific tradition to a depot which hosted the received Greek knowledge for a while before conditions were ripe for its transport to Europe. This view was built on the basis of the history of the European reception of Islamic scientific tradition. In the twelfth century, Europe looked toward Islamic civilization with respect and expectation, even awe; it invested in creating the right mechanisms for reception and translation of scientific and philosophical texts. This westward movement of knowledge from the Islamic civilization went through several phases of reception, analysis and absorption, and it witnessed several highs and lows, but it continued until the seventeenth century. This intense activity emerged through a 'spirited community of scholars eager both to pursue the language and heritage of Islam and to provide their contemporaries with learned bi-lingual editions of primary works from Arabic and not merely translations as had been the case during the first translation movement'. This included the establishment of several Arabic chairs at European universities and the travel of scores of scholars in search of instruction in Arabic language and of Arabic manuscripts. Indeed,

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'various publishers as well as individual scholars acquired Arabic type in anticipation of a significant publication enterprise' (Feingold, 1996a, pp. 441-2). During the first phase of the translation movement, Latin translations were produced from original Arabic texts, but between 1580 and 1680, European scholars became more interested in producing bilingual editions, annotated versions of Arabic texts, and commentaries on the original Arabic works. This change in direction, while indicative of an attitude formed by Reformation and humanism (as noted by Feingold), was also the result of the changed intellectual atmosphere and the specific theological debates that proliferated in Europe during the sixteenth and the seventeenth centuries. As I have noted elsewhere (Iqbal, 2002, ch, 6), whatever the reasons, the study of Arabic became an indispensable component of the late Renaissance humanist curriculum, where it was applied to gain access to the cherished classical texts preserved and enriched by Muslim scholars. In Feingold's words: 'The dignity conferred upon Arabic by the greatest scholars of the day further boosted its status' (1996a, pp. 441-2). Although this phase of the transmission of knowledge from Islamic civilization to Europe remains least studied,1 it is safe to say that Arabic had become an integral part of the academic world through the establishment of Arabic chairs, research programmes, and ambitious projects.2 In a public lecture delivered at Oxford in 1620, Sir Henry Savile cited the examples of Jâbir ibn Aflah, al-Battânï, and Thâbit ibn Qurra as instances of Arab mathematicians who had gone beyond their Greek teachers.3 Edward Pococke (1604-91), the first Laudian professor of Arabic, quotes John Bainbridge, the first Savilian professor of astronomy, who said that 'Brahe and Kepler had scarcely improved on the observations made by the Arabs centuries earlier'.4 This initial appreciation of Islamic scientific texts changed within the lifetime of these early enthusiasts; by the time William Laud, James Usher, John Selden, and Gerard Langbaine died, the entire scene had changed. Europe now looked at the Islamic scientific tradition with scorn. This was largely due to the triumph of early modern science, which had, by then, surpassed the achievements of Muslim scientists. It may have also been due to the distaste for authority and scholastic learning which accompanied the rise of modern science. Francis Bacon seems to have put the last nails in the coffin when, in a remarkable reversal of the verdict cited by Pococke, he declared: 'The sciences which we possess come for the most part from the Greeks, for what has been added by Roman, Arabic, or later writers is not much nor of much importance; and whatever it is, it is built on the foundations of Greek discoveries' (Bacon, 1905, p. 275).5 Bacon's authority was sufficient for subsequent generations to repeat his verdict ad nauseam: 1 Our knowledge of this neglected phase of transmission has been enriched by Toomer (1995). Also see Feingold (1996b). 2 For instance, Sir Henry Savile, a highly respected mathematician and Greek scholar of seventeenth-century England, established geometry and astronomy chairs at Oxford in 1619 and considered knowledge of the Islamic scientific tradition indispensable. 3 Quoted by Feingold (1996a) p. 446. 4 Thomas Smith, 'Commentariolus de vita et studiis...Joannis Bainbridgii', in Vitae quorundam eruditissimorum et illustrium virorum (London), pp. 10-11; The Works of Francis Bacon, Carmen Tograi (Oxford, 1661), both quoted in Feingold (1996a) p. 447 n. 9. 5 Bacon adds in a footnote: 'M. Chas les appears to have shown this with respect to the principle of position in arithmetic. We derive it, according to him, not from the Hindoos or Arabs, but from the Greeks.'

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For only three revolutions and periods of learning can properly be reckoned; one among the Greeks, the second among the Romans, and the last among us, that is to say, the nations of Western Europe, and to each of these hardly two centuries can be assigned. The intervening ages of the world, in respect of any rich or flourishing growth of sciences, were unprosperous. For neither the Arabians, nor the Schoolmen need be mentioned; who in the intermediate times rather crushed the sciences with a multitude of treatises, than increased their weight, (ibid., p. 279)

This verdict from the history of science was later applied to all fields of learning; in time, it was engraved on the European conscience, and almost every historian of science and philosopher since then has left a testimony of disrespect toward Islamic tradition. For instance, George Starkey said of Ibn Sïnâ, whose Qanünfíl-tibb had been taught in European universities for three centuries as the summa of medical sciences: 'Avicenna was useless in the light of practical experience' (Greaves, 1969, p. 90). By the turn of the eighteenth century, this verdict could be articulated in broad terms: 'It is certain that the Arabs were not a learned People when they over-spread Asia,' wrote William Watton (1666-1727), 'so that when afterwards they translated the Grecian Learning into their own Language, they had very little of their own, which was not taken from those Fountains' (1694, p. 140). Eventually, the narrative about Islamic science took a definitive shape: between the eighth and the tenth centuries, camel loads of manuscripts and books of Greek learning arrived in Baghdad because of the personal interest of a few enlightened caliphs; a translation movement came into existence through their patronage and that of high officials of the £Abbasid government and liberal philanthropists; and within the span of these two centuries, almost the entire existing scientific knowledge in Greek, Hindu, and Sassanid sources was translated into Arabic. This translation movement proceeded despite the strong hostility of Islamic orthodoxy, which was opposed to science and philosophy writ large. The received knowledge was then set aside as though stored in some depot; a few liberal scientists and philosophers made limited use of it, but by and large it remained 'parked' in Arab lands until its rightful heir, Europe, took possession of it. This understanding generated contempt for what Leonhart Fuchs (1501-66), the German physician often considered one of the three founding fathers of botany, described as 'Arabic dung dressed with the honey of Latinity'. He was also to declare his 'implacable hatred for the Saracens' in equally strong terms: 'as long as I live shall never cease to fight them. For who can tolerate a past and its ravings among mankind any longer - except those who wish for the Christian world to perish altogether. Let us therefore return to the sources and draw from them the pure and unadulterated water of medical knowledge' (Pagel, 1977, p. 384). This dismissive attitude toward Islamic scientific tradition was somewhat blunted by George Sarton (1884-1956), the Belgian chemist and historian of science who is often described as inaugurating the discipline of the history of science.6 The publication of his groundbreaking, three-volume Introduction to the History of Science (1927^8) restored a certain degree of 6

Sarton's passionate undertaking took him to North Africa and the Near East (1931-32) to study Arabic and Islam; in 1936, he founded Osiris, ajournai dedicated to articles longer than those which Isis published; he wrote and lectured extensively and mapped out the history of science like a geographer, combining biography and science, using secondary sources. As a result, he slighted Egyptian and Babylonian sources and relied heavily on Greek and medieval Arabic ones, which were more available to him. All of his works emphasized the continuity of science and its close affinity with

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respectability to the Islamic scientific tradition, which - Sarton noted - had lasted longer than the Greek and the Latin medieval traditions. By the time Sarton wrote his work, however, the standard narrative had become so powerful that all he could do was add a footnote to the solidified, almost ossified tale described above.7 Sarton's notion of an early demise of science in Islamic civilization was also misleading; he had set the eleventh century as the end of the vigour of the Islamic scientific tradition and the twelfth and (to a lesser extent) the thirteenth century as 'centuries of transition of that vigor to Europe' (1927^8, vol. 2, pp. 131^8), even though his periodization was severely skewed by the fact he was working with secondary sources. He was probably unaware of the enormity of untapped and unstudied sources necessary for writing a more comprehensive history of Islamic science.

IV The new perspectives on history of Islamic scientific tradition initially emerged on the basis of mounting evidence which suggested that the standard narrative has fundamental flaws.8 It gained momentum through the slow but consistent work of a few historians of science who were fascinated by the discovery of new manuscripts and instruments in their fields of specialization, such as mathematics, astronomy, chemistry, medicine, physics, and optics. Initially, these studies did not produce a broader narrative, but the accumulative weight of evidence from these specialized studies has now allowed even the most careful historian to challenge the veracity of the standard narrative. For instance, Ahmad Dallai notes that the 6 Arabo-Islamic sciences are not reducible to what came before, nor is their significance simply on account of what happened after' (2010, p. 10). Part I of this volume presents a sample of writings which have contributed toward the emergence of the revised understanding in several key areas, including the broad concerns of historians regarding the applied sciences in Islamic societies (King, Chapter 1); the transmission of Greek scientific texts into Arabic (Rashed, Chapter 2); the dating of decline (Abdalla, Chapter 3); interaction between philosophy and mathematics (Rashed, Chapter 4); premodern cosmology (Arif, Chapter 5); and a study on two treatises recording an interesting episode in the history of science which developed procedures and methods to allow geometrical control of observations and thus detachment of the phenomenon under consideration from meteorology (Rashed, Chapter 6). One aspect of the new perspectives on the history of Islamic science is the bold attempt of historians to redefine the theoretical framework of the field. Thus, while the stress on the translation movement, which produced Arabic versions of Greek scientific texts, remained magic. He officially became professor of the history of science at Harvard in 1940 and retired in 1951. He continued to lecture and write until his death. 7 See introduction to Volume 1 of this series for more details on Goldziher's hypothesis on 'Islamic orthodoxy versus natural sciences'. 8 One of the earliest figures to challenge the existing narratives was Pierre Duhem (1861-1916), the French physicist and philosopher who discovered a series of remarkable medieval texts and authors, including the works of Jean Buridan (d. c.1358) and Nicole Oresme (d. 1382), which led him to formulate his influential but flawed theories about Oresme's anticipation of Copernicus' theory of the diurnal rotation of the earth, Descartes's analytic geometry, and Galileo's law relating time and distance travelled in free fall. See Duhem (1913-59), vol. 7, p. 534.

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the main focus of earlier historians, the new attempts to understand this reception are simultaneously concerned with the mode of reception, its integration into existing research agendas, the translators themselves, the reasons for their interest, and many other social, economic, and scientific aspects. In short, as opposed to 'a vision of transmission that may well distort analysis' because it is 'a vision that is all-inclusive, passive and scholarly', the new studies seek to understand the process of transmission 'as one of conversion, reactivation, and even occasionally the renewal of one or more disciplines' (Rashed, Chapter 2, p. 17 below). Part II presents a sample of new studies which are the building blocks of a new narrative on the history of Islamic science. The sheer weight of this research has expanded our understanding of the enterprise of science in Islamic civilization; a great many historians of science are now convinced that this tradition needs to be studied on its own terms and not merely as a storehouse of Greek science or as a precursor to modern science. This is a development that avoids either exaggerated emphasis on Muslim contributions to science or a dismissive attitude toward these contributions. The significance of this development is more fully appreciated if we remember the gross generalizations which had been made about the enterprise of science in Islamic civilization with such consistency and for so long that they had become engraved truths, repeated ad nauseam in general histories and textbooks. As Dallai notes, 'the specialized studies of Edward Kennedy and his students on the exact sciences in Islam opened new horizons in the field after generations of nonspecialized commentaries on Islamic sciences' (2010, p. 12). Historians who have significantly contributed to the opening up of new vistas in various branches of science include George Saliba, who has extensively studied the history of reform tradition in Islamic theoretical astronomy (1994, 2007); David King, who has produced several studies on practical astronomy;9 Roshdi Rashed, who specializes in mathematical sciences;10 the work of M. Ullmann (1970, 1978), Michael Dois (1984), Lawrence Conrad (1994), Emilie Savage-Smith (Pormann and Savage-Smith, 2007), Ibrahim Ibn Murad (1991), Ahmad Tsà (1939), Max Meyerhof (1984),11 and others in the field of medicine and life sciences; A.I. Sabra's work on optics (1994, 1989);12 the pioneering work of Ahmad Y. aï-Hassan and Donald Hill (1986) in the field of Islamic technology (see also al-Hassan, 2009, 1979, 1980, 1998; aï-Hassan et al, 2001); and the bibliographies produced by Fuat Sezgin (1967- ) and Gerhard Endress.13 Another important area of history of science that has opened new possibilities of research is the link between Islamic scientific tradition and modern science. This is explored more fully in Volume IV of this series, but one important essay by George Saliba (included in this volume because of its broader thematic relevance) shows how Islamic scientific tradition played a direct role in the emergence of modern science during the sixteenth century. It thus demonstrates 9

For a comprehensive bibliography of King's works see http://web.uni-frankfurt.de/fbl3/ign/ ign2/people/publications%20king.pdf. 10 See a listing of Rashed's works at http://philpapers.Org/s/Roshdi%20Rashed. 11 For Meyerhof s bibliography, see http://www.worldcat.org/identities/lccn-n80131019#linkworksby 12 For a comprehensive bibliography of Sabra's works, see http://www.people.fas.harvard. edu/~sabra/PDF/publications05.pdf. 13 For a bibliography of Sezgin's works, see http://web.uni-frankfurt.de/fbl3/igaiw/publication/ publication.html; for Endress's bibliography, see http://www.ranker.com/list/gerhard-endress-booksand-stories-and-written-works/reference.

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the inadequacy of the standard narrative which misconstrued the role played by the Islamic scientific tradition in the emergence of modern science. In Chapter 20, Saliba establishes that Guillaume Postel (1519-81), a junior contemporary of Copernicus (1473-1543), had studied astronomical texts from Islamic scientific tradition in their original Arabic and in fact wrote marginal notes on the Arabic manuscripts he owned. It shows that the absence of a Latin translation of a given text is not negative proof of its isolation from later developments, as scientists like Postel had direct access to the Arabic manuscripts. 'Once this interaction between Renaissance Europe and the Islamic world is fully appreciated,' according to Saliba, we can 'better understand the conditions under which the well documented mathematical works that were first developed in the Islamic world could have been transmitted to people like Copernicus without having those original Arabic works necessarily translated into Latin' (p. 116 below). Postel's was not an isolated case; the work of historians such as Otto Neugebauer, Edward Kennedy, Willy Hartner, Noel Swerdlow, and others has traced many other specific connections between the two scientific traditions which followed each other chronologically and which are seldom connected in standard science textbooks. Copernican astronomy has received a great deal of attention in recent studies and it has been conclusively shown that Copernicus could not have developed his system merely on the basis of classical Greek mathematical and astronomical works such as Euclid's Elements and Ptolemy's Almagest. In particular, two mathematical theorems used by Copernicus had first been developed almost three centuries before him by astronomers in the Muslim world who were, like Copernicus, attempting to reform Greek astronomy. What is more important here is the context within which these theorems first appear in Islamic astronomical sources, including the shukük literature which was increasingly casting doubts (hence its name) on Greek astronomical models. As opposed to the assertion of the old narrative - that Islamic science was merely a pale shadow of Greek science - the new perspectives on the history of Islamic science have pinpointed numerous specific advances made by Muslim mathematicians, physicists, and astronomers in their respective disciplines. The case of astronomy has been studied in more detail than other branches of science, but one can on this basis infer that major advances were also made in other branches of science; this was certainly the case with mathematics and geometry, both of which were extensively used in Islamic astronomical sciences. Saliba has further argued that 'with the work of Muhammad b. Musa b. Shâkir, during the first half of the ninth century, regarding the properties and the admissibility of the existence of the ninth sphere, the stage was set for undertaking a total overhaul of the entire Greek astronomical edifice' (2007, p. 132). On the basis of new research, one can say with confidence that, after the initial reception, Greek scientific knowledge went through a process of scrutiny which began with the shukuklistidrak (doubts/recapitulation) literature, passed through the efforts to provide alternative theorems and models - for instance, the work of al-Tusï, al-'Urdï, alShïrâzï, and Ibn al-Shatir alluded to above - and matured into attempts to produce new models which were distinctively different from the Greek. The work of al-Qushjï (d. 1474) and Shams al-Dïn al-Khafrï (d. 1550), for instance, represents this trend. These are late attempts, but even as early as the eleventh century there are clear breaks with Greek scientific concepts, as testified by the correspondence between Ibn Sïnâ (d. 1037) and Abu Rayhân al-Bïrunï (d. 1048), which is rich in doubts expressed by the latter on various aspects of Aristotle's physics,

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especially his De Cáelo (On the He ovens).14 The new perspectives on the history of Islamic science have systematized shukük literature and this organization has helped to bring into fuller view certain aspects of history of science which were never discussed before (see, for example, Saliba, 2007, ch. 3). In this regard, see also the essay by Adi Setia included here as Chapter 17, which develops al-Razfs atomistic conception of time, motion, distance, and change, especially as read through the Matâlib al- Aaliyah. Al-Râzï concludes his Shark 'uyun al-hihma by arguing that the Platonic position on such concepts is 'closer' to what can be demonstratively supported than the Aristotelian conceptions - 'yet, despite this, complete knowledge of the realities of things (haqâ ïg al-ashyâ ') is but only with God the Sublime, the Transcendent' (p. 409 below). Islamic scientific thinkers developed Greek scientific knowledge in novel directions and, perhaps more significantly, transformed the epistemic framework out of which it is read. New perspectives on the history of Islamic science have demonstrated the vacuity of the earlier claims that Islamic science was merely auxiliary to Greek science, that it added nothing to scientific knowledge but merely translated, repeated, and preserved what was already known. A systematic and analytical survey of the Islamic science on the basis of new discoveries has yet to be undertaken, but a certain amount of scholarship has already framed many overarching themes. It shows that, as early as the eleventh century, many Muslim scientists were dissatisfied with aspects of Greek science. Several chapters in Part II directly or indirectly explore various aspects of the reception of Greek science (see the essays by Rashed, Houzel, and Sidoli and Kusuba; Chapters 7, 8, and 16, respectively). The Arabic edition of Theodosius's Spherics, for instance, was not merely a translation; rather - as Sidoli and Kusuba show in Chapter 16 - its Arabic rendering by Nasïr al-Dïn al-Tusï involved a considerable agenda of his own: he wanted to 'revitalize the text of Theodosius's Spherics by considering it firstly as a product of the mathematical sciences and secondarily as a historically contingent work' (p. 355 below). This he performed through editorial practices, including 'adding a number of additional hypotheses and auxiliary lemmas to demonstrate theorems used in the Spherics, reworking some propositions to clarify the underlying mathematical argument and reorganizing the proof structure in a few propositions. For al-Tusi, the detailed preservation of the words and drawings was less important than a mathematically coherent presentation of the arguments and diagrams' (ibid.). As opposed to the standard narrative, which posited an imagined Islamic orthodoxy against 'isolated instances' of research in natural sciences, numerous studies have established that there was no such opposition; in fact, at times there was direct interaction between the mosque and science. For instance, A.I. Sabra has shown, in his 1996 landmark paper ' Situating Arabic Science: Locality versus Essence', that the mosque was itself sometimes a significant locus of scientific activity, especially in Mamlük Egypt and Syria (1250-1517). Some of the most significant research in this area of the Islam and science discourse is that of David King, whose work over the last twenty years has been largely responsible for altering the terms of the decline narrative. As noted above, it has served to push back the date of the decline of Islamic science on the basis of the development and flourishing of various regional schools of astronomy, each with their distinctive interests and methods (see Chapter 14). 14

Ibn Sïnâ and al-Bïrunï (1352 AH /1973 AD); English translation by Rank Berjak and Muzaffar Iqbal in eight instalments, published in Islam & Science between 2003 and 2007.

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The study of scientific instruments and technologies has also been the focus of extensive new research. The discovery of instruments is always fascinating, but a special contribution of later research is the link it attempts to establish between instruments, their makers, and various social, scientific, and intellectual aspects of the Islamic tradition. The essays included here by King, Samsó, Calvo and Puig, and Kennedy and Paris, all involved in some way with astronomical sciences, further demonstrate the kind of groundbreaking research that interrupted the earlier narrative of science in Islamic civilization. In Chapter 11, David King examines a mathematical device, constructed in Baghdad, that was previously not known to exist - and which establishes that the existence of solar/calendrical scales on Islamic scientific instruments is not a function of Andalusï influence. Julio Samsó studies two western (Maghrebi and Andalusï) cases of the use of 'lunar mansions' for the purposes of timekeeping in Chapter 10. Emilia Calvo and Roser Puig revisit, in Chapter 18, two treatises on the construction and use of an eleventh-century Andalusï universal plate, presenting new analyses of its morphology and of the use of its mater in conjunction with its rete. Then Edward Kennedy and Nazim Paris discuss, in Chapter 19, the sections relating to solar eclipses in the ninth century zij (astronomical handbook) of one Yahyâ bin Abï Mansür, with reference to explications by his contemporary al-Khwârizmï as well as Ibn al-Shatir. Such comparisons allow us to triangulate some provisional conclusions regarding the transmission of knowledge and technologies across porous geographical and civilizational divides.

V The sole essay in Part III of the present volume (Chapter 21) steps back from the historical work of Part II to present some metadisciplinary reflections by Roshdi Rashed on what it might mean to conceptualize a history of science at the dawn of the twenty-first century especially as embarked upon in the postcolonial context, in which the universal ambitions that once held sway in the discipline have been provincialized. The relationship between contingency and necessity, Rashed concludes, variously configured in differing intellectual traditions of history of science, requires both a singular reflexivity and a complementary enterprise of social research on the sciences. In many ways, the twenty-one articles included in this volume are a backdrop for the studies presented in Volume IV of the series, which explores links between scientific traditions which existed before and after the Islamic scientific tradition. That fascinating tale of knowledge in motion could not have been constructed without the groundbreaking work of historians of science who have painstakingly gathered data for new perspectives on the history of Islamic science. What the present volume contains is merely a sample of the rich harvest which has fundamentally changed our view of the enterprise of science in Islamic civilization from the way it was viewed at the beginning of the twentieth century. Wuddistân 14 Shawwâl 1432/12 September 2011

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References Bacon, F. (1905), The Philosophical Works of Francis Bacon, éd. J.M. Robertson, London: George Routledge & Sons. Brentjes, S. (2010), Travellers from Europe in the Ottoman and Safavid Empires, 16th—17th Centuries: Seeking, Transforming, Discarding Knowledge, Farnham, Surrey: Ashgate. Conrad, L. etal. (eds) (1994), The Western Medical Tradition: 800 BC to AD 1800, Cambridge: Cambridge University Press. Dallai, A. (2010), Islam, Science, and the Challenge of History, New Haven, CT: Yale University Press. Dois, M. (trans.) (1984), Medieval Islamic Medicine: Ibn Ridwân s Treatise 'On the Prevention of Bodily Ills in Egypf, Arabic text éd. A.S. Gamal, Berkeley: University of California Press. Duhem, P. (1913-59), Le Système du Monde, 10 vols, Hermann: Paris. Feingold, M. (1996a), 'Decline and Fall: Arabie Science in Seventeenth Century England', in J.F. Ragep and S.P. Ragep (eds), Tradition, Transmission, Transformation, Leiden: E. J. Brill, pp. 441-69. Feingold, M. (1996b), 'Oriental Studies', in Nicholas Tyacke (éd.), The History of the University of Oxford, Oxford: Oxford University Press, pp. 449-504. Greaves, R.L. (1969), The Puritan Revolution and Educational Thought, New Brunswick: Rutgers University Press. Aï-Hassan, A.Y. (1979), A Compendium of the Theory and Practice of the Mechanical Arts by al-Jazari, Aleppo: Institute for the History of Arabic Science, University of Aleppo. Aï-Hassan, A.Y. (trans.) (1980), Kitab al-hiyal (The Book of Ingenious Devices} ofBanu Musa, Aleppo: Institute for the History of Arabic Science, University of Aleppo. Aï-Hassan, A. Y (1998), Kitab al-Furusiyya wal-Manâsib al-Harbiyya of Hasan al-Rammah (On Gunpowder and Incendiary Weapons}, Aleppo: Institute for the History of Arabic Science, University of Aleppo. Aï-Hassan, A. Y (2009), Studies in al-Kimya: Critical Issues in Latin and Arabic Alchemy and Chemistry, New York: Georg Olms Verlag. Aï-Hassan, A. Y and Hill, D. (1986), Islamic Technology: An Illustrated History, Cambridge: Cambridge University Press. Al-Hassan, A.Y, Ahmad, M. and Iskandar, A.Z. (eds) (2001), The Different Aspects of Islamic Culture. Science and Technology in Islam, Vol. IV, Parts I and II, Paris: UNESCO. Ibn Murad, I. (1991), Buhüth fi Târikh al-Tibb wal-Saydala lind al-'Arab, Beirut: Dar al-Gharb alIslâmï. Iqbal, M. (2002), Islam and Science, Aldershot: Ashgate. Isa, A. (1939), Târïkh al-Bïmâristânâtfîl-Islâm, Damascus: Al-Matba'at al-Hâshmiyya. King, D.A. (1999), World-Maps for Finding the Direction and Distance to Mecca, Leiden and London: E.J. Brill and Al-Furqan. King, D.A. (2004), In Synchrony with the Heavens - Studies in Astronomical Timekeeping and Instrumentation in Islamic Civilization, 2 vols, Leiden: Brill: Vol. 1, The Call of the Muezzin. Studies I—IX ; Vol. 2, Instruments of Mass Calculation. Studies X-XVIII. Krisciunas, K. (1993), 'Ulugh Beg', in E.S. Kennedy (éd.), Cambridge History of Iran, Cambridge: Cambridge University Press, p. 11. Meyerhof, M. (1984), Studies in Medieval Arabic Medicine: Theory and Practice, London: Variorum. Pagel, W. (1977), 'Medical Humanism: A Historical Necessity in the Era of the Renaissance', in F. Maddison, M. Pelling and C. Webster (eds), Linacre Studies: Essays on the Life and Works of Thomas Linacre c. 1460—1525, Oxford: Clarendon Press, pp. 375-86. Pormann, P. and Savage-Smith, E. (2007), Medieval Islamic Medicine, Washington, DC: Georgetown University Press.

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Sabra, A.I. (1989), The Optics oflbn al-Haytham: Books /-///, London: Warburg Institute, University of London. Sabra, A.I. (1994), Optics, Astronomy and Logic: Studies in Arabic Sciences and Philosophy, Aldershot: Variorum. Sabra, A.I. (1996), 'Situating Arabic Science: Locality versus Essence', Isis, 87, pp. 654-70. Saliba, G. (1994), A History of Arabic Astronomy: Planetary Theories during the Golden Age of Islam, New York: New York University Press. Saliba, G. (2007), Islamic Science and the Making of the European Renaissance, Cambridge, MA: Massachusetts Institute of Technology. Sarton, G. (1927-48), Introduction to the History of Science, 3 vols, Baltimore: Williams & Wilkins: Vol. 1, From Homer to Omar Khayyam (1927); Vol. 2, From Rabbi Ben Ezra to Roger Bacon (1931); Vol. 3, Science and Learning in the 14th Century (1947-48). Sezgin, F. (1967- ), Geschichte des Arabischen Schrifttums, 9 vols, Leiden: Brill. Ibn Sïnâ and al-Bïrunï (1352 AH), Al-As'ilah wal-Ajwibah (Questions and Answers), Including the Further Answers of al-Bïrunï and al-Ma'sumï' Defense of Ibn Sïnâ, éd. with English and Persian introductions by S.H. Nasr and M. Mohaghegh, Tehran: High Council for Culture and Art, Center of Research and Cultural Coordination; English translation by R. Berjak and M. Iqbal in eight instalments, published in Islam & Science between 2003 and 2007. Toomer, G. (1995), The Study of Arabic in England during the Seventeenth Century, Oxford: Oxford University Press. Ullmann, M. (1970), Die Medizin im Islam, Leiden: Brill Academic. Ullmann, M. (1978), Islamic Medicine, Islamic Surveys, II, Edinburgh: Edinburgh University Press. Watton, W (1694), Reflections upon Ancient and Modern Learning, London: Printed by J. Leake for Peter Buck.

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Parti Theoretical Underpinnings

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REFLECTIONS ON SOME NEW STUDIES ON APPLIED SCIENCE IN ISLAMIC SOCIETIES (8TH-19TH CENTURIES) David A. King Recent research on Arabic scientific and legal manuscripts, as well as on astronomical instruments, has led to a new understanding of the different ways in which Muslim scholars over many centuries applied scientific methods to determine the times of prayer and the sacred direction (qiblah). Keywords: New studies on the history of Islamic science; qiblah; times of prayer; World-Maps for Finding the Direction and Distance to Mecca; The Call of the Muezzin; Instruments of Mass Calculation; The Sacred Geography of Islam; Islamic Philosophy, Theology and Science Series.

Muzaffar Iqbal kindly invited me to pen a few thoughts for this journal as I see through press the third of four books dealing with aspects of applied science in Islamic civilization. I have been fortunate enough to work in manuscript libraries and museums all over the world for over 30 years, and these books are the main fruits of this enterprise. (Believe me, the frustrations of such activities and the attendant discomforts sometimes outweigh the pleasures.) The books, I would maintain, deal with topics of fundamental importance to the history of Islamic civilization, yet these topics have not been dealt with previously, because only a very few unrepresentative sources had been unearthed. Both Muslim scientists and Muslim legal scholars addressed what I have called "science in the service of Islam", that is: (1) the regulation of the strictly lunar Muslim calendar; (2) the organization of the times of prayer; and (3) the determination of the sacred direction (qiblah) towards the Kacbah in Makkah. David King is Professor of the History of Science and Director of the Institute for the History of Science at the Johann Wolfgang Goethe University in Frankfurt am Main. Address: IGN-FB 13, Frankfurt University, 60054 Frankfurt am Main, Germany.

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These new books supplement my three volumes of Variorum reprints published a few years ago and dealing mainly, but not exclusively, with these same three topics. All of my studies clearly distinguish between: (l)the scientific tradition pursued by the select few in Islamic societies, and (2) the folk scientific tradition (devoid of any mathematics beyond simple arithmetic and of any astronomy other than what can be observed with the naked eye) favored by the legal scholars of Islam. An appreciation of the dichotomy between the approaches of the scientists and the legal scholars is essential to an understanding of why scientific activity flourished for so long, but also eventually declined, in Islamic societies. This is never mentioned by anyone who has written on the nature of science in the Islamic world, let alone on its decline. It is also important for the notion of "Islam and Science" or "Science in Islam", for when Muslim scientists, using mathematics, addressed problems provided by the tenets of Islam, they came up with completely different solutions from those proposed by the legal scholars, who used the Qur*an and the hadith, together with the simple procedures of folk science. For a modern example, consider the two schools of North American Muslims regarding the qiblah: one group maintains it is north of east in North America (based on geography and mathematics) and the other favor south of east (based on a naïve 1. Islamic Mathematical Astronomy (London: Variorum, 1986, 2nd rev. edn., Aldershot: Variorum, 1993); Islamic Astronomical Instruments (London: Variorum, 1987, repr. Aldershot: Variorum, 1995); and Astronomy in the Service of Islam (Aldershot: Variorum, 1993). 2. David A. King and Julio Samsó, with a contribution by Bernard R. Goldstein, "Astronomical Handbooks and Tables from the Islamic World (750-1900): An Interim Report" in Suhayl—Journal for the History of the Exact and Natural Sciences in Islamic Civilisation, Barcelona, 2 (2001), pp. 9-105. 3. For overviews see Daniel M. Varisco, "Islamic Folk Astronomy" in Helaine Selin, éd., Astronomy across Cultures—The [!] History of Non-Western Astronomy (Dordrecht, etc.: Kluwer, 2000), pp. 615-50 and David A. King, "Folk Astronomy in the Service of Religion: The Case of Islam" in Clive L. N. Ruggles and Nicholas J. Saunders, eds. Astronomies and Cultures (Niwot: University Press of Colorado, 1993), pp. 124-38.

New Perspectives on the Histoiy of Islamic Science David A. King* 45

modern kind of folk geography). In the sequel, I shall briefly describe the contents of each of the new books. I shall also discuss the problem that, because of the nature of the transmission of knowledge these days, this flurry of new books on practical aspects of Islamic ritual and scientific highlights of Islamic civilization will probably never reach a serious Muslim scholarly audience in the form that I am publishing them. The first book, entitled World-Maps for Finding the Direction and Distance to Mecca and published in 1999, examines the way in which Muslim scholars for over a millennium dealt with the determination of the qiblah. Here we witness the ingenuity of scientists from the 9th to, say, the 15th century, as they confronted a complicated problem of mathematical geography: their results are impressive by any standards. A large part of the book is devoted to a detailed study of two remarkable newly-discovered world-maps from Safavid Iran (late 17th century) fitted with a cartographical grid so devised that one can simply read the direction and distance to Makkah at the centre. In the book, I hypothesized that the brilliant idea underlying the grids on the maps must go back to earlier (9th or 10thcentury) Islamic sources, which alas I had been unable to locate (though see below). I had, however, investigated numerous Safavid works, finding them all lacking the kind of initiative in evidence behind the map grids, and I also considered the possibility of influence from European sources, with negative conclusions. This book was published in the series Islamic Philosophy, Theology and Science: Texts and Studies by Brill Academic Publishers, with a subvention from the Al-Furqan Islamic Heritage Foundation that made it affordable. Muzaffar Iqbal reviewed the book and the underlying methodology favorably in the first issue of this journal, although he found me incapable of penetrating "the realm where the Islamic scientific tradition is perceived in its totality with all its integral links to the metaphysical doctrines of Islam intact". The second book, The Call of the Muezzin, is available from E. J. Brill as of January, 2004. It contains a comprehensive collection of essays devoted to astronomical timekeeping by the sun and stars and 4. World-Maps for Finding the Direction and Distance to Mecca: Innovation and Tradition in Islamic Science (Leiden: E. J. Brill and London: Al-Furqan Islamic Heritage Foundation, 1999). 5. Islam ¿r Science Vol. 1 (2003) No. 1, pp. 135-42.

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the determination of the times of Muslim prayer, as practiced in Islamic societies for over ten centuries. A large part of this book— written already in the 1970s—deals with tables for time-keeping by the sun and stars and for regulating the times of prayer; it is based on over 500 manuscripts that nobody had ever looked at previously in modern times. The materials come from all over the Islamic world from Fez to Yarqand and from Crete to Taiz. The book also contains sections on the origins of the definitions of the times of prayer that became standard (but which are not specifically mentioned either in the Qur^dn or the hadith), on the simple methods for timekeeping that were used by the scholars of the sacred law, and on the activities and social status of the muezzins and muwaqqits. Since no sponsor could be found for this book, it will sell at four times the cost of the first. In my first book, I had hypothesized the existence of an early Islamic tradition of Makkah-centred world-maps, of which the two Safavid examples were the sole surviving evidence. In the second book, I present a third Safavid map of the same kind. I also present evidence, discovered by my colleague Jan Hogendijk of Utrecht, that Muslim scientists in the 10th century (Baghdad) and 11th century (Isfahan) had discussed the solution of the qiblah problem using ellipses, such as are found (sensibly approximated by arcs of circles) on the Safavid maps. This should quieten those ungenerous colleagues in the history of European astronomy and cartography who preferred to see European initiative behind the Safavid world-maps. The third book, entitled Instruments of Mass Calculation, deals with astronomical instruments from the Islamic world and is to appear with E. J. Brill later in 2004. I coined this title because we searched for such instruments in Iraq, and indeed all over the Islamic world, and we found enough evidence to prove that Muslim astronomers had serious programs of instrumentation from the 8th to the 19th century. My book is my contribution to the "war against ignorance". It reveals for the first time the range and sophistication of the long and rich tradition of Islamic astronomical instrumentation. It was already well 6. In Synchrony with the Heavens—Studies in Astronomical Timekeeping and Instrumentation in Islamic Civilization, 2 vols., vol. 1: The Call of the Muezzin. Studies I-IX, (Leiden: E.J. Brill, 2004). 7. In Synchrony with the Heavens—Studies in Astronomical Timekeeping and Instrumentation in Islamic Civilization, 2 vols., vol. 2: Instruments of Mass Calculation. Studies X-XVIII, (Leiden: E.J. Brill, 2004).

New Perspectives on the Histoiy of Islamic Science David A. King* 47

known that medieval European instrumentation was highly indebted to the Islamic tradition, but now it is clear that only after ca. 1550 did European instrument-makers make technical innovations that had not been known to Muslim astronomers previously. This comes as quite a surprise to colleagues who work on Renaissance European instruments. My book includes an essay on the earliest known astrolabe, from 8th-century Baghdad, which at least until the 2003 invasion of Iraq, was housed in the Archaeological Museum in Baghdad. (I have no idea where it is now.) It continues with a description of all known astrolabes from late-9th- and 10th-century Baghdad, some 13 in number, taken from my unpublished catalogue of medieval Islamic and European instruments. I also include an essay showing that the idea behind the most sophisticated instrument of the Renaissance, the universal horary dial for finding time by the sun for any latitude, is most probably of early Islamic origin. Although I did not find precisely this instrument mentioned in Arabic texts, I did locate some years ago a treatise on a more complex instrument for the more difficult problem of timekeeping by the stars from 9th-century Baghdad. Certain colleagues in the history of European astronomy have accused me of indulging in a kind of cultural contest, and I have to admit to a certain amount of pleasure in establishing that various instruments previously thought to be European inventions were actually invented by Muslim astronomers centuries previously. 8. See my review of Gerard L. E. Turner, Elizabethan Instrument Makers—The Origins of the London Trade in Precision Instrument Making (Oxford: Oxford University Press, 2000) in Journal of the History of Collections (Oxford) 15:1 (2003): 147-50, especially pp. 149-50. 9. François Charette and Petra G. Schmidl, "A Universal Plate for Timekeeping with the Stars by Habash al-Hasib: Text, Translation and Preliminary Commentary" in Suhayl—Journal for the History of the Exact and Natural Sciences in Islamic Civilisation (Barcelona) 2 (2001): 107-59. 10. For these colleagues I have published summaries of the discoveries outlined in Instruments of Mass Calculation (see note 6), Xlla and Xllb, separately in "A Vetustissimus Arabic Treatise on the Quadrans Vetus" in Journal for the History of Astronomy 33 (2002): 237-55, and "14th-Century England or 9th-Century Baghdad? New Insights on the Origins of the Elusive Astronomical Instrument Called the Navícula de Venetiis" in Centaurus 44 (2003): 204-26.

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At this stage, I should mention that my young colleague, François Chare tte, has just published a major contribution to our understanding of Islamic instrumentation. For some years now we have known of the existence of a treatise by an enigmatic Egyptian scholar Najm al-Dïn al-Misrï (ça. 1325), in which he describes and illustrates over 100 different instrument types known to him or invented by himself. Charette has published a model edition and translation of this complicated treatise, together with a detailed commentary. There is a sense in which his book provides a kind of "instant supplement" to my new book on instruments. The fourth book, The Sacred Geography of Islam, was written in the 1980s but never published: I was on the point of submitting it to a publisher in 1989 when the first of three Safavid Makkah-centred world-maps showed up and absorbed my attention for several years. What I mean by "sacred geography" is the notion of the Kacbah at the centre of the world, and the way sectors of the world are organized around the sacred edifice. Various Muslim scholars of folk astronomy, geographers, and legal scholars discussed this notion, and their schemes of the world about the Kacbah are often illustrated. In these schemes, the qiblah in each region is defined in terms of the risings and settings of the sun and various bright stars. The qiblah for each region is inevitably different from the values derived by Muslim scientists. Some 20 different schemes of sacred geography recorded in some 30 different sources are described in this book. I hope to submit the manuscript to Brill this autumn. So why did I write these books? They mark the culmination of my preoccupation for over 30 years with the primary sources of the history of Islamic science. I worked on these because I found them exciting and rewarding. It was my firm conviction 30 years ago that this was the least researched area of the history of Islamic science, though colleagues who work on the history of Islamic mathematics, cosmography, optics and medicine could actually make similar claims for their chosen fields. I write primarily as an Islamicist rather than as 11. François Charette, Mathematical Instrumentation in Fourteenth-Century Egypt and Syria—The Illustrated Treatise of Najm al-Dïn al-Misrï (Leiden: E. J. Brill, 2003). 12. The World about the Kacba—The Sacred Geography of Islam, to be submitted to E. J. Brill.

New Perspectives on the Histoij of Islamic Science David A. King* 49

a historian of science, since my interests in the field of Islamic Studies are broad, but my activities in the History of Science are restricted to the Islamic period and the European Middle Ages. Muzaffar Iqbal called me a positivist, and I was happy to show this remark of his to my wife, who finds me too "negativist" on a variety of issues. Is it so bad to be a positivist? What it means to me is being involved in the old "Quellen und Studien" approach to cultural history: find a source and publish a description of it that captures the essence of what was intended by the original compiler. (I am well aware that some colleagues are positivist to the point of being petty and essentially irrelevant to any undertaking beyond filling the pages of very boring scholarly j ournal s. ) Take the case of a 14thcentury Muslim scholar who compiled a table displaying the qiblah in degrees and minutes for each degree of latitude and longitude difference from Makkah to serve the entire Muslim world. The table was investigated for the first time in 1970. Before that time, it was not known that Muslim scientists compiled such tables. What greater tribute to that early scholar's brilliant achievement than to edit his table from the available manuscripts, reconstruct the original values where they have been distorted by copyists, and provide the cultural and historical context for the table? Most of the entries are so accurately computed (with no errors in the minutes) that we have still not been able to determine the procedure whereby they were originally computed. If this is "positivism" on my part, then it is in order, for at least the achievement of the original compiler has been saved from oblivion, and others now have access to it. He compiled this table not only because he was a Muslim but because he was a mathematician and a Muslim. In fact, he was one of the leading mathematicians anywhere in the world at the time. Other approaches to such a qiblah table, such as art-historical or palaeographical—"the table is framed in a ..." or "the entries are written in a dark brown ink ... "—can only be labeled inadequate. Another copyist may have preferred ink of a different color. The apologetic approach—"with such tables, Muslims were able to face the qiblah correctly for over a millennium ... "—is superficial and also historically incorrect, for, in fact, the table was known only in 13. King, "al-Khalili's Qibla Table" in Journal of Near Eastern Studies 34 (1975): 81-122, repr. in idem, Islamic Mathematical Astronomy, XIII.

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a very restricted geographical and chronological milieu. Contemporaneous legal scholars were proposing completely different means for finding the qiblah anyway and would never have considered using a table for that purpose. It happens that we now know of nine different tables displaying the qiblah for each degree of longitude and latitude in the Muslim world, the first of which dates, inevitably, from ninth century Baghdad. Nevertheless, the often curious orientations of medieval mosques in each region of the Muslim world prove that scientists were seldom consulted on the qiblah. Many of these orientations are of the kind proposed in the medieval schemes of sacred geography. All of these orientations are towards the qiblah: it just depends what procedure was used to determine the qiblah. (Much nonsense has been written by historians of Islamic architecture who have noticed that this or that mosque did not face the direction they thought it should.) Why did I publish these books with Brill? First, their Islamic Philosophy, Theology and Science series has produced already 55 volumes since its inception around 1990. Second, I have a long association with Brill through my contributions to their monumental Encyclopaedia of Islam. Some Muslims seem to find the Encyclopaedia problematic; it is indeed written from an objective, "positivist" if you like, point of view, if one can credit orientalists—see below—with objectivity. Anyway, like it or not, it is the basic (and only) reference work on Islamic civilization in all its facets. Interested readers who cannot access my books will at least find there my survey articles such as "Qibla" on the sacred direction of Islam; "Makka, As centre of the world" on sacred geography; "Mïqât" on astronomical timekeeping and the regulation of the times of prayer; "Samt" for the first mention of Makkahcentered world-maps; and on various categories of instruments: "Mizwala" on sundials; "Rubc" on quadrants, "Shakkâziyya" on universal instruments; "Tâsa" on the magnetic compass; and "Zidj" (with Julio Samsó) on astronomical tables. All of these supplement the earlier and long out-of-date article "Asturlâb" on astrolabes. There is one further reason why I publish with Brill: their editors do not mess about with my text, and their printers know what they are doing, a rare combination these days. 14. I am sick and tired of editors who mess up texts - for example, by inserting bibliography into footnotes, of translators who have no

New Perspectives on the Histoiy of Islamic Science David A. King* 51

What will happen to these books of mine? They will automatically reach the major national and university libraries that subscribe to the Brill Series, as well as the libraries of some centers for Near Eastern Studies or History of Science. Some copies will end up in the private libraries of colleagues in those two fields. A few of these will have received free copies for reviews in the major journals of these two disciplines. And by the time any Muslim scholars outside the Western world hear about them and their contents—we are talking about the first histories of tahdld al-qiblah and tahdld mawáqlt al-salat—the books will be out of print and will have become collectors' items. It's rather sad, but the same is true of most publications on the history of Islamic science over the past 50 years. Modern Muslim scholars who write on Islam and science generally have no idea of what a small group of scholars of diverse nationalities, including Arabs, Iranians, Turks and Indians, has achieved in the past 50 years. There are journals devoted almost entirely to new discoveries in this field \Journalfor the History of Arabic Science (Aleppo), Suhayl-Journal for the History of the Exact and Natural Sciences in Islamic idea what they are translating, and of printers who mess up edited texts because they do not respect the authors' requests. The worst example I can cite is an article on "Science in the Service of Islam" that I was invited to submit to UNESCO's scientific journal Impact of Science on Society in 1991, and which was to have appeared in various languages. First, the editors removed all of the direct quotes from the Qur^dn and the (Sunni and Shfi) hadlth. This enabled the person who was entrusted with the preparation of an Arabic translation to add a series of footnotes to the effect that "the author does not seem to know that in the Qur^àn... ". The translator further did not recognize one hadlth I had cited, which happened to be a Shfi hadlth (and had been clearly identified as such in my original paper), and he consequently accused me of fabricating it! He also converted all dates in my text as though they were Hijra dates, so that Cairo became founded in 969 H or 1561. The disastrous Arabic translation was fortunately withdrawn and never published. Thus the first account of "Science in the service of Islam" was published in English, French, Portuguese, Chinese and Korean, and since then also in German, Italian and Persian, but not in Arabic. Also worthy of mention is an English printer entrusted just last year with an article heavy on Arabic transcription: he succeeded, it is not clear how, in converting half of each batch of long vowels to a different long vowel, so that the entire lot had to be corrected individually by hand.

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Civilisation (Barcelona), Arabic Science and Philosophy (Cambridge), Zeitschrift fur Geschichte der arabisch-islamischen Wissenschaften (Frankfurt), SCIAMVS-Sources and Commentaries in Exact Sciences (Kyoto), and now Islam ¿7 Science. For an overview of what is being done I can recommend the website: www.ou.edu/islamsci/ There are many websites set up by well-meaning but poorlyinformed Muslim student groups at various Western universities that are an insult to the splendid achievements of the Muslim scientists of the Middle Ages. They are invariably based on sources that are decades out of date. In fact, I do not know of one that is well informed or realizes that the history of Islamic science is a subject that is still being researched. In order to remain sane during the 2003 invasion of Iraq I compiled a bibliography of writings on the exact sciences in Baghdad during the 8th-10th centuries. I have mentioned above the designation "orientalist", a word that has become tainted by modern savants who have no conception of what most orientalists actually do. Their criticism of orientalists focused on some of the "bad guys", of whom, I admit, there were a few with their own dubious agendas. The vast majority of orientalists I know, however, have a healthy respect for the cultures they study. Those working in the history of Islamic civilization often have knowledge of other cultures, be they Classical, Byzantine, Indian, Jewish, Sasanian, or whatever. These insights help them to see Islamic civilization in a clearer perspective than those who know only the Islamic one. Certainly, when dealing with Islamic science, it helps to have a foundation in Greek, Indian and Sasanian science. A curious situation arose decades ago when historians of science, interested primarily in the early history of Western science, perceived Islamic science solely as an agent for the transmission of superior Greek science to eager but still ignorant Europeans in the Middle Ages. Or, to put it another way, they were only interested in Islamic works that were transmitted to Europe. Now the astronomical works of, say, al-Khwârizmï (Indian and Sasanian influence) and al-Battânï (Greek influence), and the mathematical works of the same alKhwârizmï (essentially Babylonian algebra and Indian arithmetic), 15. See

http://www.uni-frankfurt.de/fbl3/ign/astronomy_in_baghdad/

bibliography, html.

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were particularly influential in Europe, regardless of the fact that they were already out-dated and surpassed in the Islamic world. The preoccupation with these particular works has accounted for the fact that they have been better served by historians: all available materials have been edited and translated into European languages. This activity partly led to the neglect of virtually all of the other Islamic texts on astronomy and mathematics, but a few orientalists and/or historians of science have certainly remedied that situation. Witness, for example, the rediscovery over the past century of the works of alBïrunï, the greatest scientist Islamic civilization ever produced. But alKhwârizmï, al-Battânï and even al-Bïrunï, were part of a scientific tradition that knew no rival for many centuries. Thus, when E. S. Kennedy compiled his 1956 survey of Islamic astronomical handbooks with tables, he identified some 125 examples. Benno van Dalen, who has continued the work of Kennedy in spectacular directions, now counts some 250 such works compiled in the Islamic world between 750 and 1900, and his forthcoming publication on Islamic zy'es is awaited with anticipation. I make no apologies to anyone for being an orientalist. What this means to me is that I took great pains to learn some languages, read some medieval manuscripts that nobody else had looked at for centuries, and wrote about what I found. (I admit again that some orientalists with a religious penchant of their own have proposed partisan theories that have been since shown to be untenable: a good example is the literature on the development of the ritual of five prayers in standard Islamic practice, most of which—pushing Jewish, Christian or Zoroastrian connections—has been rendered invalid by further research.) Muslims need to recognize what many unbiased orientalists have achieved over the past few centuries, in order to begin to profit from and to participate in this exciting venture. Now even the discipline "History of Science" is in some danger. In German it used to be called Geschichte der Naturwissenschaften, history of the natural sciences. This is now out of favor, and Wissenschaftsgeschichte, meaning, more or less, the history of science in its cultural context, is in vogue. My own university actually appointed a Professor 16. E. S. Kennedy, "A Survey of Islamic Astronomical Tables" in Transactions of the American Philosophical Society, N. S., 46:2 (1956):

123-77, repr. with separate pagination, n.d. [ca. 1990].

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for Wissenschaftsgeschichte recently without even informing or consulting myself, the Professor for Geschichte der Naturwissenschaften. (Happily, as a result of the fact that they did not really know what they were doing, they selected a highly-competent historian of mathematics, so all is not lost.) In Wissenschaftsgeschichte, there is a great danger that people waffle about science in Islamic civilization without knowing anything about Islamic science, the history of Islamic institutions, or modern research on the history of Islamic science. There are plenty of academics, fortunately none colleagues of mine, who would do this. One danger is that the field attracts scholars who have no background in the texts compiled by the Muslim scholars. One problem is that the history of Islamic institutions has been written by scholars who had little perception of the scientific activity pursued in those institutions. This was not always their fault, because the medieval biographical dictionaries tended to concentrate on scholars with training in the religious sciences. I would like to see somebody work on the long-neglected biographical dictionaries of scientists by Ibn Abi Usaybica and Ibn al-Qifti; the last person to have looked carefully at these seems to have been Heinrich Suter, when he compiled his monumental 1900 survey of mathematicians and astronomers writing in Arabic. To his credit, he included in his survey numerous scholars known for their teaching activities and intellectual interests, but who did not "publish". There is serious work to be done in the future, and Dimitri Gutas and Sonja Brentjes, independently, have outlined some of the problems and proposed possible guidelines. As an example of the limitations of old-style Geschichte der Naturwissenschaften compared with the potential virtues of new-style Wissenschaftsgeschichte, I can cite one close to my heart. I would be the first to admit that some of my earlier writings are inadequate by the 17. Dimitri Gutas, "Certainty, Doubt and Error: Comments on the Epistemological Foundations of Medieval Arabic Science" in Early Science and Medicine—A Journal for the Study of Science, Technology and Medicine in the Pre-modern Period 7:3 (2002), pp. 276-89; Sonja Brentjes, "Between Doubts and Certainties: On the Place of the History of Science in Islamic Societies within the Field of the History of the Science" in NTM - International Journal of History and Ethics of Natural Sciences, Technology and Medicine, N.S., 11:2 (2003): 65-79.

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standards of today. For example, in 1983, I published an essay entitled "The Astronomy of the Mamluks". I wrote this based on my familiarity with dozens of Mamluk astronomical treatises and a few surviving Mamluk instruments. I did not investigate the information in the available biographical dictionaries on Mamluk scholars (although I since tried to encourage one potential doctoral student, a native-speaker of Arabic, to do just that). So I wrote, for example, that one Ibn al-Majdi in the mid-15th-century had compiled some ingenious auxiliary tables for computing the solar, lunar and planetary positions needed for annual ephemerides (taqwïm, pi. taqdwïm). I just did not know that Ibn al-Majdi was—in addition to being a professional astronomer at al-Azhar—a legal scholar who taught fîqh, a philosopher who taught hikma, an astrologer who counseled the sultan, as well as a sufi, who after becoming head of a madrasah converted it to a khânqâh. I agree that my essay would have been much richer if I could have included this kind of information. In my own defence, I can claim that at least we have an essay on the technical writings of the astronomers of the Mamluk period, which nobody at the time knew anything about, and on which somebody else can now improve. Also, in my own defence, I can still claim that we seem to have no biographical information whatever on certain Mamluk astronomers beyond the scant references in their astronomical works. Islam emerged out of a religio-cultural milieu that helped to fashion it. Otherwise, for example, the Qur^dn would not originally have been revealed in Arabic with dialectal and foreign lexicographical influence. The Muslim who believes in Islam as the ultimate revelation can take pride in the achievements of Islamic civilization. The orientalist, unless he/she happens to be a Muslim, investigates the history of Islamic civilization with a certain amount of distance. One does not need to be a Muslim to write on the history of any aspect of Islamic civilization, anymore than one need be a Christian to write on the history of any aspect of Christian civilization. (In fact, also solely out of intellectual curiosity, I have recently published on a number-notation used by monks in the European Middle Ages, and on a medieval saint whose history I found to have been completely distorted by virtually all previous writers, so that the entries on her in standard dictionaries of saints are mainly drivel. No Western reader will pose the question: does this author believe in the metaphysical implications of the cosmic triumph of Jesus Christ?)

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On Jan 31, 2004, an American convert to Islam, with a Jewish father and Christian mother, was interviewed by CNN about the hajj. He mentioned that the Kacbah, the physical centre of the world of Islam, was in itself nothing more than bricks and mortar. The interested reader will find a lot more about the significance of the layout of the rectangular base of the Kacbah—based on medieval texts written by Muslims—in the first and fourth of the books mentioned above. When I was teaching at New York University in the early 1980s, I had a doctoral student begin a dissertation—alas never finished—on medieval texts dealing with the Kacbah. The history of the Kacbah still has to be written, but it is just one amongst many topics that demands our attention. The task of the orientalist, or rather, an orientalist with my kind of interests in the practical interaction between Islam and science over many centuries, is to pose questions like the following and seek their answers. Why is the sacred direction in Islam called qiblah, from the root q-b-l? Why is the term salât for the Islamic prayer ritual written with a wâw? Is it significant that the major axis of the rectangular base of the Kacbah is aligned towards the rising-point of the star Canopus over the horizon of Makkah, and the minor axis is aligned to the solar rising at the summer solstice? Muslims centuries ago certainly thought it was. How have Muslims determined the qiblah and the prayer-times over the centuries? Why do medieval mosques face all sorts of curious directions, when any medieval astronomer could have advised on a qiblah in accord with contemporaneous geographical knowledge? What is the origin and significance of the distinctive definition of the beginning of the time of the casr prayer in terms of the increase of the gnomon shadow over its midday minimum by an amount equal to the length of the gnomon? Where did this definition, still in use today, but neither in the Qur^án nor in the hadïth, come from? Why was there in certain Muslim communities in the Middle Ages a sixth prayer at midmorning called the duhd? Some ahddïth have the Prophet himself performing the duhâ prayer, others maintain that he disapproved of it. And why is there no conflict in modern Muslim societies about the times of prayer, but chaos often reigns at the beginning and end of Ramadan? These are valid questions on subjects somewhat far from the metaphysical doctrines of Islam, and Muslims can learn a lot about Islam (and about Muslims) from their answers. These answers add to the richness of Islam rather than detract from it.

[2] PROBLEMS OF THE TRANSMISSION OF GREEK SCIENTIFIC THOUGHT INTO ARABIC: EXAMPLES FROM MATHEMATICS AND OPTICS Roshdi Rashed

Centre National de la Recherche Scientifique, Paris Historians of science have frequently stressed the significance of the transmission of the Greek and especially Hellenistic heritage into Arabic for the history of scientific thought, until the eighteenth century at least. They have not waited until now to appreciate the importance of this phenomenon for Arabic, Hellenistic and Latin sciences. The emergence of Arabic science itself is incomprehensible unless one refers to the reception of its Greek heritage; nor can one hope to reach a full understanding of the achievements of Greek science itself without the substantial part that has survived only in Arabic, as for example, Apollonius and Diophantus. The same holds for the history of the relationship between Greek and Latin science whose understanding requires the examination of Greek texts translated into Arabic and then into Latin. Given these conditions, one might therefore expect to encounter an abundance of detailed works on a question whose importance for the history of ancient and classical science is undisputed. But this is not the case. Infrequent as they are, such investigations consider the problem from only one angle, that of translation; moreover, most of them share a vision of transmission that may well distort analysis: a vision that is all-inclusive, passive and scholarly. Allinclusive, in so far as transmission, of both philosophy and science, confined to translation is considered all in one piece; and consequently, the transmission of Greek science and philosophy is viewed en bloc. Passive, since it is based on the affirmation of what one might call the law of the three estates that governs both the logical and the historical sequence of translation, assimilation and creative production in Arabic.1 Lastly, scholarly, in so far as scientific and philosophical knowledge can circulate only via translated books. Now against an all-inclusive vision of history, we have upheld a differential approach, which respects the cleavages not only between science and philosophy, but also between the sciences themselves. We oppose the image of transmission as passive reception with one of conversion, reactivation, and even occasionally the renewal of one or more disciplines.2 On this point let us recall two elementary facts known to all: first, the transfer of knowledge does not occur on either the geographical or the cultural level: it is essentially

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linguistic. Is it necessary to recall that this knowledge was mainly developed on the spot, i.e. in the centres, regions and peoples of ancient Hellenism who, after Islam, changed their language and the majority their religion? To forget this fact is to overlook another: transmitted science was not only scholarly; the administrative texts translated in the eighth century included metrology and geodesy and the inherited craft techniques included geometry, hydrostatics, optics, and agronomy. However, the history of these indispensable vehicles for the transmission of science remains to be written. It would be useless to pretend here and now to remedy the inadequacy of research. I shall confine myself to one theme: the relationship between translation and research, since all questions refer to this one. How can one reflect on the identity of translators, the works they translated, and why they translated, without returning to the state and organization of research when they were translated? Similarly, it is impossible to question translation methods if contemporary scientific disciplines and linguistic studies are ignored. This approach may perhaps avoid two pitfalls: an exposé where an author lavishes methodological advice or rather didactic recipes, all the easier since he has not put them into practice himself; or yet again the danger of an exposé on the archaeology of a fragment, where the transfer of words is assimilated with those of concepts. Without going into too much detail, I shall therefore start by pinpointing some aspects of translation, before taking up the points just raised, on the basis of two examples taken from mathematics and optics. Let us go back to Baghdad in the early ninth century and note that the translation movement is no longer in its early stages, but is entering a second phase which will bring it to its zenith. From the first period only a few vestiges3 have survived, occasionally a title; for instance, from Ibn al-Nadïm we know about the existence of an ancient translation of Theon's Introduction to the Almagest. However, these scattered references do not enable us to draw a faithful picture of the translating activity, they merely indicate individual initiatives. In the course of the second period, of incomparable importance — and the subject of this paper — translation has become a part of a much wider activity that may be designated by the evocative title "the institutionalization of science".

I This progressive movement started by spreading to newly created disciplines directly linked to the new society, its organization and its ideology: the science of language, jurisprudence, theology, history, hermeneutics, etc. In the middle of the eighth century new questions arose in the field of linguistics, hermeneutics, theology, jurisprudence; the number of scholars and writings in these

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fields increased considerably, specialization became more pronounced and one witnesses the emergence of rival schools marked by an increasingly defined professionalization.4 However, the Hellenistic scientific legacy, particularly in the mathematical sciences, was affected by this movement only in Baghdad and in the ninth century. A closer examination would show that interest in the Greek legacy was partly linked to this research activity in Islamic disciplines. Oft-repeated anecdotes about the specialists in these disciplines, such as the linguist al-Khalïl, are a good illustration.5 From now on it is understandable why the movement did not reach the legacy of Hellenistic science before the ninth century; and also why the translating enterprise in Baghdad involved several disciplines at the same time — medicine, as well as geometry and astronomy — and was not confined, as has been written, to medicine and astrology, i.e. disciplines that present a practical interest. The error of perspective that results from such a limitation cannot be sufficiently emphasized. But why did the institutionalization of the Hellenistic scientific legacy get under way at that time and in that place? Two reasons must be considered, the first of which is common knowledge: the existence of a social need. All studies on the transfer from Greek to Arabic relate facts and anecdotes that show that caliphs and patrons founded libraries and observatories and graciously encouraged translation and research. But what is never said is that not only individuals but also groups are to be found in the new institutions, one might even call them 'teams', sometimes rival and competing, These groups and the social positions created for translation and research were to be a means of integrating Hellenistic science into the 'scientific city' as it was developed and expanded. As a reminder, let us recall that the renowned House of Wisdom in Baghdad included astronomers such as Yabya ibn Mansür, translators such as al-Hajjàj ibn Matar — the translator of Euclid and Ptolemy — and mathematicians such as al-Khwârizmï. Another group also connected with the House of Wisdom, the Bánü Musa, three brothers and scientists, included the translator of Apollonius, Hilàl ibn Hilâl al-Himsï and the translator and eminent mathematician Thâbit ibn Qurra as well. Lastly, it is also known that scientists gathered around Hunaîn and al-Kindï, among others. This organization of translation clarifies one of its most striking aspects at that time: its large-scale appearance. In fact, in the space of a few decades, Euclid's Elements were translated three times, Ptolemy's Almagest twice and also other books of Euclid and Ptolemy; and Apollonius's Conies. Over the century several of Archimedes's treatises were translated, seven books of Diophantus's Arithmetica, and among others, the works of Hero of Alexandria and Pappus, Though on a large-scale, the work of translating was neither systematic, nor organized according to an increasing order of difficulty, nor even according to the historical sequence of Greek authors. One might as well say the translating

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venture was not dictated by a preconceived programme. Nevertheless, it would be a mistake to assume that the translations were made haphazardly, i.e. depending on the random discovery of texts. Several accounts by contemporary translators bear witness that it was, on the contrary, a deliberate undertaking: the text to be translated was selected and then the manuscripts of the text were tracked down.6 All these aspects, the large-scale, unsystematic translations which were nevertheless deliberately organized, are connected with the second reason which explains why the institutionalization of the Greek heritage developed in Baghdad and in the early ninth century. Insufficiently stressed though obvious, the second reason is the deep-seated connection between translating and research: the latter, depending on the circumstances, preceded translation itself or was contemporary with it, or yet again was more-or-less indirectly set in motion by the translation of another text in a neighbouring domain. The aim of the translation of scientific texts at that time was not to write the history of science but make available in Arabic, texts necessary for the training of researchers or even the advance of research. For instance, the translation of Archimedes's work was to facilitate studies on the measurement of areas and volumes, certainly not as a contribution towards the writing of the history of this chapter, nor for commentaries on Archimedes. If we call attention to this point it is because it influenced the choice of the text to be translated and governed the method and style of the translation. In other words, the underlying order behind the choice of works for translation and the succession of translations makes sense only in reference to contemporary research activity. At the same time light is shed on the fourth characteristic of scientific translation: it was often the work of first-class researchers such as Hunaïn, Thàbit ibn Qurra, and Qustâ ibn Luqà, who, as we already know, were also scientists fully conversant with Greek. Though it is true that the bulk of scientific work was translated directly from Greek without recourse to Syriac, it was however the work of scientists equally concerned with meaning, to such an extent that its literal aspect might conceal interpretations and even corrections of the text. But in order to grasp the characteristics just pointed out at work, it would be preferable to support our argument with meaningful examples. I shall therefore select two examples, one from mathematics, the other from optics. II

To start with, let us take the translation of the seven books of Diophanthus's Arithmetica, four of which are still lost in Greek. Before examining the Arabic translation, two introductory remarks are necessary.7

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The first concerns Diophantus's alleged aim in the preface to the first book of Arithmetica, and the nature of his contribution. The author intended to construct an arithmetical theory, api9|ir|TiKr| Oecopia, The constituent elements of this theory are numbers — considered according to the Euclidean concept, i.e. as pluralities of units, ^lovaSow 7rX,f|0oc, and fractional parts, like the fractions of magnitudes. These elements of theory are not only present 'in person', but as species of numbers. Diophantus mentions three species: the linear number, the plane number and lastly, the solid number. The other species are engendered from these three by composition, and each of their powers is necessarily a multiple of 2 or 3. One will look in vain for the fifth or seventh power in the statement of Greek or Arabic problems of the Arithmélica. Light is thus shed on the composition of the Arithmetica: it concerns combining species with each other under certain conditions, and with the aid of the operations of elementary arithmetic. For instance, one seeks two cubes whose sum is a square; a given square is divided into the sum of two squares. In each case, to solve these problems amounts to trying to proceed "until there remains one species on either side". In the course of his solutions, Diophantus applied the substitution, the elimination, and the transfer of species, in short, using algebraic techniques. The Arithmetica is not however, as is understood, a work on algebra, but is really a treatise on arithmetic. Our second introductory remark leads us back to the early ninth century when al-Khwarizmi conceived algebra as an independent discipline and devoted his famous book to the subject. This book does in fact conclude a set of problems of indeterminate analysis of the first degree. Like all the other chapters in this work, the problems are set forth and dealt with using new concepts and the new terminology of algebra. Al-Khwàrizmï's successors, notably Abu Kàmil, pursued the chapter of indeterminate analysis as an integral part of algebra though ignorant of Diophantus's Arithmetica. However, it was precisely during this momentous period of research on indeterminate analysis — or according to modern terminology, rational Diophantine analysis — that Diophantus's Arithmetica was translated. The new title given by the translator to Diophantus's book, The art of algebra, belonged neither to the Greek lexicon nor to the conception of Hellenistic mathematicians. Taking place right in the heart of active research on algebra, this translation later contributed to the pursuit of the works of the tenth century algebraists, such as Abu al-Wafà' al-Buzjànï and especially al-Karaji. It is therefore a striking example of a translation prompted by an already welladvanced research. This situation will explain moreover the lexical and stylistic traits of the Arabic text. In fact, though literal, the translation surprises the reader by its algebraic appearance: the translator deliberately drew on the algebraic vocabulary of alKhwàrizmï and his successors to seek out terms that designate not only

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entities on which Diophantus was working but also operations that are applied to them. For instance, the Greek TcXeupa, usually translated by Science • Vol. 3 (Winter 2005) No. 2

that from the ninth century onwards, the passage of Aristotle, Plotinus, and Proclus, among others, to the Islamic philosophers had taken place safely, without the slightest trouble. But this historical account is advanced not without some serious consequences: not only does it paint for us a very pale and an impoverished picture of philosophical activity, it also transforms the historian into an archaeologist whose skills he happens to lack. Indeed, it is not at all rare that historians set themselves the task of rummaging through the terrain of Islamic philosophy in search of vestiges of Greek works whose originals are lost but are thought to be preserved in the Arabic translations, or that, for lack of better resources, they are at least satisfied with the traces of writings of the philosophers of Antiquity, often studied with the competence and talent characteristic of the historians of Greek philosophy. It is in this manner that the history of Islamic philosophy is transformed into archaeology, so to speak. It is true that aside from the Greek heritage some historians have recently turned their attention to doctrines developed in other disciplines, such as philosophy of law, masterly developed by the jurists; philosophy of kalam, which reached important depths and stages of refinement; the Sufism of the great masters like al-Hallaj and Ibn Arabi, and so on. There is no doubt that studies of this sort go a long way towards enriching and rectifying our vision and better reflecting the philosophical activity of the time. Science and mathematics, however, are far from having received the same favourable attention given to law, kalam, linguistics, or Sufism. Furthermore, the examining of the relationships, which we regard as essential, between the sciences and philosophy, and notably between mathematics and philosophy, is completely disregarded. This serious lacuna is not the sole responsibility of the historians of philosophy; it is that of the historians of science as well. It is true that the examination of these relationships requires various competencies and an in-depth knowledge of these areas: in addition to a linguistic knowledge which goes beyond that called for in geometry (there one might do with elementary syntax and a poor lexicon), one is also asked to have a grasp of the history of philosophy itself. If we realize these requirements are not often met, and on top of that the conception of the relationships between science and philosophy is inherited from an oft-ambient positivism, we may come to better appreciate the profound indifference exhibited by the historians of science vis-à-vis the kind of examination we are calling for. This is despite the well-known fact that

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the links which science and philosophy enjoy are but an integral part of the history of sciences. As a matter of fact, the situation is quite paradoxical: while scientific and mathematical research of the most advanced standards had been developed and worked out in Arabic in the urban centres of the Islamicate for a period of seven centuries, is it at all conceivable that philosophers, who were often themselves mathematicians, doctors, and so forth, would have remained recluse in their philosophical activity, totally oblivious to the mutations taking place under their eyes, and completely blind to the successive scientific results that were then being achieved? Moreover, when faced with such an outburst of new disciplines and also success (an astronomy critical of Ptolemaic models, optics reformed and renewed, an algebra created, an algebraic geometry invented, a Diophantine analysis transformed, a theory of the parallels discussed, projective methods developed, and so on) can it be imagined that philosophers remained unperturbed by these developments, as to deduce that they were strictly confined to the relatively narrow frame of the Aristotelian tradition of neo-Platonism? The seemingly impoverished philosophy in the classical period of Islam, which emerges as a result of such accounts, is due to historians rather than history. Actually, to examine the relationships between philosophy and science, or between philosophy and mathematics—which is our only concern here— as they appear in the works of the 'pure' philosophers, amounts to only a third of the quest desired here. There is a further need to address in this instance, and that is to bring in the views of both the mathematicianphilosophers and the 'pure' mathematicians. But why have we from the beginning taken the view that we should limit our consideration in this instance to mathematics? This idea deserves an explanation, particularly as this approach is by no means exclusive to Islamic philosophy. No other scientific disciplines have contributed to the genesis of theoretical philosophy as mathematics have, and none other than mathematics have established links with philosophy which are not only numerous but also ancient. Indeed, since antiquity, mathematics had never ceased to present to the philosophers' reflection central themes of vital importance: it is owing to mathematics that philosophers acquired their methods of exposition, their argumentation procedure, and were provided even with instruments which they appropriated for their analysis. Mathematics are themselves presented to the philosopher as

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an object of study, when the latter devotes himself to the clarification of mathematical knowledge, studying its object, methods, whilst inquiring on the characters of its apodictic. Throughout the history of philosophy, questions about this mathematical knowledge (its genesis, its power of extension, the nature of certitude it attains, its place in the classification of knowledge) have been asked relentlessly. In that regard, philosophers of Islam during the classic period are no exception to the rule: al-Kindï, al-Fârâbï, Avicenna, Ibn Bâjja, Maimonides—to name only a few—are no exception to the rule. Links other than these have also been established between mathematics and theoretical philosophy, albeit in a more subtle and discrete fashion. Whether the aim is forging a method, even logic (as in the meeting of Aristotle and Euclid in relation to the axiomatic method), or the appeal of al-Tusï's combinatory analysis in order to solve the philosophical problem of the emanation from the one, their collaboration is again not rare. There is, however, in all those possible forms of relationship, one that is of a particular significance, and one which is instigated by the mathematician and not the philosopher: those doctrines mathematicians worked out in order to justify their own practice. The most opportune conditions for such theoretical constructions are gathered at the time when the mathematician spearheading the research of his period is hindered by an unsurmountable difficulty: namely, when the available mathematical techniques are deemed inadequate in the face of the emerging and spreading new objects. One could think of the diverse variants from the theory of parallels, particularly from the time of Thâbit ibn Qurra, to the sort of analysis situs conceived by Ibn al-Haytham, for the doctrines of the invisibles in the seventeenth century. The relationships between theoretical philosophy and mathematics are essentially found in three types of intellectual oeuvre: those of the philosophers; those of the philosophers-mathematicians like al-Kindï, Nasïr al-Dïn al-Tusï, etc.; and those of the mathematicians of the avantgarde, such as Thâbit ibn Qurra, his grandson Ibrahim ibn Sinân, alQuhi, Ibn al-Haytham, and so on. If we restrict ourselves to this group or the other when examining the relationships philosophy and mathematics enjoy with one another, we are bound to lose an essential dimension in this domain. We have endeavoured on many occasions to exhibit some of the themes of this philosophy of mathematics simply by digging here and there, our aim being to unearth samples demonstrating the richness of this domain

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rather than its systematic examination, which is not our purpose here. We do recognize that such a project deserves quite a large book. Yet, what seems most suitable to us is to move away from the pure relation of the views, which philosophers may have expressed on mathematics and their importance; our way is mostly interested in the themes that were debated, in the intimate relationships that unite mathematics to philosophy, and their role in the propping up or scaffolding of doctrines or systems. We are, in other words, seeking the organising role of mathematics. We will first highlight how the philosopher-mathematicians proceed in their search for mathematical solutions to philosophical problems, a fruitful approach which generates new doctrines and even new disciplines. As we look at the mathematicians we will bring into relief their attempts at solving philosophically mathematical problems. It will become clear that such an intellectual enterprise is indeed necessary and of far-reaching consequences. To clarify the aforementioned typology, I will now mention some examples in brief. I. Al-Kindï as Philosopher-Mathematician An appreciation of the relationships between philosophy and mathematics is essential for the reconstitution of al-Kindi's system. Is it not this very dependence which drives the philosopher to write a book entitled Philosophy Can Only be Acquired Through the Mastery of Mathematics and an epistle by the title On the Quantity of Aristotle's Works, in which he presents mathematics as a foundational course prior to the teaching of philosophy? In that epistle he even goes so far as to call the student of philosophy, warning him that he is in fact before the following alternative: either to start with the study of mathematics prior to embarking on the works of Aristotle, as grouped and ordered by al-Kindï, and then the student could hope to become a real philosopher—or else he could skip the study of mathematics altogether, and be only an imitator, so long as his memory does not fail him in this task. It is clear that for al-Kindï mathematics form the very base of the philosophical course. If we were to delve into their role in the philosophy of al-Kindï—which is not what we are doing here—we could then grasp more rigorously the specificity of his oeuvre. Historians tend to look at al-Kindï's philosophical edifice under two clearly distinct lights. According to the first interpretation, al-Kindï comes across as a Muslim who represents the Aristotelian tradition of neo-Platonism—that is, a philosopher of a doubly-late antiquity. The second sees in him a

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continuator of speculative theology (kalám)—that is, a theologian who had to switch languages in order to speak of Greek philosophy. But if we were to grant mathematics the true role they play in the elaboration of philosophy, then al-Kindi's fundamental options would be brought to relief: one of them stems from his Islamic convictions, as they are explicated and formulated in the tradition of the speculative theology, particularly that of al-Tawhïd, which holds that revelation brings us the truth to which reason can attain; the other falls back and refers to Euclid's Elements as a model and as method: the rational can also be attained by way of the truths inherent to reason, which need to comply with the criteria of the geometric proof, and are therefore independent of revelation. These truths of reason, which here serve as primitive notions and postulates, are, during the period of al-Kindï, brought about by the Aristotelian Tradition of neo-Platonism. It is these truths that are then chosen to replace the truths offered by revelation to speculative theology, so long as they can satisfy the exigencies of geometric thinking and allow for an exposition that is axiomatic in all appearances. It is in this way that 'the mathematical examination' (al-fahs al-riyadl) has become the instrument of metaphysics. Epistles in theoretical philosophy such as First Philosophy as well as On the Finitude of the Universe are in fact a case in point. In relation to the latter, for instance, al-Kindï proceeds in an orderly manner in order to demonstrate the inconsistency of the concept of the infinite body. There he begins by defining the primitive terms: magnitude and homogenous magnitudes. He then introduces what he calls an "absolute/assertoric proposition" (qadiyya haqq), or as he explains elsewhere, "first premises, true and intelligible through immediate inference" (al-muqaddimdt al-uwal al-haqqiyya al-maqula bi-la tawassut), or, again, "first premises, evident, true and immediately intelligible" (al-muqaddimat al-ula al-wadiha alhaqqiyya al-maqula bi-la tawassut)', that is to say tautological propositions. These are formulated in terms of primitive notions, relations of order thereof, operations of reunions and separation thereof, and predications: finite and infinite. It is to do with propositions such as of homogenous magnitudes, the magnitudes of which are not greater than the others are equal; or, if to one of the equal homogenous magnitudes is added a magnitude homogenous to it, the magnitudes would be unequal. Finally, al-Kindï proceeds by demonstration, through reductio ad absurdum, using a hypothesis: the part of an infinite magnitude is necessarily finite.

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II. Nâsir al-Dïn al-Tusï as Mathematician-Philosopher (or A Mathematical Resolution of a Philosophical Question) In this example, we are called to reflect on other relationships between mathematics and philosophy in classical Islam: the ties that are established between the two in the instance when the philosopher borrows an instrument from mathematics with the aim of solving a logicometaphysical question. Nevertheless, the situation which is of particular interest to us here has a specific trait: this borrowing returns dividends to the mathematical domain which provided the instrument, enhancing its progress and advancement. The exchange between combinatorics and metaphysics is an excellent illustration of this double movement: did not Ibn Sina give, on the basis of his ontological and cosmogonical conceptions, a formulation of the doctrine of the emanation from the One? And did not al-Tusï, when endeavouring to derive multiplicity from the One, manage to see that the doctrine as developed by Ibn Sïnâ could still be dotted with a combinatorial armature, which was borrowed then from the algebraists? For al-Tusi's move to work, however, the rules of combination of the algebraists had to be interpreted in a combinatorial manner. And it is this very combinatorial interpretation that finally marked the birth of this discipline called combinative analysis, much exploited after al-Tusï by mathematicians like al-Fârisï and Ibn al-Banna', among others. On the basis of this contribution, al-Halabï, a philosopher of a later period, will attempt to organise the elements of the new discipline, assigning to it a name as a way of demarcating it and underscoring its autonomy. It is imperative for us to, nonetheless, distinguish this movement from the kind of progression like that of Raymond Lulle. Lulle has combined notions following mechanical rules, the results of which appeared later to be arrangements and combinations. But Lulle has borrowed nothing from mathematics and his approach does not have the slightest consideration for mathematics. This is unlike al-Tusï whose approach comes very close to that of Leibniz, despite the differences that may exist between the two projects: the first, as we have already stated, intends to solve mathematically the issue of the emanation of the multiplicity from the One, which in the end brought him to galvanise the Avicenian doctrine of creation with a combinatorial armature; the second wanted in fact to build an ars inveniendi on the combinatorial. The emanation of the intelligences, of the celestial bodies as well as the other worlds—that of nature and that of corporeal things—from the One, is one of the central doctrines of Avicenna's metaphysics. This doctrine

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raises a question which is ontological and noetic at the same time: how is it that from one being, unique and simple, there could emanate a multiplicity, which is also a complexity that comprises in the end both the matter of things and the form of the bodies and the human souls? This ontological and noetic duality raises an obstacle, as both a logical and metaphysical difficulty that must be disentangled. From this we understand, at least in part, why Ibn Sïnâ time and again had returned to this doctrine, and implicitly to this question. A study of the historical evolution of Ibn Sïnâ's thought on this issue, in light of his different writings, would reveal to us how he managed to amend an initial formulation with such a difficulty in mind. Let us confine our field to his al-Shifa and al-Ishârât wa al-Tanbïhât. There Ibn Sïnâ exposes the principles of this doctrine as well as the rules of the emanation of multiples from a simple unity. His explication seems articulate and orderly, but is short of constituting a rigorous proof: in fact, he does not provide there the syntactical rules apt to espouse the semantic of the emanation, while it is precisely in this that the difficulty of the question related to the derivation of the multiplicity from the One resides. Indeed, this issue of derivation had been perceived as a problem for a long time. The mathematician, philosopher, and commentator of Ibn Sïnâ, Nasïr al-Dïn al-Tusï (1201-1273), not only grasped the difficulty, but he also wanted to come up with the syntactical rules which were then lacking. In his commentary on al-Ishârât wa al-Tanbïhât, al-Tusï introduces the language and the procedures of combination to follow the emanation until the third order of beings. He then stops the application of these procedures to conclude: "if we were to exceed these three orders [the first three], there may exist an uncountable multiplicity (Id yuhsâ cadaduha) in one single order, and to the infinite". Al-Tusi's intention is thus clear, just as the procedure he applied for the first three orders leaves us with no doubt: the proof and the means that Ibn Sïnâ lacked must be put forward. At this stage, however, al-Tusï is still far from the aim. It is one thing to proceed by combinations for a number of objects, and it is another thing altogether to construct a language with its syntax. Here, this language would be that of combinations. And it is precisely for the introduction of this language that al-Tusï strives in a separate essay, whose title leaves no ambiguity in the air: On the Demonstration Concerning the Mode of the Emanation of Things in Infinite [Numbers] from the Beginning of the First and Unique Principle. In this instance, al-Tusï proceeds generally through

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the combinatorial analysis. Al-Tusï's text and the results it contains will not disappear with their author; they are found again in a later treatise which was completely devoted to the combinative analysis. Thus, not only does al-Tusï's solution mark out a style of research in philosophy, it also represents an interesting contribution to the very history of mathematics. III. Al-Sijzi as Mathematician (or A Philosophical Solution to a Mathematical Problem) In proposition fourteen of his book On the Conies, Apollonius proposes to demonstrate that the asymptotes and the hyperbole come closer to one another indefinitely without actually ever meeting. This proposition obviously calls for that formidable notion of the infinite. Firstly, the infinite is presented as an object of knowledge, since what is at issue are mathematical beings whose existence entail infinite processes. This is but a trait peculiar to any asymptomatic behaviour. The idea of the infinite, however, also comes to the fore as a means for knowledge called for by the infinite mathematical construction, such as the infinite construction of the rest of the distances between the curve and its asymptote: one needs to ascertain that it is always possible to reiterate the same construction. Now, it is not hard to understand that this notion of the infinite, as professed by Apollonius, must have bothered both mathematicians and philosophers. For if the former could not have remained indifferent to an obvious difficulty in the demonstration, mainly due to the use of a notion which was never clearly drawn, the latter must have been attuned to a new problem which happens to be emerging at that very conjuncture, and whose traces had continued to persist even during the eighteenth century viz., the gap between our ability to conceive of a property and our capacity to actually rigorously establish it. Can we establish a mathematical property which we can not distinctly conceive? We may need to take a few steps back in order to localise the commencement of this philosophical interrogation. In the eyes of al-Sijzi, this proposition covers up a problematic which he tries to elicit in the rather inflected language of Islamic Aristotelian philosophy. In line with the Aristotelian Islamic philosophers, al-Sijzi seems in fact to admit that mathematical knowledge, like any other knowledge, may be characterised by the twosome "conception/judgment" (tasawwur/tasdïq); whereas in mathematics this twosome is confined to that of "conception/demonstration", in that here judgment is considered but a demonstrative syllogism. Again in line with the Aristotelians, al-

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Sijzi only recognizes that conception which is 'essential' and revealed by way of a rational intuition or expressed in a definition. In his case, as in others indeed, we may paraphrase that famous text of the Second Analytics: conception "shows what a thing is, whereas demonstration shows whether a thing is or is not attributed to a given other". Following this terminology, Apollonius' proposition raises the problem of those affirmations which are demonstrable while they remain inconceivable or hardly conceivable at the very least. Having said that, we know that to establish the proposition of Apollonius rigorously one needed to make use of concepts and techniques which alSijzï as a mathematician had not yet possessed: these are the concepts and the means for the analysis. But, in this case, it is worth noting that philosophical elucidation allows the mathematician to actually elbow in and make a dent till the plotting of future mathematical pathways is laid out. And if the mathematical difficulty calls for a philosophical thematic, philosophical explication is in turn presented as a means for the reflection of the mathematician. It is these two tasks together which completely characterise al-Sijzi's approach. In the first instance, he is driven to make a comparison between conception and demonstration with the aim of establishing a typology of mathematical propositions, which will then permit him to close in on the exact type of Apollonius proposition. Following the Aristotelian philosophers, he begins by recognising two extreme types, the confrontation of which shows clearly that there can not be a conception of all that lends itself to demonstration: this is precisely the case with the proposition advanced by Apollonius. We could, on the other hand, seize the essence of the object of a proposition, and conceive of it without having recourse to a demonstration. Between these two extreme types are the others, the intermediary ones; and it is then that al-Sijzi brings to relief the classification of the mathematical propositions. 1. Propositions which are directly conceivable on the basis of philosophical principles. 2. Propositions which are conceivable prior to attempting their demonstration. 3. Propositions which are conceivable only once an idea of their demonstration is formed. 4. Propositions which are conceivable only once they are demonstrated.

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5. Propositions which are hardly conceivable, even after they had been demonstrated. Thus, al-Sijzï has provided us with one of the earliest classifications of mathematical propositions from the twosome "conception/ demonstration". IV. The Philosophical Problem of the Unity of Mathematics: the Mathematicians' Examination Let us recall, although it goes without saying, that the heirs of Hellenic mathematics had been accumulating results and methods through active research for more than two centuries, and were thus led to conceive of disciplines unknown to the Greeks: algebra, the entire Diophantine analysis, and the algebraic theory of the cubic equations, to name only a few. Again, with their access to works in astronomy, optics, and statistics, mathematicians were also led to 'renew' Hellenic geometry, introducing new chapters to it. Among the renewed disciplines, one could list infinitesimal geometry, spheric geometry, and so on. As for the new chapters, they deal with geometry of position and form, particularly on the study of geometrical transformations. The language of the quadrivium had proven inept to contain such diversity, and things had already got a bit jammed with that of the theory of proportions. Consequently, a search began for another mode of demonstration that could be algebraic and undertake projections both through proportions and folding-backs. It still remained that the global landscape—the development of an increasing diversity on the one hand and the persistence of a wooden language on the other—was begging, as it were, for both a logical examination and a philosophical elucidation. Philosophers of the calibre of al-Fârâbï appear to have anticipated some of the difficulties engendered by this situation. The latter had for instance conceived a new ontology of the mathematical object and an architecture other than that of the quadrivium, for the purpose of the composition of an encyclopaedia of mathematics and of other forms of knowledge in general. However, for reasons that were at once theoretical as well as practical, it behoved the mathematicians alone to face to these difficulties, and indeed, soon thereafter they came up against them, especially in their compositions on the analysis and the synthesis. This encyclopaedic aspect of the analysis and the synthesis has since recalled a vibrant problem, but one obscured in this context: to render an account of the new disciplines,

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and restore the unity of mathematics. By the end of the ninth and beginning of the tenth century, the term 'mathematic' and the term 'geometric' pertained to a host of dispersed disciplines, which from then onwards could be contained by the increasingly narrow frame of the quadrivium. As a matter of fact, it is no longer possible to gather all of these disciplines under one denomination, like that of the 'theory of the magnitudes', for instance. How is the unity of mathematics thought out in these conditions? This is a question at once necessary and difficult: there had been no means at the time, and for a long time still, to attain this unity. Algebra was still far from being the discipline of the algebraic structures, and was not formalised at all. It could only do some partial unifications, such as the geometry of conies and the theory of equations. As the algebra of structures was yet to be created, mathematicians had no other choice but to find another way: the idea was to find a discipline that was logically prior to all of the other mathematical disciplines, but which did not predate them historically, and was necessarily posterior to all of them, so that it was able to actually provide them with the unifying principles. In the meantime, no determination of the nature of this discipline or its methods and objects was a priori called for. The analysis and the synthesis had manifestly played the role of this unifying discipline. Ibn Sinân (909-946) does not preoccupy himself with the entire field of mathematics, but only with geometry, although the unification he did is brought to bear on the gamut of the analysis and synthesis procedures, and the reasonings deployed, independently of the realm of geometry in which they apply. The discipline which justifies the method, viz. the analysis and synthesis as a discipline, is a sort of programmatic logic, in that it allows one to associate an ars inveniendi to an ars demonstrandi. Ibn Sinân's contribution is of a particular interest: it is the first substantial essay, to our knowledge, which deals with this kind of philosophical logic of mathematics. The author has thus brought the fundamental problem of the unity of geometry to this logico-philosophical discipline of the analysis and the synthesis, inaugurating in this way an entire tradition that can be traced throughout the tenth century all the way to the algebraist alSamaw^al in the twelfth century. Indeed, it is also following Ibn Sinân and against him that Ibn al-Haytham would develop his project. With Ibn Sinân we cannot say thatwe have reached the middle of the great century when the mathematical activity is at its zenith. The differentiation between the disciplines was, nonetheless, following its course; geometry

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of projections had received a strong jolt at the hands of mathematicians like al-Quhi and Ibn Sahl; geometrical transformations had become an object of reflection and application for the mathematicians; a chapter on geometrical constructions with the help of the conies had taken shape and developed. For geometrical demonstrations we now increasingly have recourse to a folding-back, to punctual transformations, and to the asymptotic properties of conical curves to demonstrate their points of intersection. Simply put, two types of exigencies had then emerged: demonstrative structures have to be conceived for the new objects as well as providing for their plan of existence. It was recognized the accomplishment of these two intimately linked approaches also requires that the methods employed would have to be founded on the basis of a discipline. This would have to also be general enough as to be able to offer the means of existence to the new geometrical objects, without being reduced to a pure logic; but additionally, it would have to precede logically all the other mathematical disciplines in order to provide foundations to the diverse demonstrative structures. It is this monumental task that Ibn al-Haytham has tackled, no doubt by choice, but by necessity as well. We owe to him the undertaking of innovative research of the highest degree not only in all the branches of geometry, but also in arithmetic and the Euclidean theory of numbers, and these are precisely the domains that would occupy him the most. We have indicated above four situations in which philosophermathematicians, mathematician-philosophers, and 'pure' mathematicians delved into the topic of the philosophy of mathematics, and brought forth as much evidence as is possible for the blossoming of this field from the ninth century onwards. To forget these contributions not only impoverishes the history of philosophy, but it goes as far as to truncate the history of mathematics as well.

Translated from the original French by Redha Ameur

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[5] THE UNIVERSE AS A SYSTEM: IBN SINA'S COSMOLOGY REVISITED Syamsuddin Arif This article explores Ibn Sina's cosmological views and analyzes the underlying assumptions and arguments in support of the theories to which he subscribes. These include the notions of the central and stationary position of the earth in a finite, spherical cosmos, the impossibility of the existence of many universes, and the metaphysical forces that drive, guide, and maintain the perpetual movement of cosmic bodies. Keywords: Ibn Sïnâ, Islamic cosmology, geocentric universe, multiverses, cosmic motion, celestial spheres, celestial bodies, celestial intelligences.

Ibn Sma (d. 428/1037) is one of the most celebrated 'scientist-philosophers' the Muslim world has produced.1 Besides the influential Liber Canonis on medicine, Ibn Sïnâ wrote Kitâb al-Shifa3, a multi-volume encyclopedic masterpiece embodying a vast field of knowledge from logic and metaphysics to mathematics, astronomy and music, which was in part translated into Latin and exerted tremendous influence in subsequent centuries. This article aims to discuss some aspects of Ibn Sina's cosmology. An outline of his picture of the physical universe is given together with an exposition of its philosophical underpinnings, followed by an analysis of his views about the nature and motion of heavenly bodies. 1. For further details, see G.W. Wickens (éd.), Avicenna: Scientist and Philosopher (London: Luzac & Company, 1952); and S. M. Afnan, Avicenna: His Life and Works (London: George Allen & Unwin, 1958).

Syamsuddin Arif is Assistant Professor, Department of General Studies, KIRKHS, International Islamic University Malaysia (HUM). Email: [email protected].

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1. General Picture of the Cosmos Drawing on Aristotle's cosmology and Ptolemaic astronomy, Ibn Sïnâ views the universe as consisting of nine concentric spheres contiguously nested, one within the other, from the lowest sphere of the moon to the outermost starless sphere. These spheres are thought to be concentric because they seem to share a common center, which is the center of the universe, taken as coincident with the earth's center. On this model, each of the seven known 'wandering stars' or planets (al-kawdkib al-mutahayyirah]—namely, the moon, the two inner planets (Mercury and Venus), the sun, and the three outer planets (Mars, Jupiter, and Saturn)—and the 'fixed stars' (al-thawabit) are assumed to be attached to eight solid but transparent spheres that carry them as they revolve around the earth.2 There is a ninth, outermost sphere (kurah khdrijah canha muhïtah), which defines the edge or boundary of the universe and supposedly contains no star (ghayr mukawkabah), posited to explain the daily motion of the heaven, whereas the motion of the eighth sphere (that of the fixed stars) is said to be due to the precession of the equinoctial points (nuqtatà al-ftidal)? Each of these spheres, according to Ibn Sïnâ, is governed by an intelligence and a soul, which are respectively the remote cause and proximate principle of their motion. Ibn Sïnâ's model rests on four fundamental assumptions, namely: (1) that the universe is one in number; (2) that it is finite in extent and spherical in shape; (3) that it has a center; and (4) that the earth lies at its center. Let us first consider the third and fourth assumptions. Ibn Sïnâ argues for the central position of the earth by means of a logical argument which essentially de2. Ibn Sma, Shifa\- Ilahiyyat, éd. Y. Musa, S. Dimya and S. Zayed (Cairo: Organisme General des Imprimeries Gouvernementales, 1960), 401 lines 6-17; Skiff: Riyádiyyát: cllm al-Hafah, ed. Muhammad Mudawwar and Imam Ibrahim Ahmad (Cairo, 1980), 463; and Shiftf: al-Tabl'iyyat: al-Samtf wa al-'Alam, ed. Mahmud Qasirn (Cairo: Dâr al-Kâtib al-Arabï: 1969), 37 line 12; cf. Ibn Hammüdah, Mukhtasar cllm al-Hay^ah li al-Shaykh al-Rd'is Abi CAU ibn Sïnâ in Kitáb al-Mahraján li Ibn Sïnâ (Le Livre du Millénaire d'Avicenne) (Tehran: Société pour la Conservation de Monuments Nationaux, 1956), III: 1-10. Cf. "The Arabie version of Ptolemy's Planetary Hypotheses," ed. B. Goldstein in Transactions of the American Philosophical Society, 57 (1967) 4: 27-9.

3. Shiftf: Ilahiyyat, 392 lines 10-14; cf. Maqàldt al-hkandar al-Afrûdisïfi

al-Qawlfi

Mabâdf al-Kull, mAristû cind al-cArab, 265 = Charles Genequand, Alexander ofAphrodisias on the Cosmos (Leiden: E. J. Brill, 2001), 12 and 82-5. Cf. C. A. Nallino, 'Astrologia e astronomia pressi i Musulmanni," Raccolta di scritti editi e inediti (Rome: Istituto Per L'Oriente, 1944), 5: 64-6 and 75, cited in G. Endress, 'Averroes' De Cáelo: Ibn Rushd's Cosmology in his Commentaries on Aristotle's On the Heavens" Arabic Science and Philosophy 5 (1995), 43-4; and R. Walzer, al-Fàràbï on the Perfect State (Oxford: Clarendon Press, 1985), 364.

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rives from the Aristotelian physical theory of four elements (earth, water, air, fire) and their natural motion and place. For him as for Aristotle, any motion of natural bodies (that is, anything capable of motion and change, whether animate or inanimate) is either simple or composite, natural or unnatural. Simple motion, which belongs to simple bodies (as opposed to composite bodies), is either rectilinear (mustaqïmak) or circular (mustadïmh). Simple rectilinear motion is either motion away from the center, motion toward the center, or motion about the center.4 Motion away from the center toward the cosmic circumference, termed upward motion, is natural to light bodies, whereas motion toward the center, called downward motion, is natural to heavy bodies.5 The motion of a body is said to be natural (tabfiyyah) if it drives the moving body toward the place where it will rest 'naturally', that is, by nature and not by an external force, whereas unnatural motion is that which is due to some external force contrary to the thing's nature6—"nature" being identified as an intrinsic principle of being moved and being at rest.7 Since the sub-lunar elements ('anâsïr) are natural simple bodies (bastfit), their motions must be both simple and natural,8 but also rectilinear and not circular because, in the absence of any hindrance, each of the elements will by nature either move straight up or straight down, seeking its natural place.9 By 'natural place' (hayyiz tabici) is meant the place to which a natural body is moved or inclined to move and where it will rest naturally,10 namely, the cosmic center for heavy bodies, and the circumference for light ones. Given all these principles, it is reasonable for Ibn Sïnâ to conclude that the earth must lie at the center of the universe. This is so because the earth, being the heaviest of all the elements, must naturally move toward the center and cannot be placed anywhere but where it belongs by nature. Indeed, even if at any time it should not have been at the centre of the cosmos, it would have been bound to reach it long ago by natural rectilinear motion which, because of the finiteness of directions (tanàhï al-jihat) within the universe, cannot be perpetual. And now that it is situated in its natural place, the earth must be at rest and motionless. That is to say, given its present natural position, the earth cannot have rectilinear motion; nor can it revolve about an axis at the center of the 4. Shifa*: Tabfiyyat: Sama" wa cAlam, 6 lines 5-7. 5. Ibid., 7 line 18 and 8 lines 1-6. 6. See Ibn Sïnâ, Kitab al-Najat (Cairo, 1938), 109-10. Unless indicated otherwise, subsequent references are to this edition. 7. Ibn Sïnâ, Shifà*: Tabïciyydt: Sama3 Tabïï, éd. Said Zayed (Cairo: Organisme General des Imprimeries Gouvernementales, 1983), 34 lines 8-9. 8. Shifâ\- TabFiyyàt: Sama" wa cÂlam, 9 lines 17-8. 9. Shiftf: Tabfiyyât: Sama" Tabïï, 318 lines 5-17 and 319 lines 1-9. 10. Najât, 134-5.

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universe, because circular motion belongs only to celestial bodies.11 Interestingly, Ibn Sïnà discards other arguments for the geocentric thesis on the grounds that they all share one wrong assumption, namely, that "the earth is forced to stay at the center (al-ard maqsurah calâ al-qiydmfï al-wasat)." For how, he asks, can a thing be forced [to remain somewhere] except when it is not in its natural place?12 Thus Ibn Sïnà rejects, for example, the theory which claims that the earth stays as it is and does not fall downward because it floats on water, or that it remains stable by virtue of its dryness. For still can one ask, Ibn Sïnà contends, the further question of what then supports the water. He also rejects the idea that the earth is at rest because it is like a cylinder in shape (tabliyyat al-shakl), having an extended plane surface top and bottom (musattahat al-qacr munbasitah). Equally unacceptable to him is the idea that the earth has a ball-like shape (kuriyyah) and that it stays aloft and motionless, not supported by anything but staying where it is because it is pulled to every direction with the same force by the celestial sphere and therefore remains at the same distance from everything.13 That this cannot be the case is explained by Ibn Sïnà in the following passage: As for those who say that [the earth is at rest and motionless] because of the attraction (jadhb) of the celestial sphere from all directions equally, their claim and opinion are flawed in several respects. First, if we suppose that this attraction has vanished, then the earth would either stay still in the center or it would rather move. Now if it were to move, then it certainly would move toward the sphere—for those people think that the sphere contains [the earth] and that the earth is in the middle—so that if it moved toward the sphere, then it would have turned its natural motion upward, which is impossible. But if it stays where it was, then the reason they give for the earth's quiescence is superfluous; even without that reason [the state of] being at rest would still be there. [For if there is] something whose very existence does not require the existence of something else, [then] this something else cannot be the cause for that thing which does not need it at all. Therefore, such an attraction cannot be the cause for the earth's quiescence. Secondly, small things would be attracted faster than big things; but why is it that a piece of earth is not attracted toward the sphere, and instead is moving away from it toward the center? Also, things near [to the sphere] would be attracted more than things far away, according to their nature; now, a piece of earth thrown up [to the air] is [on such an assumption] approaching the sphere, so that it should have been attracted to its [the sphere's] nearest point, rather than to the whole earth. Furthermore, as you know, rectilinear nat11. Shifa\- Tabfiyyat: Sama" wa ^Alam, 55 lines 5-7. 12. Ibid., 57 lines 6-7. 13. Ibid., 56 lines 7-18 and 58 lines 6-16.

New Perspectives on the Histoij of Islamic Science Syamsuddin Arif • 131 ural motion must lead to the place of rest (jihat al-qamr) naturally, and a piece of earth simply moves in order to be at rest, be it at the sphere [i.e. the periphery] or at the supposed center; but it does not move toward the sphere—for otherwise the opposite direction of its motion would be more appropriate, since it is nearer. Therefore, it [the piece of earth] must have moved toward the center to be at rest by nature.14

As we can see, here and in the subsequent passages Ibn Sïnà emphasizes clearly that it is neither 'by force' (qasrari), nor 'by choice' (ikhtiyàrari), nor 'by chance' (hi al-bakht), but rather 'by nature' that the earth stays where it is, at rest at the center of the universe. It cannot be due to some coercive factor, he says, because it is impossible for the sphere surrounding the earth to change the earth's inclination (mayl) by repulsion (daf'ari). For if it were possible, then a piece of earth falling toward the center would move less quickly the closer it is to the earth, because the speed of a body moved by force diminishes the farther away it is from the moving agent. Nor can we say that it chooses to be so, because being inanimate the earth cannot have choice or will of its own, but simply behaves in accordance with its nature. Ibn Sïnà also rejects the view that the earth owes its stability to chance on the grounds that what happens by chance cannot be perpetual and is itself due to some cause.15 As we can see, all these arguments for the stationary and central position of the earth ultimately rest on his theory of mayl which says, inter alia, that "every body will lose its inclination once it reaches its natural place."16 Turning to the idea that the universe is finite in extent and spherical in shape, having the outermost, starless sphere as its circumference and the earth at its centre, Ibn Sïnà seems content with making only a brief argument. For him, as for Ptolemy whose Almagest he paraphrases, the sphere is the only figure most fitting for circular motion such as that of celestial bodies, and is the noblest (ashrafal-ashkal)^ most encompassing (azyaduhâ ihatatari),18 and most perfect because of its unique form limited by a single surface. Most importantly, it is the only one which, by rotating on its axis, can move within its own limits without change of place. Indeed, sphere is among bodies as the circle is among plane figures; it is the most uniform of all solid figures, since it is equidistant every way from centre to extremity. Now, according to Ibn Sïnà, one can infer the universe's sphericity from the circular motion of the heavenly bodies. The cosmic sphere cannot be infinite, because an infinite body is 14. Ibid., 59 lines 7-19 and 60 lines 1-7. 15. Ibid., 61 lines 1-13. 16. Ibid., 69 lines 1-2. 17. Shifá*: Tabfiyyát: Sama* Tabïcï, 41 line 14. 18. Shijiï: Riyàdiyyàt: cllm al-Hay"ah, 16 line 11 and 19 lines 5-10.

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logically impossible. Being spherical, the universe is said to exhaust all space, so that there exists neither body nor place nor void outside this all-embracing cosmic sphere.19 This view has led Ibn Sïnâ to maintain, paradoxically, that the universe is not in a place, since 'place' is defined as that in which a body is found and that which contains or surrounds the body20—a definition which doubtless presupposes the existence of at least two contiguous bodies, 'place' being the innermost surface of the containing body in direct contact with the contained body, and implies that no two bodies can occupy one and the same place at the same time.21 Now it is easy to see why the universe or heavens as a whole cannot be said to be in place: the whole body (that is, the universe) is surrounded neither by another body nor by a void, since it is assumed that there is no such thing and there exists no material body beyond the universe to serve as its container. To be sure, denial of a place to the last, outermost sphere constituting the whole universe is a consequence forced upon Ibn Sïnâ in order to avoid an infinite regress of material places; for if the outermost sphere is contained by another sphere, the latter, in turn, would require a further containing sphere, and so on ad infinitum, a process that would inevitably lead to the assumption of an infinite universe. Not only the whole cosmos is believed to be spherical but also the earth is thought of as having a ball-like shape.22 That the earth cannot be flat almost necessarily follows from the theory of elemental motion according to which the heavy element earth is naturally inclined toward the center of the universe, while light elements by nature tend to move up toward the circumference. Thus, supposing that the earth was originally in a state of dispersal, when the dispersed particles of earth traveled to the center (i.e. to the earth), they would naturally impinge upon one another and form a spherical body, because any anomalies (tadàrïs) would be self-correcting: a lump on the sphere would be heavier than the counter-balancing portions of it, and so it would continue to press toward the center until all was in balance, just like the case of water seeking its own level, although such a process would no doubt take a very long time, being gradual, and hence—given the earth's dryness and hardness—hardly noticeable.23 Indeed, for Ibn Sïnâ the sphere is just the natural shape (shakl tahfi) of simple bodies,24 which is why each of the elements is supposed to seek and stay at their proper natural place, forming its own 19. Shifá": Tabfiyyát: Sama" Tabïcï, 104-5. 20. Naját, 118.

21. Shifá": Tabïciyyat: Sama" Tabï'ï, 263 line 14. 22. Ibid., 41 line 8.

23. Shifá": TabFiyyát: Sama" wa cAlam, 19-21; cf. Naját, 135. 24. Naját, 135; cf. Shifd": Riyâdiyyât: cllm al-Hay"ah, 19 lines 7-10.

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sphere and surrounding one another.25 Furthermore, given its central position and being mostly composed of the heaviest element, the earth cannot but be spherical, for only a spherical body could be equidistant (fî sawa3 al-wasaf) from all the points on the cosmic circumference.26 The sphericity of the earth can also be inferred from the curved, crescent-like (hilàlï) or even sometimes circular shadow which the earth casts on the moon's surface no matter at what position it passes the moon.27 Added to that is the observation that the portion of the sky that is visible changes as one moves even quite a short distance north or south on the earth's surface.28 2. Impossibility of Many Universes Along with Plato and Aristotle, Ibn Sïnà denies the existence of other universes apart from our own. For him there cannot be more than one universe, and he adduces two arguments in support of this view. First, he says, if there were many universes (cawâlim kathïrah) then a given body (say, water) would have several natural places differing only numerically yet placed and scattered in diverse directions. The body would consequently be subject to contrary natural motions (simultaneously towards and away from the centre, as some would move downward while others upward). Since natural motions and natural places are interdependent, indétermination of motion would imply indétermination of place. This would, moreover, result in a contradiction, because places would be determinate (since they would form a universe) and yet, at the same time and in the same respect, also indeterminate (since they would be the goals of contrary motions). If [assuming that there were many universes] every universe is the same in form as another, such that in each universe there exist similar earth, fire, water and air, then bodies of the same species would tend [to move] to many natural places that vary in position or in nature, and this we have shown to be absurd. Rather, as we have explained in [the treatise on] the universal principles, there must be one place where all earths would gather forming a single sphere 25. Najàt, 136-7 and 144-5. 26. Shifiï: Riyàdiyyàt: cllm al-Hafah, 21-3. 27. Shifff:

Tabfiyyàt: Samâ" Tabïï, 42 line 13.

28. Shifâ: Riyàdiyyàt: cllm al-Hafah, 20-1; cf. Shijiï: Tabïiyyàt: Sama" Tabïcï, 41 line 17. Ibn Sïnâ does not, however, invoke the a priori argument found in Aristotle that all heavy bodies fall at equal angles to the earth's surface, that is, that the angles between the line of fall and all lines on the earth's surface radiating from the point of impact are equal. Consequently, lines of fall (that is, the lines directed toward the center of the universe) are not parallel to each other, for only if the earth were like a flat disk would lines of fall, vertical to the earth's surface, be parallel. See Aristotle, De Cáelo, 296b 16-25.

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Secondly, if there were many universes, then there would be more than one center. But such a situation is impossible because, Ibn Sïnà argues, the earth of each universe, each being the center, must by virtue of their similar nature eventually gather in one place, forming a new center; there is no reason why they should not do so (hâdhà al-ijtimâc mimmâ là mâni'a lahu canhufïtabcihi), for one and the same nature cannot be separated and differentiated (fa inna al-tabïcah al-wdhidah al-mutashabihah la taqtadl al-iftimq wa al-tabâyuri)?0 That is to say, if there were another universe, its elements would be one and the same as those in our universe; and since all elements are essentially the same everywhere and so are moved toward their respective natural places, each element would be moved to its proper place in our universe—for example, that earth would be moved to the center of our world—which is impossible because, from the point of view of its own universe, that earth would be moved upward (that is, away from its center), just as the earth from our universe would be moved upward if moved toward the center of another cosmos. All earths are one in [that they have the same] natural form. And as mentioned earlier, things that are one [that is, similar] in form must have the same natural place in which all of them should gather—as scientific verification and explanation has shown. It follows that all other earths cannot remain in various places naturally and have no choice but [to move and rest in] their natural place. Also, the earth that has reached its natural place will not move rectilinearly, as we already know; but neither will it move circularly, because by nature earth can only have rectilinear motion. And as we have explained, no single body can have a natural tendency for both rectilinear and circular motions.31

In short, the assumption of more than one universe entails not only denial of the identical natures of the elements and the oneness of their respective 29. Shiftf: Tabïiyyàt: Sama" wa cAlam, 74 lines 5-14. 30. Ibid., 75 lines 1-3. 31. Ibid., 54 line 17 and 55 lines 1-7.

New Perspectives on the Histoij of Islamic Science Syamsuddin Arif • 135 motions throughout the different universes, but also denial of place as the principle rendering the cosmos determinate in respect to direction—that is, in respect to "up," "down," and "middle." For the natural motion of each element is defined in relation to its place in the universe; and it is either away from the center and toward the circumference (min al-markaz ilâ al-muhït), or toward the center and away from the circumference, or about the center.32 In other words, if there were many universes existing in an infinite space where there is neither center nor circumference, there would be no motion, since bodies would have no place to serve as the goal of their motion and one could not point to one direction as up and another as down. Furthermore, how can there be [many cosmic] heavens (samdwdt) for different places? What is it that makes their places different, such that there should be numerous centers? Indeed from the foregoing theses it is clear that heaven constitutes the cause for determining all other places, and therefore all other places cannot be the cause for defining its place. So the cause for [defining] the different places [of those heavens], in such a way that they do not pass across one another and do not share one common place, must be something other than their own nature; nor can it be some other bodies whose very places are defined by them [i.e. the heavens]. And no doubt, it must be by force since it is not something natural—both in respect to the [celestial] body and in respect to the other [non-celestial] bodies. But we have said that compulsory change of place (unnatural locomotion) is impossible in the case of this [celestial] body Therefore, since it is impossible for the defining bodies that are similar in nature (al-muhaddiddt al-mutashabihat al-tibiï—i.e. the heavens of the presumed universes) to have different places by nature, and impossible too by compulsion, there cannot be many centers. Such being the case, we have made it clear that there cannot be many universes with similar elements having similar natures.33 3. Celestial Nature and Motion Before dealing with Ibn Sïnâ's theory of celestial motions, it is worth discussing his views on the nature of heavens. According to Ibn Sina, heavenly substances differ fundamentally from earthly things in many respects. First of all, celestial things are simple in that they are not composite, and, second, they are made of a unique simple substance called aether (athïr), which, unlike the four sublunary elements, is eternal and changeless in the sense that it is neither 32. Ibid., 6 lines 5-7; cf. Ibn Sina, cUyun al-Hïkmah, éd. cAbd al-Rahmaii Badawi (Cairo: Institut Français cTArchéologie Orientale, 1954); repr. in Rastfil Ibn Sïnà (Qomm: Intishârât Bïdâr, 1980), 35 (page reference to the reprint). 33. Shifà\- Tabïciyyàt: Sama* wa cÀlam, 75 lines 3-13.

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generated nor destructible (làyaqbal al-kawn wa alfasdd).M This is because generation and destruction apply only to composites—i.e., things which contain contrary qualities, and represent change into and out of opposites, as will be explained below. Indeed, this so-called 'fifth element' (al-jism al-khamis or altabïcah al-khdmisah,^ the quinta essentia of the medieval scholastics) is immune not only to the process of generation and destruction (substantial change) but also to other kinds of change, such as locomotion (which entails movement to natural place in search of rest), alteration (qualitative change), and growth and diminution (quantitative change), since all these changes imply contrary qualities, whereas heavenly bodies are simply devoid of contraries (lays lahà cunsur ayy shay" qdbil Ifl-diddayn).^ The simple celestial substance (the aether), Ibn Sïnâ tells us further, moves only in a circle, circular motion being the only simple motion natural to it on the grounds that the other simple motion (rectilinear) is natural and belongs to the four simple terrestrial elements (fire, air, water, earth) or anything composed of them in which one element predominates (hi hasab al-ghàlib)?7 For given that each of the simple (terrestrial) bodies has only one natural motion (e.g. either upward or downward) and since a motion can, if at all, have only one contrary, the conclusion is drawn that circular motion (which, however, has no contrary) cannot be the unnatural motion, let alone be the natural motion of one of the four elements; rather, it should belong to another simple element, namely the 'fifth body'.38 Moreover, since it has no inclination (mayl) for rectilinear motions, the heavenly substance is neither heavy nor light, whether actually or potentially, for heaviness implies downward motion towards the centre, and lightness implies motion away from the centre.39 Above all, the reason why the celestial element deserves all these properties lies in the fact that it is ever actual, its matter being always attached to its form (mawqufah calâ suratihâ),40 its form having no contrary and its properties unchanged.41 The sphere (falak) has a physical reality (jawhar jismànï), is round in shape, and circular in motion by nature [sic!]; it never leaves its natural place and yet does not rest at one fixed position within its natural place; to its power and nature are due all that happens 34. Ibid., 34 line 6. 35. Ibid., 25 line 9 and 15 line 6. 36. Ibid., 28-34; the quoted sentence is on page 31 line 1. 37. Ibid., 17-18; cf. Najât, 134-5. 38. Ibid., 11-12. 39. Ibid., 7-9 and 64-5. 40. Ibid., 30 line 17, 31 lines 1-3, and 34 lines 7-11. 4L Ibid., 33 lines 4-5.

New Perspectives on the Histoij of Islamic Science Syamsuddin Arif • 137 in the [terrestrial] world of elements. Its circular motion, which is meant for glorification (tasbîh), is due to God's command (li amr Allah). It is absolutely impossible for it to have a rectilinear motion; nor can it be affected by elemental bodies (al-ajsdm al-cunsuriyyah, i.e., terrestrial elements)42...which [in contrast to celestial spheres] will not move at all [once they are] in their natural places and will not move at all according to [their] nature except when they are in foreign [i.e. unnatural] places; indeed they do not move by nature except in a straight line, and are constantly affected by aetherial bodies (al-ajsam al-athiriyyah).43 He elsewhere remarks that: Every body which is generated has in it a principle or innate impulse for linear motion (mabda* harakah mustaqïmah), and every body lacking this principle for linear motion is not generated. Now, a body which has such a principle for circular motion by nature is not generated out of another body, nor is it found in the place of another body. Rather, it is originated [not out of pre-existent matter] (mubdcf) and, therefore, [is the one that] preserves time and never fails to do so (láyukhill). Consequently it needs no other body to determine its direction, for [all] directions are determined by it. Nor does it ever leave its [natural] place, because if it did, then it could not be the essential determinant of directions. We also maintain that its "nature" has no contrary.44 It should be noted that the term "nature" as used in the passage just cited refers to the principle of any motion, rest and other perfections (kamâlât) which every natural body may have within and by itself. As Ibn Sïnâ explains it, 'nature' is the first of the three kinds of powers (quwa) which pervades the body and preserves its perfections (e.g., its shape, its natural place, and its action).45 It is an internal source or cause of being moved and being at rest, that within things by virtue of which they move (taking 'motion' in its broadest sense which includes all kinds of change) and come to rest. Whereas for living beings the intrinsic mover is their soul (nafs), for the elements and other nonliving things it is the inclination (mayl) of each to reach and rest in its proper, natural place. Thus nature is identified with soul as well as inclination in the case of animals (ensouled bodies) and inanimate objects respectively. But in both cases nature expresses itself in the thing's motion, motivating the thing to actualize its potentialities and achieve its existential purpose. Let us now turn to Ibn Sïnà's theory of celestial motions. To begin with, 42. Risalahfi al-Ajram al-cUlwiyyah in Tisc Rasrfil, 57 lines 1-7. 43. Ibid., 57 lines 11-14. 44. Shifà0: Tabï'iyyàt: Samà* wa cÀlam, 28 lines 6-12. 45. Kitob al-Najat, ed. Majid Fakhry (Beirut: Dâr al-Âfâq al-Jadïdah, 1985), 137; cf. Aristotle, Physics, ILL

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Ibn Sïnà rejects Aristotle's quite complicated theory according to which the motion of celestial spheres is due to forty-seven or fifty-five unmoved movers, the first of which, identified as theos, is said to be directly responsible for moving the outermost sphere of the fixed stars.46 That is to say, the stars and the planets are rotating because they are attached in some way to a series of rotating spheres, each of which is moved by an unmoved mover. Instead, like Alexander of Aphrodisias before him, Ibn Sïnâ adopts the simplified version of the theory, positing only nine spheres, while at the same time appropriating the remaining Aristotelian views: that the so-called Prime Mover, being both the efficient and final cause in the sense of an object of both love and thought (to orekton kai to noêtori),47 produces motion while all other things move by being moved, and that the first moving sphere, which embraces all the orbs involved in the daily motion, seeks to become as much like the Prime Mover as possible and thus wishes to come to rest in imitation of the First Unmoved Mover. Nevertheless, since it is impossible for any celestial sphere to acquire such a state of perfection, the first moving sphere remains in a continuous, eternal state of rotational motion as it strives for its unattainable goal. The celestial motion is eternal, partly because of its circularity—since it is assumed that a body which moves in a circle is perpetual and is never at rest—but mainly by virtue of the eternal, unchanging First Principle of Being (he arkhe kai to proton ton ontôn akinêtori).48 Ibn Sïnâ's position is explained in the following passage: You know that the essence of the First Beloved Good is one; and it is impossible for the whole universe (jumlat al-sama*) to have more than one first mover. It is true that each one of the celestial spheres has its own proximate mover as well as its own beloved and object of desire, according to the First Teacher and subsequent peripatetic scholars. But they deny multiplicity to the mover of the [universe as a] whole (muharrik al-kull), although they affirm plurality to the separate movers as well as the non-separate movers for each one of the spheres, thereby making the first of these specific movers responsible for moving the first sphere—namely, that of the fixed stars, according to those before Ptolemy, or the outermost, all-embracing one that contains no star, followed by those which move the succeeding spheres, according to either opinion, and so on. Thus, they [i.e. the commentators] think that the cosmic mover is one and that each of the succeeding spheres has its own mover, whereas the First Teacher assumed the number of the moved spheres, ac46. Aristotle, Metaphysics, XII.8. 1074a 1-14 and 1072b 26-30; cf. P. Merlan, "Aristotle's Unmoved Movers," Traditio 4 (1946), 1-30; J. Owens, "The Reality of Aristotle's Separate Movers," Review of Metaphysics 3 (1950), 319-37 and J. G. deFilippo, "Aristotle's Identification of the Prime Mover as God," Classical Quarterly 44 (1994) 2, 393-409. 47. Aristotle, Metaphysics, XII.7. 1072a 26-7. 48. Aristotle, Metaphysics, XII.8. 1073a 24-34.

New Perspectives on the Histoij of Islamic Science Syamsuddin Arif • 139 cording to the data available to him at the time, to correspond to the number of the separate principles [of motion]. But some of his companions [sic, namely, Alexander of Aphrodisias] gives the most correct opinion as he asserts in his treatise "On the Cosmic Principles" (Fî Mabâdf al-Kull) that the mover of the whole heaven is one and cannot be many in number, even though each one of the spheres has a mover and a beloved of its own.49

Crucial to understanding the whole theory is the general principle, first enunciated by Aristotle and adopted by Ibn Sïnâ, that 'everything that moves is moved by some agent.' Specifically, this means that all natural bodies owe their motion to a certain cause or principle, which can be either intrinsic (can dhatiha) or extrinsic (bi-sabab khàrij). The external factor capable of producing and/or obstructing motion in a body is called Torce' (qásir), and its effect 'violent' or unnatural motion. The intrinsic principle, on the other hand, is further classified into that which brings about 'voluntary' motion (hi iradah), and that which causes involuntary but non-violent (and hence natural) motion (la c an irddah wa Id can taskhïr qásir), the former being identified as soul (nafs), the latter as nature (tabïcah).'M In short, if anything is in motion, it must be moved by something else: either by nature, by soul, or by force. These assumptions entail that nothing is, strictly speaking, self-moved. Indeed, self-motion is impossible because motion broadly defined is the first perfection (kamdl awwal) or actualization of a potency (quwwah),51 a process that requires an agent (namely, the cause or principle of motion) which itself must be actual and perfect. Thus, the moving principle must already be in the state at which the motion of the patient is aimed because otherwise we would have an infinite series of such agents, which is absurd. It is clear that each moving object presupposes some cause Çillah) which sets and sustains it in motion. However, since the series of such causes cannot regress indefinitely, therefore, the motion of each moving object must be ultimately sustained by a first cause, which moves the rest but itself is unmoved.52 On Aristotle's account, there exist no less than fifty such unmoved movers, whereas Ibn Sïnâ recognizes only ten, which he identified as separate intelligences (cuqül mufáriqak), apart from the First one (al-cAql al-Awwal).^ According to Ibn Sïnâ, the circular motion of celestial bodies cannot be natural, because natural motion can occur only when a body is located elsewhere from its proper place. But celestial bodies are and have always been 49. Shifiï: Ilàhiyyàt, 392 lines 7-17 and 393 lines 1-2. 50. Shiftf: Tabïiyyàt: Sama" Tabïï, 29-30. 51. Ibid., 83 lines 2 and 5. 52. Najat, 235. 53. Shiftf: Ilàhiyyàt, 401 lines 6-14.

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in their natural place.54 A second reason is that natural motion is aimed at rest (U ajli talab suküri), which is characteristic of rectilinear motions, whereas the circular motion observed in celestial bodies is perpetual. However, such a motion cannot be said to be unnatural or enforced either, since it is assumed that there cannot be any force greater than that of celestial bodies themselves which could move them contrary to their nature. Now, since the circular motion of celestial spheres is neither by nature nor by constraint, it must originate from the voluntary power (quwwah irddiyyah) of ensouled bodies or living beings.55 This view seems to contradict his statement elsewhere that the celestial bodies move circularly by nature (hi al-tibac).56 Nevertheless, one need only to recall the distinction Ibn Sïnâ maintains between the nature of terrestrial elements (or bodies composed thereof) and that of the fifth element that constitutes celestial bodies. Nothing could be more natural to such simple but animated bodies as the heavenly spheres than circular motion. Whereas in the case of bodies of the sublunary region 'nature' and 'soul' are differentiated, in the case of celestial bodies they are identical. Since the heavenly bodies are simple and changeless, only circular and everlasting motion is proper to them. However, since they are believed to be ensouled and alive (hayy dhü nafs),57 their motion is, strictly speaking, voluntary. At best, one could say with Ibn Sïnâ that the celestial motion, apart from being intellectual in a sense, is quasi-natural' (ktfannahu tabiciyyah).58 The celestial sphere is moved by [its] soul (nafs), the soul being its proximate principle of motion. This [celestial] soul is blessed not only with renewed conception and volition (mutajaddidat altasawwur wa al-imdah) but also with imagination (mutawahhimah); that is to say, it can perceive changeable things such as particulars, and it has got desire for particular, concrete things. It [i.e. the soul] represents the perfection (kamal) of the celestial body and is the latter's form. Indeed, if it were not so—that is, if it were self-subsistent in every respect—then it would have been pure intelligence, unchanged, unmoved, and unmixed with anything potential. The proximate mover of the celestial spheres, being itself not an intelligence, is nevertheless preceded by an intelligence which is the prior cause of the [celestial] motion.59

Thus, while their simple circular motion is due to their soul, the perpetuity of the motion is due to their intelligence; the former serves as the interme54. Naját, 109. 55. Shiftf: Tabfiyyát: Sarna" Tabïcï, 302 lines 16-17 and 303 lines 1-3.

56. For example in Risalahfï al-Ajmm al-cUlwiyyah in Tisc Rastfil, 57 line 2. 57. Najátf 145 line 1. 58. Mabda* wa Macad, 53 (last line). 59. Shiftf: Ilàhiyyât, 386 lines 14-17 and 387 lines 1-3; cf. Najâtt 240-1.

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diate cause of motion. It is their intelligence, whose sole concern it is to attain to the Pure and True Good (al-khayr al-mahd al-haqlqi) and to contemplate the First Principle and to strive to become like Him, that actually causes their soul to continuously revolve the celestial body around it, and always in the same way.60 For intellectual contemplation alone is not accompanied by motion; nor are mere desire and volition sufficient to produce motion. The celestial soul, we are told, must not only will and comprehend the objective of its motion, but also has to 'imagine each one of the successive motions' (tatakhayyal al-aynat aljuz'iyyah) that are required to satisfy its eternal longing for Pure Intelligence, its desired object, just as a man who has resolved to travel from one place to another must know his destination and imagine each one of the successive steps that are required for him to cross the distance.61 Indeed, according to Ibn Sïnâ, there is a great affinity between the celestial and human souls in terms of capacities and inclination.62 The human souls have three kinds of desire (shawq; ishtiydq) or love (cishq), namely: appetite (shahwati), passion (ghadaty, and free will (irddah) or rational choice (ikhtiyar), corresponding to the soul's three faculties—the vegetative, the animal, and the rational.63 In the case of the heavenly bodies, however, since they are said to be changeless and eternal, one can only ascribe to them intellectual desire and rational will, because the two lower kinds of desire are appropriate only for the changing and perishable beings of the sublunary region. Thus, despite their seemingly mechanical movements, celestial substances do exercise free choice precisely because their souls, being their direct moving principle, are endowed with eternal will that is ever renewed.64 The point is summarized neatly in the Risalahfi al-cishq as follows: It has been explained that one who knows something good will naturally love it (ya'shiquhu). We have also indicated that the First Cause is loved by the divine souls (al-nufus al-muta"allihah). Furthermore [as we have made it clear] since the perfection of both the human and angelic souls lies in (1) comprehending the intelligibles as they really are as much as they can in order to become similar to the essence of the Absolute Good (al-khayr al-mutlaq) and (2) producing fair deeds proper to them, such as [acting in accordance with] human virtues as well as the imparting of motion by the angelic souls to the celestial substances (al-jawdhir al-culwiyyah) with a 60. See Najat, 262-73. 61. Ibid., 241. 62. Shiftf: Ilâhiyyât, 387 lines 4-8. 63. Ibn Sïnâ uses the terms shawq, ishtiyaq, tashawwuq and cishq interchangeably, a fact which seems to suggest the influence of Alexander's Mabadi\ See Genequand, Alexander on the Cosmos, 37; and Walzer, al-Farâbï, 391. 64. Najat, 241.

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New Perspectives on the Histoiy of Islamic Science 142 • Islam & Science • Vol. 7 (Winter 2009) No. 2 view to preserving [the continuous process of] generation and corruption—again in an attempt to imitate the Absolute Good.... Now, this love exists in them eternally, without ever ceasing (wa hádhá al-cishq ghayr za°il al-battah).65 It should be added that unlike that of terrestrial animals, the celestial intelligences, being the remote and final cause of their motion, are possessed of infinite power (quwwah ghayr mutanâhiyah), pure and wholly free from all the determinations which belong to matter, such that they have nothing to lose, nor to gain, from what is below them.66 Otherwise they would be subject to change and hence could not be eternal. The motion of the celestial spheres cannot be due to its own innate power because the heavens as a whole, being a finite body, cannot contain the infinite power capable of causing and sustaining its eternal motion over an infinite time.67 Since an infinite power cannot be in a body, Ibn Sïnâ concludes that the power which causes the eternal, circular motion of the heaven (and which is infinite in the sense of exerting its action during an infinite time) must be incorporeal, separated from matter; that is, Intelligence.68 One might wonder why circular motion is deemed most appropriate for the celestial bodies. To this Ibn Sïnâ has the following reasons. First of all, circular motion is prior (awlâ bi al-taqaddum) and superior (awlà bi al-sharaf) to rectilinear motion, because it alone is numerically one (wahid bi al-cadad), wellbalanced (mustawiyah), and most prior and most complete of the two simple motions (aqdam wa atamm al-basitayn). In contrast to circular motion, a rectilinear motion is—if the distance is finite and should the motion turn back—in fact a composite of two contrary motions, while if it does not turn back and stops at a terminal point, then the motion is incomplete. On the other hand, if we suppose the distance is infinite (which is impossible, given the finitude of the cosmos) and the motion does not turn back but goes on to infinity, then it is incomplete. Indeed, for Ibn Sïnâ, there is no such thing as an actually infinite straight line, and even if there were, it could not be traversed by anything in motion, for the impossible does not happen and it is impossible to traverse an infinite distance.69 Furthermore, circular motion is considered complete because one cannot add to it without repeating its course (idhd tarnmat al-dawrah fold yuzdd calayhd bal takarrarà), whereas rectilinear motion can 65. Risalahfial-clshq, in Rastfil Ibn Sïnâ, 391 lines 15-18 and 392 lines 1-2 and 1011; and Emil L. Fackenheim, "A Treatise on Love by Ibn Sïnâ," Mediaeval Studies 7 (1945), 224. 66. Shijiï: Ilàhiyyàt, 387 lines 2 and 8. 67. Shifá": Tabfiyyát: Sama" Tabïï, 228-32. 68. Najât, 127; cf. P. Lettinck, Aristotle s Physics and Its Reception, 662-3. 69. See Shifâ": Tabïiyyat: Sama" Tabïï, 215 lines 6-15 and 217 line 9.

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always be added to and extended infinitely—potentially, of course, without such a consequence. Finally, given the eternity of celestial substance, only circular motion is proper to it, precisely because it is ceaseless and perpetual, since in circular motion every destination is a fresh starting-point (idhà tammat dawrah ïbtadtfat min raisin).70 On Ibn Sïnà's account, no motion is eternal except the celestial, since in all rectilinear motions rest must occur once the moving body arrives at its proper, natural place; and with the occurrence of rest the motion has perished. A further reason is that circular motion has no contrary, which is not the case with simple rectilinear motions. Unlike circular motions, rectilinear motions are the contraries of each other, since they set out from opposite startingpoints and proceed in opposite directions (upward and downward).71 Motions around the circumference of a circle, on the other hand, even if in opposite directions, are nevertheless motions from and to the same point. Two motions are said to be contrary to each other only if they start from and end in two opposite points (fa al-harakdt al-mutadaddah hiya allatl tataqabal atrafuha)^ While he appears to accept Ptolemy's theory of epicycles in order to account for the retrograde motions of the 'wandering stars' in the course of their revolutions around the earth, Ibn Sïnà adopts Alexander's view in pointing out the reason behind those irregular and complex motions of the planets. To recall, ancient astronomers in the time of Plato had discovered that the planets' apparent motions are actually not uniform; they noticed that the circular course of each planet is at certain times interrupted by a movement in a loop: the planet retards its movement and turns back, moving for a certain while in the opposite direction; then it stops and once again advances beyond the turning-point, and so on.73 As is well-known, Ptolemy proposes that a planet's motion may be represented geometrically either by an eccentric circle (falak khârij) possessing a center other than the earth's center; or, if the earth's center is to be retained, an epicycle (falak tadwlr) must be added to the circumference of the deferent circle (falak hamil)', or finally, some combination of eccentric and epicyclic circles could be employed.74 Having accepted this solution, Ibn Sïnà gives a further explanation: whereas the regular, daily motion of the planets from east to west is due to the desire felt by their souls for a common beloved (ma'shuq mushtarak), namely the First Principle, and is but the mechanical effect of the motion of the outermost, first moving sphere, their other 70. Ibid., 266 lines 1-9. 71. Ibid., 282 lines 5-15. 72. Ibid., lines 15-16; see also 289 lines 2-3. 73. See S. Sambursky, The Physical World of the Greeks (London: Routledge and Kegan Paul, 1987), 58-64. 74. Shijiï: Riyàdiyyat: 7/m al-Hay"ah, 466 ff = Ptolemy, Almagest, Bk. IX, Chap. 3 ff.

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irregular motions reflect their having different principles of motion as well as different objects of longing after the First—that is, because each of them is guided by its own intelligence.75 For us it is correct [to hold], as it has been established in Almagest, that the celestial motions and spheres are many [in number], just as they vary in direction and velocity. It follows that for each motion there is a mover [i.e. soul] as well as a beloved (mutashawwaq) different from one another, for otherwise there would be no variety in direction and speed. And we have explained that these lovers are themselves pure good (khayrat mahdah) separated from matter. And it is the love for the First Principle, which is common to all the spheres and motions, that makes it possible for them to participate in the perpetuity and circularity of [cosmic] motion.76

As one might notice, there seems to be a contradiction in the foregoing account. On the one hand, it is said that celestial bodies are changeless, while on the other we are told that they do nevertheless move, albeit with a circular motion. The difficulty arises because motion is defined and understood as equivalent to if not synonymous with change. How does Ibn Sina explain this? It is true that since they lack the primary contrary qualities (hot, cold, dry, moist) that are indispensable for manifold and continuous changes, celestial bodies cannot be said to be generated or destructible any more than they undergo change in terms of quality or quantity, for they have always been in the same state, as astronomers have recorded from the earliest times. So, it is argued, we have good reason to believe that celestial bodies do not move or pass from one quality to another and that they seem to continuously remain as they are. But what about their motions? According to Ibn Sïnâ, the motion of celestial bodies, far from being locomotion or change of place, merely entails positional changes or motion in position (hamkahfial-wadc), which allows the heaven as a whole to remain where it is while its parts move and change their different positions. As he explains in the following passage: As to whether something can change its position (yatabaddal wafuhu) only, without changing its location, we may know its possibility from the motion of the [celestial] sphere (harakat al-falak), which can be in either of these ways: like that of the highest sphere which is not in place' (laysafi rnakari) in the sense of being the defining end of the all-embracing entity (nihâyat al-hawl al-shamil) that we call 'place' or, alternatively, it is said to be in place except that it does not leave its place as a whole, the change being confined to the relation of its parts to the parts of [i.e., various points on] its very location (innarna tataghayyar calayh nisbat ajzà'ihi ilà ajzrfi makdnih) which it [always] retains. Indeed, nothing occurs [in ce75. Shija*: Iláhiyyát, 399 lines 4-8. 76. Shijà*: Ilâhiyyât, 393 lines 6-10.

New Perspectives on the Histoij of Islamic Science Syamsuddin Arif% 145 lestial spheres] except this change [in position], but the location remains unchanged (thabit). Now, since this kind of change is change of relation, and since this relation represents position (wa hadhihi al-nisbah hiya al-waf), therefore, such a kind of change is change in position.77

It is interesting to note that this idea of positional change is found nowhere in Aristotle's works. Whether Ibn Sïnâ got it from some no longer extant Arabic commentaries on Aristotle's Physics is difficult to ascertain given our present-day knowledge. Conclusion Ibn Sïnâ envisages a universe that is one in number, finite in extent, and spherical in shape. The cosmos is divided into two realms: first, the supra-lunar region of eternal, immutable, ungenerated, and incorruptible celestial spheres, and, second, the sublunar region of the four elements subject to generation and corruption. On this model, the universe is structured as a set of nested spheres, all centered upon the center of the universe, which coincides with the earth's center. Nearest the center are the sublunary spheres of earth, water, air, and fire. It is within these spheres that all fundamental changes involving the elements occur, such as locomotion, alteration, growth and diminution, and generation and corruption. Beyond those four central spheres are the nesting crystalline solid but transparent spheres made of a fifth element, aether, that carry around and move the celestial bodies, namely the moon, the sun, all the planets, and the fixed stars. Ibn Sïnâ corroborates his theses with a set of arguments, mostly a priori in kind and largely derived from the Aristotelian physical system. The geocentric thesis, the arrangement of the spheres, the immobility and spherical shape of the earth, and the impossibility of other universes similar to ours are all explained in terms of Aristotelian theories of natural and forced motions, simple and composite motions, and circular and rectilinear motions. Ibn Sïnâ differs from Aristotle, however, when it comes to the metaphysical question as to what causes the celestial motions. Whereas Aristotle posited forty-seven or fifty-five unmoved movers, Ibn Sïnâ not only reduced the number into one single unmoved mover for all, but also gives a non-Aristotelian explanation for celestial phenomena from a religious point of view, saying that the circular movement of celestial spheres is meant for glorification (tasbih) and is due to Divine Command (li amr Allah).

77. Shiftf: Tabfiyyàt: Sarna" Tabïï, 104 lines 10-14.

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[6] AL-QUHÏ: FROM METEOROLOGY TO ASTRONOMY ROSHDI HASHED

I The reader of a treatise on meteorology, whether ancient, medieval, or even classical, is immediately struck by some features that are, at first glance, paradoxical. Whereas, according to Aristotle, this is a discipline that should not be confused with any other, and which deals with all phenomena concerning the four elements "which we may consider as accidents",1 yet this discipline deals with such a wide variety of subjects that it can be defined only negatively. We encounter in it the most diverse phenomena, which today belong to sciences as different as astronomy, geography, chemistry, seismology, volcanology, meteorology, and optics. All efforts to identify a unifying principle - exhalation, for example - behind this variety are condemned to defeat in advance, or at the very least to arbitrarily excluding part of the Stagirite's Meteorológica as apocryphal. On the contrary, it is as though this diversity was in accordance with the Stagirite's intentions, in so far as he seems to have wished to relegate to the Meteorológica all the sublunary phenomena which were not retained in the physical treatises: the Physics, On the Heavens, and On Generation and Corruption. This situation, created by the philosopher, lasted more than two millennia, as is still attested by Descartes' Les Météores. By their number as well as by their variety, the phenomena studied by the Meteorológica ensured a certain popularity for the discipline. Literary authors have often been interested in them, as have philosophers, physicians, and even theologians. Take the example of shooting stars in classical Islam, which we shall study in this article: the philosophers had been concerned with them since al-Kindï2; and literary authors and theologians 1

Aristote, Météorologiques, texte établi et traduit par Pierre Louis, Collection des Universités de France (Paris, 1982), vol. I, 338b, 20-25. 2 The ancient bibliographers attribute to al-Kindi a treatise entitled "On the effect

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examined them when they dealt with certain Koranic texts.3 Thus, this single theme of shooting stars lent itself easily to several historical readings, according to one's area of interest: literature, Koranic commentary, philosophy, etc. It was the object of at least two redactions, one of which belongs to the history of doctrines, and the other to the history of science. These two redactions are obviously interdependent, and one would have to be naive indeed to wish to separate them. Nevertheless, we shall limit ourselves here to the studies which pertain to the history of science, for the following reasons: The phenomena dealt with in the Meteorológica pertain to the domain of experience. Some, however, pertain to it in a particular sense: that is, to the realm between heaven and earth. Rainbows, shooting stars, etc., are sublunary phenomena, without, however, being objects which are accessible to a direct treatment: that is to say, they require the construction of a model. To remedy this situation, we must know how to observe, and above all, how to control our observations. As we raise this question, however, and undertake the research necessary for such control, we modify the very status of our study. Thus, we have shown previously with regard to the phenomenon of the rainbow,4 that once we substitute rigorous methods in the place of uncontrolled observation and naive geometrical representation of the phenomenon (as with the research of Ibn alHaytham on burning spheres, and that of Kamàl al-Dïn al-Fàrisï on the model of the water-filled sphere), research on the rainbow became detached from the Meteorológica in order to become part of another domain: that of reformed optics.5 which appears in the atmosphere, and which is called a star" (Fl al-athar alladhi yazharu fi al-jaww wa-yusamma kawkaban)". See al-Nadim, Kitab al-fihrist, ed. R. Tajaddud (Teheran, 1971), p. 319. 3 Several Koranic verses explain how demons (jinn) are struck by "shuhub" - that is, brilliant flames - when they surreptitiously reach the heavens in order to eavesdrop; for instance in Sürat al-hijr, Sürat al-mulk. The commentators interpreted these "brilliant flames" as shooting stars; cf. for instance al-Zamakhshari, alKashshàf, ed. Muhammad 'Abd al-Salàm Shàkùn (Beirut, 1995), vol. IV, p. 565; alRàzï, al-Tafslr al-kablr, 3rd ed. (Beirut, n.d.), vol. X, p. 169 and vol. XXIX, p. 61. 4 "Le modèle de la sphère transparente et l'explication de l'arc-en-ciel: Ibn alHaytham, al-Fàrisï", Revue d'histoire des sciences, 23 (1970): 109-40; reprod. in Optique et Mathématiques: Recherches sur l'histoire de la pensée scientifique en arabe, Variorum reprints (Aldershot, 1992), III. 5 Géométrie et dioptrique au Xe siècle: Ibn Sahl, al-Quhï et Ibn al-Haytham (Paris, 1993).

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Our goal here is the similar: first of all, we wish to ask the same questions about this second phenomenon of meteorology: shooting stars. We intend to show when and how the introduction of controlled observation and of the necessary rigorous methods led this phenomenon, in its turn, to detach itself from the Meteorológica, in order to become part of astronomy. Here 6 again, Ibn al-Haytham plays an important role, but only after 7 Abu Sahl al-Qùhï. Since he was interested in the mathematical control of observations, al-Quhï also studied a second phenomenon which, although it is not part of the Meteorológica, is related to them. This was the question of the rigorous analysis of that part of the sea or the sky which can be observed from the top of a building of a known height, which rises perpendicular to a plane (for instance, the surface of the sea). It is thus a new field of research that al-Quhi inaugurated. In both cases, however, the goal was to invent methods to control observation, both linguistically and technically. II

Abu Sahl 8al-Quhï, a mathematician of genius and an astronomer, was at best indifferent to all forms of speculative thought. His contemporary, the critic Abu Hayyàn al-Tawhïdï,9 reports this crucial attitude, which has been insufficiently understood. As we have pointed out elsewhere,10 al-Tawhïdï recalls al-Quhi's aversion to metaphysical discussions. He took pleasure in refuting those of the Stagirite's theses that were upheld by the Aristotelians of his time, some of whom, like him, circulated at the court of 'Adud al-Dawla, and then, after him, 6 Ibn al-Haytham wrote on the same theme, following al-Qùhï; cf. R. Rashed, Les Mathématiques infinitésimales du IXe au xf siècle, vol. V, in preparation. It was, moreover, in order to understand the contribution of Ibn al-Haytham that we returned to the study of al-Qùhï. 7 Cf. below. 8 Cf. Yvonne Bold, "Al-Qùhï", Dictionary of Scientific Biography (1975), vol. XI, pp. 239-41; and R. Rashed, Les Mathématiques infinitésimales du IXe au XIe siècle, vol. I: Fondateurs et commentateurs: Banü Musa, Thàbit ibn Qurra, Ibn Sinàn, alKhàzin, al-Quhï, Ibn al-Samh, Ibn Hud (London, 1996), pp. 835-8. 9 Abu Hayyàn al-Tawhïdï, Kitàb al-imtâe wa al-mu'ânasa, éd. A. Amin and A. alZayn (reproduction Bùlàq, n. d.), first part, p. 38. 10 R. Rashed, Les Mathématiques infinitésimales du IXe au xf siècle, vol. I, p. 835.

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of his two sons. Recently, we analysed his refutation of two theses on motion which Aristotle set forth in the Physics, and we showed that each time, he proceeds with the help of geometry, and by means of a thought experiment. Obviously, this approach was not accidental, but reflected a deliberate epistemic position, which al-Quhi formulated several times. For him, it is mathematics that provides the ideal of knowledge. He says in the treatise we have edited below: With regard to the people that neither Galen nor anyone else could criticize - they could not criticize either them or their science, for they relied upon demonstrations in all their sciences and their books - they are the mathematicians.12

Al-Quhï did not hesitate to proclaim this mathematical ideal of knowledge loud and clear, when addressing the King in person. Here are his words: The science of geometry is a model which we observe for truth, and a guide we follow for veracity, for its principle is established, its reasoning constant and continuous, and not susceptible of grievances. No weakness nor corruption affects it; no blow may touch it; no denial nor refusal changes it; it is incomparable with regard to the truth, and without analogy with regard to nobility.13

This praise of geometry and mathematics, reiterated throughout his writings, becomes the echo of an epistemic position that has an affinity with certain modern currents of thought. As we shall see, such a position could not be blended with the doctrine of Aristotle, nor with that of the Aristotelians contemporary with al-Quhi, in order to explain the mechanism of shooting stars. Yet what precisely did he know of this doctrine? And what are the conditions that would make possible a geometrical study of this phenomenon? We shall have to consider these two questions before we return to the contribution of al-Quhi himself. With regard to the first question, al-Quhi is of no great help. He does not mention any name, not even that of Aristotle; nor does he mention any title, not even Aristotle's Meteorológica. 11

R. Rashed, "Al-Quhï vs. Aristotle: On motion", Arabic Sciences and Philosophy, 9.1 (1999): 7- 24. 12 See infra, p. 176 and Additional note, p. 203. 13 See al-Quni's introduction to the construction of the regular heptagon in R. Rashed, Les Mathématiques infinitésimales du IXe au xf siècle, vol. III: Ibn alHaytham, Théorie des coniques^ constructions géométriques et géométrie pratique (London, 2000), p. 766.

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This is not surprising; the Aristotelian thesis was well known and widely diffused at the time. The Arabic version of the 14 Meteorológica by Ibn al-Bitrïq 15was available, as was the Compendium of Hunayn ibn Ishàq. There were also the Arabic versions of the Greek commentaries on Aristotle's work: those of Alexander,16 Olympiodorus,17 and the Pseudo-Olympiodorus.18 What could this literature have taught al-Quhï about shooting stars? According to Aristotle, they are an atmospheric phenomenon; that is, they take place beneath the sphere of the moon. They have their origin in the exhalation in the form of hot breath which rises into the upper atmosphere, which is therefore inflammable. As he writes in the Meteorológica: [...] so that a little motion often makes it burst into flame, just as smoke does, for flame is the ebullition of a dry exhalation. So whenever the circular motion stirs this stuff up in any way, it catches fire at the point at which it is the most inflammable.19

Shooting stars thus occur "if the whole length of the exhalation is scattered in small parts and in many directions and in breadth and depth alike".20 Thus, for Aristotle, shooting stars are an atmospheric phenomenon connected with the earth, the form of which is 14 C. Petraitis, The Arabic Version of Aristotle's Meteorology, A Critical Edition with an Introduction and Greek-Arabic Glossaries, Recherches publiées sous la direction de l'Institut de Lettres Orientales de Beyrouth. Série I: Pensée arabe et musulmane, vol. XXXIX (Beirut, 1967), see pp. 30-2 of the Arabie text. 15 H. Daiber, Ein Kompendium der aristotelischen Météorologie in der Fassung des Hunayn ibn Ishàq, Aristóteles Semítico Latinus 1 (Amsterdam-Oxford, 1975). 16 According to al-Nadïm, al-Fihrist, p. 311, Olympiodorus' commentary on the Meteorológica was translated by Abu Bishr and glossed by Abu 'Amr al-Tabari (on this point, cf. A. Hasnawi, "Un élève d'Abü Biêr Mattà b. Yunus: Abu 'Amr alTabari", Bulletin d'Études Orientales, 48 [1996] pp. 35-55, particularly pp. 41-2); and Alexander's commentary was translated into Arabic, but not into Syriae. It was only later that Yahyà ibn 'Adi translated it from Arabic into Syriae. 17 A. Badawi, Commentaires sur Aristote perdus en grec et autres épîtres (Beirut, 1986), contains the critical edition of the Ps.-Olympiodorus' commentary on the books of Aristotle's Meteorológica, the translation by Hunayn ibn Ishàq, and revised by his son Ishàq ibn Hunayn, pp. 83-190; cf. ibid., p. 95 on shooting stars. 18 We can also add the translation by Qustà ibn Luqà of the Placita Philosophorum, in which Ps.-Plutarch reviews the opinions of the ancients on shooting stars. Cf. H. Daïber, Aetius Arabus die Vorsokratiker in arabischer Überlieferung (Wiesbaden, 1980), pp. 39-41. On the totality of the Meteorológica in Arabic, see the study by Paul Lettinck, Aristotle's Meteorology and its Reception in the Arab World (Leiden, 1999). 19 Aristotle, Meteorológica, I, 4, 341 b 20 ff. [The translation is that of E.W. Webster (Oxford, 1923)]. 20 Ibid., 341 b 32-35; translation Webster.

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explained by exhalations. It is part of those phenomena which "happen beneath the moon. This is shown by their apparent speed, which is equal to that of the things thrown by us; for it is because they are close to us, that these latter seem far to exceed in speed the stars, the sun, and the moon".21 This Aristotelian doctrine became the communis opinio. It was discussed, and even criticized, but its nucleus, which we have briefly recalled here, remained intact. Shooting stars are not extraterrestrial objects, but phenomena, produced beneath the sphere of the moon. Thus, in his comments on Aristotle, Alexander writes: He (Aristotle) says that so-called shooting stars (TOÙÇ ôiaaaovTaç àarépaç) sometimes occur in that way, when the fuel which underlies the celestial bodies is ignited by their movement, and in turn sets ablaze the body contiguous to it. Sometimes as well, they occur in the following way: the heat enclosed within, encircled by the cold surrounding air and gathered together in a single, compact mass, finds itself, as soon as it is ignited, violently expelled from the air constituted by cooling (which has its position beneath the fuel). Its trajectory is then similar to that of fruit-pits22 which we squeeze between our fingers, with the fire remaining the same and identical without igniting that which is adjacent to it. These are the two ways in which the so-called shooting stars seem to occur.23 That these compositions (gustaseis) and trajectories take place under the moon, he thinks is shown by the apparent speed of these things in their trajectory: for just as the things we throw seem to us to move more quickly than the stars, because of their proximity, whereas in fact they are very far from traveling at the same speed, so the so-called shooting stars seem to us to been moved more quickly than the stars, because of their proximity (oi)T P / sin P whenever a>p (a = EGA, p = BAC). In his second proposition,3 Ibn al-Haytham considers^ another arc of circle DG with a point E on jt such that DE>EG\ if the angle subtended at the center by DG is less that the corresponding angle relative to AC, then AB / BC = DE / EG implies AB¡ BCHR / RI. Then an application of the lemma to the triangle ARH and the point 7 of RH gives HR / RI>HAB / IÂB, so that

and, "composing",

(by hypothesis). On the continuation_pf AIB beyond B, let S be suchjthat AIB / BS = DE I EG>AlB I IB (fourthjaroportional), so that BS is similar to EG and ÁBS is similar to DEC', then AB / BS = DE / EG. But BSCÂB \ CÂL Thus

this amounts to ÁB ¡ BC>AI \ CI = DE \ EG in virtue of the hypothesis.

Fig. 5. With the preceding notations and ju = EG / DË, the proposition states that

implies that a>|3 and ju>ta Let us put x - sin tax, y - sin ju|3 and u - sin (1 + X)a / sin tax = sin (1 + ju)|3 / sin ju|3, so that sin (1 + i)a = ux and sin (1 + ju)|3 = uy\ then a = Arc sin ux — Arc sin x, |3 = Arc sin uy — Arc sin y, A, = Arc sin x / (Arc sin i¿x — Arc sin x) and ji = Arc sin y ¡ (Arc sin uy — Arc sin y). The statement is equivalent to: if x>y, Arc sin ux — Arc sin x> Arc sin ¿¿j> — Arc sin y and Arc sin ux I Arc sin x> Arc sin z/j> / Arc sin y. Proposition 45 sa^s that, if DGDE/ÉG and that AC/BC>DG/EG implies 4 5

/6id., pp. 278-83; commentary, pp. 56-9. Ibid., pp. 282-93; commentary, pp. 59-64.

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ÁC/BC>DG/ÉG. Moreover, when AC and DG are similar, it remains^ true that AC/ BODG / EG implies AC I BODG / EG; when AC and DG are larger than a semi-circle, it remains true that AB I BODE / EG Amplíes ÁB / BC>DE / EG. ^Indeed, _if ^AB / BCAB and CKCB, AI/ CI>AB I EC and DG / EG>AB / EC contradicting the hypothesis. _ _ _ _ _ _ _ _ In the same manner, if AC ¡ BC AI¡ CI= DE ¡ EG. In other words, sin a / sin }ux>sin P / sin |u|3 or sin (l + X ) a / sin ^a>sin (1 + ja)|3 / sin ju|3 implies 1 / X>1 / JLÍ. The first implication is true for if |3