Teaching and Learning the Sciences in Islamicate Societies (800-1700) 9782503574455, 9782503574462

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Teaching and Learning the Sciences in Islamicate Societies (800–1700)

Studies on the Faculty of Arts History and Influence

Volume 3 Editors Luca Bianchi (Milano) Jacques Verger (Paris) Olga Weijers (Paris) Editorial Board Amos Bertolacci (Pisa) Dragos Calma (Dublin) David Lines (Warwick) Colette Sirat (Paris)

Teaching and Learning the Sciences in Islamicate Societies (800–1700) by

Sonja Brentjes

F

Cover illustration: Folio from a Mihr-u Mushtari (The Sun and Jupiter) by Shams al-Din Muhammad Assar Tabrizi (d. ca. 1382); verso: Mihr at school; recto: text, Shah Shapur sends Mihr and Mushtari to school. Freer Gallery of Art, Smithsonian Institution, Washington, D.C.: Purchase – Charles Lang Freer Endowment, F1932.5.

© 2018, Brepols Publishers n.v., Turnhout, Belgium. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, ­mechanical, photocopying, recording, or otherwise without the prior permission of the publisher. A shorter and modified version of a part of chapter 2 has already been published in IHIW Volume 5 number 1-2, 2017, Brill. D/2018/0095/80 ISBN 978-2-503-57445-5 eISBN 978-2-503-57446-2 DOI 10.1484/M.SA-EB.5.112709 Printed on acid-free paper.

TABLE OF CONTENTS

INTRODUCTION

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CHAPTER 1: CONTEXTUALIZING LEARNING AND ­TEACHING OF THE SCIENCES IN ISLAMICATE SOCIETIES 17 1.1. The Beginnings 18 1.2. The Early Abbasid Period 19 1.3. A Period of Consolidation, Synthesis, and Contests 21 1.4. B  reakdown, Reorientation, and Reconfirmation in the Wake of the Mongol Conquests 24 1.5. C  hange as the Norm? A Further Wave of New Empires and Dynasties 26 1.6. Consolidation, Climax, and New Challenges 27 1.7. Comparisons 30 1.8. Postface 31 CHAPTER 2: TEACHERS AND STUDENTS AT COURTS AND IN PRIVATE HOMES (EIGHTH–TWELFTH CENTURIES) 33 2.1. Limited Resources 35 2.2. S tories about the Transfer of Philosophy and Medicine from Alexandria to Baghdad 37 2.3. Teaching the Mathematical Sciences 38 2.4. Teachers and Students 42 2.5. Postface 65 CHAPTER 3: SCHOOLS OF ADVANCED EDUCATION 3.1. The Legal Status and Formalities of Advanced Education 3.2. Teaching Non-Religious Disciplines at Religious Institutions 3.3. Processes of Professionalization and Specialization 3.4. Secretaries, Animals, and Foreigners

67 68 70 71 75

CHAPTER 4: THE SCIENCES AT MADRASAS 4.1. Mathematical Disciplines 4.2. Medicine and Pharmacology

77 77 91

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4.3. Natural Philosophy 4.4. Divination, Magic, Alchemy 4.5. Postface

98 107 111

CHAPTER 5: OTHER TEACHING INSTITUTIONS 5.1. Learning and Teaching at Hospitals 5.2. Family Education 5.3. Travel for the Sake of Knowledge 5.4. Postface

113 115 131 135 144

CHAPTER 6: TEACHING AND LEARNING METHODS 6.1. Meetings, Teachers, and Goals 6.2. Reflections on Creativity and Professional Control 6.3. Reading, Writing, Speaking, Seeing 6.4. Tradition, Ingenuity, and Discursive Method 6.5. “The Etiquette of Scholarly Disputation” 6.6. Commentaries and Super-Commentaries 6.7. Postface

147 149 155 161 168 177 181 185

CHAPTER 7: ENCYCLOPAEDIAS AND CLASSIFICATIONS OF THE SCIENCES 187 7.1. Philosophical Perspectives and Works 194 7.2. Administrators and Their Encyclopaedias and Knowledge Systems 204 7.3. Madrasa Teachers as Writers of Summas and Divisions 211 7.4. Postface 221 CHAPTER 8: TEACHING LITERATURE AND ITS TEMPORAL GEOGRAPHIES 223 8.1. Euclid’s Elements and the Middle Books 227 8.2. Other School Texts for Geometry 237 8.3. Arithmetic, Algebra, and Number Theory 239 8.4. Astronomy and Astrology 243 8.5. Medicine 247 8.6. Logic and Natural Philosophy 255 8.7. Postface 262

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APPENDICES Table 1. I slamicate Dynasties Prominently Mentioned in this Book Table 2. Ancient Scholars  Table 3. Scholars from Islamicate Societies Table 4. Muslim Rulers

263

BIBLIOGRAPHY Primary Sources Secondary Sources

289 289 292

INDEX

305

263 264 266 286

INTRODUCTION

The learning and teaching of scientific disciplines has a long history in Islamicate societies. The societies that play a role in this history may appear surprisingly numerous to some readers. Contrary to the older historiography that claimed that the sciences declined or even disappeared from Islamicate societies at some time – the precise timing of such a “decline” varied from author to author, ranging from as early as the eleventh century to as late as the sixteenth – questions about nature, the heavens, human bodies, numbers, surfaces, and solids continued to be taught and studied at schools in many Islamicate societies well into the nineteenth century. Since no one can cover all of them exhaustively, I had to make some choices. The obvious selection criterion was the extant material about particular societies and its relevance for a history of learning and teaching scientific disciplines. As a result, we will visit Baghdad, Isfahan, Shiraz, Samarkand, Mecca, Damascus, Cairo, Tunis, Tlemcen, Sivas, and Istanbul as important centres of learning and teaching. But we will also hear of provincial towns, villages, or fortresses, where some manuscripts were copied, read, and annotated. The main primary sources of this book are handwritten texts, but also images of various kinds, instruments, and other material objects. They are today found in museums and public libraries across the world. Too many are also stored away in private collections, often not accessible for research. The loss of pertinent information through this private policy of investment and exclusion is tremendous. The scientific disciplines that will be discussed in this book appear in Arabic, Persian, or Turkic texts and schemata under different classifications. The starting points can be found in Arabic and Syriac translations of ancient Greek philosophical, medical, and doxographical texts composed in the learning and teaching environments of the different Greek philosophical and medical schools in Athens, Alexandria, Pergamon, and Rome, to name only a few cities where such schools flourished in Antiquity. Although Christian, Jewish, and Muslim scholars adhered closely to what they learned from such translations, the many changes in intellectual life caused visible modifications, rearrangements, and

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i­nnovations in the ways they classified the sciences. Over time, the originally much more narrow term ʿilm (religious knowledge), and in particular its plural ʿulūm, opened up to include all kinds of knowledge, ranging from religious disciplines through philological, philosophical, and mathematical disciplines to literary, historical, and the ghariba disciplines, often summarily translated as “occult sciences”. Some of the last were clearly seen as mathematical sciences. In some societies, they were even considered the most valuable of the sciences. Examples are magic squares of numbers and letters, geomancy (a method of divination through arrangements of groups of points in sand), and astrology. In the eyes of its practitioners, astrology shared with alchemy a scientific status grounded in natural philosophy, metaphysics, mathematics, empirical knowledge, and experience. In this book, I will allow some room for these disciplines, although our knowledge of how they were learned and taught is often fairly limited. That is why my focus will be on the mathematical sciences, as understood by their practitioners in past Islamicate societies. For them, the mathematical sciences included number theory, geometry, astronomy, and theoretical music as the fundamental sciences of mathematics, and optics, the science of weights/heavy bodies, magic squares, algebra, systems of calculation, burning mirrors, the science of timekeeping, and others as branches of these fundamental sciences. I will also address medicine, and questions belonging to natural philosophy in so far as the primary and secondary sources available to me speak about their presence in the classroom or the textbook. My geographical and historical focus in most of the following chapters will be on Egypt, Syria, Iraq, and Iran, partly because it is for cities in those regions that I have information about what was taught and which methods were applied in the classroom. But I will also – as far as possible – pay attention to North Africa west of Egypt, Anatolia, parts of Ottoman Europe, Central Asia, and India. I will rarely mention al-Andalus, South East Asia, and sub-Saharan Africa, simply because I do not know enough about the schools, their literature, and the teaching methods in those regions. My explicit acknowledgment that students are as important to a history of education in the scientific disciplines as teachers reflects the individualistic and informal character of education in Islamicate societies before the introduction of modern Western systems to the Middle East, North Africa, and South Asia during the nineteenth century. This is not

Introduction

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to say that no institutions of learning and teaching existed. Christian and Jewish communities in different Islamicate societies ran their own schools at monasteries, the houses of lay teachers, or taught scientific knowledge like a craft in families of medical and other practitioners. Learning and teaching the abovementioned scientific disciplines in Muslim communities were organized similarly. In the first centuries, they were taught as private education at courts, in the houses of the rich, and perhaps occasionally at mosques, although we have no reliable information about such sessions before the twelfth or thirteenth centuries. Other early locations of learning and teaching were circles of discussion and entertainment, or the exchange of letters and epistles between scholars and patrons across hundreds or even thousands of kilometres. Most students studied with prominent scholars. Others were autodidacts. Another important form of private education was travelling. The motivation for medium- and long-distance travel varied from person to person. Trade and pilgrimage ranked highest for most who left their homes for months or years. Finding a position and a patron and building one’s reputation certainly motivated many others. Many, in particular young men and junior scholars, traveled to acquire the newest books and oral instruction on a broad range of disciplines in the centres of knowledge like Baghdad, Damascus, Cairo, Tlemcen, Tunis, or Shiraz. The great cultural change in learning and teaching scientific disciplines is linked to the integration of these disciplines into the teaching practices of scholars with formal posts at madrasas and mosques. This began presumably in the twelfth century, at first in cities of Iraq, but spread quickly into Syria, Egypt, Anatolia, and probably Iran. North Africa, South Asia, as well as Central Asia followed suit in the thirteenth and fourteenth centuries. Logic, the mathematical sciences, medicine, and parts of natural philosophy were the main beneficiaries of this fundamental change in which learning and teaching were institutionalized. Medicine occupied a unique place in learning and teaching. Some schools from pre-Islamic times survived among Christian communities or were imitated by Christian physicians in the Abbasid caliphate’s newly founded capital of Baghdad in the later eighth and early ninth centuries. Homeschooling or craft-like training (apprenticeship) were two further forms of medical education. Families of physicians taught their sons (and daughters, though only rarely, as far as our sources suggest) the skills and

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secrets of the craft. They gave them theoretical education and practical training. Hospitals provided this knowledge at the latest from the tenth century, but not always and everywhere. Education in all scholarly disciplines, including medicine, in past Islamicate societies was first and foremost a textual enterprise, regardless of whether it was communicated orally or in writing. Some disciplines also included practical training. Medicine, botany, astronomical disciplines, and alchemy are examples for such hands-on training, at least in some recorded cases. The first chapter of this book tries briefly to contextualize its subsequent chapters. Chapter Two discusses how we know about the forms of private learning and teaching before the foundation of schools of advanced education. It offers a number of examples from the mathematical sciences and natural philosophy that historians of the ninth, tenth, or eleventh centuries or the scholars themselves reported in their chronicles, autobiographies, or scientific treatises. Chapters Three and Four describe the processes through which the mathematical sciences, medicine, natural philosophy, and parts of the “occult sciences” were integrated in the new institutions for advanced education, which focused primarily on the legal sciences and the foundations of faith and law. They discuss the many features that this tremendous innovation introduced into learning and teaching scientific disciplines as well as the setbacks it brought with it over time. Chapter Five surveys other institutions of learning and teaching. It focuses primarily on hospitals and some of the historiographical difficulties that pertain to their interpretation as teaching sites. Other sections present surveys of the relationship between education within families and external training and travelling as a central means of learning and teaching. Chapters Six, Seven, and Eight look at important aspects of learning and teaching in the environment of texts, paying special attention to methods used in classrooms as much as they can be traced in extant school texts and learning genealogies documented in so-called catalogues, programs, or dictionaries. I will discuss the transfer of teaching bestsellers between major centres of learning, the evolution of different kinds of textbooks, and the emergence of collections of teaching texts. The development of encyclopaedic works will be examined as products for disseminating knowledge outside the scholarly elites, multidisciplinary introductions for beginners, and as expressions of scholarly educated, professional administrators.

Introduction

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Although the book as described deals with some of the most important features of learning and teaching scientific disciplines in past Islamicate societies, it is not comprehensive. At the moment, only a very small number of academic studies are available on this topic. Hence, the task of writing about the history of learning and teaching any of the sciences in Islamicate societies faces many challenges. These challenges are conceptual, historiographical, and material in nature. Historiographical problems include chronology, periodization, macro- versus micro-historical analysis, or how to differentiate teaching materials from other genres of scientific texts. Questions about which kinds of contexts are most conducive for understanding the content, forms, and methods of learning and teaching the sciences are also historiographical in nature. Conceptual challenges consist in how to balance a history of learning and teaching with a history of the disciplinary content, how to determine the content of teaching proper, or how to differentiate between methods of teaching and disciplinary methods. I was not always certain where to draw the borderlines. It is clear that a history of learning and teaching needs to talk at least summarily about the content. But when it is often unclear whether a specific text was indeed read between a teacher and one or more students, then precise statements about what was taught at a school in a specific location at a concrete moment of time become very difficult to formulate. Even notes in manuscripts often do not help to settle such issues. I have tried to paint with broad brushstrokes to ­provide at least some provisional impressions of institutions, teachers, texts, subject matters, and methods over the millennium and the large territory this book covers. For the many names of people, dynasties, and books that appear in it, I provide some help through tables in the appendix. Material challenges concern the abundance of elementary teaching texts for the period after about 1150, when madrasas, mosques, and other educational institutes increasingly opened their doors to teachers, students, readers, and copyists of scientific texts, while there is a dearth of such texts clearly identifiable as teaching and learning material for the period between the eighth and the early twelfth centuries. These material challenges generate their own historiographical problems that need to be addressed. How does one, for instance, identify any scientific text as a source of learning and teaching if its author did not declare his work to be so? Is an encyclopaedic survey of one or several disciplines a teaching tool

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or a product of patronage structures or both? How many readers does a text have to have before we can call it a teaching text? Do we need to find notes in a text that testify to readers trying to understand its content or does it suffice for recognizing it as a textbook if its author says so? Since there were no ministries for education, boards for quality control, or commercial publishers of schoolbooks, can we ignore issues like the spread of specific texts either across space or time and other forms of institutionalizing learning and teaching? Since for most Islamicate societies there are no documents prescribing the choice of specific texts to be used in schools, how did teachers know which texts to privilege and how did visiting scholars find out which texts to study in any given city? Some of these problems will be touched upon in this book. Others need to wait for another historian interested in how scientific disciplines were learned and taught in past Islamicate societies. Although I agreed to write this book on the history of learning and teaching of scientific disciplines, I actually believe that what was taught and learned in most centuries were not disciplines, but texts. Perhaps this is too general and too big a claim. Maybe it is more appropriate to say that while scientific disciplines seem to have been studied and taught in the educational forms that existed before the rise of the madrasa, in the centuries dominated by advanced education at madrasas, mosques, and similar kinds of religious houses the desire to study or teach a scientific discipline in its entirety retreated in favour of learning and teaching individual texts. The question here is how to measure the difference. But I hope that at the end of the book readers will better understand what it meant in some Islamicate societies to study or teach a scientific discipline. I did not envision this book as a platform of discussion against the growing number of academic and non-academic amateurs who produce books about the history of the sciences in Islamicate societies. Nonetheless it serves as a rebuttal of the often profoundly wrong depictions of scholars and institutions in those societies and their interests, curiosities, preferences, and achievements for both types of amateurish writings – writings that denounce and denigrate as well as those that glorify and exaggerate. I thank my daughter Rana, my friend Amber Romasa, my colleagues Leigh Chipman, Nahyan Fancy, Maribel Fierro, Hossein Kamaly, Miri Shefer-Mossensohn, Peter Barker and his students, and participants in the colloquium of Department III of the Max Planck Institute for the

Introduction

15

History of Science in Berlin for reading various stages of this book and for highlighting their shortcomings. I am also very grateful to the following colleagues for their support in finding manuscripts, editions, colophons, and other relevant information about madrasas, teachers, and teaching texts: Gerrit Bos, Hüseyin Sen, Jan P. Hogendijk, Giovanni Carrera, Bink Hallum, Charles Burnett, Sabine Schmidtke, and Nathan Sidoli. Finally, my thank goes to the Max Planck Institute for the History of Science in Berlin and in particular its director Jürgen Renn. Without his personal as well as the institutional support, this book would not have been possible. I dedicate this book to my daughter and to my colleagues and friends Menso Folkerts, David A. King, and E. Scholz.

Chapter 1 CONTEXTUALIZING LEARNING AND ­TEACHING OF THE SCIENCES IN ISLAMICATE SOCIETIES

R

eading unprepared about a foreign culture – whatever the precise subject might be – is usually the wrong approach. Too many names, places, customs, doctrines, legends, languages, and so on are unfamiliar and decrease one’s reading pleasure. A simple list of such names, etc. is not very helpful either, because already their transliteration and pronunciation poses great obstacles. Integrating excursions into specific Islamicate societies and their conditions of learning and teaching with the planned chapters of this book is probably the wisest way to proceed. But the page numbers available for the book as a whole do not suffice for this approach. Hence, I decided to start the book with a very brief bird’s eye view of relevant contextual issues concerning the mathematical sciences, medicine, philosophy, and the “occult sciences”. The thread of this introduction is not political, social, or general history. I  rather chose as my organizing principle the relationship to – or, as I will call it: the distance from – the ancient sciences as known through Arabic translations in Islamicate ­societies since the early Abbasid caliphate. This is one of the issues that was often discussed by academic experts in the twentieth century. Today, it is debated mainly by amateurs in academia and elsewhere. In addition to the historiographical, ideological, and political relevance ascribed to this issue, the problem of the unmanageability of any other format for several hundred societies over one thousand years in an introduction of at most twenty pages motivates my choice. My third motif for choosing this approach is to highlight how deeply the intellectual life in major Islamicate societies was anchored in an active interaction with, and broad acceptance of, ideas and practices developed in the millenium before the rise of Islam as a religion and to point out that various political, social, and intellectual cultures relied on some kind of interpretation of pre-Islamic types of knowledge as doctrines, texts, instruments, and other practices.

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1.1. The Beginnings Historical chronicles and biobibliographical works report that healers were known among the Arab tribes before their conversion to Muhammad’s teachings. They also speak of members of the family of the Umayyad caliphs (ruled 661–750) who were interested in alchemy and invited Christian monks to share their knowledge with them. But they have little to nothing to say about where, with whom, and how these early experts acquired their knowledge. Moreover, modern research identifies these healers as non-scholastic magicians. Hence, my history of learning and teaching the sciences begins only with the Abbasid dynasty that through rebellion, ­religious and other kinds of propaganda, and military campaigns conquered the lands of the Umayyad caliphs from Central Asia to Egypt between 719 and early 750. The Abbasids were successful, because Umayyad rule had disaffected many Arab Muslims and other subjects. Major points of contention were their wars against Muhammad’s nephew ‘Ali (murdered by a Kharijite – another group fighting the Umayyads – in Kufa in 661) and the husband of Muhammad’s daughter Fatima (died in 632), the murder of ‘Ali’s younger son Husayn in the Battle of Karbalah in 680, the possible instigation of the poisoning of ‘Ali’s older son Hasan by his wife in 670, other wars and rebellions, famines, and further disastrous political and economic decisions. In addition, non-Arab Muslims felt alienated by Umayyad policies privileging Arabs with regard to access to high-ranking offices and properties. Many armed upheavals shook the Umayyads’ hold on power and prepared the ground for the Abbasid success. With the Abbasid dynasty the first major rupture in the cultural and political contexts of the mathematical sciences, medicine, ­philosophy, and the “occult sciences” took place in Islamicate history. By its end almost the entire corpus of ancient Greek mathematical, medical, and philosophical works of almost all scientific heros of Antiquity had been translated into Arabic and a good number of texts also into Syriac. In the early phase of this cultural transformation astrological, logical, and h ­ istorical texts were translated from Middle Persian and astrological-astronomical as well as medical handbooks from Sanskrit into Arabic. These translations were not the first such activities in the Middle East. Rather, they had predecessors in Syriac (an Aramaic dialect) and Armenian from approximately the fifth to the eighth centuries. But the translations undertaken under

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the Abbasids certainly attained a much larger scope and a greater depth. They created the foundation for the slowly emerging hybrid knowledge cultures in Islamicate societies. Over the course of almost a millenium, these new cultures compared and measured themselves to those earlier cultures, themselves clearly hybrid formations. The comparisons and measurements took a plenitude of forms. They could be scornful, condescending, or glorifying and deeply appreciative. In this sense, one can organize a history of learning and teaching the mathematical sciences, medicine, natural philosophy, and the “occult sciences” along a trajectory of distances from or engagements with ancient Greek, Middle Persian, and Sanskrit authors and texts in Arabic translations. 1.2. The Early Abbasid Period The first two Abbasid centuries appear on such a trajectory of distances as dominated by the translation and study of works produced in different philosophical, medical, and mathematical schools from different historical phases of the ancient Mediterranean world – classical Greek city states, Hellenistic kingdoms, the Roman Empire, and its offspring, Byzantium, and Sasanian Iran. Religious debates among Muslim ­scholars in the eighth and ninth centuries motivated those interested in such translations to adapt Aristotelian, Neoplatonic, and Christian scientific teachings to Muslim beliefs in several instances, such as the questions of the creation and duration of the universe and the formation of its components like natural bodies on Earth or celestial bodies in the heavens. These two c­ enturies are the period when specific components of Indian knowledge such as the decimal positional system and the belief in two additional ­planets, representing the intersections of the lunar orb with the eclipse, were integrated into the new hybrid knowledge systems, forever to stay there. They also were the time of a close scientific collaboration between translators, astrologers, and physicians from different religious ­communities as well as of serious struggles over cultural priority. They were times of great courtly and urban patronage for the new sciences, in which scholars of non-Arab origins dominated. Astrology became a highly appreciated and successful courtly discipline based on Aristotelian natural philosophy. A  number of astronomical observations were carried out for religious as well as scientific reasons, and partly financed

TEACHING AND LEARNING THE SCIENCES

The Atlas of Islam 22003, 6.

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by Abbasid rulers. Works on issues of central ­meaning for Muslims like prayer times, prayer directions, or the beginning of a new month began to be written. On the material, social, and cultural level, shifts from papyrus to paper and from orality to literacy took place, which found their expression in a quickly diversifying manuscript production and the emergence of the new profession of paper and book traders. Closely linked to those changes were debates about values in learning and teaching, which would continue over the centuries. Should a master know his products by heart without committing them to paper or should he share property rights with copyists, students, and stationers? Should a student learn through listening to a reciting teacher or was it permissible to learn by reading? Could the latter be done alone or did one need a teacher? A final aspect of these nascent new forms and modes of teaching and learning was the dynastic support of hospitals as a tool of healing, but also as a place for training new generations of doctors. 1.3. A Period of Consolidation, Synthesis, and Contests The tenth, eleventh, and twelfth centuries saw the emergence of great systematizing and synthesizing works, which, while deeply grounded in the teachings of the translated texts, acquired their own Islamicate status, structure, and flavour. Some of them, in particular Ibn Sina’s ­philosophical and medical encyclopaedias, ensured the survival of this multifaceted knowledge culture for several centuries thanks to their authors’ teaching activities and their students’ production of new encyclopaedia-style manuals. These two centuries saw the emergence of numerous local dynasties all over the Abbasid caliphate, which multiplied the opportunities for patronage for scholars and allowed for more diversity with regard to religious creeds, legal schools, philosophical doctrines, languages, and literature. New Persian began to evolve, finding its space first in poetry and historical epics. But scientific works, again often encyclopaedias, followed suit, written primarily for local patrons in Central Asia and eastern Iran. The relationship between religious scholars and philosophers changed. The question which was superior – law or philosophy – was answered by both sides differently and caused much irritation, debate, and ridicule. This question too remained on the table for several centuries.

TEACHING AND LEARNING THE SCIENCES

The Atlas of Islam 22003, 10.

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Major religious schools began to compose refutations of philosophy, while important members of those schools wrote texts on geometry, arithmetic, algebra, logic, or integrated liberal doses of pre-Islamic philosophical concepts, methods, and theories into their writings about kalam (reasoning about matters of faith). One of the most prominent, but by far not the only, exponent of these processes was Fakhr al-Din al-Razi (died in 1210). The process of rewriting important ancient teachings continued, now transforming for instance the concept of the Prime Mover into that of the Necessary Existent. New scientific developments included an increasing willingness to treat ancient Greek authorities and their texts in a critical manner. Doubts were raised against Ptolemy, Euclid, Galen, or Aristotle. While conservatism was victorious with regard to Euclid’s Elements, the process of constructing non-Ptolemaic models for planetary movements gained in speed. Higher-level mathematical books by ancient authors such as Apollonius or Archimedes were studied, commented on, challenged, and completed or extended. The sciences, medicine, and philosophy in Islamicate societies had reached adulthood. Political and socio-economic changes of great importance for later centuries occurred. The emergence as well as subsequent disappearance of Shiʿi movements, dynasties, and even empires of different creeds shaped history, as did the advancement of nomadic, mostly Turkic, tribes of Sunni creed from Central Asia westwards and southwards. Sufism – in different forms of social organization and religious commitment – spread. The first Nizamiyya madrasas were founded in the eleventh century by a vizier of the most powerful of the Sunni tribal dynasties – the Great Saljuqs (ruled 1034–1194). In the twelfth century, this form of organizing learning and teaching expanded into regions ruled by other Sunni dynasties. With this last development, another fundamental cultural rupture occurred, the emergence of an educational institution with posts and salaries for teachers and stipends for students. This institution is called the madrasa. For a long time, it focused on teaching the doctrines of the major Sunni law schools. But the integration of logic, the mathematical sciences, medicine, various parts of philosophy, and some of the “occult sciences” into the new institutional landscape soon became part of this tremendous cultural change. In addition to the madrasa, other spaces for teaching religious topics continued to exist, like the mosques, or were added as further institutions where teaching could take place, such as the houses of the

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Qur’an and/or hadith. In these more specialized institutions, classes on the mathematical sciences, medicine, logic, or natural philosophy only rarely took place. But in some cases, the libraries also included literature on these fields of knowledge. It is thus possible that in those cases some forms of learning or teaching also happened. Mosques, in contrast, sometimes even included chairs for teachers of medicine, if the donor prescribed them. Relating these changes to the trajectory of the ancient sciences and their authorities, differences can be easily recognized. If logic and ­philosophy were taught at madrasas or mosques, their teachers most often ­followed the writings by Muslim authors. In contrast, teachers of medicine or the mathematical sciences tended more often to mix texts by ancient authors with those by medieval scholars. 1.4. Breakdown, Reorientation, and Reconfirmation in the Wake of the Mongol Conquests The thirteenth century saw the arrival of the Mongol tribal confederation, which brought much death and sorrow to large parts of the Islamicate world, destroying states in Central Asia, Iran, the Caucasian Mountains, Iraq, Syria, and Anatolia. In 1256, they terminated the last Ismaʿili state in the Middle East and in 1258 the Abbasid caliphate. The destruction wrought by the Mongol armies included schools, libraries, and books. But the new Mongol dynasty, called the Ilkhans (ruled 1256–1335), soon created conditions for the recovery of intellectual activities. They brought together leading Shiʿi and Sunni, Christian, and Jewish physicians, astrologers, and other scholars at their new capital Maragha in northwestern Iran, fostered the exchange of medical, astronomical, calendrical, and agricultural texts with their overlords, the Great Khans, in China, and gave the administration of their empire into the hands of Iranian Jews, Muslims, and Christians. The so-called Pax Mongolica enabled long-distance travel to China for more scholars than ever before, brought Catholic Christians from western Europe to their courts, and provided the conditions for the revival of intellectual life among Syriac Christians in Iran, Iraq, and Anatolia. Despite the Mongol enmity against the Mamluks (ruled 1260–1517), who defended Egypt and Syria against the former’s repeated efforts at conquest and finally defeated the Crusaders, scholarly exchanges between Egypt, Syria, Iran, Iraq, and Anatolia flourished. The building of madrasas and hospitals

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thrived. A new astronomical discipline, the so-called science of timekeeping, emerged in the late thirteenth century, perhaps in Cairo. Planetary theory matured thanks to the work of Sunni and Shiʿi scholars at the new observatory in Maragha. New non-Ptolemaic models for the Moon, the Sun, and Mercury were proposed and new mathematical devices and theorems created. Important teaching manuals with long-term impact on learning and teaching the mathematical sciences and philosophy were compiled by scholars in Iraq and Iran. Many ancient mathematical and astronomical texts, translated during the eighth and ninth centuries, were collated, corrected, edited, and rewritten. The same process took place for several texts written by scholars in Baghdad during the ninth century. These new editions of ancient and medieval mathematical and astronomical texts became the most often taught textbooks in a number of Islamicate societies in the centuries after the fall of the Ilkhanids. It is, however, not always easy to trace their usage for all dynasties, urban centres, and regions. The most important representatives of these new editions were the works of the Shiʿi legal scholar, philosopher, and ­astrologer Nasir al-Din al-Tusi (1201–1274). He was also one of the ­leading lights in the development of planetary theory and in the changes of methods and rules for writing philosophical commentaries. A further development of long-term impact was the turn of two Muslim scholars and one Jewish philosopher to the oeuvre of the Iranian religious scholar and philosopher Shihab al-Din al-Suhrawardi (executed in 1191), the founder of a new type of philosophy called illuminist, or in al-Suhrawardi’s terminology “the philosophy of light”. This philosophy of light considered Ibn Sina’s teachings as its lower part for beginners and doctrines from ancient Egypt, Iran, Mesopotamia, and pre-Aristotelian Greek philosophers as higher-level philosophies, which needed to be recovered and brought together. Parallel to these developments in Iran and Iraq, a philosophically-grounded type of Sufism was promoted by Muhyi l-Din Ibn ʿArabi (1165–1240) from al-Andalus, who died in Damascus. 1.5. Change as the Norm? A Further Wave of New Empires and Dynasties The fourteenth and fifteenth centuries saw far-reaching political changes in Central Asia, Iran, Anatolia, and North Africa. New dynasties of Turkic

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and Berber origin with clear Sufi leanings emerged, side by side with small, local ruling families of different backgrounds and shorter survival rates. Most of them shared strong interests in astrology and the magic properties of numbers and letters that – so they believed – gave them access to the divine and hence enhanced their power over enemies and subjects. In Central Asia and Iran, Timur (ruled 1370–1405) headed a nomadic confederation and conquered large territories, including incursions into Anatolia, where he defeated the ruling Ottoman sultan, and India. In order to support his claims to legitimate rule, he revived several Mongol customs, from marriages to the arts and the sciences. Traces of Chinese motifs are easily recognizable in the arts. In the sciences, Nasir al-Din al-Tusi’s works and those of his colleagues and students were studied and copied, particularly in Samarkand. In philosophy, there was a new interest in Abu Nasr al-Farabi’s (died c. 950) oeuvre and in works attributed to him, although the circles who sponsored the copying of these works are not well known. Both sets of ­writings clearly embody either edited translations of ancient Greek ­teaching texts or responses to Greek philosophy. Nonetheless, it is unclear whether these features were valued. In Mamluk territories, interests in the mathematical sciences, medicine, logic, and philosophy focused undoubtedly on Muslim authors who lived between the eleventh and the fifteenth centuries. Even in the mathematical sciences, translations of ancient Greek texts beyond Euclid’s Elements were barely studied. Since Anatolian scholars acquired their advanced education in this period primarily in Cairo and to a lesser degree in Damascus or in Iran, the pattern of their education also shows a clear distance from works from Antiquity. The same seems to apply to North Africa. The socalled “occult sciences” grew in importance. The science of magic letters and numbers profited in particular from this trend. It became seen as a new kind of philosophy and was placed at the top of all disciplines. 1.6. Consolidation, Climax, and New Challenges The sixteenth and seventeenth centuries experienced a significant change with respect to the organization and content of advanced education. The study of ancient mathematical texts in Nasir al-Din al-Tusi’s editions and of ancient philosophical works grew slowly in India from about the second half of the sixteenth century and in Iran some decades later, both

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The Atlas of Islam 22003, 12.

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The Atlas of Islam 22003, 13.

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as independent processes. In India, this intellectual shift resulted from the decision of the Mughal emperor Akbar (ruled 1556–1605), a scion of the Timurids, to reform the program of the madrasa as one measure in his political, religious, and cultural decisions to integrate Hindus into the administration, scholarship, and military class of his state. In Iran, the turn to philosophical writings from Antiquity and the ninth and tenth centuries reflects a desire to build a Shiʿi ­philosophical identity. Since Ibn Sina’s philosophy and its impact on kalam was ­understood by the Safavid intellectual elite of the late sixteenth and seventeenth centuries as married to Sunni Islam, turning “back” to other forms of Neoplatonic philosophy and integrating their reading into Shiʿi religious doctrines appeared a reasonable solution. Suhrawardi’s illuminist philosophy also gained greater recognition in those circles. Nonetheless, the study of Ibn Sina’s works continued throughout the entire Safavid period, in particular since the founder of the Mansuriyya madrasa in Shiraz, Sadr al-Din al-Dashtaki (1425–1498), had argued in the late fifteenth century for a return to the original works of the ­philosopher and their cleansing from the layers of interpretation through commentaries, supercommentaries, and transformations in kalam texts. Madrasa studies in the Ottoman Empire, in contrast, continued to follow the older approach to Ibn Sina’s works, reading in particular his Pointers and Reminders together with the commentary literature all the way down from the eleventh to the late fifteenth centuries. In natural philosophy, these studies were accompanied by reading the textbook literature compiled in the thirteenth century. 1.7. Comparisons Hence, in three different ways there was a renewed rapprochement to texts and teachings translated, or derived with adaptations and transfor­ mations, from ancient philosophical and mathematical traditions. Copies of Euclid’s Elements and to a lesser degree of other translations of ancient mathematical texts suggest that a similar process took place for the mathematical sciences in North Africa. Nothing similar, however, is visible for philosophy. After 1300, medicine as a whole seems to have remained ­distanced from these intellectual changes and diversifications with regard

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to ancient medical school literature with the exception of Dioscorides’s De Materia medica. The  latter’s exceptional status is suggested by the new copies of Dioscorides’s De Materia medica made in Safavid Iran and Golconda in western India. The “occult sciences” crossed lines with some of the philosophical debates in Safavid Iran, Mughal India, and the Ottoman Empire, since astrological and talismanic texts ascribed to Aristotle or Plato were again copied more often. Considering all so far known documents, however, Islamic forms of divinatory knowledge dominated the scene. Supported by apocalyptic expectations towards the end of the first Islamic millenium in 1591/2, divinatory knowledge was more highly appreciated as a political tool than in the centuries before, although many earlier dynasties had also used various divinatory techniques, in particular before and during military campaigns. 1.8. Postface Introducing the reader to the history of learning and teaching the mathematical sciences, medicine, philosophy, and the so-called “occult sciences” through the relationships between Antiquity and Islamicate societies was a tool to cut a short path through almost one thousand years of intellectual development in the environment of schools and other learning and teaching institutions. It is an outsider’s view that highlights one important feature of this history, too often undervalued in Western societies. But it is certainly not an insider’s portrayal of this history, which would be better served by relating these disciplines and their studies to the coterminous development of the religious sciences. I did not choose this latter path because it would have required introducing many concepts unfamiliar to most of the readers of this book.

Chapter 2 TEACHERS AND STUDENTS AT COURTS AND IN PRIVATE HOMES (EIGHTH–TWELFTH ­CENTURIES)

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his chapter surveys learning and teaching activities between the mid-eighth and the second half of the twelfth centuries. The main institutional form of teaching was that of a private tutor for well-off families, beginning from the very top of society at the caliphal court and descending down to administrative officers and wealthy merchants. Caliphs, viziers, and other courtiers hired well-known scholars as the teachers of their sons. In the ninth and tenth centuries, such scholars were paid to teach Arabic and literature, religious knowledge, the mathematical sciences, and philosophy. It is unclear whether basic medical concepts or alchemical, physiognomic, and related types of knowledge also were part of this advanced education. There is no information about the kind of teaching that girls received in this period, although there are exceptional cases of women as a recipient of a textbook, a secretary at a dynastic court, or participants in instrument making. The textbook for Rayhana will be discussed in this chapter. The secretary Lubna in al-Andalus and the one daughter of an instrument maker in Aleppo – whose name is often mentioned in modern popular medias as Maryam, but cannot be found in medieval sources – will certainly have mastered elementary arithmetic, geometry, and writing. The daughter of the instrument maker learned from her father. It is also likely that Lubna learned her skills in her family, but no evidence has survived the centuries. An important stimulus for educational goals at courts, at least during the ninth and tenth centuries among the Abbasids and the new dynasty of Buyid amirs (ruled 945–1055), were the versions of stories told about Aristotle’s role as Alexander’s teacher and its interpretation as a fatherson-relationship. In Kraemer’s view, the Arabic translations of these mostly spurious texts added the concept of the “enlightened philosopher-king” to the ideal of the “just ruler” anchored in Sasanian traditions

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translated from Middle Persian into Arabic, and enriched by Qur’anic concepts (Kraemer 1992, 19–20). This material, combined with equally spurious (?) Sasanian stories about Buzurgmihr – a name connected with a member of the Sasanian aristocracy and vizier of two Sasanian rulers in the sixth century as well as a physician who lived in the same time and to whom the translation into Middle Persian of a Sanskrit set of fables teaching princes how to rule is ascribed – also gave the figure of the teacher a high social reputation among the philosophically interested scholars of the tenth century and their courtly patrons (ibid., 144). The ideological impact of such translations formed the basis for major parts of the educational program pursued among the elites in Iraq and Iran in this period and hence for the integration of philosophical subjects into the training of the sons of well-off families. The missionary work of Ismaʿili preachers also included debates about philosophical themes and encouraged wealthy administrators, like Ibn Sina’s father serving the Samanid dynasty (ruled 819–999) in Bukhara, to hire tutors for philosophy, the mathematical sciences, and medicine. Although there is no modern study of the socio-cultural forms of teaching the mathematical sciences and philosophy to boys and young men except for special cases like that of Ibn Sina, the level of specialized knowledge and newly produced results found in treatises and books written in this period leaves no doubt that systematic access to teaching and learning these disciplines must have been available to many of those who became their leading representatives. It is difficult to conceive that all of these highly gifted authors of the ninth, tenth, or eleventh centuries were autodidacts, although some of them indeed claimed to have acquired their knowledge and skills solely by reading texts. During the last half century, the focus of research on the history of the mathematical, medical, and philosophical disciplines has been above all on tracing progress, innovation, and invention. It unveiled many previously unknown features of the intellectual life in several Islamicate societies between the second half of the eighth and the later twelfth centuries. As a result, appreciation for the scholarly achievements during this period has increased tremendously. The drawback of this research orientation was the more or less complete neglect of issues like teaching or circulation of knowledge, scholarly networks, and cultural practices of knowledge such as patronage or library formation. Hence, there is no secondary literature

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available for most themes of this chapter, and primary sources need to be analyzed before they can be used as resources for this book. It is clear that I can compensate for this gap only with a small number of exemplary cases. 2.1. Limited Resources A comprehensive history of the learning and teaching of scientific disciplines in Islamicate societies should survey all communities that undertook educational activities. In addition to various Muslim communities, this applies above all to different Christian and Jewish denominations. The source material available for such a broad survey is unfortunately very limited. Moreover, the extant texts do not depict all communities in equal measure. Arabic sources are the main material accessible to me for the early Abbasid caliphate. In the late tenth and even more so during the eleventh centuries, the first New Persian texts were composed which have some bearing on this history. Syriac, Coptic, and Greek sources produced in Islamicate societies are less well explored, although Syriac studies have contributed new editions, translations, and interpretations of texts translated, copied, or newly composed between the seventh and tenth centuries and again in the thirteenth century (Watt 2010a, Watt 2010b, D.  King 2010, D.  King 2015, Aydin 2016). Despite the famous examples of the Syriac ­philosophers of the tenth century, their training in monasteries in Iraq, and their teaching of Christian and Muslim students in Baghdad, there is no clear picture available about where Syriac speakers in general studied ancient or contemporary scientific doctrines and texts until the twelfth century, the period to which this chapter is dedicated. The few monasteries of the sixth and seventh centuries that are famous for their teaching of ancient Greek scientific, medical, and philosophical texts like Qenneshre or the so-called school of Nisibis either do not survive into the Abbasid period (Nisibis) or are destroyed in the early ninth century (Qenneshre). Methodological shortcomings have led to false statements or purely speculative claims about the translation of mathematical texts into Syriac before their translation into Arabic. This applies in particular to evaluations of the translation of Euclid’s Elements. The mere existence of translated texts or reports about such translations in medieval Arabic sources contributes nothing to our knowledge of where for instance Syriac texts were taught or

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studied. How little certain our knowledge about ­educational practices in Syriac communities indeed is, is shown by Watt’s statement: “Education in rhetoric was, after all, the staple of late Greek education, and well educated Syriac speakers in the major bilingual cities such as Edessa who also knew and admired Greek must surely be presumed to have received instruction in the basic principles of classical rhetoric” (Watt 2009, 141–42, emphasis mine). Where Coptic and Greek speakers in Islamicate societies studied the mathematical sciences, medicine, natural philosophy, or the “occult sciences” is even less clear than in the case of the two major Syriac communities. Monasteries, private homes, and private schools are, as in Late Antiquity, the most likely locations of teaching and learning. Monasterial libraries like that of Qenneshre (until 815) on the Euphrates, Mar Mattai near Mosul, or Dayr Qunna near the new Abbasid capital of Baghdad kept philosophical and astronomical manuscripts. One of the most important Syriac philosophers of the tenth century, Abu Bishr Matta b. Yunus (died 940), learned his art in the monastery of Dayr Qunna. In Baghdad, he taught philosophy to Syriac students of different denominational affiliations as well as to at least one Muslim student who later outshone his Christian classmates – Abu Nasr al-Farabi. But the increasing turn to ascetic lifestyles in monasteries, a process that began long before the rise of Islamicate polities, seems to have left less and less space for secular teaching and learning in monasterial contexts. Physicians continued to teach their relatives, but also gave classes privately, whether in schools or hospitals. Others invited students to their homes. Over time, many of the Arabic historical or scientific sources focus increasingly on matters concerning exclusively Muslim communities. Thus, it is not surprising that most of our knowledge about teaching and learning in territories ruled by the Abbasid dynasty during the first centuries of its existence concern Muslims of different religious orientations who taught at the caliphal court in Baghdad or at the courts of other, newly emerging dynasties in Iran, Central Asia, Syria, or Egypt. We know that numerous prominent Muslim scholars of the mathematical sciences between the ninth and the twelfth centuries also worked as teachers. Several of them taught sons of ruling families. In particular the Buyid dynasty, which arose from the military struggles for power within the Abbasid caliphate and whose members were originally mercenaries from Daylam on the southern shores of the Caspian Sea, hired well-educated viziers and scholars

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to ­educate and train their male children. Less prominent scholars tried to gain their livelihood as itinerant teachers. Anecdotes preserved in historical chronicles speak of the insufficient knowledge of the sciences of some of those itinerant educational labourers. Despite this asymmetric preservation of information about the teaching and learning of the mathematical sciences, natural philosophy, medicine, or the “occult disciplines” across different faith groups, I will include information about non-Muslim teachers and students whenever possible and appropriate. In particular, the ninth and tenth centuries saw a continuous collaboration between members of different faith communities with regard to translating, studying, and teaching scientific texts, constructing scientific instruments, and undertaking astronomical and other observations and explorations. During the ninth century, teaching knowledge of Arabic grammar and good speech or public sharing of knowledge about how to read and understand the Qur’an or about Muhammad’s alleged or true sayings and deeds (hadith) became important for social reputation and success. In Baghdad, teaching professional knowledge of medicine equally served as a measure to boost a physician’s social standing and hence access to well-paying clients. It also may have contributed to the creation of a pool of adjuncts helping in the daily chores of medical labour. But what were the socio-cultural gains to be made by a teacher of philosophical knowledge, including the ­mathematical sciences, beyond the prospect of becoming the teacher of a member of a ruling family, be it the Abbasids in ninth-century Baghdad or the new dynasties of the tenth century in Iran and Central Asia? Was teaching such knowledge indeed becoming in these two centuries a stable part of being a scholar of the philosophical sciences writ large or did it remain the outcome of the personal decisions of individual scholarly personalities? These are questions I cannot answer due to a lack of research so far. 2.2. Stories about the Transfer of Philosophy and Medicine from Alexandria to Baghdad As early as the late eighth or early ninth centuries, Syriac Christian scholars began telling stories about the connection between their knowledge and scholarly works and the learning and teaching of philosophy and medicine in Alexandria in Late Antiquity. Over the centuries, Muslim and Jewish

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philosophers and physicians picked up these stories and presented them in greater elaboration. An important part of them talk about the transfer of the Alexandrinian traditions, texts, and teachers to Antioch in Syria and from there either straight to Baghdad (medicine) or via a stay at Harran (philosophy). Umayyad caliphs, Christian teachers, and Christian as well as Muslim students were the protagonists of that transfer. Modern historians have interpreted these transfer stories as well as other, earlier parts of the complex narrative about the learning and teaching of philosophy and ­medicine in Late Antiquity and the Umayyad and Abbasid caliphates in very contradictory and often unsatisfying manners (Meyerhof 1930, Strohmaier 1987, Gutas 1999, Watt 2009). The few known examples of Greco-Syriac learning and teaching under the Umayyad and the Abbasid dynasties indicate without doubt that these stories of a simple, straightforward transfer of philosophical and medical knowledge from Alexandria to Baghdad present too simplistic an image. Their layers about Augustus’s role in establishing or reviving philosophical classes in Alexandria, the transfer of philosophy to Rome, the awakening of the Seven Sleepers of Ephesos (a legendary group of seven young men who hid in a cave near Ephesos to escape persecution) during the reign of Theodosius II (ruled 416–50), and other such features all point to the merging of different kinds of stories produced in various periods of Antiquity and enriched by Christian and Muslim narrators after the middle of the seventh century. Arabic versions of Greek philosophical, medical, and mathematical texts and the specific literary forms of a number of them support the nucleus of these stories, namely their origin as school texts in Alexandria. Examples of such school texts are paraphrases of medical works by Galen and Hippocrates, Porphyry’s Introduction to Aristotelian logic, Euclid’s Elements, Nicomachus of Gerasa’s Introduction to Arithmetic, Ptolemy’s Almagest, and the mathematical texts by Autolycus of Pitane (flourished c. 360-c. 290 bce), Hypsicles of Alexandria (c. 190c. 120 bce), Theodosius of Bithynia (flourished c. 160-c. 100 bce), and Theon of Alexandria (flourished c. 335-c. 405). 2.3. Teaching the Mathematical Sciences I am not aware of a single work of the mathematical sciences newly written in Arabic or Persian, designated as a textbook, and composed in the period on which this chapter focuses. The standard textbooks of geometry

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and astronomy were Arabic translations of ancient Greek texts: Euclid’s Elements, the texts of the so-called Middle Books, Ptolemy’s Almagest. The later Buyid amir and from 978 to 983 head of the Buyid family ʿAdud alDawla (ruled 949–83), for instance, is reported to have distributed generous alms after he had finished his study of Euclid’s Elements. One of his teachers, who perhaps also read the Elements with the young prince, was ʿAbd al-Rahman al-Sufi (903–86). Other scholars who taught princes were the philosopher Abu Yusuf Yaʿqub b.  Ishaq al-Kindi (died after 870) and the astrologer Abu Jaʿfar al-Khazin (died between 961–71). Al-Kindi was the teacher of philosophy, including the mathematical sciences, of Ahmad (died in 866), son of the Abbasid Caliph al-Muʿtasim bi-Llah (ruled 833–42) and later Caliph al-Mustaʿin bi-Llah (ruled 862– 66). Abu Jaʿfar al-Khazin came as a mediator or envoy in the service of the Samanid amirs from Samarkand to Rayy, negotiating a truce after a Samanid vassal had failed to conquer the Buyid city (Kraemer 1986, 29). The head of the Buyid family, Rukn al-Dawla (ruled 935–76), invited al-Khazin to stay in his employ, teaching his children, setting precedence for his vizier Ibn al-ʿAmid (vizier 940–70), and working as an astrologer at an observatory built by the latter (Kraemer 1992, 252). Rukn al-Dawla and his vizier also hired teachers of logic, administration, statemanship, grammar, and literature (ibid., 37, 52, 242, 252, 275–76 and passim). A short note found in an early modern collection of Arabic texts of the mathematical sciences as well as in a twelfth-century Latin manuscript transmits a list of the Middle Books ascribed to Ishaq b. Hunayn (died in 911). This provides a small window into the form of this collection in the second half of the ninth century as known in Baghdad. The Latin manuscript adds this information to a list of the Arabic works translated by the Italian cleric Gerard of Cremona (died in 1181) in the forty years of his stay at Toledo in cooperation with a Mozarab adjunct and possibly other people, and Gerard’s scholarly biography (Burnett 2001, 274–75). Order of what is to be read after Euclid, found in a manuscript in the handwriting of Ishaq b. Hunayn: Book of Optics by Euclid, one chapter; The Spherics by Theodosius, three chapters; The Moving Sphere by Autolycus, one chapter; The Phenomena by Euclid, one chapter; The Inhabited (World) [On Habitations] by Theodosius, one chapter; Risings and Settings

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TEACHING AND LEARNING THE SCIENCES by Autolycus, two chapters; Nights and Days by Theodosius, two chapters; Ascensions by Inqila’us [Hypsicles], one chapter; Distances of the Planets and Their Sizes by Aristarchus, one chapter. These are thirteen chapters (ms. Beirut, St Joseph University, 223, microfilm, picture 64).

In later centuries, the collection grew. Further translations of ancient mathematical treatises were added as well as works by scholars of the ninth century (Banu Musa [ninth century]; Thabit b.  Qurra [died in 901]), the thirteenth century (Nasir al-Din al-Tusi), and occasionally also of other centuries (Thābit ibn Qurra 2008, 22–29, in particular 28–29). In a sense, the Middle Books fused the ancient Little Astronomer with Pappus’s (second half of the fourth century) idea of a teaching canon of geometrical works (Mansfeld 1998). Thus, they served both as a preparatory course for Ptolemy’s Almagest and as a survey course of higher geometry. The most difficult books such as Apollonius’s (flourished c. 262-c. 190 bce) Conics, or more specialized treatises, as for instance on the parallel postulate or the trisection of an angle, had to be studied after this canonical collection. In the middle of the thirteenth century, Nasir al-Din al-Tusi edited this collection anew. A copy from the second half of that century, preserved in the National Library of Tabriz in Iran, shows some of the modifications that al-Tusi introduced into the Middle Books. In addition to the titles listed by Ishaq b. Hunayn, this copy contains five further translations of ancient Greek texts, one Arabic treatise, and one Arabic translation of a Persian treatise by Nasir al-Din al-Tusi: Euclid (Data), Archimedes (Lemmas; On Sphere and Cylinder; Measurement of the Circle), Menelaus (On Spherical Figures), Thabit b. Qurra (Data), and Nasir al-Din al-Tusi (On the Sector Figure) (Tusi 2005). Al-Tusi was neither the first nor the last who altered the content of this collection. The Middle Books were a reflection of the vivacity of the learning and teaching of the mathematical sciences to students on their way to higher astronomy. An exploration of texts written for people named as students or about people described as teachers in different sources shows that in addition to such a more systematic reading of ancient and recent texts, the mathematical sciences were also taught through discussing and solving problems and learning methods in private group meetings. Examples of such meetings and the discussion of mostly geometrical problems are extant in short treatises by

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Apollonius, Conics, Beginning of Book VII, ms. Oxford, Bodleian Library, Marsh 667, f. 162b, copied in 1070.

scholars of the tenth century. Muhammad b. Ahmad al-Shanni (flourished in the last third of the tenth century) was one of them. He reports about one of his teachers who had been challenged in one such meeting by a participant concerning the determination of the area of a triangle when the length of the three sides is known. We may regard this as a very simple task, but the dispute arose about how to prove the rule. Al-Shanni wished to defend his teacher and to stop the challenger. He thus offered what he knew about the problem. The outcome of this dispute was the short treatise by al-Shanni extant in a microfilm of a sixteenth-century collection of mathematical and mechanical treatises, whose original was lost in the Lebanese Civil War (ms. Beirut, St Joseph University, 223, unpaginated; microfilm, pictures 9–10).

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All in all, despite our lack of knowledge about many locations and times, we can conclude that in general plane and solid geometry was learned and taught with Euclid’s Elements, spherical geometry with a number of texts collected in the Middle Books, and conic sections with Apollonius’s Conics or commentaries on this book by scholars from Islamicate societies. Specific geometrical problems and methods like analysis and synthesis were studied with specialized literature. How many students took such classes and how many teachers offered them remains, of course, unknown. 2.4. Teachers and Students In a number of cases, medieval sources inform us about teachers and their students in cities of Iraq, Iran, Egypt, and Central Asia. Examples are al-Kindi, Thabit b. Qurra and his offpring, Abu Zayd al-Balkhi (died in 932), Ibn Sina, Ibn al-Haytham, Abu Jaʿfar al-Khazin, Abu l-Wafa’ (948– 98), al-Mubashshir b. Fatik (eleventh century), and others. A ­particular case is the relationship between Abu Nasr Mansur b.  ʿAli b.  al-ʿIraq (lived c. 960–1036) and Abu l-Rayhan al-Biruni. Not all of them can be presented here. The chosen examples are al-Kindi, Thabit b. Qurra and his grandson Ibrahim b. Sinan, Ibn al-ʿIraq, and al-Biruni. 2.4.1. Abu Yusuf Yaʿqub b. Ishaq al-Kindi Al-Kindi came from a noble family of the Arab tribe of Kinda, which had been very important in southern Arabia and Iraq during the fifth and sixth centuries. Al-Kindi’s grandfather and father were high-­ ranking officials in the service of the Abbasid dynasty. His grandfather is ­believed to have settled in the port town of Basra, where Ya‘qub was born. He became the first famous representative of philosophical knowledge in the ancient sense among the people who shaped intellectual and cultural life in Baghdad during the ninth century. He was one of the first Arabs whose name lived on over the centuries for his active involvement as a scholar and a patron in what is called the translation movement. He paid bi- and tri-lingual Syriac and perhaps also Greek Christians who translated philosophical, medical, mathematical, and other ancient texts for him.

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According to Ibn abi Usaybiʿa’s (1203–1270) history of physicians, al-Kindi received his education (adab) in the Abbasid capital Baghdad (Ibn Abi Usaybiʿa 1965, 207). We do not learn from him, however, with whom al-Kindi studied which branches of knowledge. But it is clear that over time, al-Kindi became proficient in very many disciplines, among them philosophy, medicine, geometry, astronomy, theoretical music, number theory, optics, mechanics, astrology, burning mirrors, prognostication from boiled shoulder blades of sheep, and other suitable subjects of magic and divination. The description of al-Kindi’s works and skills by Ibn al-Nadim, Ibn Abi Usaybiʿa, and other historical writers suggest that al-Kindi’s education followed patterns of Neoplatonic philosophical training. The close connection between the translation of Greek texts that al-Kindi paid Christian scholars to produce and his own writings makes it clear that education, research, and appropriation of ancient knowledge were closely intertwined in al-Kindi’s learning and writing. In addition to these well-established disciplines, al-Kindi also learned and then wrote about how to produce perfumes, swords, glass, dyes, colours, how to remove stains, or how to distinguish true from fake gemstones. Other areas of his learning included knowledge about birds, bees, crossbreeding of doves, earthquakes, tides, and the causes of rain, snow, lightening, and thunder. These latter themes show ties to Aristotelian natural philosophy, while the treatises on perfumes, swords, and related matters seem to reflect al-Kindi’s close connection to the Abbasid court and the practical interests of his caliphal patrons (Adamson 2007, 8). 2.4.1.1. al-Kindi’s students

The preserved names of al-Kindi’s students as well as remunerated collaborators point to two main groups – Syriac-speaking Christians and Iranian language-speakers from northeastern Iran and Balkh, today in northern Afghanistan. The three students of al-Kindi best known for their own scholarly careers were Abu Zayd al-Balkhi, Ahmad b. al-Tayyib al-Sarakhsi (lived c.  833 or 837–99 when he was executed), and Abu Maʿshar al-Balkhi (died in 886). Al-Kindi’s fourth prominent pupil was the Abbasid prince Ahmad mentioned above. Several of the very brief epistles written by al-Kindi were addressed to this prince and can possibly be regarded as teaching material.

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A few more students are mentioned in al-Kindi’s epistle on rain and moisture and in Qalonymos ben Qalonymos’s (1268-after 1328) Hebrew translation of an Arabic paraphrase of Nicomachus of Gerasa’s (second century) Introduction to Arithmetic. The short meteorological treatise is dedicated to a student called Habib. The proposed identification of this student as Habib b. Bahriz (late eighth-early ninth centuries), the metropolitan of the Church of the East in Harran, Mosul, and Hazza, is in all likelihood wrong (Steinschneider 1893, 518, 564; Freudenthal-Lévy, 2004, 483). The compiler of the paraphrase of Nicomachus’s Introduction to Arithmetic also was al-Kindi’s student as the many quotes from his class in this text show (ibid., 481–83, 514–17). 2.4.1.2. al-Kindi’s Classroom Work and “Teaching Material”

Arabic was the exclusive language of al-Kindi’s teaching as it was the only language of his treatises. Thematically, he focused on the philosophical and mathematical disciplines. He accepted Galen’s view about the importance of the mathematical sciences for a future philosopher or a scientifically educated physician. His On the Subject that Philosophy Cannot be Acquired Except through the Knowledge of the Mathematical (Sciences) introduces the reader to this approach to learning (Ibn al-Nadim n.d., 318–19; compare Ibn al-Nadim 1970, vol. 2, 616). In addition to the number of theoretical works and the treatise on weather forecasting for Habib mentioned in the previous section, we find many other shorter or longer works among al-Kindi’s texts that were written for students, could be used as introductory material for autodidactic studies, or are marked as topics of his classes. Examples are letters to prince Ahmad, a further epistle on weather forecasting, letters answering questions about natural philosophy, the epistle mentioned above that one needs to know mathematics before studying philosophy, texts about the arrangement of Aristotle’s books, Aristotle’s intention in the Categories, “what they aim at, and their subject matter”, and The Encouragement for Learning Philosophy, as well as a number of other texts on The Essence of Science and Its Division, The Divisions of Human Learning, Scientific Evaluation, Questions Asked about the Benefit of Mathematics, or several introductory texts on logic (ibid., vol. 2, 616). The list of such possible teaching texts is surprisingly long. My impression that they represent al-Kindi’s work as a teacher is based on their formal and substantial

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s­ imilarities with the manner of teaching that Mansfeld, Watt, and others describe for late antique schools among Greek and Syriac communities (Mansfeld 1994, 1998; Watt 2009, 2010a, 2010b). If this can be corroborated in future research then al-Kindi was indeed very intensely involved in teaching. In the text called That the Elements and the Outermost Body are Spherical in Form written for the Abbasid prince, al-Kindi is outspoken about his didactic goal: I have sketched of this (topic) as much as I thought congenial to the power of your virtuous self and the skill of your perfect understanding (Rescher 1968, 9).

The content focuses on the thesis that the bodies of the fixed stars and of the two elements around the center of the universe, namely Earth and Water, are spherical and concentrically placed. Al-Kindi bases his arguments on Aristotle’s Physics and Ptolemy’s Almagest. Going beyond the two Greek scholars, he casts his arguments prevalently in geometrical form, working with diagrams and formal geometrical proofs. In order to understand the text’s arguments, the princely student had already to be familiar with a series of philosophical ideas, mathematical concepts, and geometrical methods. The philosophical ideas include, for instance, the claim that the universe is constrained by limits, that the outermost body revolves around its center, and that beyond this outermost body there is neither void nor plenum. He also had to have learned beforehand Aristotle’s theory of the natural place, movement, and rest. With regard to geometry, Ahmad had to be familiar with Books I and III of Euclid’s Elements (Rescher 1968,  10). As an adult, Ahmad commanded as a patron the translation of ancient mathematical texts into Arabic, among them texts of the Middle Books and Heron’s Mechanics. Al-Kindi’s letter to Habib about metereological phenomena and the revision of the summary of al-Kindi’s teaching about Nicomachus’s Introduction to Arithmetic offer further clues in addition to what we have seen in the letter to Ahmad. In the introduction, al-Kindi tells Habib: I have noticed your request to compose a short treatise for you, in which I would explain to you the principles of meteorology, phenomena of the atmosphere, gales, and the causes of moisture and dryness, insofar as the philosophers had clear, settled opinions

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Al-Kindi follows this explanation (whether rhetorical or real) with an immediate reply about the shortcomings of the astrologers’ ­methodology. Then he explains the structure of his text: After this introduction I have divided my treatise for you into five chapters. In the first chapter I discuss all the phenomena of the planets and their causes. In the second chapter I discuss the differences of the phenomena of the planets in the quadrants of the orb and their causes. In the third chapter I discuss the moist and dry quadrants of the year and how knowledge of this can be acquired. In the fourth chapter I discuss the general rules on moisture and rain in every clime and why winds can vary on one and the same day. In the fifth chapter I discuss the way to find out the times of moisture and rain in every place on earth and their cause (ibid., 162).

Al-Kindi’s introduction to this letter to Habib contains some of the standard preliminary components characteristic of ancient Greek philosophical, mathematical, and medical books, in particular the just quoted survey of the epistle’s structure, the brief outline of the thematic scope of the letter, and the critique of the astrologers. Other introductory elements characteristic of ancient Greek scientific texts are absent. As far as I can judge ninth-century Arabic scientific production, the complete ten-point set of ancient Greek introductory rhetoric did not become a standard convention for scholars in Islamicate societies (Mansfeld 1994). Recently, searching for images of star constellations, I looked up The Great Introduction of al-Kindi’s student Abu Maʿshar. There he criticizes his contemporaries for ignoring this ancient Greek i­ ntroductory

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set-up, although he only speaks of seven instead of ten points: the purpose, the usefulness, the title, the author’s name, when to read the text, i.e. before and after which other text, its position in the entire textual or doctrinal corpus, and finally the division of the corpus in treatises and books (ms. Oxford, Bodleian Library, Or. 565, f. 2a). This critique suggests that Abu Maʿshar too was seriously interested and engaged in matters of teaching. The didactic character of al-Kindi’s letter to Habib is highlighted by the text’s overwhelmingly dialogical mode (Bos-Burnett 2000, 164, 184, 188–92, 197–200). Although such a dialogical form is not unusual, in particular in ancient philosophical texts, it is a rare occurrence in ninth-century scientific texts. Moreover, al-Kindi’s style seems to be a genuine conversation, not the standard formulas used in Euclid’s Elements, for instance. It thus seems to support the case for a teaching text. Al-Kindi writes, for instance, in chapter 2: “The philosophers agree that the planets are as I have described to you, and that they are not fiery and that their light is not fiery” (ibid., 164). A further didactic feature is the use of examples in order to simplify matters for the student (ibid., 174). The abovementioned text on Nicomachus’s book on number theory has been interpreted as the product of one of al-Kindi’s students based on notes made in the classroom (Freudenthal-Lévy 2004, 481–82, 485–86; Freudenthal-Zonta 2007, 68). Its addressee might even have been a classmate of the text’s author (Freudenthal-Lévy 2004, 481). This interpretation challenges our standard view of the teaching mode in Islamicate societies, according to which the teacher reads out loud a finished text – either written by himself or by some previous scholar – in class, commenting occasionally (or more often) on difficult, obscure, or otherwise relevant points. Students were allowed to ask questions for clarification. I do not know, however, a case of students in this period ever producing their own text based on such a classroom procedure. Thus, if the proposed text is indeed not merely a copy of al-Kindi’s teaching procedure introduced by a specifically requested explanation of Nicomachus’s philosophical introduction, it is an exceptional document testifying to a student’s superior scholarly qualification acquired from al-Kindi’s teaching as well as his breach with the social norms of ­teaching in his time.

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A teacher in a mixed class exercising to read words and short phrases written on wooden slates. Fritware dish. Kashan, late 12th century. The David Collection, Copenhagen, inventory number 50/1966, Pernille Klemp.

The texts discussed so far are not the only treatises that might have had a teaching and learning function. Four of the other extant epistles and one long work on optics present themselves as specifically written for either an unnamed brother, i.e., a friend or an acquaintance, or for two named people, Muhammad b. Jahm [al-Barmaki] (died in the early ninth  century) and Ahmad b.  Muhammad al-Khurasani. The subject matter of the four short epistles is taken from philosophy. The letter addressed to Ibn Jahm explains God’s unity and the finiteness of the body of the world. The one addressed to Ahmad b. Muhammad al-Khurasani treats the finiteness of the body of the world. The two letters to unnamed addressees speak about the infinite and the finite and the topic of agency and agents, respectively.

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Al-Kindi’s edition of Euclid’s Optics differs in many respects from the four short epistles. The differences include length and depth, disciplinary content, treatment of ancient authorities, style of argumentation and proof, and rhetorical choices. The five texts share nonetheless a few properties. Al-Kindi’s Optics addresses a friend and ends with the brief assurance that what had been written “suffices (as a reply) to your request” (Rashed-Jolivet 1997, vol. 1, 254–55. 334–35). Thus, this work on optics belongs to Bos and Burnett’s category of a technical manual or textbook (Bos-Burnett 2001, 35). A reader of this manual must have already been well educated in the theoretical mathematical sciences. If not, he would not have understood al-Kindi’s deductive-axiomatic style of presentation. The few examples that I could introduce here briefly suggest that alKindi taught classes for beginners, middle-level students, and perhaps even for people who had already progressed quite far in the mathematical sciences and natural philosophy. We find the same breadth of teaching in the case of the Sabian scholar Thabit b. Qurra. 2.4.2. Thabit b. Qurra Thabit b.  Qurra came from a family of star worshippers in Harran, ­northern Mesopotamia, who are called Sabians in Arabic historical sources. He spoke Syriac, Greek, and Arabic. At some point, probably before 866, he moved to Baghdad after he had met Muhammad b. Musa (died in 873), allegedly during the latter’s travel to Byzantium for manuscripts. In his youth, Thabit is said to have worked as a money-lender. Thus, he will have received his professional education from a craftsman, perhaps a family member. He certainly could count and calculate, thus had ­arithmetical skills. He also could run a balance and identify weights. This means that he also knew how to read and probably write in at least one of the languages he spoke. Furthermore, his religion may have demanded some knowledge of the heavens. Ibn al-Nadim reports that Muhammad b.  Musa was impressed by Thabit’s eloquence. Hence, he invited him into his household, trained him in the mathematical sciences, and paid him for translating scientific texts from Greek into Arabic (Ibn al-Nadim 1970, vol. 2, 647). We possess no information about the details of either of the two stages in Thabit’s education, but we are on safer grounds with Thabit’s activities as a teacher.

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TEACHING AND LEARNING THE SCIENCES 2.4.2.1. Thabit’s Bibliographies

The Ayyubid vizier Ibn al-Qifti (1172–1248) preserved a bibliography of Thabit compiled by al-Muhassin (died in 1010), Thabit’s great-greatgrandson, in about 970. Al-Muhassin built on information already collected by Thabit’s son Sinan and his grandson Thabit b. Sinan (died in 973/4) (Ibn al-Qifṭī 1903, 120–22; Gutas n.d., 4). For almost a century, Thabit’s family cherished and preserved this scholarly heritage. Ibrahim b.  Hilal b.  Ibrahim (lived c.  925/6–994), the father of al-Muhassin, copied several of Thabit’s texts, among them at least one that Thabit may have written for students. It clarifies a proof or construction by Ptolemy (ms. Istanbul, Süleymaniye, Fazil Ahmed Pasha, 1435). In 980, Ibrahim copied the treatise on the construction of the fourteen-faced polyhedron enclosed in a known sphere (Rashed 2009, 330–31). In a similar manner, a family preserved the library at their mosque in Chennai in the nineteenth and twentieth centuries, protecting the fragile books against temperatures, humidity, insects, and worms. Al-Muhassin mentions one book by Thabit for instructing his son Sinan in medicine and philosophy (Gutas n.d., 9, no. 17). He also lists answers to questions and problems or replies to texts by other scholars. The second class certainly was part of scholarly debates. The questions and problems belong to the type of learning-and-teaching literature, which we already met in the previous section on al-Kindi. In Thabit’s case, their recipients were Caliph al-Mu‘tadid, the courtier ‘Ali b. Yahya alMunajjim (flourished between 847 and 861), the court astrologer Sanad b. ‘Ali (flourished in the second and third quarter of the ninth c­ entury), and religious scholars like Abu Sahl al-Nawbakhti (died in 923) (ibid., 10, 12–14). Although formally none of them was Thabit’s student, they all asked for information and instruction. 2.4.2.2. Thabit’s Students

Al-Muhassin also reports that Thabit had composed “a number of abridgements on astrology and geometry, which I saw in his own handwriting, and whose translation is also in his hand” (ibid., 12, 45–46). The recipients of these treatises were young boys (ibid., 12, 46). Thabit apparently wrote those abridgements in Syriac, translating them afterwards into Arabic. Thus, it seems that Thabit taught Syriac as well as Arabic students. One of his pupils was Nu‘aym, a son of Muhammad b. Musa (ninth/tenth

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century). Nu‘aym’s collection of geometrical problems reflects Thabit’s teaching of higher-level courses (Hogendijk 2003, 60). Ibn al-Nadim’s Fihrist shows that Thabit wrote epistles like al-Kindi. This coincidence suggests that teaching did not merely take place in a classroom as a reading, writing, and commenting exercise. An important element of teaching obviously was writing short texts addressing specific questions. This format became a standard during the ninth and tenth centuries. One of the question-and-answer epistles listed by Ibn al-Nadim as a work by Thabit was actually written by his student ‘Isa, at a time when the latter was already married and father of a son named Musa. ‘Isa describes this exchange with his teacher as a long conversation in which he challenges Thabit several times until he even enters into a controversy with him (M. Rashed 2009, 642–43). Thus, it is of a different kind than the text by one of al-Kindi’s students briefly discussed in the previous section. 2.4.2.3. Textbooks, Manuals, and Other Teaching Material

On 3 August 1228, a certain Muhammad b.  Abi Bakr b.  Muhammad copied the last lines of Thabit b.  Qurra’s work on compound ratios (ms. Istanbul, Topkapı Sarayı Kütüphanesi, Ahmet III, 3464, f.  188a). Compound ratios are – to our way of thinking – products of ratios. A product of two ratios is a double ratio, one of three a triple ratio, and so forth. Historians of mathematics consider the Book on Compound Ratios a research text. Muhammad b. Abi Bakr (or one of his predessors), however, saw it as text for students. He included this information in its title: Book of Abu l-Hasan Thabit b. Qurra al-Harrani to the Students on the Compound Ratios (ibid., f. 171b). Muhammad also copied other texts from the Middle Books, which I will discuss again in Chapter Eight. It is easy to see why some reader thought that this book addresses students. It is one of Thabit’s few texts that is divided into chapters with headers. Research texts of this period usually do not possess such a structure. In the first chapter, Thabit explains with Euclid’s Elements what a ratio is: “The ratio … is a certain (relationship) of two homogenuous quantities, of the one to the other, according to the measure” (Crozet 2009, 428–29). Then he comments on each single term: ratio, a certain (relationship), quantity, homogenuous, according to the measure. Finally, he rephrases the definition explaining that it applies only to geometrical magnitudes, but not to numbers, since the term

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quantity does not include the latter. Afterwards, he surveys the definitions of ratio and proportion from Book V of the Elements (ibid., 430–33). Chapter Two systematically explains the determination of the quantities in double and triple ratios according to their possible cases. Thabit enters the combinations into tables, thus allowing the reader to keep track (ibid., 432–83). The final chapter teaches how to solve problems with compound ratios (ibid., 482–535). It begins with an explicit reference to students. Thabit wishes to simplify matters for them and to provide examples (ibid., 482–83). Throughout the chapter, Thabit again organizes the exercises in tables and diagrams. Hence, Muhammad b. Abi Bakr (or his predecessor) was right when he judged Thabit’s book on compound ratios as a “textbook”, the arena of explaining how to do things and illustrating the explanations by concrete examples and visualizations. Thabit’s list of works shares further, more specific elements with that of al-Kindi, but also shows significant differences. Like al-Kindi, Thabit produced introductions to and paraphrases of logic, Euclid’s Elements, number theory, theoretical music, and medicine (Gutas n.d., 8–14). Like al-Kindi, Thabit wrote short letters to his contemporaries. But Thabit’s work list contains a further type of texts called compendium or synopsis that are not known for al-Kindi. Nine of Thabit’s compendia summarize Galenic works, including at least one commentary by Galen on a book by Hippocrates. Other compendia introduce Aristotle’s First Analytics and Ptolemy’s Tetrabiblos (ibid., 10–11,  14,  45,  47–49). Undoubtedly, this class of texts imitates late antique teaching material. Some are even translations of Galen’s own synopses. We do not know, however, whether Thabit or one of his students translated them. Given Thabit’s work profile, it is also possible that he revised translations made by someone else. Titles of other compendia on Thabit’s list of works belong to the question-and-answer genre (ibid., 47–48, 58–59). Thabit’s treatises written to simplify the doctrines or methods of other authors are a further difference to al-Kindi’s oeuvre. According to al-Muhassin their purpose was to facilitate understanding. Gutas calls them “study aids”. An example of this type are (different?) treatises simplifying Ptolemy’s Almagest (ibid., 9,  34–35). I  prefer to call them “aide-memoires”, since these texts only present definitions and rules. In contrast, the textbook on compound ratios represents a “study aid”.

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Thabit’s replies to questions and requests by contemporaries cover music, logic, metaphysics, astrology, astronomy, natural philosophy, and religious issues (ibid., 10, 41, 56–57). Further texts are gifts for high-ranking courtiers who did not ask for them, or at least their request is not made explicit. The vizier Isma‘il b. Bulbul (died in 892) received a text on geometry. The vizier ‘Ubayd Allah (died in 901) was the recipient of an explanation of the astronomical handbook produced for Caliph alMa’mun. ‘Ubayd Allah’s son and successor al-Qasim (died in 904) was the addressee of two works, a compendium on medicine and an epitome of Aristotle’s Metaphysics (ibid., 29, 41, 48–49). Works with the word problems in their title, such as On Geometrical Problems, may have been inspired by ancient Greek problem-texts (Endreß 1987, 464; Filius 2006, 33–54). The relationship of these often short pieces to research or teaching is unclear, because they have been neglected so far. 2.4.2.4. Two Textual Examples

Two texts linked to Thabit b.  Qurra contain terms characteristic of learning and teaching situations. The first studies the unequal-armed balance, the steelyard. The second text contains definitions from Book I of Euclid’s Elements. The Book on the Steelyard describes classroom activities in two different terms. Two copies say that it was dictated by Thabit ( Jaouiche 1976, 168–69). The third copy states twice that it is the result of listening to Thabit speaking about the steelyard (ms. Florence, Biblioteca Laurenziana, Or. 118, ff. 71a,1 and 72b,19). As far as we know, both terms, dictation and listening to someone, are used in the ninth century to describe teaching and learning only in other than the scientific disciplines (Gruendler 2016). In later centuries, these terms are regularly used in biographical dictionaries, including the mathematical sciences. The text on Euclid’s definitions opens with the following statement: “ Yusuf, the calculator, informed me that Abu Ya‘qub Ishaq b.  said: I  dictated to Thabit b.  Qurra the definitions of the First Chapter of Euclid’s Book called The Elements” (ms. Tehran, Malik Museum, 3586, unpaginated [f. 243b]). Abu Ya‘qub Ishaq b. Hunayn, the best known son of the most highly appreciated translator and physician in ninth-century Baghdad, Hunayn b. Ishaq (died in 873), was a colleague and friend of Thabit b. Qurra. Like his father, Ishaq was a p­ hysician and a

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t­ ranslator. He translated numerous mathematical, astronomical, and natural philosophical texts from Greek or Syriac into Arabic, among them Euclid’s Elements (Rosenthal 1954, 61, 72). But why did he dictate the definitions of Book I to Thabit? Does this claim mean that the two friends worked together when Ishaq translated the Greek text? According to Arabic historical chronicles and biographies, Thabit was the better mathematician and the friend who checked Ishaq’s translations of scientific texts. Hence, “to dictate” here does not seem to say that Ishaq taught Thabit geometry. The Book on the Steelyard unites fragments of ancient Greek origin. They present the balance as exemplifying circular movement, a lever, a straight line, and finally as a material beam. The order of the text is somewhat unsystematic for a theoretical mathematical work. A ­general statement of the type of a postulate opens the treatise; others pop up somewhere in its middle part. Comments interrupt the flow of the theorems. Methodologically, the text also possesses interesting features. Several proofs combine geometrical with natural philosophical arguments. Some proofs are easy to grasp, but others presuppose a higher level of scientific education. Thabit was not content with this situation. His unease is reflected by medieval and modern scholars. Unknown readers added comments and further theorems to the text. Thabit overhauled this first version substantially. In the introduction to the new text, he talks to an unnamed partner. The two debated the fragments, their further distortions by translators and copyists, and their theoretical inconsistencies for some time. Aiming to clarify matters, Thabit’s acquaintance wrote a faulty analysis of the balance. Hence, Thabit decided to revise his Book on the Steelyard. This revision is only extant in the Latin translation Liber ­karastonis by Gerard of Cremona. From it we learn important information about what Thabit considered superfluous, deficient, or too difficult and how he tried to overcome such shortcomings. He deleted a theorem and two general statements, transformed a comment into a fully developed theorem, and added a further theorem to correct a proof. He tackled difficulties with the help of numerical examples, more detailed explanations, and the omission of all natural philosophical arguments. The difficult indirect proof for the case of an infinite number of weights suspended from a balance was also deleted. Instead, the Latin translation offers a circular, hence faulty, but elegant direct proof. Whether this was Thabit’s decision and work is contested. In a postface, Thabit explains in a more detailed

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manner than previously how to determine the counterweight needed to keep a material beam in equilibrium (Moody-Clagett 1952). These modifications show that here Thabit deliberately crossed the boundaries between teaching activities and research. 2.4.3. Ibrahim b. Sinan b. Thabit b. Qurra Ibrahim b. Sinan (908–46) was a grandson of Thabit b. Qurra and a very gifted mathematician. He died as a young man at the age of thirty-eight. He wrote a scientific “autobiography” some time after his twenty-fifth birthday. There, he focuses on his work, unfortunately for us ignoring his upbringing and education. But because his father Sinan b. Thabit was the personal physician of Caliph al-Muqtadir bi-Llah (ruled 908–32), he was probably trained by several tutors, perhaps also by his father, who in addition to his medical profession was well versed in the mathematical sciences and a good historian. Ibrahim reports in what has been called his autobiography, but rather is a report about his scientific production, that he began writing mathematical texts at the age of fifteen. A major motivation for his writing was to contribute to maintaining and increasing the scholarly reputation of his family. This he succeeded to do already in the eyes of his contemporaries, for Ibn al-Nadim wrote that “[d]uring his time no one appeared who was more brilliant than he was” (Ibn al-Nadim 1970, vol. 2, 649). Another of his goals was to correct mistakes and shortcomings in the study of geometry and the usage of its methods. That is why he composed three works on the ancient methods of analysis and synthesis, which were much practiced by mathematicians of the tenth century, but in a form considered by Ibrahim to be abbreviated and insufficient. The intended recipients of these three treatises on Tangent Circles, Analysis and Synthesis, and Selected Problems were students who should learn the execution of these methods according to both the contemporary abbreviated style and Apollonius’s full form as described in his Cutting Lines in Ratios (Berggren-Van Brummelen 2000). These texts, then, are higher-level teaching texts. Another important piece of information in Ibrahim’s account concerns his differentiation between writing for his peers and writing for artisans. Ibrahim reports that he wrote first a treatise on the ­armillary sphere for his colleagues and later, “in other terms”, an explanation of this instrument for the craftsman who produced it for him (Berggren

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2008). Instructing craftsmen and secretaries about rules, constructions, tricks, and proofs was an important form of knowledge transfer between the scholars of the mathematical sciences and practitioners in the tenth and the late eleventh/early twelfth centuries. In some cases, like that of Ibrahim or his younger contemporary Abu l-Wafa’, the transfer was from the scholars to the artisans. In other cases, artisans instructed scholars in the craft of instrument making, as may have been the case of ‘Abd al-Rahman al-Khazini (died after 1125) and his construction of a celestial globe. This globe rotated over the course of a day due to a weight attached to it and moved through the leaking of a sand box (Lorch 1995, IX). Ibrahim’s father may not have taught his son, but he certainly gave classes. Ya‘qub al-Kaskari (flourished in the first half of the tenth ­century), a physician at numerous hospitals in Baghdad, reports that he studied logic with Sinan b.  Thabit (Pormann 2010a, 351). This suggests that practicing physicians like Sinan and al-Kaskari both taught and studied logic as part of their medical education, as well as those parts of natural philosophy related to medical theory and – as documented in other sources – some of the mathematical sciences (arithmetic, astronomy/ astrology, possibly geometry as needed for the former). 2.4.4. Abu Nasr Mansur b. ‘Ali b. al-‘Iraq and Abu l-Rayhan al-Biruni Our knowledge about the ancestors of Abu Nasr Mansur b.  al-'Iraq (hereafter: Ibn al-‘Iraq) comes from two different sources: al-Biruni’s works, and archaeological excavations with their recovered objects and sites. Most of their details do not agree. It is unknown which problem causes the greater inaccuracies: al-Biruni’s lack of ancient sources and his prejudices against the Arab invaders of the eighth and ninth centuries or the loss of most written sources of pre-Islamic Khwarazm (Bosworth 2011, vol. 1, 743–45). Hence, for our purposes we simply register that Ibn al-‘Iraq probably was a prince of the ruling dynasty of the Khwarazmshahs (Afrighid family) and that al-Biruni is believed to have been born in a suburb of Kath, the ancient capital of this state. Ibn al-‘Iraq’s family was overthrown in 995 by the neighbouring Ma’munid amir of Gurganj, possibly a ripple effect of the westward drive of nomadic tribes in Central Asia. For Biruni, this began a long period of travel. He apparently went first to Buyid Rayy (Bulgakov 1966, 13). In 997, he was back in Kath observing a lunar eclipse in cooperation with

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Abu l-Wafa’ in Baghdad. One year later, he left again, moving to the court of the Ziyarid ruler Qabus b.  Vushmgir (ruled 977–81,  997–1012) in Gurgan on the south-eastern shores of the Caspian Sea.  Although the Ziyarid court was a flourishing cultural and scholarly centre at that time, al-Biruni was not too happy there, complaining in his later works about the lack of instruments and opportunities for scholarly research (Rozenfel’d-Rozhanskaya-Sokolovskaya 1971,  11). Possibly receiving an invitation, al-Biruni returned during the first decade of the eleventh century (the precise year is contested) to Khwarazm, serving at the last Ma’munid ruler’s court in Urgench until 1017 as a boon companion, princely adviser, and skilled diplomat (Bosworth 2011, vol. 4, 274–76). There he made the acquaintance of Ibn Sina and one of his teachers, Abu Sahl ‘Isa b. Yahya al-Masihi (died in 1012). It is unknown when Ibn al‘Iraq came to the Ma’munid court and served its rulers ‘Ali b. Ma’mun (ruled 997–1009) and Abu l-‘Abbas Ma’mun (ruled 1009–1017). In 1017, the political turmoil once again changed the lives of both men dramatically. Since 1008, the new Ghaznavid dynasty with their capital in Ghazna (today in Afghanistan) had become the regional superpower. The Khwarazmshahs tried to maintain their dominance by forging alliances with the Abbasid caliphs in Baghdad and the Ghaznavid ruler Mahmud (ruled 997–1030). This policy finally failed in 1017 when Mahmud sent an ultimatum to Abu l-‘Abbas Ma’mun. He wished to be accepted as Ma’mun’s overlord, to receive a hefty tribute, and to be sent the group of leading scholars assembled at Ma’mun’s court. Al-Ma’mun paid for his willingness to obey Mahmud with his life. His nobles and army leaders rebelled, enthroning al-Ma’mun’s young nephew Abu l-Harith Muhammad b. ‘Ali (died 1017?). Four months later, Mahmud’s army conquered Khwarazm, “avenging his brother-in-law’s murder” (Bosworth 2011, vol. 1, 744). It seems that only then were al-Biruni, Ibn al-‘Iraq, and two other scholars moved to Ghazna, where they spent the rest of their lives with varying fortunes at the Ghaznavid court. 2.4.4.1. Teachers, Students, Companions

When the prince and the orphaned pauper met is unknown. Their childhood and youth were not recorded by historians. On the basis of their later scholarly papers we can gain some glimpses of both boys’ education. It included classical Arabic, New Persian, and the mathematical sciences.

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They learned to recite the Qur’an and studied other religious literature. Poetry also seems to have been part of their education. Philosophy and medicine, on the other hand, do not figure prominently in their work and thus may not have been an important part of their school years. Given this scarcity of information, it is very difficult to determine who their teachers were. Ibn al-‘Iraq allegedly received his mathematical and astronomical training from one of the leading scholars of the mathematical sciences of the Buyid era during the tenth century – Abu l-Wafa’, from Buzjan in eastern Iran. Since Abu l-Wafa’ moved in 959 to Baghdad, when Ibn al-‘Iraq was at best nine years old, this is difficult to accept, because there is no evidence that Ibn al-‘Iraq spent any significant portion of his life in the Abbasid capital. Thus, if the two men met and talked about the mathematical sciences, this must have happened somewhere in Iran, possibly at one of the Buyid courts. At an unidentified date, but before 998, Ibn al-‘Iraq wrote a treatise on azimuths that he claimed Abu l-Wafa’ had read (Samsò 1969, 28–29). In about 990, al-Biruni observed the altitude of the Sun for the spring and autumn equinoxes in his hometown (Bulgakov 1972, 27). Four years later, he constructed astronomical instruments and perhaps a terrestrial globe. Thus, al-Biruni’s higher education in the mathematical sciences must have taken place before 990, when he celebrated his seventeenth birthday. Perhaps his early observations, constructions of instruments, as well as his early texts written in the same period, may be regarded as components of his training as a young scholar. Seen in this manner, alBiruni’s experience of learning differed from that of al-Kindi’s students, who apparently focused predominantly on the acquisition of knowledge through the reading and explaining of texts. It also seems to have differed from the classes Thabit b. Qurra taught, which in addition to the study of scientific matters through texts included the training of skills in translating from Syriac (and perhaps also from Greek) into Arabic. Although Thabit’s astronomical texts leave ample testimony to his own astronomical observations, I did not come across a passage where students of his participated as adjuncts, let alone as independent observers. Analyzing several of Ibn al-‘Iraq’s and al-Biruni’s extant writings, Samsò pointed to al-Biruni’s unique approach to several scholars in his environment. They allegedly wrote treatises in al-Biruni’s name (Samsò 1969, 18–19). Two of them are said each to have written twelve such shorter

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or longer treatises: Ibn al-‘Iraq and Abu Sahl al-Masihi. Al-Biruni asked Ibn al-‘Iraq for an explanation and proof of problems in works by earlier authors, in practices of craftsmen, or for determining their errors. Ibn al-‘Iraq appears here in a double role – that of a teacher and perhaps the technically more apt scholar, and that of an adjunct of al-Biruni whom – Samsò believes – Ibn al-‘Iraq wished to free from detailed, pedantic labour for more ambitious projects (ibid., 21). If Samsò’s reflections on the possible dating of some of these texts are correct, then al-Biruni continued to ask for such services over a period of about three decades, until he was almost fifty years old, and Ibn al-‘Iraq complied with such requests even when he was over seventy. 2.4.4.2. al-Biruni’s questions to Ibn Sina

Al-Biruni did not study only in direct contact with his teacher Ibn al‘Iraq. He also learned through sending short treatises or letters to other scholars like Abu l-Wafa’ or Ibn Sina. Al-Biruni’s letters to Ibn Sina raise ­philosophical, astronomical, optical, and related scientific questions. They express curiosity, challenge, dissatisfaction, and criticism. It is believed that this exchange took place around 1000, when al-Biruni was at the court of Qabus b. Vushmgir and Ibn Sina, then about twenty years old, was still in Bukhara (Glick 2005, 88; for the date of Ibn Sina’s flight from Bukhara see Gutas 1988, 334). Ibn Sina is said to have defended “orthodox Aristotelian” views, while al-Biruni showed his “independent” mind by accusing Ibn Sina of relying too much on authority and abstaining from making observations (Glick 2005,  88). The year 1000 as a date for the exchange is, however, doubtful in terms of chronology. While Ibn Sina answered the first two letters with eighteen questions in person, he gave al-Biruni’s last question to his student Abu Sa‘id Ahmad b. ‘Ali al-Mas‘umi (late tenth-first half eleventh centuries), exasperated and angry at al-Biruni’s choice of words and continued challenge (Reisman 2007, 197). This contradicts an early dating of the exchange, since Ibn Sina seems to have had students whose names we know only from 1013 onwards (Gutas 2014, 19). With regard to Ibn Sina’s and al-Biruni’s intellectual positions in these letters, things are neither simple nor clear cut. One strong current in them is al-Biruni’s rejection of any theoretical claim that can be shown to deviate from empirical observations. Ibn Sina, on the other hand, points to ­al-­Biruni’s weaknesses in his knowledge and interpretation of ­philosophical theories and tries to determine the books from which he might have derived

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ms. London, British Library, Or. 8349, restored cover page of a copy of alBiruni’s Book of the Stars for Rayhana from 1435. It shows the book’s title at the top of the page, the name of the author at the bottom, and in between a kind of colophon with the date.

his views. This does not mean that Ibn Sina does not mention e­ xperiments in his replies. But as a rule, he embeds them in references to mostly Aristotelian books, in particular On the Heavens, On the Soul, On Generation and Corruption, Meteorology, and On Sense and Sensibility. The overall character of al-Biruni’s questions and Ibn Sina’s and alMas‘umi’s answers is that of a scientific dispute, in which al-Biruni mostly, but not always, challenges Aristotelian positions. He also asked ­questions

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free of polemical character, which suggests that one reason for this exchange might indeed have been to acquire knowledge, which he did not possess, i.e., to learn. Question 10, for instance, is free from polemics: The Tenth Question: What causes transformation of elements into each other? Is it the result of their proximity or intermingling or some other process? Let us take the example of air and water: when water transforms into air, does it become air in reality, or is it because its particles spread out until they become invisible to the sight so that one cannot see these separate particles? (al-biruni_ibn-sina-correspondence)

Ibn Sina’s reply begins with a brief summary of his views, then names Aristotle’s books (On Generation and Corruption; Meteorology; On the Heavens, Book III) where al-Biruni could find more detailed information, and finally offers an example with the aim to clarify the philosophical methods and demonstrations used for this problem. In this sense, we can consider the letters between al-Biruni and Ibn Sina as documents of high-level teaching and learning. 2.4.4.3. Science for Rayhana

Between 1027 and 1029, al-Biruni wrote in Ghazna a voluminous book in the form of 530 questions and answers on astronomy and astrology, calling it The Book on the Understanding of the Principles of the Art of the Stars [hereafter: The Book on the Stars]. The recipient was a young woman by the name of Rayhana, daughter of al-Hasan. According to al-Biruni’s introduction to the book, Rayhana was from Khwarazm and had asked for instruction. Al-Biruni must have appreciated her intelligence and capacity to learn highly, since instead of writing a brief epistle for her, he wrote a full-fleged course on the four sciences of the quadrivium, extended in various ­directions. Al-Biruni introduced Rayhana into plane and solid geometry and the geometry of the sphere. He taught her the theory of proportions, number theory, systems of counting and calculating, and algebra. He presented to her Ptolemaic astronomy, timekeeping, and the astrological doctrines of Hellenistic and Late Antique, Indian, Iranian, and Muslim authors. Some questions also pertain to balances and weighing, roots and powers defined in accordance with the definitions of Book X of Euclid’s Elements, or arithmetical rules not found in Greek treatises. Al-Biruni justified his choice of the dialogical format as being better suited for learning and easier to understand (Beruni 1975, 21).

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Four questions and answers must suffice to provide a glimpse of this substantial textbook: [Question 1:] What is geometry? [Answer 1:] It is the science of the magnitudes and the quantities in relationship to each other, the teaching of the properties of their forms and figures, as they pertain to a body. It transforms the science of numbers from the particular into the universal and transfers astronomy from guesswork and opinions into truth (ibid., 21). [Question 64:] How many figures can enclose a sphere? [Answer 64:] If they have equal sides and angles, which are from one genus, then there are only five, which relate to the four elements and the celestial sphere from the aspect of similarity. But if they are composed from different kinds, then they are neither limited nor numbered. As for the first five figures, one of them is the cube with six square faces. It is called the earthy (one). The second has twenty equal-sided faces. It is the watery (one). The third has eight triangles (of the same kind). It is the airy (one). The fourth, the spiny (one), has four triangular faces. It is the fiery (one). The fifth has twelve pentagons as faces (ibid., 36). [Question 123:] What is the heaven? [Answer 123:] The word “heaven” means everything that is above you and towers above you so that by restriction this word means the clouds and the roofs of the houses. In a free (sense), it is the ceiling that is visible to the world, which is the heavenly sphere whose description was introduced before. The Persians call it in their language asmãn, i.e., (something) similar to a millstone (due to?) its circular movement (ibid., 51). [Question 385:] Which are the male and which are the female planets? [Answer 385:] The three upper panets and the Sun are male, whereas Saturn is a eunuch [having no influence on birth]. Venus and the Moon are female. Mercury is a hermaphrodite, because it is male together with the male planets and female together with the female (ones). When it is, however, alone, it is male. Some consider Mars as female, but this opinion is not accepted (ibid., 180–81). Al-Biruni created a superb teaching document marked by its comprehensiveness. He continuously talks directly to Rayhana, explaining one matter, comparing the other, or offering a name in another language. The many terms, concepts, and possible difficulties are represented by diagrams and

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ms. London, British Library, Or. 8349, f. 31b; al-Biruni, Book of the Stars, Moon phases, copied in 1435.

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tables, visualizing and ordering the taught knowledge. As a result, Rayhana, if she ever read the book from cover to cover, would have been capable of understanding fairly high-level scientific texts or of participating in scholarly conversations, if allowed into the male circle. She could also have acted as a teacher to other women. But nothing of this has aroused a historian’s curiosity and hence she remains hidden in the dust of history. One thing, however, al-Biruni did not teach her are technical skills, i.e., how to observe and measure the altitude, declinations, azimuths, and other coordinates of heavenly bodies, and how to calculate values derived from them. Although The Book of the Stars shows al-Biruni as a gifted teacher, no other teaching activities of his are known. But due to his transfer to Ghazna and the military campaigns into northern India, which he had to accompany, in his adult life he engaged in a series of learning activities in a foreign cultural environment. 2.4.4.4. al-Biruni’s Knowledge of Indian Sciences

Al-Biruni’s learning – like that of other students of the mathematical sciences in Islamicate societies – also included knowledge from non-Islamicate sources in India as a result of the translation of Sanskrit texts on astronomical, astrological, and chronological subjects during the eighth century. Although translations of ancient Greek texts were of a g­ reater impact in most of the mathematical disciplines, a good number of ­particulars from Sanskrit traditions survived within Arabic and Persian scientific knowledge practices. In addition, al-Biruni used the opportunities offered to him by his transfer to northern India. He learned Sanskrit, the high language of learning in Indian cultures. After many years of exposure to northern India, al-Biruni wrote a book about it. There, he outlines fairly well the difficulties a foreigner encountered when learning Sanskrit, although he does not name all of them. After his study of the language, al-Biruni went to look for teachers of the disciplines he was most interested in: philosophy, astronomy/astrology, arithmetic, and literature. He was upset at the socio-cultural ideas of the Brahmins who considered him impure and refused to interact with him. In his view, the Buddhists were not much more welcoming. But he himself harbored his own ideas of superiority: At first I stood to their astronomers in the relation of a pupil to his master, being a stranger among them and not acquainted with their peculiar national and traditional methods of

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science. On having made some progress, I began to show them the elements on which this science rests, to point out to them some rules of logical deduction and the scientific methods of all mathematics, and then they flocked together around me from all parts, wondering, and most eager to learn from me, asking me at the same time from what Hindu master I had learnt those things, whilst in reality I showed them what they were worth, and thought myself a great deal superior to them, disdaining to be put on a level with them (Alberuni’s India 1992, 23).

Unfortunately, al-Biruni does not provide any information about the men who taught him the language and any of the other kinds of knowledge found in his book (ibid., xxxv). Equally, he did not talk much about his learning experience. Only once does he state that it was very difficult for him to enter into Indian scientific doctrines, despite his love for the ­subject. He admits to have spent much time and money in buying books, even from remote places, and paying teachers (ibid., 24). His goal in writing the book about India was not autobiographical. Rather it was meant to offer his Muslim readers an opportunity to get acquainted with India and its intellectual cultures (ibid., 110, 122, 147). 2.5. Postsface I have tried to outline my general views about the forms and content of learning and teaching the mathematical sciences and natural philosophy between the middle of the eighth and the second half of the twelfth centuries. Most of these activities took place either as one-on-one learning and teaching endeavours in the house of the student or in small groups in the house of the teacher. Reading and commenting on texts was the dominant form practiced in these encounters. Knowledge of instruments and ­instrument making seems to have been a more specialized training. It took place either in the shop of a craftsman or with an expert astrologer. The ­qualification of teachers was only tested when they exercized their craft. While families of the elites could afford to pay famous scholars to teach their sons, middle-class families had to trust their luck when hiring an itinerant teacher. There are complaints about men offering to teach the mathematical sciences, logic, philosophy, or medicine without having mastered more

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than a minor part of Euclid’s Elements, Ptolemy’s Almagest, or Aristotle’s philosophy. Encyclopaedias, autobiographies, and treatises on the classification of knowledge leave no doubt that like in Antiquity texts formed the backbone of teaching, not a comprehensive disciplinary approach. They also indicate that texts were not taught in isolation from each other, but in sequences depending on the kind of knowledge that was pursued. In this sense, despite the various differences between learning and teaching in Antiquity and in Islamicate societies until the later twelfth century, the studied texts provided a systematic survey of the fundamental questions, problems, and methods as needed by a later scholarly expert in philosophy, medicine, or the mathematical sciences. Some of the works written in this period, like Ibn Sina’s Canon of Medicine or his Book of Healing on philosophy, soon became major textbooks for learning and teaching. A few other, much shorter, treatises on the astrolabe by Qusta b. Luqa and al-Biruni or astronomy by Muhammad b. Kathir al-Farghani (died after 861) acquired a similar longstanding reputation as texts for learning and teaching. The time of textbook-writing, however, only began in the following period with the inclusion of classes for various mathematical sciences, medicine, and parts of philosophy in the madrasa, which is the content of Chapters Three, Four, and Eight. This lack of recognizable textbooks leads to the strong visibility of geometry and astronomy as the mathematical disciplines most often taught in this period. This does not mean that other disciplines were not taught. We simply have less unequivocal evidence for their teaching and learning contexts. Mostly anonymous treatises on algebra show the interest in learning how to solve problems that we identify as linear and square equations. The basic text referred to time and again is the early ninth-century survey by Muhammad b. Musa al-Khwarazmi (flourished between the late eighth and the second third of the ninth centuries), which also became the starting point for learning and teaching algebraic techniques in Latin Europe. Various oral and written calculation methods were taught to children and shop apprentices, but also among students of the religious disciplines, where this knowledge was needed for calculating inheritance shares and donations. Although this kind of mathematical literature never made it into the canon of the Middle Books, it is most likely that teachers of those texts also trained their students in how to count, calculate, and determine unknown quantities, because they were necessary skills for the practicing astrologer.

Chapter 3 SCHOOLS OF ADVANCED EDUCATION

A

t the end of the period described in Chapter Two, the teaching of the mathematical sciences, medicine, and philosophy slowly began to move into schools, mosques, houses for the reading of the Qur’an or hadith collections, and similar public religious spaces. This happened in different regions of the Islamicate world at different times. The earliest hints at such an integration of the non-religious disciplines into advanced education for Muslims come from the famous Nizamiyya madrasas in Baghdad and Mosul during the mid-twelfth century. These schools took their name from their founder, the Persian vizier Nizam al-Mulk (1018–1092) who served two Saljuq sultans, Alp Arslan (ruled 1063–1072) and Malikshah (ruled 1072–1092). Modern interpretations of Nizam al-Mulk’s motives for founding these schools vary greatly. The older view saw this as a move to revive Sunni Islam in the caliphate after the century of rule by the Buyids, who were Shiʿis. A less grandiose interpretation sees Nizam al-Mulk’s educational activities as support for the Shafiʿi law school against the Hanafis. A third perspective emphasizes the schools as one of the numerous tools that the vizier created for building his personal power basis and network of support. In addition to Isfahan, Baghdad, and Mosul, Nizamiyya madrasas were founded primarily in eastern cities: Nishapur, Amul, Balkh, Herat, and Merv. Soon other rulers as well as other affluent or pious men and women donated their houses, orchards, fields, shops, and other property for creating a religiously protected legal foundation (waqf) for education, prayer, or support of needy travellers, the poor, or the sick. Madrasas proliferated in Iran, Iraq, Anatolia, Syria, and Egypt during the twelfth century. In the following centuries, madrasas were also built in North Africa, Central Asia, and India. In some regions like North Africa, they remained the prerogative of the rulers, while elsewhere individuals outside the ruling families also participated in such commendable activities. The main focus of learning was the religious disciplines, in particular law according to different schools, and the study of the Qur’an and the sayings and customs of the Prophet (hadith).

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Nineteenth-century painting of Sultan al-Hasan’s (ruled 1347–1351 and 1354– 1361) Mosque and Madrasa in Cairo, built between 1356 and 1363.

Since there are only very few studies of regional or even urban traditions of teaching and learning the mathematical sciences, medicine, natural philosophy, and the “occult” disciplines, I depict in this chapter first briefly the general background of advanced education, focusing, however, on the non-religious disciplines. In the following chapter I will describe in greater detail the learning and teaching conditions for the four disciplinary areas treated in this book. 3.1. The Legal Status and Formalities of Advanced Education The legal status of a madrasa was defined by a religious donation (waqf) of a building for at least one teacher (mudarris) and a group of students together with monetary and/or natural funds like orchards or shops for salaries, stipends, and maintenance. The donor often added jobs for a doorman, a water carrier, a reader of the Qur’an, and an administrator. The last-mentioned often came from the donor’s family. Wealthy donors provided for more than one teacher. Dynastic donors often added other posts, for instance a post for a timekeeper or for a physician or other

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healers. A donor could stipulate the type of classes to be taught (mostly related to specific law schools) and regulate at how many madrasas a teacher was allowed to hold a position. A teacher read with his students a text together with commentaries and then signed copies made by students in class with an ijaza (certificate of teaching, literally: permission), a declaration allowing the student to teach the copied text. This permission to teach a learned text took many forms and variants. It is very rare in natural philosophy and appears significantly less often in the mathematical sciences and medicine than in the religious disciplines. There is no survey documenting such ijazat (plural of ijaza) for the sciences or medicine. Neither is there any explanation offered why they did not become a standard tool in those disciplines. But this does not mean that there are no ijazat for the mathematical sciences or medicine. Examples can be found in manuscripts or in Shams al-Din al-Sakhawi’s (1428–1497) collection of biographies and manuscript titles (al-Sakhawi n.d., vol. 6, 285; vol. 7, 113; mss. London, British Library, Or. 3129 and Or. 5659). When students reached a higher level of education they could earn additional funds as a repetitor. This meant that they reread with less advanced students a text that had been taught in class. In later Ottoman centuries, it also could mean that they ran preparatory classes before such a reading in class by the teacher. After they finished their education, many students followed a master as a disciple for quite some time. This relationship often focused on one particular text or a set of texts that were studied together. In medicine, such disciples also acted as adjuncts, helping the physician in preparing remedies and drugs, writing prescriptions, copying texts, or caring for the sick in a hospital, the physician’s house, or the sick person’s private home. Whether there were exams at any level of advanced education in the mathematical, medical, philosophical, or “occult” sciences is difficult to say. For a long time the ijaza has been considered as a kind of exam or even as a degree-awarding event. But this is not supported by the sources. In Mamluk Egypt and Syria, however, the terminology of some biographical dictionaries seems to suggest that public performances were obligatory at the end of the study of a text in a religious field and that other teachers in town participated in such a procedure, which we may perhaps understand as an examination. In a few cases, the word imtihan (test, exam, probe) is explicitly used. In one case it

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even seems to include the mathematical sciences. Al-Sakhawi reports on Ibn al-Fadl b. al-Imam (1437–1475?) and his two teachers Muhyi l-Din al-Kafiyaji (died in 1474) and Zayn al-Din Tahir (fifteenth century): The two gave him ijazat in fatwa-writing, teaching [of law], inheritance regulations and [their] appended [fields] after an imtihan (al-Sakhawi n.d., vol. 7, 55).

The Ottoman regulations for educational and juridical career patterns used a different term for something that describes the transition from years of studying to one’s first regular position – mülazemet. Modern researchers interpret the meaning of this concept differently. Some believe it describes a formal examination, while others understand it as a waiting period with specific entrance rules that were regulated by legal ­prescriptions ­concerning the rank of teachers, judges, or other religious officials who were entitled to propose junior scholars for positions, as well as the events in which such a transition from the years of learning to the years of waiting and then into the ranks of scholarly officialdom (ʿilmiyye) could take place (el-Rouayheb 2015,  126–28; Beyazıt ­2012–2013, 201, 203–06). In the latter interpretation, someone who had entered this period was a mülazim, a candidate for a post (ibid., 204). 3.2. Teaching Non-Religious Disciplines at Religious Institutions Under the rule of the Saljuq, Zangid, and Ayyubid dynasties non-religious fields of knowledge entered these new forms of institutionalized learning in Iraq, Syria, Egypt, Anatolia, and Iran, although we do not know the precise chronological development of these processes. Historical sources speak of an early entrance of philosophical studies of Ibn Sina’s books into the Nizamiyya madrasa at Nishapur, and mathematical texts were copied at its sister institutions in Mosul and Baghdad. Kalam or the rational debate of articles of faith and with it logic, parts of metaphysics and natural philosophy, the mathematical sciences – in particular arithmetic, algebra, geometry, and astronomy – and medicine found their representatives and students at madrasas more or less regularly for seven to eight hundred years, in particular at the ostentatious princely foundations. Over time, texts from these fields of knowledge were also taught and studied at mosques, tombs, houses for timekeepers, libraries, Sufi

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lodges, and occasionally also in specialized houses for reading the Qur’an or hadith. This spread of the secular disciplines beyond the houses of teachers and madrasas – which in many cases were one and the same thing – was accompanied by their spread through the legal schools and the Sufi orders. Many manuscripts, biographies, and historical chronicles demonstrate that members of all major doctrinal and communal groups accepted learning and/or teaching some of these disciplines, most often logic, the basic mathematical fields, and over time some of the “occult” disciplines, but also medicine. The place of natural philosophy is not well studied. It is not often mentioned in the historical sources. But its inclusion in the main teaching manuals produced during the thirteenth century suggests that it too was studied more often than is usually thought. 3.3. Processes of Professionalization and Specialization Several processes of professionalization and specialization characterize the presence of the mathematical, medical, and philosophical sciences at advanced educational institutions in different parts of the Islamicate world. They concern the professional status and designation of those who taught these fields of knowledge, the emergence of newly institutionalized fields of knowledge, and the regional differences between the acceptance of any of these disciplines as teaching subjects at madrasas, mosques, and other institutions. In parallel to the move of these fields of knowledge into the religious teaching institutions we lose more and more access to the educational practices of minority groups – whether Muslim or others – within the majority societies. This is partly the result of the character of the extant historical sources and partly the result of modern research interests. The rare examples of Jewish, Christian, or Shiʿi students in Sunni circles of learning, or of libraries of patriarchs or Jewish physicians, that I am aware of suggest that the scientific disciplines, which had developed together in the previous period across the various religious communities, had now become hegemonic. They were learned and taught not only at Sunni institutions of advanced education, but also at Shiʿi madrasas and mosques and amongst the Christian and Jewish communities. In Shiʿi communities no houses for reading the Qur’an and hadith seem to have been founded. The main teaching position at a madrasa was that of a mudarris ­(teacher). The task of this position was primarily to teach Sunni or Shiʿi

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law. Over time, other religious fields of knowledge and languages, mostly Arabic, were also taught by such head teachers. The position of a m ­ udarris was rarely allocated to the non-religious disciplines. Exceptions to this rule were medicine and timekeeping under the Mamluk and Ottoman dynasties, and medicine, the mathematical sciences, and some of the “occult” disciplines under some Timurids, Mughals, and possibly other Muslim dynasties in South Asia. Teaching remained, however, informal and individual. This means that teachers were socially more important in a scholar’s self-representation than institutions. Entries in biographical dictionaries, collections of information on a person’s education, or colophons at the end of copied texts, and anecdotes highlight three types of information as essential markers of education: numbers, names, and titles, i.e. the numbers of teachers and studied texts and the names of teachers and texts. Institutions and classmates clearly mattered less, unless one of the latter had become a scholar of high reputation or one of the former had a particular distinction. Some division of labour among the teachers emerged over time in various regions. Seen first in weak forms under the Zangids in northern Iraq and Syria and then extending during the Ayyubid dynasty into Egypt, teachers of law or disciplines called the foundations of law and religion (or: faith) read texts by Ibn Sina on metaphysics, the classification of the fields of knowledge, and sometimes natural philosophy, as well as treatises on logic by an ever growing number of authors. Some of them also taught theoretical astronomy. The latter, in the form of planetary theory, developed during the fourteenth century into a stable field of instruction at Sunni madrasas in Iran. An important center for such classes emerged in the late phase of Mongol rule in Shiraz, which remained active under the following dynasties and even survived the difficult transformation of Sunni madrasas into Shiʿi institutions under the early Safavid shahs in the first half of the sixteenth century. A second process of specialization emerged in the late thirteenth century in Mamluk Egypt and Syria. Similar trends can be found in Rasulid Yemen, al-Andalus, and North Africa. This specialization appropriated spherical geometry, the calculation of astronomical parameters, and the construction of instruments from their previous disciplinary homes and unified them with the new designation of “the science of timekeeping”. Their practitioners even received a specific disciplinary name as “timekeepers” (muwaqqit). Their tasks consisted of compiling tables

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and teaching this knowledge at madrasas. Occasionally, timekeepers maintained sundials and other public instruments in the town. In some cities such as Cairo they were also responsible for predicting eclipses and explaining their aspects, in particular in cases of predictive or interpretive errors. Tables had to be established for the five daily prayer times, the directions of prayer towards Mecca, and the rising of the new lunar crescent for determining the beginning of a month, of particular relevance for Ramadan. Many of these timekeepers received positions for producing tables at mosques and sometimes at madrasas. Over time, Mamluk madrasa founders and administrators also hired timekeepers as teachers of law. Due to the flexibility and informal c­ haracter of teaching, these specialists often also taught classes on some of the other mathematical sciences in addition to other disciplines of their preference. Teachers of the mathematical sciences and their students could combine these specializations with one or more of the following disciplines of the transmitted or the rational sciences: logic, Arabic, the two disciplines called “foundations of religion (or: faith)” and “foundations of law”, exegesis, and law. This means that they received or provided education in the main branches of madrasa teaching, enriched by their specialization in the mathematical sciences. It is not clear to me, however, whether this comprehensive training was in place from the early years of mathematical classwork in madrasas in the twelfth century or whether it took time to evolve until it was apparently the rule in the fifteenth century, at least in the Mamluk territories (al-Sakhawi n.d., vol. 7, 3). A parallel trend combined such religious disciplines with the study of medical texts. Again, others did not specialize in one of these minor branches of madrasa education, but only read a few texts in the mathematical sciences, medicine, and philosophical and related matters (ibid., vol. 7, 6). A stricter format of centralized regulation and control began to take shape under the Ottoman sultans after the conquest of Constantinople in 1453. After founding the so-called eight madrasas, together with his mosque complex called Fatih (the Conqueror), in the 1470s, Mehmet II Fatih (ruled 1444–1446,  1451–1481) prescribed in one of his legal codices rules for the ranking of the schools in his realm and therewith for the scholarly and juridical career of their students. Parts of this legal codex were rewritten in the early sixteenth century and thus reflect a moment in time some four decades after the schools’ foundation. The codex deals

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Gazanfer Aga Madrasa, Istanbul.

more with the ideal career of a student, who had finished his education, than with the education itself. Afterwards, other Ottoman sultans reedited similar legal stipulations or ordered the compilation of new ones. This set of proclamations created a regularity of expectations on the side of young and middle-ranking scholars, as well as on the side of the state, even if the practice did not always agree with them to the letter. After finishing his education, a young man would become a candidate waiting for a few years for promotion to the lowest regular position (Beyazıt 2012–2013,  203–04). These ranks were measured in terms of the daily salary (20 akşe being the lowest level and 100 akşe and more representing the uppermost level) and geography (madrasas in the provinces being less valuable than madrasas in the three Ottoman capitals; within the capitals themselves madrasas were ranked according to their founders). The rise through the system ideally took place in steps of 5 akşe. But in practice, excellence, family background, and social connections or the lack thereof often altered conditions profoundly. Petitioning helped to speed up one’s career, as did the promotion of one’s teacher (Imber 2009, 212–15; Beyazıt 2012–2013, 205). The death of a former teacher or celebrations like a military victory, the

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accession of a new s­ ultan, or the circumcision of a prince also contributed to extraordinary chances for promotion (ibid., 204–06). The legal codices of the sixteenth and early seventeenth centuries also included prescriptions for the minimal time span a student should stay in the educational system, the books to study at the minimum before proceeding to the next level, and the punishment to be meted out against students and teachers who violated these rules (Imber 2009, 215). The named books are limited to the disciplines of transmission (mainly the reading of the Qur’an, exegesis, hadith, law), some of the religious disciplines belonging to the rational sciences (kalam, the foundations of law and faith), and logic (İzgi 1997, vol. 1, 63–64, 67). In parallel to these institutional and professional changes, the epistemological classification of the various fields of knowledge changed substantially at least twice, as I will discuss in Chapter Seven. The classical division into the “sciences of the moderns”, the “sciences of the ancients”, and the “Arabic sciences” of the previous centuries was superceded by the new trio of the “transmitted”, “rational”, and “mathematical sciences”. Sometimes, a fourth class was argued for: “the sciences of philosophy or wisdom”. This change included a new grouping of some of the religious disciplines, previously all located under the header of the “sciences of the moderns”, with some of the ancient sciences. Logic, metaphysics or “divine science”, natural philosophy, and the disciplines of practical philosophy formed the rational sciences together with kalam and the two disciplines of the foundations (law, faith). Further members of this group were ­medicine, pharmacology, which was not always named separately, and occasionally alchemy. Some authors also added the philological disciplines to this new group (Brentjes 2002). The mathematical sciences were separated from philosophy and often received their own group, enriched by disciplines which we would consider unscientific, but which used mathematical methods, such as astrology and different forms of divination. 3.4. Secretaries, Animals, and Foreigners A long-established specialized professional group were the secretaries, the administrative officials of the state. The integration of knowledge like tax calculation procedures and other professional duties of this group is not a very visible theme in biographical dictionaries or historical chronicles. But at least in the Mamluk case, some specialized domains of

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knowledge relevant to administrators were indeed sometimes taught by madrasa ­teachers. Later high-ranking Muslim administrators appear in biographical dictionaries among madrasa students. Some of them also took classes in medicine and those parts of the mathematical sciences that fell into the domains of timekeeping and the theoretical disciplines (al-Sakhawi n.d., vol. 6, 235; vol. 8, 113–14; vol. 10, 230). Mamluk texts composed by madrasa teachers suggest that in some cities knowledge about animals and their diseases, in particular horses, as well as about war machines, was also occasionally taught at school (Shehada 2013). The march of the mathematical sciences, medicine, and parts of philosophy into the schools of advanced education profited moreover from the teachers’ mobility across the large area of Islamicate societies, although not all regions participated in the same manner in this circulation of people, books, and knowledge. Different factors stimulated the wanderlust of scholars and students: wars, tribal movements towards the West, the search for positions, teachers, or spiritual guides, professional or political activities as merchants and envoys, and pilgrimage. Teaching thus was not exclusively local or regional, but was nourished by manpower, material, and theories from faraway territories. Chapters Five and Eight will pay particular attention to travelling students and scholars and the territorial spread of books and doctrines.

Chapter 4 THE SCIENCES AT MADRASAS

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n this chapter, I present the mathematical sciences, medicine, natural philosophy, and the “occult” sciences as learned and taught at madrasas and related educational institutions. I discuss teaching material and summarize their content. For this survey of the learning and teaching activities in the scientific disciplines I draw more on primary than on secondary sources. The picture that I can paint in this manner is partial and confined to a few cities. With regard to disciplines which do not belong to my area of expertise such as medicine or philosophy, I  rely mainly on a small number of primary sources, prefering concrete data about one or two local cases over generalizations from surveys without systematic analysis behind them. I added astrology to the mathematical sciences, because many scholars of the latter earned their living as practitioners of the former. As I will show in Chapter Seven, however, not all scholars considered astrology to be a mathematical science. Some saw it as a lower part of natural philosophy, while others elevated it to the queen of philosophy or even of all the sciences. 4.1. Mathematical Disciplines In 1125 and 1158, anonymous scribes copied ʿAbd al-Rahman al-Sufi’s Star Catalogue and Theodosius of Bithynia’s Spherics at the Nizamiyya Madrasas in Baghdad and Mosul (Theodosius 2010, 4; Oriental Manuscripts and Miniatures 1998,  34). Only shortly thereafter, in 1161, further mathematical texts were copied in the same madrasa in Baghdad. These are the earliest known references to astronomical and geometrical texts produced within the confines of a madrasa. From then on we find many more texts copied in Nizamiyya madrasas as well as in other big and small schools founded in Baghdad, Mosul, and elsewhere by wealthy or humble donors and scholars. For this early time, there is only rare proof that copying such manuscripts in Nizamiyya madrasas was undertaken by

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specialists in the mathematical sciences. A brief extract from a once larger text on arithmetic, today preserved in the Schoenberg Collection at the University of Pennsylvania, is the only precious witness to the presence of mathematical experts at the Nizamiyya Madrasa in Baghdad known to me. Its colophon states that in Safar 590 (February 1194) the calculator Muhammad b. ʿAbdallah b. al-Mahall (?) al-Baghdadi copied the first part of the work called The Explanation at the Nizamiyya Madrasa in Baghdad (ms. Philadelphia, University of Pennsylvania, lsj 293, f. 86a). A second copy of Theodosius’s Spherics was the work of Muhammad b.  Abi Bakr, the scribe who also copied Thabit b.  Qurra’s textbook on compound ratios in the summer of 1228, as discussed in Chapter Two.  Around the same time, Muhammad copied several other mathematical texts, among them Theodosius’s treatises on The Habitations and Days and Nights, Euclid’s Phenomena, and Autolycus’s The Risings and Settings (Theodosius 2010, 3; Thābit ibn Qurra 2008, 22). Another early copy of a text that appears in numerous Arabic collections of the Middle Books, that is the Spherics of Menelaus (lived c. 70–140), shows further features of the teaching and learning process and its spread beyond Iraq. It states clearly that it was copied in Damascus in 1153 from a book owned by the well-known physician and scholar of the mathematical sciences Ibn al-Salah al-Sari (died in 1154). It was copied during Ibn al-Salah’s lifetime and contains many comments by this scholar, who is known to have taught the mathematical sciences to other students. These comments are today unfortunately incomplete and thus lack important parts, due to having been cut off by an incompetent collector or conservator. They sometimes correct the text. In other cases they explain a term or a problem. Other comments report on the different translations and editions of the text, their authors, and the difficulties that these differences pose for the users of the text. Thus this particular copy of Menelaus’s Spherics is most likely the result of the teaching procedures to be discussed in Chapter Six (ms. London, British Library, Or. 13127). But early copying activies in Nizamiyya madrasas were not confined to texts of the mathematical sciences. Dioscorides’ (died c. 90) book on materia medica, for instance, was copied in 1240 in one of them (Savage-Smith 2011, 43). The thirteenth century saw several scholars in Syria, Iraq, and Iran engage in the revision of the collection of ancient Greek teaching texts of the mathematical sciences and in the translation of a small number of

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ms. Oxford, Bodleian Library, Arab. d 138, f.  2b, Dioscorides, De materia medica, Books 3–5, copied in a Nizamiyya madrasa in 1240.

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these texts into Persian, from Euclid’s Elements through the Middle Books to Ptolemy’s Almagest. Some of these editors were viziers, who headed courtly administrative offices (diwan), like Najm al-Din Ibn al-Lubudi (1210-after 1267) in Syria or Nasir al-Din al-Tusi in Iran. Others were court astrologers like Mu’ayyad al-Din al-ʿUrdi (died c.  1266) or Ibn Abi Shukr al-Maghribi (lived c. 1220–1283), first in Syria, and after the Mongol conquests in Iran. A third group of these editors were madrasa teachers in Iraq, Iran, or Anatolia like Athir al-Din al-Abhari (1200– 1265) or Qutb al-Din Shirazi (1236–1311), who, as a young man, had been a physician in Shiraz. The most famous and most successful of these editors was Nasir al-Din al-Tusi, a towering scholar of Shiʿi law, kalam, philosophy, and the mathematical sciences including astrology and ­divination from sand figures, as well as mineralogy. The Middle Books were not the only collections of mathematical works that were used either for autodidactic or school education. Special collections were produced in particular by individuals interested in the mathematical sciences. One example is a collection of mathematical texts, which was preserved in the Catholic College of Beirut, now St Joseph University. In addition to texts on mechanics and specific weights by Thabit b. Qurra, al-Biruni, and ʿAbd al-Rahman al-Khazini, this interesting collection, which was unfortunately lost in the Lebanese civil war, contained works on astronomy (methods of stereographic projection, the construction and use of the sextant) and trigonometry. Also included are geometrical treatises by scholars of the tenth and eleventh centuries, for instance, al-Biruni, al-Khujandi (c.  940–1000), al-Shanni, ʿAbd alJalil al-Sijzi (tenth century), and Abu Nasr Ibn ʿIraq, most of whom we met in Chapter Two. Another collection unites works by other important scholars of these two centuries such as Abu Sahl al-Kuhi, ʿAbd al-Jalil al-Sijzi, Ibn Sina, ʿUmar al-Khayyam (c. 1048–1125), or al-Muzaffar al-Isfizari (died c. 1125). It was copied by a lover of mathematics in the Ottoman administration called Mustafa Sidqi (died in 1769), who also owned the copy of Menelaus’s Spherics from 1153 mentioned above. In this case, the collection was clearly meant for self-education. These two examples indicate that in addition to the traditional teaching texts from Antiquity and the newly composed introductory works that flourished within madrasas and private study circles after 1300, there

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was a continued interest in higher-level mathematical treatises by authors from the classical period among individual scholars. Such information is found in manuscripts produced in Iran and Central Asia under the Timurids, in Iran under the Safavids, and in Anatolia, Syria, and Egypt under the Ottomans. The teachers of such classical, higher-level mathematical treatises worked above all at the courts of the Timurid princes Iskandar Sultan in Shiraz and Isfahan and Ulugh Beg (ruled 1409–1449) in Samarkand. Madrasas in Shiraz were another important setting for such educational activities. In the Safavid period, some teachers and students in the capital Isfahan again studied Apollonius’s Conics. 4.1.1. Arithmetic, Algebra, and Astronomy under the Mamluks and in North Africa Madrasas, however, did not always and not even primarily teach the Middle Books, Euclid’s Elements, or Ptolemy’s Almagest. We have only very meagre information about them for Mamluk Syria and Egypt, where two of the teachers of the mathematical sciences presented below are occasionally mentioned as giving classes about Euclid, which most likely means the Elements – Jamal al-Din al-Maridani (died in 14?9) and Ibn al-Majdi (1359–1447) (al-Sakhawi n.d., vol.  10,  27; Charette 2007a, 561–62). We have no such information for the early Ottoman Empire, the various Mongol and Tatar dynasties north of the Black and the Caspian Seas, or the smaller Islamicate states in India and Africa. Instead, we have substantial – and in some cases even abundant – data about the teaching texts newly composed in some of those regions. The two most often taught mathematical subjects at madrasas in Mamluk Syria and Egypt were arithmetic and the science of timekeeping. Specialized teachers in these two fields whose texts and names survived several centuries and found acceptance and appreciation outside the borders of the Mamluk state in Iran, India, Anatolia, or North Africa were, for instance, Ibn al-Majdi in Cairo, Ibn al-Ha’im (c.  1352–1412) in Jerusalem, and Jamal al-Din al- Maridani in Cairo, and his grandson Badr al-Din (1423–1501), who was known as Sibt al-Maridani, the son of the daughter of al-Maridani. These four men, their students, and their successors as teachers in Cairo are mentioned time and again in al-Sakhawi’s biographical dicitionary of famous men and women of the fifteenth century. We learn from these entries that the mathematical disciplines and their legal relatives

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Ibn al-Majdi, Treatise on the drawing of hour lines on three kinds of sundials (horizontal, vertical, oblique), copied in 1481 by a certain ʿAli b.  Hasan, Arts of the Islamic World 2011, 94.

that they taught most often were inheritance regulations, arithmetic, algebra, and timekeeping. Al-Sakhawi himself also took classes in three of these disciplines with Ibn al-Majdi (al-Sakhawi n.d., vol. 8, 4). But some students did not study texts from all of these fields together with the same teacher. They chose themes depending on individual teachers. A student

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from the Hijaz in the Arabian Peninsula, whose family had emigrated from Fez, for instance, studied inheritance regulations with Ibn al-Majdi and another teacher, arithmetic with those two and two more teachers, but timekeeping and a special type of quadrants with Ibn al-Majdi alone (ibid. vol. 6, 155). A migrant from Ardabil in Iran made similar choices. He studied inheritance regulations, arithmetic, timekeeping, and other subjects with Ibn al-Majdi, inheritance regulations, timekeeping, Arabic, and other subjects with a second teacher, but three subjects (inheritance regulations, timekeeping, Arabic) with another three different teachers, one for each subject (ibid., vol.  8,  75). These two examples also indicate that a student could find more than one teacher of mathematical knowledge in a big city like Cairo, if he wished to. Widely studied authors and teachers of mathematical textbooks in North Africa and al-Andalus, whose texts were also read in Mamluk, Ottoman, and sometimes even Safavid madrasas, were Ibn al-Yasamin (died in 1204), a Berber poet at the court of the Almohad dynasty (ruled c. 1121– 1269) in Seville, and the jurists Ibn al-Banna’ (1252–1321) in Marrakesh and al-Qalasadi (1412–1486) in Tunis, Cairo, and Almería. Ibn al-Yasamin composed didactic poems on arithmetic and algebra. Ibn al-Banna’ wrote introductory and middle-level texts on arithmetic, algebra, geometry, and astronomy. Al-Qalasadi focused on arithmetical and algebraic themes. Ibn al-Yasamin received his initial education in the religious, philological, and mathematical disciplines in Seville, where he later taught law and the mathematical sciences. He wrote three or four mathematical texts, among them two didactic poems on the extraction of roots and on algebra. The second poem was particularly successful and was studied for centuries across North Africa, reaching far into the Ottoman lands and even Iran and parts of India. Among its many students and commentators we find al-Qalasadi, Ibn al-Ha’im, and Sibt al-Maridani. Each line of Ibn al-Yasamin’s poems consists of two verses, which are separated ­physically on paper by an empty space. Algebra rests upon three

amwāl, numbers, then roots;

māl is every square number

and its root one of the factors;

absolute number relates

neither to the amwāl, nor to the roots.

Be it understood!

(Abdeljaouad 2004, 4)

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The concepts memorized in these lines are: māl (plural: amwāl; literal meaning: wealth, riches; in algebra it means, as the poem specifies: x2), root (means: x), and absolute number, which signifies the third component of a quadratic equation. 4.1.2. The Mathematical Sciences in Iraq, Iran, and India In Iran and Iraq, where the Abbasid caliphate was destroyed by Mongol armies in 1258, teaching manuals emerged throughout the thirteenth century in several disciplines, among them astronomy, natural philosophy, and logic. They spread quickly throughout Iran and Iraq and from there to Anatolia, Syria, Egypt, Yemen, Tunisia, and further west. The two main introductory textbooks on astronomy, which were taught until the modern period, are Sharaf al-Din al-Jaghmini’s (first half of the thirteenth century) Epitome on Plain Theoretical Astronomy and Nasir al-Din al-Tusi’s Memoir on Astronomy. Numerous commentaries were written on both texts, which were used as an aid when studying al-Jaghmini’s or al-Tusi’s textbook in class or at home. Many authors of commentaries came from cities in Iran, India, and Anatolia. Others lived in cities in North Africa or Central Asia. Some of these commentaries were relied upon in higherlevel classes as more advanced texts (S. Ragep 2007, 584; S. Ragep 2016). Characteristic for this two-level usage is the vivacity of the two textbooks and their commentaries. Al-Jaghmini’s textbook, in particular, was repeatedly enriched by more recent material (S. Ragep 2007, 585). S. Ragep claims that “thousands of copies” are extant today in manuscript libraries all over the world (ibid.; S. Ragep 2016, 1). Al-Tusi’s Memoir did not survive in such abundance, but it too found many commentators and for several centuries inspired some of the brightest minds in their discussions of planetary models. Other astronomical teaching manuals also came from al-Tusi’s pen. Often studied and commented on, they treat the astrolabe and the preparation of the calendar. Related texts, mostly commentaries or supercommentaries, by Ilkhanid, Timurid, and early Safavid scholars like Nizam al-Din al-Nisaburi (died in 1328/9), Qadizade al-Rumi (died after 1440), ʿAli b. Muhammad al-Qushji (1402–1474), and ʿAbd al-ʿAli al-Birjandi (died in 1525/6) on planetary theory, calendars, and astrolabes belonged to the standard schoolbooks taught at Mamluk, Ottoman, and Safavid madrasas. Some of these works were also taught in Islamicate societies in India. Students of these texts thus learned the structure of the Ptolemaic universe

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in its modifications by Ilkhanid scholars, how to design a calendar (one of the most important tasks of a court astrologer), which parts an astrolabe contained, and how to draw its various curves. Extant Safavid and Mughal astrolabes and globes indicate that parts of this technical knowledge continued to be taught in artisanal workshops, transmitted from father to son or other male relatives (King 2004). Higher-level knowledge of planetary models and the surrounding philosophical and mathematical discussions was also acquired at the madrasas of Shiraz, where Shams al-Din al-Khafri (died in 1550) learned and taught. The teachers of this city had a long tradition of engaging with Ilkhanid and Timurid astronomical works, in particular those of Qutb al-Din alShirazi and ʿAli b. Muhammad al-Qushji. Saliba believes that the models proposed by al-Khafri went beyond the previous scholars’ achievements (Saliba 1994 and 1997). Cooper, however, considers al-Khafri more a bookish astronomer than a practical observer (Cooper 2007,  623–24). This fits well with late Timurid and Safavid astronomical learning, which was seen as the theoretical starting point and basis of astrological practice. The most often studied introductory text for arithmetic, algebra, and surveying in seventeenth- and eighteenth-century India, Iran, Anatolia, and southern Europe was Baha’ al-Din al-ʿAmili’s (1547–1621) Essence of Arithmetic. This is an interesting phenomenon in two ways. First, because the author was a well-known Shiʿi scholar and as the highest religious official (shaykh al-islam) an active supporter of the Safavid dynasty, which was in repeated military conflict with its western Sunni neighbour, the Ottomans, and involved in some wars with its major eastern neighbour, the Mughals. Second, the situation clearly differed in geometry and astronomy, where the traditional teaching texts from Antiquity and the thirteenth century prevailed, enriched by commentaries of Timurid and early Safavid authors, texts by Andalusian emigrants, and treatises by authors from the ninth to the eleventh centuries, among them Qusta b. Luqa and al-Biruni, whom we met in Chapter Two. Higher level-knowledge of arithmetic and algebra was taught after the introductory classes on al-ʿAmili’s text. The two main texts used for this purpose, sometimes as a kind of commentary or advanced explanation of the Essence of Arithmetic, were Nizam al-Din al-Nisaburi’s The Epistle on Arithmetic for Shams [al-Din] and Ghiyath al-Din al-Kashi’s (died in 1429) Key of Arithmetic or Key of the Calculators.

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A study of mathematical and astronomical manuscripts in Iranian libraries suggests that madrasa teachers in Isfahan, Shiraz, and (apparently to a lesser extent) elsewhere offered the study of the classical teaching texts in the editions of Nasir al-Din al-Tusi, that is Euclid’s Elements and the Middle Books, enriched by reading sessions about Apollonius’s Conics. This occurred more often during the later decades of the sixteenth century and through most of the seventeenth century than at the beginning of the Safavid dynasty. It is unclear, however, whether this renewed interest in the classical teaching literature of the mathematical sciences without the study of Ptolemy’s Almagest continues Timurid traditions of the madrasas in Shiraz or other Timurid cities or whether it was more closely linked to the changes in the philosophical teaching and learning culture in Isfahan in the Safavid period. The works listed in this section as teaching material for the mathematical sciences cover a very broad range of themes, problems, and methods on different levels of qualification. In the first half of the fourteenth century in Cairo, the physician Ibn al-Akfani (died during the plague in 1348) produced a classification of sixty scientific disciplines. Eleven of these sixty sciences were main sciences, subdivided into eight theoretical and three practical ones, and forty-nine were branch sciences. Included in this classification are lists of book titles. Hence, Ibn al-Akfani’s booklet also offers a kind of study guide, in which he classifies the levels of learning and teaching as those of the beginner, the intermediate student, and the advanced student. For each level, he presents a list of suitable textbooks (Ibn al-Akfani 1989, 45–64). Altogether, he names some four hundred plus titles (ibid., 21). This list is part of the author’s discussion of the entire set of knowledge disciplines. I will discuss some of the book titles in Chapters Six and Eight and Ibn al-Akfani’s classification of the sciences in Chapter Seven. With the expansion of Islamicate societies on the Indian subcontinent, Muslim forms of learning and teaching slowly made their way first in the north and later to the centre and the south. About the early Islamicate societies in India (eleventh to sixteenth centuries) and their teaching methods and literature we know only very little. Information becomes more plentiful and detailed for the Mughal state (1526–1856) and the so-called Deccan Sultanates (1527–1686). Madrasas and p­ rivate tutors seem to have dominated. The first reference to teaching the

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r­ ational sciences in India comes from a chronicler of one of the rulers of the Delhi Sultanate in the thirteenth and fourteenth centuries (Speziale 2013, 166). The most famous ruler of the Mughal dynasty, Akbar (ruled 1556–1605), reformed the educational system in his realm and established the study of the rational and mathematical sciences as a duty. The disciplines prescribed by Akbar included arithmetic, administrative shorthand (siyaq), geometry, astronomy, surveying, agriculture, medicine, logic, and the theoretical and practical philosophical disciplines according to their ancient classification (ibid.). An important participant in this reform was the Iranian Shiʿi scholar from Shiraz, Fath Allah (died in 1598). He introduced teaching patterns from the madrasas of his hometown to Mughal India. Speziale argues that this educational reform was one of several elements in Akbar’s cultural and religious politics, which had the goal of strengthening the power of his dynasty over a predominantly Hindu population. Other elements were the introduction of Persian as the language of administration and the arts, the subordination of religious scholars under the dynasty’s thumb, the declaration of a policy of “universal tolerance” vis-à-vis all other religions, and the abandonment of the poll tax for non-Muslims. One consequence of this new policy was the entrance of Hindu students into the madrasa, a feature of Mughal education, which continued until the final destruction of the dynasty by the British Raj in the nineteenth century (ibid.). 4.1.3. Themes, Problems, and Methods Arithmetic taught the nine Indian signs for the digits plus zero and the rules for calculating with them as integers and fractions, carried out either on tablets covered with dust or on paper, in the head or with the fingers. It also introduced calculating with the sexagesimal numbers used in astronomy and timekeeping. Algebra was taught using two different approaches. One line of learning dealt with linear and quadratic equations, the other taught how to calculate with positive and negative powers of x (this is a modern form of expression). Combinatorial problems and the solution of commercial and inheritance problems and other s­ eemingly practical tasks were also taught in classes on arithmetic or algebra. Calculating areas and volumes, however, belonged to a branch discipline of geometry called surveying. Classes on timekeeping taught the astronomical and geodetical interpretation of circles and arcs on a

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sphere (horizon, ecliptic, meridians, altitudes, declination, hour angles, latitudes, longitudes), the qibla (the direction of prayers towards Mecca), and issues related to calendars and chronology. Planetary theory focused on the composition of the universe, divided between the sublunar world with its four elements Earth, Water, Air, and Fire and the supralunar world with the orbs, the movements of its celestial bodies, together with the sizes and distances of the Earth and the planets, which included the Moon and the Sun. On a higher level, classes on arithmetic, algebra, and geometry – if they took place – taught the extraction of higher than cubic roots, decimal fractions, the binomial triangle, occasionally cubic equations, conic sections, and other more difficult geometrical problems. Classes on timekeeping or planetary theory taught the construction of instruments such as astrolabes or quadrants of different kinds and the modelling of planetary movements. Teachers at madrasas or mosques usually taught the basic arithmetical methods of oral and written addition, multiplication, subtraction, division, factorization, and the extraction of square and cubic roots, the construction of plane and simple stereometric figures, and the solving of linear and quadratic equations. Higher-level classes presented the construction of conic sections, arithmetical and geometrical solutions of astronomical and geodetical problems through multi-entry tables, analemmas, or the reading of instruments, and the compilation of the various ncessary astronomical and astrological tables. These higher levels of mathematical knowledge were often acquired as a disciple of a teacher. Many teaching texts served the beginner and are accordingly very elementary. Their sheer number overshadows the fact that higher-level learning and teaching also took place, albeit apparently less often. As I will explain in Chapter Six, flyleaves and notes by students confirm what S. Ragep wrote about al-Jaghmini’s introduction to astronomy (S. Ragep 2007; S. Ragep 2016). These very elementary texts were read together with other books, either commentaries or independently written works. Some of these books were more extensive and taught more complex problems and methods. The collections discussed here testify to pockets of broader and higher mathematical studies across a large territory and several centuries. Thus, the idea of exclusively low-level mathematical ­teaching after about 1500 must be modified in the light of such material.

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Not all themes were taught in the same manner and frequency in all Islamicate societies. For many societies we have little to no information about mathematical education. For those whose historians and scholars reported their work in biographical dictionaries, historical chronicles, or the colophons of manuscripts, we know that in Iran, Central Asia, and later also in India, scholars focused in particular on planetary theory, which is rarely mentioned in Syrian, Egyptian, or North African biographies. In those regions, in contrast, the science of timekeeping was the most visible astronomical field in education. Individual biographies and single manuscripts show nonetheless that such broad-brush pictures hide the specifics of local conditions as well as individual interests. In the 1460s, a high-ranking Mamluk officer, probably from the Ashrafiyya corps of Sultan al-Ashraf Barsbay (ruled 1422–1438), commissoned a copy of one of Qutb al-Din al-Shirazi’s books on planetary models, which was a higher-level commentary on al-Tusi’s Memoir. The copy was produced at the Old Zahiriyya Madrasa in Cairo. Its date of completion is 1467. Several, most likely Ottoman, scholars, among them a court astrologer, studied or owned the book from the early seventeenth to the early nineteenth centuries (ms. London, British Library, Add. 7482). Planetary theory was clearly taught at madrasas, tombs, or shrines, in particular in Cairo, but also in Syria and even in Mecca, during the fourteenth and first half of the fifteenth centuries (al-Sakhawi n.d., vol. 1, 204; vol. 4, 12; 7, 259–61; vol. 10, 189, 259) A prominent teacher of this field was the Turkish scholar from Saruhan, al-Kafiyaji (ibid., vol. 7, 259–61). He had studied the elementary introduction to planetary theory by Mahmud b. Muhammad al-Jaghmini and written a commentary on it. It is unclear whether he also taught more advanced texts like Nasir al-Din alTusi’s Memoir or Qutb al-Din al-Shirazi’s Royal Gift. Ibn al-Akfani surprisingly does not list al-Jaghmini’s Epitome on Plain Theoretical Astronomy as a short text for study, but Athir al-Din al-Abhari’s edition of the Almagest and al-Tusi’s Memoir. As medium-level texts he presents works by the Andalusian scholar Ibn Aflah (died c.  1160) and by Mu’ayyad al-Din al-ʿUrdi. The latter had worked at the court of the last Ayyubid ruler of Aleppo and Damascus, Nasir al-Din Yusuf (ruled 1250–1260), before the Mongols overran both cities and accepted al-ʿUrdi’s plea to let him live, because he was a skilled astrologer. They took him to the new Mongol capital in Maragha (northwestern Iran), where he became an

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important member of Nasir al-Din al-Tusi’s crew of scholars at the observatory. Ibn al-Akfani named as higher-level books first al-Biruni’s astronomical masterwork The Masʿudi Canon, dedicated to al-Biruni’s patron, the Ghaznavid Sultan al-Masʿud I (ruled 1030–1040). Afterwards, he lists Abu l-ʿAbbas al-Nayrizi’s (died after 922) Commentary on the Almagest, and Qutb al-Shirazi’s The End of Perception on the Science of the Celestial Orbs (Ibn al-Akfani 1989, 57). Although other sources confirm that alBiruni’s Canon and Qutb al-Din al-Shirazi’s two astronomical books were known to Mamluk scholars in Syria and Egypt, I am unaware of further evidence that the texts named by Ibn al-Akfani were indeed studied with any kind of regularity, except for al-Tusi’s Memoir, which al-Sakhawi mentions as one of the books on planetary theory read at madrasas in Cairo in the fifteenth century (al-Sakhawi n.d., vol. 3, 110). For Mecca, al-Sakhawi mentions al-Sayyid al-Sharif al-Jurjani’s (1339–1414) commentaries on al-Tusi’s and on al-Jaghmini’s works as the books on planetary theory studied with a teacher (ibid., vol. 4, 12, 78). In the same period, mechanics in the form of the study of the balance appears explicitly as a field of madrasa teaching in Cairo for the first time (ibid., vol. 8, 179; vol. 9, 179). This is probably connected with greater social recognition for the men who headed the office of balances and measurement, since appelations like al-Qabbani (“the man who works with or builds balances“) now also appear in the biographies (ibid.). The existence of manuscripts with texts about the steelyard in Cairo’s central manuscript library is another proof of this renewed interest in balance studies. One such text names the student’s teacher as ʿAbd al-Majid al-Shamuli (ms. Cairo, Dār al-kutub, h.isāb 338, unpaginated [f. 8]). Its content shows that for those interested in balances the main subject matters were the methods for constructing a steelyard and the calculation of the counterweight. Hence, the study of balances appears in this text as connected to craftsmanship, arithmetic, and algebra (ibid., unpaginated [ff. 8, 25, 27]). Ibn al-Akfani, however, reports that he knew of two more themes related to issues of balances and the transport of loads – centres of gravity and the pulling of heavy bodies (Ibn al-Akfani 1989,  56). The texts he refers to were written by two authors of the tenth and the ­eleventh centuries. It is rather unlikely that this entry reflects a fourteenth-century reading practice in a larger circle of teachers and students beyond Ibn al-Akfani himself, who may even have taken his information

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from secondary literature such as Ibn al-Qifti’s biographical dictionary of the philosophers or wise men (Ibn al-Qifti 1903). In contrast, the field of pulling heavy bodies was more regularly taught in Iran, India, and to a certain extent in the Ottoman Empire, judging on the basis of extant school texts. 4.2. Medicine and Pharmacology Medicine and pharmacology constitute the second non-religious discipline that found a stable place in madrasa education. With some variations, the content of medical education built on the basic theory of the four humours, the four elements, and their qualities. The body was understood as consisting of four main liquids (blood, phlegm, black bile, yellow bile) composed like all things in the sublunar world of the four elements, whose state depended on their two qualities out of four (cold, hot, dry, humid) and their degrees. Humoural theory was also the basis for the classification, production, and application of remedies. Disease resulted from the disturbance of the equilibrium between these humours and was healed by restoring it. There was, however, not a single equilibrium for all humans. It rather depended on the specific qualities of the environment, the diet, and the individual nature of each person. On this basis, diseases were identified and classified as general or particular diseases. Other important themes of teaching were ophthalmology, anatomy, doctrines about the soul, fertilization, embryos, bonesetting, and the treatment of wounds. Similar to the long-term stability of basic teaching contents in the mathematical sciences, medical texts continued to teach practices which had been abandoned for centuries, sometimes already in Late Antiquity (Pormann-Savage-Smith 2007). 4.2.1. Teaching Chairs for Medicine and Medical Madrasas In 1227, the Abbasid Caliph al-Mustansir bi-Llah (ruled 1226–1242) founded the Mustansiriyya Madrasa in Baghdad. Its construction was finished in 1234. In addition to teaching positions for the four dominant legal schools (Shafiʿis, Hanafis, Hanbalis, Malikis), he also funded salaries for a teacher of medicine, a librarian, an inspector, and auxiliary personnel. He donated a sizeable library, which survived the Mongol conquest of the city. The physician gave classes and was responsible for

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treating sick people in the hospital joined to the architectural complex (Conermann 2004, 61). This decision by the Abbasid caliph to include a position for medicine was the first to be taken at this high level. At the same time, in Ayyubid Damascus physicians themselves began to endow their houses and libraries as a madrasa dedicated to teaching medicine. The first doctor to take this decision was a leading Ayyubid physician from Damascus called Muhadhdhab al-Din al-Dakhwar (1169/70– 1230/1). The third Ayyubid ruler al-ʿAdil (ruled 1200–1218) appointed him head of the medical community of Syria and Egypt. This office may have been split at some time, since al-ʿAdil’s son al-Ashraf Musa (ruled 1229–1237) appointed al-Dakhwar head of the medical profession in Damascus at the beginning of his reign, and al-Dakhwar returned to the city (al-Nuʿaymi 1988, vol.  2,  129). Six years before this happened alDakhwar was already residing in Damascus. He created a religious trust (waqf) and stipulated in it that his house be turned into a school where only medicine should be taught (ibid., vol. 2, 127; Pormann and SavageSmith give a much later date for the opening of the school, one year after al-Dakhwar’s death [Pormann-Savage-Smith 2007, 83]). As explained in Chapter Three, this type of religious endowment included funds for an administrator, a teacher, a doorkeeper, and further personnel as well as maintenance funds and stipends for students. The head administrators of this medical school were obviously reliable and successful, since almost two hundred years later, in 1417, the school still existed and owned sufficient funds for repairing the building (al-Nuʿaymi 1988, vol. 2, 129). ʿAbd al-Qadir al-Nuʿaymi (died in 1521) compiled a history of madrasas, which had once flourished, but were no longer active in his time. Al-Dakhwar’s madrasa is among them. He reports that al-Dakhwar was the first teacher of his new school and names several of his successors. Among them was ʿImad al-Din al-Dunaysiri (1209–1287), who founded the second medical madrasa in Damascus. Unfortunately, al-Nuʿaymi does not report anything about the classes given at the school or the books read there. Rather, he follows the style of historical chronicles and biographical dictionaries telling his readers with whom al-Dakhwar had studied medicine, Arabic, and literature, who his most famous students were, who else in his family was a physician, and which were the books he had written. Hence, we will meet al-Dakhwar and the men around him again in Chapter Six.  But al-Nuʿaymi highlighted major

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points of a­ l-Dakhwar’s education, quoting from older historical sources. Al-Dakhwar paraphrased influential medical texts by physicians of earlier times such as Abu Bakr al-Razi’s (865–925) Comprehensive Book on Medicine (ibid.). He studied philosophical texts with the religious scholar Sayf al-Din al-Amidi (1156–1233), who became famous and controversial for his interest in logic and philosophy, commenting, among other books, on Ibn Sina’s work Pointers and Reminders. He also was familiar with theoretical astronomy and astrology, two disciplines whose study was often closely interwoven with medical education and practice (ibid.). Ibn Abi Usaybiʿa, a student of al-Dakhwar, provides many more details about the various fields of knowledge that al-Dakhwar excelled in. He not only possessed numerous astronomical and astrological texts, but also instruments. This practical knowledge of the stars earned him al-Ashraf ’s patronage in 1225, a high salary, and a few years later the appointment as head physician mentioned above (Ibn Abi Usaybiʿa 1965, 477). Al-Dunaysiri, who had received his medical and religious education in his hometown and during an educational visit to Egypt, came to Damascus to serve the ruling Ayyubid family as a doctor at the citadel. Afterwards he was appointed at the city’s great Nuri Hospital, founded in 1156 by the Zangid ruler Nur al-Din (ruled 1146–1174) and which functioned until the early twentieth century. We will come back to it as a place of medical education and training in Chapter Five. Although we do not know the date, al-Dunaysiri founded his medical madrasa near this hospital. Al-Nuʿaymi does not provide further information about it. Judging on the basis of al-Dunaysiri’s didactic poems on simple remedies, the theriac (a general cure-all and antidote to poison), and Hippocrates’s introduction to medicine, we can assume that they were meant for teaching and that other texts on these subjects were also read. The last private madrasa exclusively dedicated to teaching medicine in Damascus and mentioned by al-Nuʿaymi was founded by the vizier and physician Najm al-Din al-Lubudi mentioned earlier. His father also was an important physician and administrator. The madrasa was located outside the city gates near a well-known garden or a bath called The Stars and rapidly became famous for its medical classes. Its first teacher was not the founder, but another doctor (ibid., 135–36). Private medical madrasas remained exceptional. More typical were dynastic endowments of a specialized position in medicine such as at the

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Ibn Tulun mosque in Cairo, or an entire madrasa dedicated to teaching medicine and pharmacology. They multiplied across numerous Islamicate societies after the twelfth century in Iran, Mamluk Egypt and Syria, the Ottoman territories in Anatolia and eastern Europe, and in later times also in India and Central Asia. Such foundations were often part of a building complex tied to a mausoleum of the donor built before the latter’s death. A prominent example is Cairo’s Mansuri Hospital with a madrasa attached to the funerary complex, built from 1284 to 1285 for the Mamluk Sultan al-Mansur Sayf al-Din Qalawun (ruled 1279–1290), to which I will return in Chapter Five. Qalawun’s madrasa had teachers for the four main Sunni law schools, hadith, and medicine. Some teachers held teaching positions for medicine at the same time as they served at the hospital (al-Sakhawi n.d., vol. 6, 285; vol. 10, 128). The hospital’s endowment certificates stipulate that Christians or Jews are forbidden to work there or be treated as patients (Northrup 1998, 112). I will return to this point in Chapter Five. Information about foundations combining hospitals with madrasas in a funeral complex is lacking, in contrast, for the western Islamicate societies in Africa and on the Iberian Peninsula. Similar structures began to appear in the late fifteenth century in the Ottoman Empire, often enlarged by a Friday mosque, a soup kitchen for the poor, and a library. Numerous elements of the educational practices of the Mamluk state, including timekeeping and medicine, were appropriated by the Ottomans, although we do not know the details of this process of circulating and imitating knowledge forms and their institutions. Examples are the hospital and medical madrasa in the architectural complexes of Mehmet Fatih in Istanbul (1470), of Bayezid II (ruled 1481–1512) in Edirne (1482), and of Süleyman Kanuni (The Lawgiver; in English also known as The Magnificent) (ruled 1520–1566) in Istanbul. As in the case of mosques, madrasas, or mausoleums established as single buildings, women of the upper class also participated in building hospitals as parts of larger complexes. In the Ottoman case, the Hafsa Sultan Hospital in Manisa (1522–1523) and the Haseki Hospital in Istanbul (1550) were endowed by women of the ruling family (Ihsanoğlu 2001, 567). 4.2.2. The Emergence of the “Jurist-Physician” Medicine could also be studied at madrasas without an appointed teacher for medicine. This process of teaching medicine by teachers appointed for law broadened access to medical knowledge beyond the families of doctors.

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Sabra called this process the shift from “philosopher-physicians” to “juristphysicians” (Sabra 1987, 19, 24; see also Behrens-Abouseif 1989). It had its beginnings much earlier and outside the madrasa, however. The study of the various disciplines together started in the ninth century, slowly and in a few cases at first, but gaining more widespread acceptance in the course of the eleventh and twelfth centuries. Men who later became primarily identified as physicians were also famed for their knowledge of Arabic grammar and literature. Others studied hadith or law in their youth or early adulthood. On the other hand, famous scholars of the religious sciences studied logic, Indian arithmetic, astrology, geometry, number theory, medicine, or magic. Fakhr al-Din al-Razi, one of the leading religious scholars of the twelfth century, for instance, studied the theoretical part of Ibn Sina’s Canon of Medicine, and wrote a commentary on it, which he taught and dictated to students (ms. Tehran, Danishgah, Kitabkhanah-i markazi, 7815). Hence, the terms “philosopher-physicians” and “jurist-physicians” should only be understood as keywords marking these multifaceted processes of change without, however, describing them fully. Northrup believes that in the Mamluk territories the process gained momentum due to the perception among conservative Muslim scholars like Ibn al-Ukhuwwa (died in 1329) or Ibn Taymiyya (1263–1328) that too few Muslims studied medicine, leaving it to members of other r­ eligious communities (Northrup 2014, 122). But this can be true at best in a relative sense, since in Ayyubid times the process of Muslims entering the medical profession was already in full swing. Ibn Abi Usaybiʿa listed a good number not merely of Christian and Jewish doctors and ophthalmologists in his history of physicians, but many high-ranking and well-­respected Muslim representatives of this profession (Ibn Abi Usaybiʿa 1965). There is also some evidence for a cultural shift in the education of physicians in numerous biographical entries written about the scholarly communities in the Mamluk and Ottoman states. It signifies the replacement of philosophy by law or hadith as the second main educational profile of physicians, although it does not mean the complete disappearance of philosophical education among students of medicine. In contrast to earlier views of this period, Fancy shows that in the thirteenth and fourteenth centuries physicians in Mamluk cities, Anatolia, and Mongol Iran were familiar with at least those parts of metaphysics and natural philosophy that were relevant to medical theory (Fancy 2013a).

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The shift from the “philosopher-physician” to the “jurist-physician” also marks the rise of medicine as a field of knowledge that students who focused on law or hadith could and did choose as a complementary field, reading a few introductory texts. One result of this development is the separation between medical knowlege and being able to put this knowledge into practice. Al-Sakhawi, for instance, stresses in a number of his biographical entries that a scholar either was a good or a bad healer or did not enter the profession at all (al-Sakhawi n.d., vol. 6, 125, 323; vol. 8, 217, 242; vol. 9, 151, 184; vol. 10, 196). 4.2.3. Teaching Patterns As the combination of skills and expertise changed with the opening of the madrasa for secular disciplines, teaching patterns apparently adapted to the new conditions. At the beginning of al-Sakhawi’s period of report (end of the fourteenth century), medicine seems to have been mostly studied with a specialized teacher who rarely taught any other discipline. One hundred years later, it had become one of the numerous fields studied together with the religious disciplines. Further combinations emerged. Some students studied it together either with the philological sciences and logic or with the philosophical sciences (falsafiyyat), dialectics, and geometry (ibid., vol. 8, 180–81; vol. 9, 60; vol. 10, 266). A rare case is that of a medical student who is reported to have studied it in conjunction with two philological disciplines, dialectics, logic, and natural philosophy (ibid., vol. 6, 285). Other students read texts in all disciplines taught at a madrasa (ibid., vol. 10, 266). Even al-Sakhawi himself seems to have read one medical text or another as a student, since later he wrote a treatise on what is called prophetic medicine (ibid., vol. 8, 4). Depending on the author, such texts contain either sayings attributed to the Prophet Muhammad and popular recipes mostly based on plants and honey, or a combination of such sayings and recipes with fragments of the theoretical underpinnings of Graeco-Arabic school medicine and references to its main authorities like Hippocrates, Galen, al-Razi, or Ibn Sina (Pormann-Savage-Smith 2007,  150–51). Interpretations of this medical genre vary among modern historians. Some consider it to be in conflict with Graeco-Arabic school medicine, others regard the work of some of its authors as an effort to win more orthodox Muslims over to studying medicine (ibid.; Perho 1995; Northrup 1998).

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A typical example of the bookish type of jurist-physician is the famous jurist ʿIzz al-Din Ibn al-Jamaʿa (1348–1416). In addition to the religious disciplines, he studied medicine with a physician, as well as the preparation of astronomical tables, astrology, divinatory disciplines, and logic (al-Sakhawi n.d., vol. 6, 172–73). When he held madrasa chairs in Cairo, he taught students from Egypt, North Africa, and al-Andalus a broad range of religious and philological sciences together with logic, medicine, and philosophy (hikma) (ibid., vol. 6, 114, 174, 263; vol. 10, 240). He was the teacher of ʿAla’ al-Din ʿUmar b. Muhammad (died in 1462), a member of the famous Ibn Saghir family of physicians, merchants, and administrators of Jewish (Karaite) descent (eleventh-fifteenth centuries), and knew a fair amount of ancient, classical, and contemporary medical texts in Arabic (ibid., vol. 6, 125). But al-Sakhawi never says that he ever treated a single person. Other variations of this new intellectual profile were scholars who taught medicine and preferred to be treated on their deathbed by one of their own students, who specialized in kalam (the rational discussion of articles of faith) and worked in this capacity at the hospital of Mecca or at the Mansuri Hospital in Cairo, or who practiced medicine and taught logic, by then primarily the domain of teachers of the religious discipline called foundations of religion (or faith) (ibid., vol. 9, 187, 266, 278; vol. 10, 127). Among those who studied medical texts as a kind of exercise in “general education” without the intention of practicing it was Muhammad b.  Sulayman al-Rumi, known as al-Kafiyaji (ibid., vol.  7,  259–60). An ­interesting feature of this entry in al-Sakhawi’s dictionary is the combination of medicine with law as something al-Kafiyaji did not study in depth. In contrast, the scholar’s training in the mathematical sciences is portrayed as one of his main subjects of study in addition to the philological disciplines (grammar, declension, semantics, rhetoric), foundations of faith, logic, philosophy (hikma or falsafa), and dialectics. Al-Sakhawi even depicts a clearly different spectrum of mathematical competence for al-Kafiyaji, who had come to Cairo from Saruhan in western Anatolia, than among his Egyptian, Syrian, or Meccan colleages. Instead of the disciplines of arithmetic, algebra, and timekeeping primarily taught at Cairo’s madrasas, al-Sakhawi lists for al-Kafiyaji geometry, theoretical astronomy, spherics in the tradition of the Middle Books, burning mirrors (equally a topic of ancient origin), and optics (ibid., vol. 7, 261).

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4.2.4. Shortcomings of Students and Physicians in Mamluk Times But not all was well among the alumni of Mamluk madrasas. Some only acquired a very superficial knowledge of the texts they studied. Others cheated. Still others became known for their criminal activities. Among them were also men whom al-Sakhawi described as physicians. A certain Muhammad b. ʿAbd al-Wahhab misled his colleagues in law as well as those in medicine by praising the value of Hippocrates’ works to the legal scholars and the importance of his own commentary on Muhyi l-Din alNawa’i’s (1233–1277) book on law to the physicians (ibid., vol. 8, 138). Others became famous for their political ambitions and murderous activities on their way to power. The students of medicine were not alone in such uncivilized behavior. As Chamberlain has shown, severe competition for positions and hostility among madrasa scholars was the norm rather than the exception in Syria and Egypt, in particular during the first century of Mamluk rule (Chamberlain 2002, 92–93, et passim). 4.3. Natural Philosophy Natural philosophy is the disciplinary knowledge taught at madrasas after 1200 that has been least studied by modern historians. During recent years, logic, metaphysics, and epistemology have received significant attention. Unfortunately, this is not the case for natural philosophy. Many historians of philosophy in Islamicate societies believe today that Safavid Iran saw a resurgence of philosophical studies and debates in the sixteenth and seventeenth centuries, in particular in Shiraz and Isfahan. This revival was the work of madrasa teachers of the religious sciences like Ghiyath al-Din al-Dashtaki (died in 1542), Mir Damad (died in 1631), Mulla Sadra (died in 1640), and their students. It focused on metaphysical and epistemological issues, and revived the study of texts by ancient scholars as well as of leading figures of the Abbasid caliphate, in particular Ibn Sina and al-Farabi, but also al-Kindi. Even some philosophical texts by Ibn Bajja (died in 1138) and Ibn Rushd (died in 1198) became accessible in Iran at that time. Pourjavady and Schmidtke have recently shown the extent of this renewed interest in ancient and medieval philosophical texts and doctrines (Pourjavady-Schmidtke 2015). They argue that two main trends were behind this process. In the fifteenth and sixteenth centuries,

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Sadr al- Din al-Dashtaki, Jalal al-Din al-Davani (1426–1502), and their students showed an increased interest in Ibn Sina’s works. Sadr al-Din opined that the many commentaries and supercommentaries on those works and developments in kalam had embedded Ibn Sina’s thought in unneccesary and obstructing textual layers, which needed to be removed. A “return to the sources” was his slogan. Al-Davani, in contrast, was a strong and influential proponent of this criticized tradition. He integrated parts of alSuhrawardi’s doctrines into it, but equally recommended a “return” to the original writings of ancient and medieval philosophers. His main goal in this respect was methodological. Quotes from previous authorities should be correct and hence had to be checked and verified (ibid., 254). At the end of the sixteenth century, a process of slow change set in. It pushed for a reading of the sources from an openly Shiʿi perspective, in contrast to earlier times when such a clear difference between Sunni and Shiʿi interpretations of philosophical doctrines cannot be recognized. A central element of this development was the perception that reading and commenting on Ibn Sina’s works was a Sunni enterprise. As a result, Safavid scholars began to search for an independent Neoplatonic identity as philosophers (ibid., 255, 257–59). They slowly moved towards a preference for al-Suhrawardi’s illuminist philosophy and another “return to the sources”. They revived the study of ancient Greek philosophers like Plato, Aristotle, Alexander of Aphrodisias (flourished around 200), or Polemon (died c. 270/69 bce). But they also studied Late Antique philosophers such as Proclus (412–85) and Philoponos (490–570), translated into Arabic in the early Abbasid period discussed in Chapters One and Two. Moreover, they read Muslim and Christian philosophers of the ninth and tenth centuries such as al-Kindi, al-Farabi, and Yahya b. ʿAdi (894–974), and the Andalusian philosophers Ibn Bajja and Ibn Rushd. The copying of their writings, including texts falsely attributed to them, surged during the seventeenth century. Although colophons are notoriously incomplete, often containing beside religious formulas merely a date or the name of the copyist, some of these copies say that they had been made in a madrasa. They show that despite the growing strength of the second trend in favour of Ibn Sina’s predecessors and critics, the study and copying of Ibn Sina’s works did not disappear from Safavid madrasas. Endress makes this last point quite emphatically in his study of two of several so-called “one-volume” libraries of philosophical literature compiled in Isfahan at this time (Endreß 2001, 19).

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Scholars of the late Timurid and early Safavid periods also studied and taught mathematical texts at madrasas in Shiraz, Herat, Isfahan, Tabriz, or Qazvin. There is even some indication that the turn to Ibn Sina’s philosophical works increased attention to classical mathematical texts. This does not just apply to the presence of geometry, number theory, astronomy, and theoretical music in Ibn Sina’s great philosophical encyclopaedia The Book of Healing. In one of the collections of Ibn Sina’s short philosophical treatises, at least one text on geometry is included (ms. Mashhad, Astan-i Quds 12042, ff. 13b-22b). The colophon claims that Ibn Sina wrote it for his teacher Abu Sahl al-Masihi (ibid., f. 22b,13–15). In the same kind of context, natural philosophy will have been present, as the epistle on the celestial body in this collection suggests (ibid., ff. 69a-78b). Although the impact that the two trends in the study of philosophy in the Safavid period had on the study of natural philosophy is not well known yet, one topic clearly held great interest in the classroom and beyond – the question of the eternity of the universe and its coming into being (Pourjavady-Schmidtke 2015,  266). In this context, as the extant copies show, Aristotle’s work On the Heavens was again read (ibid., 260). Other philosophical issues of interest to Mir Damad, Mulla Sadra, and their students were the role of the intellect in the world, the manner in which the intellect acquires knowledge, the nature of the soul, and the Neoplatonic process of emanation from the One (= God) accepted as standard philosophical doctrine by al-Farabi, Ibn Sina, and other p­ hilosophical writers in Islamicate societies (ibid., 266). The “one-volume” libraries, studied by Endress, show moreover the presence of elements of Aristotelian cosmology in two texts by Alexander of Aphrodisias (On the Principles of the Universe after Aristotle; On the First Cause) and questions on physics, also following Aristotle, perhaps by Polemon (Endreß 2001, 20–21). In contrast, it is generally assumed that with the exception of logic, no philosophical activities took place at madrasas in the Arabic-speaking territories of the Islamicate world. Al-Sakhawi’s biographical dictionary contradicts this widespread belief, as do manuscripts. Some of Ibn Sina’s short texts on the classification of the sciences, philosophical definitions, his philosophical enyclopaedias The Book of Healing and The Book of Salvation as well as his Pointers and Reminders were read or commented on in private houses, study circles, or at madrasas in Iraq, Syria, and Egypt, often introduced by scholars from Iran fleeing the Mongols, undertaking a pilgrimage, or travelling for e­ ducational purposes, as I will show in Chapter Five.

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Philosophy teaching is also recorded for North Africa, Anatolia, and even for Jerusalem and Mecca (al-Sakhawi n.d., vol. 6, 48; vol. 7, 60, 99, 135; vol. 8, 180–88; vol. 9, 48, 277–78; vol. 10, 136 and passim). Ibn Sina’s Pointers and Reminders was of great importance for the spread of natural-philosophical concepts and arguments both to the west and the east of Iran. However, the text’s presence in classes taught by madrasa teachers does not necessarily mean that the part on physics was read too. Works on kalam themes show, nonetheless, that a number of authors included introductions to natural philosophy along the lines of either the Pointers and Reminders and their commentaries or other works of Ibn Sina (see, for instance, Eichner 2009). Hence, the ways of bringing natural philosophy into teaching and learning within the madrasa system were manifold. 4.3.1. The Emergence of Teaching Manuals During the thirteenth century major teaching manuals were written in cities of the Middle East and North Africa dealing with logic and the theoretical disciplines of philosophy (metaphysics or “divine science”; natural philosophy; mathematics). Other such manuals combined parts of philosophy with a religious discipline and a mathematical one. Their authors were often students of Fakhr al-Din al-Razi, the eminent Sunni scholar of the so-called transmitted and rational sciences mentioned earlier. He did not only include philosophy, medicine, and the mathematical sciences, but also astrology and several of the “occult” sciences in his learning and teaching practices. His encyclopaedias in Arabic and Persian are an example, which will be presented in Chapter Seven. Other authors of such cross-disciplinary or philosophical textbooks were disciples and students of Nasir al-Din al-Tusi. A more detailed survey of the teaching literature for natural philosophy will be offered in Chapter Eight. Three of those manuals became standard textbooks in many madrasas between India and Ifriqiyya (today Tunisia) and maybe elsewhere: Athir al-Din al-Abhari’s Gift of Philosophy (Wisdom); Afdal al-Din ­al-Khunaji’s (1194–1248) Summa, and Najm al-Din al-Katibi’s (died in 1276) Wisdom of the Source. Al-Abhari’s and al-Katibi’s textbooks were lucid introductions to Ibn Sina’s philosophy with some excursions into other ­philosophical developements. In addition to Ibn Sina’s philosophy being labeled ­peripatic (mashsha’i), a second major branch of philosophical reflections emerged in the second half of the twelfth century authored by Shihab ­ al-Din a­l-Suhrawardi and called “Illumination” (ishraq).

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Scholars of the thirteenth and early fourteenth centuries like Shams al-Din al-Shahrazuri (died between 1288 and 1304), the Jewish philosopher and religious scholar Ibn Kammuna (died in 1284), and Qutb al-Din al-Shirazi (mentioned above) revived al-Suhrawardi’s philosophical teaching and helped it to find new adherents (Pourjavady-Schmidtke 2009). These “Illumination” philosophers lived under the rule of the Mongol Ilkhanids in cities of Iraq, Iran, or Anatolia. Despite the wars and the religious and political enmities between the Mongol Ilkhanids and the Mamluks, scholarly contacts continued. Al-Shirazi and others were connected with scholars in Mamluk Syria and Egypt who taught philosophical texts there (Pourjavady-Schmidtke 2009,  18). This continued in the post-Ilkhanid period, when important Iranian scholars like al-Sayyid al-Sharif al-Jurjani came to Syria and Egypt and studied as well as taught there for some time, reading not only religious, but also logical, philosophical, and mathematical books (al-Sakhawi, n.d., vol. 5, 233; vol. 6, 82; vol. 9, 22; vol. 10, 207). 4.3.2. Syriac Scientific Studies in the Thirteenth Century During the thirteenth century, secular intellectual activities of members of the clergy of the Syriac churches are again documented after almost three centuries of either silence or lost texts. The central content of this revival, also called renaissance as often is the case in Western historiography, is the translation and appropriation of Arabic scientific, medical, and philosophical texts, in particular those of Ibn Sina (Canon of Medicine, The Book of Healing on Philosophy, The Epistle on Definitions, The Sources of Philosophy, Pointers and Reminders,  etc.). These texts appreciated by Syriac scholars reflect the teaching and learning practices amongst Muslim scholars during that period. Moreover, like their Muslim counterparts, Syriac scholars read Euclid’s Elements and other classical texts in Arabic with their students. While there seems to be no information on how the lay brethren who served as doctors were educated, the safest bet is to assume that this education took place in their families and at least until the early Mamluk period also in hospitals. In the thirteenth century, some Syriac scholars emerged who did not earn their living as physicians, but were high-ranking clerics with a sound philosophical and mathematical education, which they taught to a number of students whose names have been preserved. The most famous Syriac scholars of this time and type are the Miaphysites Jacob Severus bar Shakko (died in 1241) and Bar Hebraeus

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ms. Oxford, Bodleian Library, Pococke 47, f. 177a; last page of the second book of Ibn Sina’s Canon of Medicine, dealing with medicinal simples, proofread March 10, 1126.

(1225/6–1286). Bar Shakko was the bishop of either the Mar Mattai monastery near Mosul or of Tikrit. He studied grammar with Syriac monks and the philosophical disciplines and dialectics with the Muslim jurist and madrasa teacher Kamal al-Din b. Yunus (1226–1286) in Mosul. Ibn Yunus was a famous teacher of a number of later prominent Muslim scholars of

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the religious and also the philosophical and mathematical sciences, among them Nasir al-Din al-Tusi. Ibn Yunus is known for having permitted Jewish and Christian students to attend his classes. He also studied their scriptures with them (Ibn Khallikan 1977, vol. 5, 312). His Syriac student Bar Shakko wrote, in addition to a few religious works, a Book of Dialogues consisting of two parts. The first part covers the philological sciences. The second part encompasses philosophy with its theoretical and practical parts. Although Bar Hebraeus mentions only Aristotle and Greek and Syriac authors from the second to the ninth centuries as the sources studied by Bar Shakko, it is clear that he knew texts by Ibn Sina (Nau 1896). He also was in contact with Athir al-Din al-Abhari, a Muslim student of Ibn Yunus and the already-mentioned author of one of the main philosophical textbooks studied at madrasas. Perhaps they had been classmates. Bar Hebraeus was also familiar with books of ancient Greek, Syriac, and Muslim philosophers, theologians, physicians, and scholars of the mathematical sciences, in particular Euclid, Aristotle, and Ibn Sina. He studied with his father, who was a physician, in Malatya, where he was born, and in the Crusader principality of Antioch whence the family had fled from the invading Mongol armies. In Antioch, Bar Hebraeus received a theological education. Like many students in this time and place, he travelled to other cities for further learning, including Tripoli and perhaps Damascus. In addition to this learning with teachers, Bar Hebraeus studied works like Ibn Sina’s Book of Healing and Pointers and Reminders on his own. At least two of Bar Hebraeus’s students are known by name: Taj alDawla, the son of the Ilkhanid court physician Simeon of Qalʿa Rumayta (died in 1289), and Simeon’s nephew Nemrod (died in 1292), who was elected Miaphysite patriarch in 1283 taking the name of Philoxenus. Bar Hebraeus himself rose quickly through the Syriac Orthodox Church’s hierarchy, being appointed in 1264 to its second-highest office (Maphrian of the East). Although his see was most likely at the monastery of Mar Mattai near Mosul, the new political conditions after the Mongol conquests induced him to spend most of his time in the Ilkhanid capitals Maragha and Tabriz in Iran. There he seems to have written most of his theological and philosophical works, including those of a curricular character. Since these two cities were centres of ­substantial scholarly activities, Bar Hebraeus is believed to have interacted with high-profile philosophers and scholars of the mathematical sciences at the Ilkhanid court like Nasir al-Din al-Tusi or Ibn Abi Shukr al-Maghribi (Takahashi 2003, 250).

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According to Takahashi, three of Bar Hebraeus’s philosophical works can be understood as providing a course on the subject, teaching logic, natural philosophy, and metaphysics (ibid., 252). Each of them covers these matters at different lengths and depths. The parts on natural philosophy are closely related to Ibn Sina’s book on natural sciences in the Book of Healing. Thus, a Christian reader of Bar Hebraeus’s philosophical works will have learned more or less the same kind of knowledge about the universe, nature, and humans as did a Muslim student of Nasir alDin al-Tusi and his colleagues in Maragha – a Neoplatonic version of Aristotle’s books on physics, meteorology, the sublunar world with its minerals, plants, and animals, and doctrines on the souls as summarized, modified, and enriched by Ibn Sina (ibid., 262–64). 4.3.3. A Scholar of Kalam as a Teacher of Philosophy Burhan al-Din al-Nasafi (born around 1233, died after 1277), originally from Transoxania (today Uzbekistan), spent the last years of his life after a pilgrimage to Mecca in Ilkhanid Baghdad. He was a contemporary Muslim mutakallim of Bar Hebraeus with strong philosophical interests. We know nothing about his education, but historical sources praise him as a famous teacher of many people (al-Nasafi 2015,  4). Among his students were important scholars of the Ilkhanid realm such as Sharaf al-Din al-Juwayni (died in 1286), a teacher at the Nizamiyya Madrasa of Baghdad, and Ibn al-Fuwati (1244–1323), a historian, biographer of many scholars of the period, and librarian at the very same school. After long years of teaching in Transoxania, al-Nasafi travelled to Delhi, where he worked for an unknown number of years in his capacity as a teacher (ibid., 1–2). His main reputation rests on his treatise on dialectics. But he was also appreciated for his competence in legal debate and philosophy. His commentary on Ibn Sina’s Pointers and Reminders seems to be lost. A text on algebra was extant, but it is unclear whether it has survived the years of endless war, plunder, and bombings in Iraq since 2003. In his Commentary on the Foundation of Intellectual Perspicacity, written in Baghdad, al-Nasafi treats logic, natural philosophy, “divine science”, and four mathematical disciplines (number theory, arithmetic, surveying, geometry), mostly following Ibn Sina’s elaborations in The Book of Healing with some additions from Pointers and Reminders and Sufi doctrines (ibid., 4–5, 9). Al-Nasafi divides natural philosophy into three parts (ibid., 187–233). The first part defines the concepts of simple and compound bodies and

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their usage for bodies in the supralunar and sublunar worlds such as celestial orbs, elementary bodies, and the four elements. The second part turns to the Earth. It discusses composite bodies generated above, on, and below its surface. In these short sections al-Nasafi explains views about the occurrence of rain, snow, thunder, earthquakes, minerals, gemstones, meltable bodies, sulphurs, salts, eclipses, and the astronomical division of the sphere. These standard philophical themes are enriched by references to alchemical subjects and artisanal products (ibid., 210–23). The third chapter treats doctrines of the soul and intellect. Since neither al-Nasafi’s commentary nor the text he commented on are mentioned by his contemporaries nor by later scholars, Dadkhah and Goodarznia consider both works as marginal texts in the world of learning and teaching of Ilkhanid and post-Ilkhanid Baghdad. Together with the works of the two Christian scholars and the teaching manuals composed during the thirteenth century, al-Nasafi’s commentary demonstrates the pervasiveness of Aristotelian natural philosophy in its presentation by Ibn Sina in the philosophical education that teachers at madrasas and in other contexts gave on the supra- and sublunar worlds at this time. Moreover, al-Nasafi’s commentary is a very handy compendium of the necessary basic knowledge of logic, natural philosophy, “divine science”, and parts of the mathematical sciences. It also integrates some information on alchemy, talismans, and astrology. The brevity of most sections and the tight formulations characterize the commentary as a synopsis or an aide-mémoire. The chapter on natural philosophy, for instance, begins with a description of the scope and content of this branch of philosophy: As for natural (science), it (belongs) to the theoretical arts and what (goes into) them. It has a subject (composed) from the existing or the imagined (things). That is (the reason that) this science (encompasses) the bodies with regard to the property of movements and rests. What we (included?) in this science is according to five parts, which are composed in kinds and sections as follows (ibid., 131).

The topics of natural philosophy covered by al-Nasafi are recognizably Aristotelian in kind, but occasionally include some non-Aristotelian ­opinions from unspecified Muslim sources. In addition to rare cases of highli­ ghting intellectual debates, al-Nasafi often explains natural-philosophical concepts through examples taken from geometry. The main themes of his chapter on natural philosophy treat – not always in this order – natural

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bodies and their substances, types of bodies (simple, compound) and their individual natures, matter, form, existence; dimensions, attributes; forces that allow the transformation of a body from potentiality into actuality and those that are the reason for its decay; movement and rest, the rela­ tion of movement to four of the categories (quantity, quality, place, position) and types of movement (straightness, circular form, velocity); atoms and indivisible objects; the natural place of all objects; time and place, planetary movements, eternity; vacuum and plenum, the finite and the infi­nite, the sphericity of the Earth; the supralunar world, its bodies, their movements, their light or opacity; the sublunar world, the four elements and their attributes, compound bodies; minerals and metals, plants, and animals; the nature of the soul and reason (ibid., 131–260). This fairly comprehensive survey of all relevant themes of natural philosophy built on Aristotelian doctrines indicates that while al-Nasafi’s commentary and the source text on which he wrote may have indeed not been widely read, the knowledge al-Nasafi had acquired and taught was the philosophical mainstream, which reached across disciplinary divides. Since al-Nasafi was a mutakallim, that is a scholar of kalam, his familiarity with Aristotelian knowledge about the world according to its appropriation and modification by Muslim philosophers testifies to the wide distribution of this kind of knowledge both in terms of geography and disciplinary training in the thirteenth century. The stability of madrasa teaching of natural philosophy with its concomittant adaptations to new debates and questions is highlighted by the systematic outline of similar themes in a mid-nineteenth-century text called The Fortunate Gift by Fadl-i Haqq Khaydarabadi (died in 1861). This compendium illustrates the extension of this kind of educational activities to India, where they can be found in the sixteenth century at the very latest. It apparently contains a collection of lectures given by a father to his son while travelling to the headquarters of the East India Company in Delhi. An instructive and lucid survey and discussion of the physics found in this text is given by Ahmed and McGinnis (2016). 4.4. Divination, Magic, Alchemy The institutionalization of the so-called “remarkable, strange, or occult” disciplines repeated the phases, which we encountered already in Chapter

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Two for the mathematical, philosophical, and medical sciences. They were at first exclusively taught in private settings, a form of teaching, which continued until recent times. Magic squares and the construction of talismans had been scholarly subjects since the early Abbasid period when Thabit b. Qurra was one of their early proponents. Magic squares quickly became a subject of mathematical research and many well-known scholars of the mathematical sciences wrote treatises on construction methods (Sesiano 2004). It is less well known in which circles talisman ­constructions were taught. But here too, important works were written by members of the scholarly class, among them also famous representatives of the religious disciplines like Fakhr al-Din al-Razi. Alchemy and its procedures were themes also treated in writing and practical activities from the eighth or the ninth centuries on. Al-Kindi was one of their early representatives. Basic practices were taught by craftsmen like dyers or gilders. The huge corpus of philosophically grounded alchemical writings ascribed to a heavily contested personage of the eighth century, that is Jabir b. Hayyan, probably came into being over a period of two centuries. The corpus attracted the interest of writers in many different areas of the Islamicate world, but the ways in which it was taught and transmitted remain to be studied. In the thirteenth century the disciplines of this kind of knowledge are more often discussed in historical sources. They are present in the courtly spheres of small and large dynasties in Iran, Syria, and Egypt, where patronized scholars like Nasir al-Din al-Tusi or Muhammad b. Mahmud ­al-Amuli (died in c. 1352) wrote about them. In the early fifteenth century, divinatory disciplines like sand divination and the “science of letters” joined astrology at the court of the Timurid prince Iskandar Sultan (ruled 1403–1415), who represented the “science of letters” as the pinnacle of disciplinary learning (Melvin-Koushki 2014). Whether other princes of the dynasty followed his example is not well known yet. But this modification of princely education is in tune with the usage of divinatory practices together with (or instead of ) astrology as one component of military strategy in Syria and Egypt under the Ayyubids and Mamluks. In Mamluk Cairo lived one of the teachers of Iskandar Sultan’s courtly philosopher Ibn Turka (died in 1437). Later, Ibn Turka’s texts were studied by scholars from Cairo. Ibn Turka convinced Iskandar Sultan and contemporary scholars in Iran that the “science of letters”

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was the foundation and goal of philosophical enquiry and mathematical study (ibid.). The Safavid successors of the Timurid dynasty in Iran and the Mughals in India continued various components of Timurid politics with regard to the arts, the sciences, and architecture, including courtly support for divinatory practices and literature. Under the Ottoman dynasty west of Safavid Iran, not only did the court favour various forms of divination, but an increasing number of madrasa teachers dedicated classes to these speculative areas of knowledge. This is clearly visible in Muhammad a­ l-Muhibbi’s biographical dictionary written in the late seventeenth century (al-Muhibbi 1966). In general, people who studied or practiced “letter science” also read treatises on sand divination and astrology. Other disciplinary combinations depended on individual interests. The Mamluk legal scholar from Ghazza, Ibrahim b. Muhammad al-Nawfili (1339–1413), known as Ibn Zuqqaʿa, for instance, pursued alchemy and the study of plants, undertaking explorative journeys to observe and collect them, in addition to “letter science” and astrology (al-Sakhawi n.d., vol. 1, 130). He was a wellknown Sufi and served several Mamluk sultans as advisor (ibid., 132). But as is often the case in these subject matters, some admired the man’s skills and knowledge, including his performing of miracles, while others considered him a charlatan (Shoshan 1993,  77). The famous historian Taqi al-Din al-Maqrizi (1364–1442) studied sand divination and the preparation of a complex chart called zaʿirja for predicting the fate of dynasties with Ibn Khaldun (1332–1406), in addition to the religious disciplines and some of the mathematical ones (including how to construct an astrolabe). Later in his life, he also practiced sand divination (al-Sakhawi n.d., vol. 2, 24; al-Azmeh 2003, 41). Since the Mamluk court, in contrast to many other Muslim dynasties, did not have a courtly office for astrology and since only a few writings on astrology have been preserved from the Mamluk period, it is often assumed that astrology was not a favoured discipline and not part of learning and teaching at Mamluk madrasas. In general, the inclusion of astrology in madrasa classes is more difficult to trace than that of related topics like planetary theory or timekeeping. But there are some clues, in particular remarks in al-Sakhawi’s biographical dictionary, that show that astrological texts were indeed read – at least in some cases – by scholars who specialized in timekeeping. The timekeeper Ahmad b. Ghulam Allah (died

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in 1335) from Kawm al-Rish, who moved to Cairo, was not merely well known for his texts on this discipline, but studied astrology, knew many components of judicial astrology, could handle the tables of an astronomical handbook (zij), and compiled ephemerides (al-Sakhawi n.d, vol. 2, 62). Alchemy was learned and studied primarily in a private setting. In Mamluk Egypt, for instance, some members of the scholarly class were known as practioners of this art, which they offered occasionally to a sultan. Almost all stories known to me in this regard ended either with the loss of life or wealth by the alchemist. The few alchemists whom alSakhawi registered came primarily from Sufi orders. An example is Bilal al-Habashi (fifteenth century), a Hanbali legal scholar from Aleppo, who apparently turned to alchemy due to his leanings towards Sufism (ibid., vol. 3, 18). When we turn to manuscripts we see that despite the lack of formal opportunities for learning numerous students and scholars copied alchemical manuscripts or annotated them. Here much research remains to be done. The same applies to the branches of magic dealing with talismans and incantations. Material objects of the thirteenth century show their usage for medical treatment in the Zangid and Ayyubid territories of northern Iraq and Syria. But there is little reason to doubt that they were also present in North Africa, al-Andalus, or Central Asia. Ibn Khaldun, for instance, complained about their spread in North Africa, although he himself taught – as said already above – sand divination and related matters in Cairo, possibly at a madrasa. The Central Asian scholar al-Nasafi, introduced in the previous section, acquired alchemical knowledge together with his studies of philosophy, the mathematical sciences, and religious knowledge. It may well be that his work reflects a more widespread learning practice among those who took classes or read books on philosophical matters or medicine on their own. Such an assumption seems to be supported by the writings of two major alchemical authors of the twelfth and the thirteenth/fourteenth centuries, one of whom came from Khurasan, but lived for many years in Cairo–ʿIzz al-Din Aydamir al-Jildaki (died in 1342), while the second, Ibn Arfaʿ Ra’s (d. 1197), was born and died in the west of North Africa. The geographical range of the two scholars combined with their educational and scholarly pathways points to a widespread accessibility of alchemical knowledge, even if this access might have been possible only in certain locations.

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4.5. Postface In the following chapters, I will come back to people who learned or taught at madrasas or mosques, since I will talk there about students and scholars travelling for education, methods used when teaching the sciences, and ­teaching bestsellers. We will learn in these later chapters that there is no single story linking the presence and daily practice of the sciences in schools of advanced education across the many different Islamicate societies that rose and disappeared between 1150 and 1700 across the Old World. The informal nature of learning and teaching and the social gain derived from sitting with famous teachers combined to work against a systematic, sequential, disciplinary teaching of knowledge. I do not believe in the existence of curricula that were taught for several decades, let alone centuries, at any of the educational institutions described in this chapter. There were trends, though, that linked Ilkhanid teaching collections with Timurid practices and Ottoman learning. But each of these collections had their individual histories, which need to be unravelled. We are far from understanding these individual sequences and their fates. Other trends linking Ilkhanid preferences with Timurid, Safavid, and Mughal ones or Andalusian teaching literature with that of Maghribi, Mamluk, and Ottoman societies seem to be easier to understand, if only because of similar trends in the arts or politics. Nonetheless, individual manuscripts continue to challenge these easier interpretations such as the appearance of a copy of one of Qutb al-Din alShirazi’s astronomical books on planetary models in 1467 in Cairo, copied there at the command of a Mamluk officer (ms. London, British Library, Add MS 7482, ff. 3a-3b). This type of theoretical astronomy is not otherwise visible in descriptions of scholarly activities at madrasas, mosques, or shrines in Cairo. Its presence speaks against the image painted in biographical dictionaries and by the overwhelming majority of extant teaching texts from that time and place. It reminds us that our understanding of the past always depends on the material that survived and what we care to open and browse. Our understanding of the past also depends on our prejudices about the circulation of knowledge between Islamicate societies and the level of teaching dominantly achieved at their institutions of advanced education. This may also apply to numerous other features of the history of learning and teaching as we currently describe them. Hence, caution is required whatever our judgments – negative or positive.

Chapter 5 OTHER TEACHING INSTITUTIONS

H

aving described in the previous three chapters two major types of teaching and learning – private teaching by a tutor and taking classes with a madrasa teacher – this chapter aims to survey other formalized kinds of learning and teaching the sciences in Islamicate societies. In some cases, these other institutions do not differ from those already considered since they also function primarily as a place for student-­teacher relationships. It depends on the individual teacher and his standing vis-àvis a student’s family and the details of the relationship between student and teacher to decide whether a specific case was that of a hired tutor, a coveted madrasa or royal teacher, an itinerant seller of knowledge, a skilled practitioner who shared his knowledge with apprentices, or a cherished older family member having high-elite education or long years of professional practice. In order to describe the variability of educational forms, possibilities, preferences, and expectations, I have decided to select three further types of formalized education for discussion in this chapter: learning and teaching in families, learning and teaching in hospitals, and travelling as a crucial element of learning and teaching. People in different Islamicate societies often chose several of the available forms to provide their male children with the education they could afford and which was accessible in their towns, villages, or oases. If opportunities were limited, as was often the case in provincial towns and smaller settlements, they first opted for learning and teaching within the family or sending their boys to a mosque or to a practitioner in the market place. Later they encouraged their adolescent sons to travel with a male adult family member to a larger city, or even to the capital, where madrasas, hospitals, or public teaching in other forms existed. The young people could stay behind as enrolled madrasa students with a stipend and room and board. Or they might stay in the care of another family member, an acquantaince, or as an apprentice of a merchant or some other professional.

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After years of study in such forms, adult men often decided to remain as disciples of a famous master or to begin travelling for knowledge to faraway countries, studying in several towns with all or some of the available teachers. Such travels for educational purposes could take many years or even decades. The destinations of such journeys changed over time and depended on regional developments. Early on, people from al-Andalus and the Maghrib often travelled to the Abbasid centres in Iraq, in particular Baghdad. In later centuries, their destinations often were located closer to home in North Africa itself, but could also reach as far to the east as Cairo. But in many cases, travel for education was combined with other important goals such as pilgrimage. Hence Mecca and Medina were part of the travel plan. In the first centuries of Islamicate societies, people from Central Asia and Iran also travelled mostly to the Abbasid centres in Iraq. But already in the tenth century, their travel destinations became more diverse. Towns along the southern Caspian shore ruled by small, local dynasties, and cities in southern and central Iran governed by the Buyids, became preferred goals in the search for patronage. These flows of scholars increased their reputation as places for learning and teaching. In the following centuries, cities in western Iran, northern Iraq, eastern Anatolia, and then India attracted teachers and students from Iran and Central Asia. Students and teachers from Islamicate societies in India began travelling to eastern and southern Iran, Syria, and Egypt. All of these movements left traces in biographical dictionaries, teacher lists, manuscript notes, and libraries. The presence and status of hospitals and their history in Late Antiquity and early Islamicate societies are highly contested. Many modern historians have attributed their emergence to different dynasties, cities, and historical periods. Medieval sources often present unreliable claims as part of the narratives of origin of the entire field of medicine and of the legitimacy of particular medical families, approaches to healing, or caliphal generosity (Pormann 2010a). One undeniable feature of hospitals in Baghdad and Rayy under Abbasid or Buyid patronage in the late ninth and the tenth centuries is their function as sites of learning and medical training. This kind of institution continued in several other Islamicate societies, in particular those ruled by the Zangid, Ayyubid, Mamluk, and post-Ilkhanid Mongol dynasties. The situation at Ottoman hospitals, in contrast, is highly debated. Since learning and teaching at hospitals is

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often seen as a mark of progress, Turkish scholars tend to emphasize such a function for Ottoman hospitals. Ottomanists and historians of medicine from other places of origin have been more reluctant to subscribe to such a view and believe that early-modern Ottoman hospitals actually offered very little formalized learning and teaching as part of their daily routine (Shefer-Mossensohn 2009, 142). 5.1. Learning and Teaching at Hospitals Hospitals in Islamicate societies are called in Arabic, Persian, or Turkic sources by a broad variety of names including houses for caretaking, houses for medicine, asylums, infirmaries, and hospitals. The early hospitals founded under Abbasid and Buyid patronage in Baghdad, Rayy, and elsewhere were known by their Persian designation bimaristan. Numerous stories in medieval sources link their emergence to the city of Gundishapur in western Iran and its Christian physicians of the Church of the East. But as with other stories about the late Sasanian Empire and early Abbasid times, it is very difficult to judge the reliability of these claims. For our purpose in this chapter, it is sufficient to focus on the hospitals founded by Abbasid caliphs and their mothers, as well as by Buyid emirs, in Baghdad and Rayy. These hospitals are well known as locations of teaching and learning not merely from biographical stories, but also through medical writings of different kinds and different authors working and writing in them from the second half of the ninth century onward. This multiplicity of testimonies increases the likely truth of the claim that indeed some medieval experts learned and later taught in the hospitals of Baghdad and Rayy, in particular the ʿAdudi Hospitals. These hospitals were either newly created or restored by the Buyid ruler ʿAdud al-Dawla mentioned in Chapter One. He endowed the hospital in Baghdad with twenty-four physicians of each medical subfield, including ophthalmologists and surgeons, and ordered them to teach at the ­hospital (Ibn Abi Usaybiʿa 1965, 367). 5.1.1. Hospitals in Baghdad and Rayy Pormann believes that hospitals in Baghdad were the result of a number of factors. The city’s extensive urbanization contributed to their rise in the ninth and the tenth centuries, as did epidemic and other health

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pressures, and high-profile female and male patronage as part of charity. Further contributing factors were the stabilization of formalized, theoretically grounded medical knowledge and the impact of Christian values, in particular from communities of the Church of the East, upon some members of the caliphal household and some of its high-ranking administrators. Finally, the emergence of the legal framework of religious endowments (waqf) ensured a controlled and stable building and maintenance process (Pormann 2010a, 369–75). Pormann sees the shift from exclusively caring for the poor and travellers in Christian circles in Byzantium and the Sasanian Empire to the treatment of members of the elite and openness to all religious communities, both as personnel and as patients, as distinct new features of hospitals under Muslim rule (ibid.). Recognizing the hospital as a site of teaching and learning appears to be a further element, that was, if not introduced, then promoted by the sociopolitical attention and financial support provided by the wealthy elites under the Abbasid dynasty. Gifted physicians guaranteed the hospitals’ fame and made the investment worthwhile. Hospitals were named for their endowers and increased their reputations as guardians of the faith and protectors of the population. They were thus seen as institutions, which bound together religious, political, economic, and scientific obligations and opportunities. Learning in a hospital was recommended with different arguments by a number of physicians. For some, like Yaʿqub al-Kaskari (see also Chapter Two), reading translations of ancient Greek texts such as Rufus of Ephesos’s On the Ailment of Melancholy or pharmacological works by Christian and other colleagues, such as Sabur b. Sahl’s Dispensatory, was part of his standard work practice. Only in such a manner did al-Kaskari think he could improve his own knowledge and skills in preparing remedies (ibid., 346–47, 349). Others, like ʿAli b. ʿAbbas al-Majusi (died after 982), commanded students to work in a hospital as part of their professional training (ibid., 366). Al-Majusi’s encyclopaedic work The Complete Art of Medicine, also known as The Royal Book, insisted that (i)t is also necessary for the student of this art [sc. medicine] to attend hospitals and other places where patients are present; to discuss their state and condition with intelligent professors of medicine; to observe closely their state [sc. the patients] and the symptoms present in them (quoted after ibid.).

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The Royal Book itself was an object of courtly patronage, but fairly quickly became a textbook for students of medicine. Over time, it lost ground to Ibn Sina’s Canon of Medicine. But it kept the status of complementary reading for a long time. Some medieval reports highlight the fact that the concept of “student” was different to our understanding. People might enter this state not only in their youth, but at any moment of life. More importantly, there was no limit to the time during which one could be a student. Ibn Abi Usaybiʿa, for instance, reports, from Ishaq b. ʿAli al-Ruhawi’s (ninth century) book The Education of the Physician, the testimony of one ʿIsa b.  Musa that “Masawayh, Abu Yuhanna was a student at the hospital of Gundishapur for thirty years” (Ibn Abi Usaybiʿa 1965,  191). Ibn Abi Usaybiʿa also says of this man that he had never read “a single letter in any language” (ibid.). Thus the father of the court physician Ibn Masawayh knew the art of healing without training in theoretical, formalized medicine and possibly without being capable of reading. In such a context, the word “student” may have rather meant “amanuensis” or “servant”. Hubaysh b. al-Hasan (ninth century), a nephew and student of Hunayn b. Ishaq, had another function. Ibn Abi Usaybiʿa reports that Hubaysh finished Hunayn’s important medical textbook Book of Problems, which he classifies as “an introduction to the art of medicine, because he collected in it all summas and epitomes dealing with the principles and foundations of this knowledge” (ibid., 219). According to one witness, Hunayn is portrayed here as having collected material for this textbook all of his life, apparently never finishing it. His student Hubaysh then ordered the material and added information about the theriac on his own (ibid.). Other physicians considered hospital practice indispensible for someone who wished to become a good doctor, because only there could the student or young professional encounter rare diseases unknown to the world of books. In his treatise Stimulating a Yearning for Medicine, the Christian physician Saʿid b. al-Hasan (died in 1072) argued: He [sc. the physician] should frequently enter and serve in hospitals; he can study rare diseases, which he encounters [there]. One often witnesses in such places diseases which are unheard of and which one does not see [discussed] in the written [medical literature]. […] If he sees any such rare condition, he should record it in his notebook and thus preserve it so that he and others can benefit

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ms. Oxford, Bodleian Library, Greaves 25, Hunayn b. Ishaq, Problems of Medicine for Students, completed by Hubaysh al-ʿAsam, his student; proofread in the last days of November and first days of December 1295 by Muhammad b. Ahmad b. Michael of Konya.

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from it. When he comes to the hospital, he should sit in the place, which behoves and befits him. He should clothe himself in calm and dignity, and be attentive and listen with benevolence to the complaints of the patients (quoted from Pormann 2010a, 365).

Abu Bakr Muhammad b. Zakariyya’ al-Razi, one of the most famous physicians and philosophers of the second half of the ninth and the first quarter of the tenth centuries, was inspired to study medicine by visiting a hospital in Baghdad. Reading medical literature, talking to physicians and druggists, and observing patients at the Muqtadir Hospital apparently were all part of his learning process. Later, his teaching at the various hospitals, which he headed in Baghdad and Rayy, combined treating patients with reading books. Al-Razi’s method is described in Ibn al-Nadim’s Catalogue, based on the testimony of an acquaintance, who had visitied Rayy and talked there to some old gentleman, as follows: He was an old man with a large sack-shaped head, who used to sit in his clinic with students around him. Alongside with them were (his) students, and still other students were with them. A patient would enter and describe his symptoms to the first people, who met him. If they had knowledge [of what was wrong, good] but if they did not [have the required knowledge], he would pass from them to others. Then if they hit [upon the diagnosis, good], but if not, alRazi would discuss the case (Ibn al-Nadim 1970, vol. 2, 701–02).

Nonetheless, al-Razi was not an empiricist. Like many others of his colleagues he believed in the necessity of reading the books of the ancients. This is shown in his writings, but also in the following little anecdote. One day, al-Razi was asked whom to prefer – a doctor who had seen many sick people but did not appreciate scientific books, or one who had spent his time with reading the books of the ancients and trying to understand them. Al-Razi recommended the latter (Micheau 1981, 110). The ʿAdudi Hospital in Baghdad continued to serve as a site of learning and teaching until the late thirteenth century at the very least. It seems to have survived the Mongol onslaught in 1258. A colophon written in the year 1280 at the end of a copy of Fakhr al-Din al-Razi’s Commentary on the theoretical part of Ibn Sina’s Canon of Medicine confirms the hospital’s existence. Moreover, it links the hospital to autodidactic learning there. Its scribe was ʿAbd al-Sammad b. Ahmad b. Masʿud b. Abi Bakr

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ms. Oxford, Bodleian Library, Or. 514, f. 114b, a Judaeo-Arabic copy of Abu Bakr al-Razi’s book The Sufficient on Medicine.

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b. ʿAbd al-Karim b. Abi Saʿid al-Tustari (thirteenth century), known as the servant of the ʿAdudi Hospital. He annotated for himself what “the excellent Sayyid, the Philosopher Fakhr al-Din Muhammad b. ʿUmar alRazi, may God be content with him, has dictated of the Commentary on the Kulliyat of the Qanun, much praise be upon God” (ms. Tehran, Danisgah, Kitabkhanah-i markazi, 7815). The other remarkable aspect of this colophon is ʿAbd al-Sammad’s designation of Fakhr al-Din al-Razi as a philosopher. This is certainly correct as a matter of fact, but unknown as an appellation of the great Sunni scholar. 5.1.2. New Hospitals in Damascus and Cairo In the twelfth and thirteenth centuries two newly built hospitals in Damascus and Cairo became equal in fame as places of learning and teaching – the Nuri Hospital built in Damascus in 1154 at the command of the Zangid ruler Nur al-Din Zangi (mentioned in Chapter One) and the Mansuri Hospital in Cairo opened in 1285 by the Mamluk Sultan al-Mansur Sayf al-Din Qalawun (also already introduced in Chapter One). Both hospitals were not merely royal acts of health-promotion and charity, but intricate projects of powerplay and urbanization (Northrup 1998; Ragab 2015). Here, however, the sole focus will be on their function as sites of learning and teaching. The main sources for our knowledge about who learned and taught at the hospital in Damascus, what was learned, and how it was learned, are the biographies of physicians and philosophers composed by the Ayyubid vizier Ibn al-Qifti, and the Ayyubid doctor and scion of a high-ranking medical family Ibn Abi Usaybiʿa. Mamluk historical chronicles and biographical dictionaries provide material about Qalawun’s hospital in Cairo. Further sources are the writings of the students and teachers who also worked at one of these hospitals. I  will talk about some of the teaching texts in Chapter Six, because there is no explicit evidence that they were composed or taught within the hospitals. Ibn Abi Usaybiʿa described the learning and teaching activities at the Nuri Hospital in several of his biographies, both for the time of the

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Zangid ruler and for the decades of Ayyubid rule (Micheau 1981, 120; Ibn Abi Usaybiʿa 1965, 670–71 and passim). His descriptions show that these activities had a stable pattern. Doctors took care of hospitalized and ambulant patients in the morning hours. Teaching took place in one of the free corners of the hospital’s central space, where the head physician or one of the other leading doctors assembled a group of junior and possibly a few more senior colleagues, as well as students, around him in a semicircle and read a particular medical text with them or sometimes two texts together. The truly good teachers of medicine, like Ibn Abi Usaybiʿa’s own teacher Muhadhdhab al-Din al-Dakhwar (see Chapter Four), corrected mistakes in the text read and explained difficult or obscure passages. Texts studied at the Nuri Hospital were either taken from the library that Nur al-Din Zangi had attached to the hospital or were brought by the physicians (Micheau 1981,  120). In addition to book-­ reading and writing copies of a text taught during such afternoon classes, the main advantage of learning in the hospital was the apprenticeship it provided to students and young practitioners. Ibn Abi Usaybiʿa describes his own training as having followed al-Dakhwar and another leading doctor of the Nuri Hospital wherever they went, listening to their conversations with the patients, and observing their prescriptions of therapeutic methods. He also sat close to the doctor who served the day-patients, taking notes of his exchanges and recommendations, and copying his prescriptions of remedies (ibid., 671). Among the texts that Ibn Abi Usaybiʿa read at the Nuri hospital with al-Dakhwar, as well as with Abraham, the son of Maimonides (1186–1237), at a smaller hospital in Cairo, were the so-called Sixteen Texts of Galen, texts ascribed to Hippocrates like the Aphorisms and On Epidemics, and Galen’s commentaries on such ancient Greek texts like The Oath. The so-called Sixteen Books of Galen encompass texts written by Galen for beginners. The first of them, which Ibn Abi Usaybiʿa’s uncle learned by heart at another small hospital in Cairo, are On the Sects for Beginners, The Art of Medicine, On the Pulse for Beginners, Therapeutics to Glaucon, and On Bones for Beginners (Pormann 2010b, 424). Ibn Abi Usaybiʿa and the older members of his family would also have read commentaries on those ancient works by Christian, Jewish, and Muslim physicians. The Aphorisms in particular were often chosen for commentaries. Commentators living in Damascus and Cairo

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during Ibn Abi Usaybiʿa’s lifetime were Maimonides (died in 1204), al-Dakhwar, and Ibn al-Nafis (Savage-Smith 2011, 6–7, 9, 13, 15, 18). Other texts studied by Ibn Abi Usaybiʿa with his Jewish or Christian teachers in Cairo belonged to the remedy literature specific to hospitals. Chipman suggests that he may have read the Dispensatory of Amin al-Dawla b.  al-Tilmidh (1073–1165), which in her view had already arrived at the Nasiri Hospital in Cairo, when Ibn Abi Usaybiʿa studied there with its Jewish director Ibn Abi l-Bayan (died in 1236). For his work in the hospital, Ibn Abi l-Bayan composed his own pharmaceutical handbook on compound medicinals, which he read apparently more than once with his student and which Ibn Abi Usaybiʿa corrected for his teacher (Chipman 2009, 38–39). Ragab recently proposed that the content, style, and purpose of learning and teaching at the Nuri Hospital depended on that of the ʿAdudi Hospital in Baghdad. He believes that a group of physicians, among them Ibn Mutran (died in 1191), Radi al-Din al-Rahbi (1140–1234), and alDakhwar, “read new texts, rediscovered others, and wrote summaries and commentaries in new and largely unique ways. Their intellectual genealogy extended to the famous al-Bīmāristān al-ʿAd.udī in Baghdad linking them to a longer bīmāristān tradition that colored their work and the works of their students” (Ragab 2015, 141–42). A number of his ideas for butressing this claim are speculative and in conflict with the interpretation of the sources by other historians of medicine (see, for instance, Pormann 2012). Amin al-Dawlah, a member of the Church of the East, was the long-serving director of the ʿAdudi Hospital in Baghdad, and a highly influential teacher (Ibn Abi Usaybiʿa 1965,  331). His oeuvre consists overwhelmingly of commentaries on ancient and medieval authorities, among them The Completion of the Alexandrian Epitomes, al-Razi’s Comprehensive Book of Medicine, and Ibn Sina’s Canon. He also wrote handbooks specifically for his work at the hospital, thus combining texts for teaching and healing. His Great Dispensatory replaced that of Sabur b. Sahl, first at the ʿAdudi Hospital, and over time also in other hospitals of the region, including the Nuri Hospital in Damascus (ibid., 326; Savage-Smith 1996; Ragab 2015, 144). These texts became the nucleus of what was studied in Damascus at the Nuri Hospital and later on in Cairo at the Mansuri Hospital (ibid.).

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The Mansuri Hospital, built about fifteen years after Ibn Abi Usaybiʿa’s death, has attracted repeated research attention due to the fact that several of its founding documents have survived in narrative and archival sources. Another reason for the attention paid to this hospital was Ibn al-Nafis, one of the famous medical teachers in Cairo in the second third of the thirteenth century. In the early twentieth century, Ibn al-Nafis was falsely identified as the Muslim discoverer of the pulmonary blood circulation who also predicted the existence of pulmonary capillaries. These two claims attracted many historians and physicians (Fancy 2013a, 2, 5–6; for an example, see West 1985). Fancy showed that Ibn a-Nafis did not speak of pulmonary circulation, but of a pulmonary transit of a minimal part of very fine blood, rooted in his revisions of Galenic/ Avicennan physiology (Fancy 2013a, 69, 101–12). It is generally recognized that the hospital was the central building of the funeral complex built by Sultan Qalawun in 1284 and 1285 (Northrup 1998; Ragab 2015). The entire complex served a number of political and religious goals of the Mamluk ruler, the discussion of which are beyond the subject matter of learning and teaching. Important, however, are the terms chosen by Qalawun to legitimize his choice of a hospital as the centrepiece of his funeral complex, because he styled himself as the first ruler to take care of his subjects’ bodily health and to provide funds and space for adequate medical education and caretaking. Moreover, in the following extract from his appointment decree for the first head of the new hospital, he defines medicine as a religious duty of the ruler and of the ordinary believer: We saw that every king who preceded us, even if he followed the best path in managing the flock, had been interested in the science of religion and neglected the science of the bodies, and each of [our predecessors] built a madrasa and did not care for a bīmāristān [hospital], and neglected [the prophet’s] saying science is [of ] two [types], and did not admonish any of his flock to be occupied with the science of medicine that is necessary, nor endowed a waqf for the students of this science, mentioned [in traditions], nor prepared a place of attendance for those occupied with the art, nor appointed a shaykh for [those] occupied [with medicine]. We have known of this what they had been ignorant of, and remembered of this nearness [to God] what they neglected, and connected of these religious and earthly means what

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they separated, and built a bīmāristān [hospital] that dazzled the eyes with joy (Ragab 2015, 106–07).

A further feature of Qalawun’s complex is the presence of a madrasa, added by Qalawun’s overseer of the construction, the emir ʿAlam al-Din Sanjar al-Shujaʿi (died after 1293). It clearly contradicts the emphasis the Sultan himself made in the document just quoted. Over time, however, the madrasa provided an important space for education in the context of the hospital. Physicians such as Ibn al-Nafis donated their personal libraries to the hospital, and a member of his study circle, Ibn Abi Hulayqa (1223–1308) became the first director of the hospital (Northrup 2001 and 2014, 113). The endowment deed for the hospital itself included, among other items, salaries for physicians, oculists, and surgeons as well as a bonus for the director for giving a weekly public lecture on medical knowledge (Ragab 2015, 119). The waqf also stipulated that one of the hospital’s physicians should teach all branches of medicine, at times to be set by the administrator of the hospital. Diverging from the practice at the Nuri Hospital, Sultan Qalawun wished this teacher to sit on a long bench while teaching (ibid., 130). The purpose of this expressive command remains unclear. A second waqf document clarified the teaching obligations prescribed solely for the medical director of the hospital, who at the same time was confirmed as the head physician of the Mamluk realm (ibid., 132). Qalawun’s decrees contained further, very specific details prescribing how to organize the teaching. Obviously, experts were involved in preparing these texts. The students were to be sorted according to their skills and educational goals into groups of aspiring doctors, ophthalmologists, surgeons, bone-setters, herbalists, and other medical practioners. The teacher’s task was to make them learn by heart the knowledge needed for their fields of specialization and to supervise them in their practical activities (ibid., 133). In addition to the experts mentioned in these deeds, Chipman lists as further medical labourers of the hospital cooks of syrups, rhubarbs, and foodstuffs, as well as preparers of electuaries, eye-powders, purgatives, and other medicines (Chipman 2009, 138). Several recent scholars believe that Qalawun’s directives for his waqf aimed at increasing educational opportunities for Muslim students of medicine, sidestepping family education, and providing society with more skilled Muslim doctors (Northrup 1998,  2014; Tabbaa 2003; Lewicka

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2014; Ragab 2015). Since none of them provides, however, any kind of statistics for physicians who lived during the time of Qalawun and his successors, it is very difficult to judge whether such directives achieved any visible rise in the number of Muslim physicians, at least for the capital. The continued presence of Christian and Jewish doctors in Mamluk historical sources puts such claims in doubt. Moreover, the attention paid in the deed to providing equal education for all other medical practicioners needed at the hospital should then be read in the same manner. No historian writing about the Mansuri hospital has, however, interpreted the waqf stipulations in such a form. Another way to interpret the exclusion of Jewish and Christian physicians and patients from work and treatment at the Mansuri Hospital is to assume that Qalawun interpreted the religious obligation of charitable work differently than previous Muslim rulers and administrators. The Abbasid vizier Ibn al-Jarrah clearly saw himself as responsible for the health of the non-Muslim subjects in Iraq and organized medical care for Jewish and Christian communities accordingly (Pormann 2010a, 358–59, 368). Sultan Qalawun obviously did not share this view, but considered himself responsible for his Muslim subjects only. On the other hand, as Shefer-Mossensohn has pointed out for Ottoman hospitals, Ottoman Jews often refused to receive medical treatment outside their own communities due, for instance, to differences in dietary prescriptions (Shefer-Mossensohn 2009, 127). 5.1.3 Theory versus Practice or Theory cum Practice? In his recent book, Ragab claims that Ayyubid doctors in Damascus like al-Dakhwar and his circle had little interest in theoretical medicine and focused mainly on issues relevant to practice. This alleged Ayyubid healing as well as teaching practice, he believes, had a profound impact at the Mansuri hospital. This thesis is the result of Ragab’s flawed understanding of al-Razi’s Hawi and its alleged rediscovery by al-Dakhwar’s circle, and of Ibn al-Nafis’s works, especially his commentaries on the Hippocratic Aphorisms and Ibn Sina’s Canon. Ragab suggests that Ibn al-Nafis rearranged the texts in order to focus on what he thought were the texts’ central points. Thus, these commentaries reveal “a significant practice-oriented bias. […] this practice-oriented approach was arranged around diseases; it valued anatomical knowledge that viewed diseases through their connection to the body’s anatomy” (Ragab 2015, 163). However, Ragab

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­ istakenly attributes the rearrangement of the Aphorisms to Ibn al-Nafīs, m when in fact, it had been Ibn Abi Sadiq of Nishapur (died after 1068) who rearranged the Aphorisms. Ibn al-Nafis merely reverted back to the original Hippocratic order. In the case of Ibn Sina’s Canon, Ibn al-Nafis removed the anatomical section from the section on diseases, as found in the Canon itself. He placed it at the end of Book I, which is on the universal theory of medicine and medical practice. Finally, contrary to Ragab’s claims, al-Razi’s Comprehensive Book on Medicine (Hawi) is the same text as the Jamiʿ. It was in use by physicians outside of al-Dakhwar’s circle, such as the late twelfth-century physician Ibn Jumayʿ(died in 1198) in Cairo, who incorporated it into his commentary on the Canon (Fancy 2016). Fancy, in contrast, does not see a turn to primarily practical knowledge in the teaching and learning practices of late Ayyubid and early Mamluk doctors. He emphasizes the philosophical education of a number of Ayyubid and Mamluk physicians and their contemporaries in Saljuq and Mongol Anatolia, Iraq, and Iran. He shows that subsequent commentators on Ibn Sina’s Canon and its Epitome (a text attributed to Ibn al-Nafis) recognized that the Syrian physician had challenged several of Galen’s and Ibn Sina’s medical theories and their underlying natural philosophical foundations. These commentators engaged with Ibn al-Nafis’s new theories in several different ways, all of which presuppose solid philosophical training (Fancy 2013b, 2017a, 2017b). The idea of a neglect of theoretical and philosophical education among Ayyubid and Mamluk physicians also contradicts the overall picture of these two dynasties painted in various historical sources. Philosophical and medical commentaries on Ibn Sina’s works by Fakhr al-Din al-Razi, in particular on the Pointers and Reminders and the Canon, shaped the intellectual world of Ayyubid Damascus to which al-Dakhwar and his circle belonged. Conflicts between scholars at the Ayyubid court in Damascus about what to read and what to teach focused on these books and their interpretation. Such conflicts and their misrepresentation by religious scholars who opposed any engagement, however critical, with philosophy and medicine have for a long time misled modern historians in their evaluation of the state of the sciences under the Ayyubids and the Mamluks. They took at face value stories about al-Ashraf Musa’s alleged ban on the learning and teaching of all the sciences except the religious ones in 1229 for Damascus (for a late echo of this belief, see Lewicka 2014).

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In contrast to such faulty interpretations of the historical material, in his impressive survey of the intellectual developments between the thirteenth and the seventeenth centuries, including Sunni, Shiʿi, and Sufi trends in Iran with outliers in Central Asia and India, Iraq, Syria, Egypt, and Anatolia, Endress sketches the major lines of the processes of integrating philosophy and other non-religious sciences into Muslim education as primarily focused at madrasas, but also pursued by scholars at courts (Endreß 2001). Witkam’s study of Ibn al-Akfani’s life offers further reasons for questioning Ragab’s low opinion of the scientific interests of the medical personnel at the Mansuri Hospital. Ibn al-Akfani practised as an opthalmologist and as an advisor on herbs at the hospital. He also taught medical, ophthalmological, arithmetical, optical, natural philosophical, and logical literature. Moreover, he was the successful author of at least nineteen, if not more, treatises on different fields of knowledge (Ibn al-Akfani 1989, 25–53). While Ragab considers Ibn al-Akfani, who hailed from Sinjar in northern Iraq, as the best of the hospital’s medical workers, he nonetheless claims that “[t]he majority of these physicians did not achieve any significant prestige, and many of them had other professions in addition to medicine. This indicates their limited reputation as physicians and also their limited income from medical practice” (Ragab 2015, 129–30). Witkam, in contrast, sees Ibn alAkfani as a highly appreciated member of Cairo’s scholarly community in the first half of the fourteenth century (Ibn al-Akfani 1989, 25–53). 5.1.4. Rashid al-Din’s (1247–1318) House of Healing in Tabriz Other hospitals were founded in the twelfth and thirteenth centuries by rulers of Turkic dynasties in Anatolia, in particular in Kaiseri, Konya, and Tokat; by two further Mamluk sultans, high-ranking Mamluk officials in smaller towns in Syria; and by Rashid al-Din, one of the most famous viziers of the Mongol dynasty, in Tabriz, the dynasty’s second capital in Iran (Shefer-Mossensohn 2009, 141; Chipman 2009, 139–43; Speziale 2012, 2; Chipman 2013, 116). Since the information about their learning and teaching activities is generally meagre, except for the few instructions contained in Rashid al-Din’s endowment documents, I will mention here briefly the Ilkhanid hospital in Tabriz. This hospital was much smaller than the Nuri and the Mansuri Hospitals in Damascus and Cairo. It only hired a single physician, an oculist, a surgeon, a druggist, and a guardian

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of the medical storeroom. Teaching was the prescribed task of the physician. Two students were his planned audience. They received a stipend. In order to support the students’ learning, the donor also provided funds for a repetitor, usually a more advanced student or a disciple of the teacher. In close agreement with waqf documents for madrasas, the hospital in Tabriz received funding for a gatekeeper, a housekeeper, a water-carrier, a cook, and two servants (Shefer-Mossensohn 2009, 141). 5.1.5. Learning and Teaching at Hospitals in the Ottoman and Safavid Empires, and Islamicate Societies in South Asia Hospitals in early modern Islamicate societies did not differ much from their medieval predecessors. At least this is the view of scholars who published books about them in the last decade (ibid.; Speziale 2012). They seem to have been less prominent than their predecessors in Baghdad, Rayy, Damascus, or Cairo. References to teaching in such early modern hospitals are very rare (ibid., 3). Exceptions seem to have been the royal hospitals in the three Ottoman capitals of Bursa, Edirne, and Istanbul, and a hospital in Astarabad (today called Gorgan) in northeastern Iran. In other cases, hospitals were built near to a madrasa, as happened in Isfahan, Hyderabad, and Delhi (ibid., 3, 8). Hence, this last section on teaching and learning in hospitals will briefly summarize the scarce reports of these few hospitals and their teaching and learning activities, without a deeper engagement with historiographical matters raised in the sections on the famous teaching and learning hospitals in earlier centuries in Iraq, Syria, and Egypt. In the case of Safavid Iran, only one hospital is described in the known primary sources as endowed with a teaching professor, a repetitor, and stipends for students (Floor 2012, 40). It is the one in Astarabad mentioned above. It was built by a wealthy merchant. He stipulated that the professor to be hired had to be knowledgeable in medicine (ibid.). Although a number of hospitals existed in major towns of Safavid Iran and were headed more often than not by known physicians with links to the Safavid court and the towns’ governors, no other is mentioned as a teaching and learning institution. The two primary institutions of medical learning and teaching in post-Mongol Iran up to the modern era were the master-apprentice relationship, often bound to medical families, or the madrasa, although no specialized medical madrasas are known.

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The situation in Islamicate societies on the Indian subcontinent and in the Ottoman Empire resembled that of Safavid Iran. Although sultans and their high-ranking courtiers and officers occasionally included the building of hospitals and dispensaries in their architectural activities, only a few of them are known to have included provisions for teaching and learning. One hospital that also served the education of students was built in 1595/6 in the newly founded capital Hyderabad (1590/1) of the Qutb Shah dynasty of Golconda (ruled 1518–1687). It is one of the oldest extant hospitals in South Asia. It taught medicine according to Ibn Sina, although this does not mean that its professors only read Ibn Sina’s Canon with their students (ibid.). Since the actual construction supervisor of the hospital was in all likelihood the Iranian grand vizier Mir Muhammad Mu’min (died in 1625) of Astarabad, it is not impossible that the remedy book that he dedicated to his ruler Muhammad Quli (ruled 1580–1612) was also read at the hospital (ibid., 167). Other treatises, perhaps studied at this hospital, were the writings of its first medical director Muhammad Tabib Gilani (late sixteenth/early seventeenth centuries), also of Iranian descent. One of his books dealt with sexual hygiene. The other is a dictionary of medical terms in several languagues (ibid., 168). The existence of several such multilingual medical dictionaries points to the crosscultural cooperation between Muslim and Ayurvedic doctors and druggists in these parts of India, who occasionally also worked together at a hospital. The Hyderabad hospital was part of a larger complex including a mosque, a madrasa, and a caravanserai. Speziale rejects the ideas of Indian authors according to which the madrasa was a school specializing in higher medical education. He thinks it is more plausible to assume that the classes taught at the madrasa followed the overall patterns of advanced education at madrasas in Islamicate societies on the Indian subcontinent in the early modern period. This means they functioned like madrasas in the Mamluk or the Safavid realms, teaching religious sciences, mathematics, medicine, and parts of the philosophical sciences (ibid., 168–69). In the religious disciplines, they will have shared clear similarities with Safavid madrasas, because both dynasties followed Shiʿi creeds. However, the extant sources speak explicitly only of one teacher at the madrasa in Hyderabad during the seventeenth century, who was a poet and is said to have taught the sciences of transmission, and the rational as well as the

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mathematical sciences (ibid.). Medicine is not named among his fields of teaching, but it may have belonged to the rational sciences. In the early modern Ottoman Empire, apparently only one hospital was built together with a madrasa specializing in medicine as part of one of the impressive funeral complexes of Ottoman sultans. This single example of specialized medical education in such a complex is the Süleymaniye madrasa, near Sultan Süleyman the Magnificent’s splendid mosque in Istanbul (Shefer-Mossensohn 2009, 142). Today this madrasa contains one of the richest manuscript libraries in the world. Shefer-Mossensohn rejects the claims of Turkish historians regarding the importance of hospitals for the medical training of Ottoman physicians. She considers the extant evidence as too scanty (ibid.). The Persian term shagerd, often translated as student and used in the waqf documents related to the hospital built by Mehmet II the Conqueror, is too ambiguous to know exactly what it describes. It could signal a beginner, but also an advanced learner, or a support person like an apprentice (ibid.). Shefer-Mossensohn suggests that a shagerd was not a student, but an intern who had completed his formal education at a madrasa or with some master. This would make the shagerd’s position similar to other practices in Ottoman institutions relying on previous education. Madrasa students of religious disciplines, for instance, who wished to become a judge, or a teacher at a madrasa, had to work for some time as a candidate before they received their first full-time positions (ibid.). The name given in the administration to such a junior clerk was shagerd. Finally, the medical shagerd was a member of the retinue of a senior doctor, similar in status to Ibn Abi Usaybiʿa during his learning practice at the Nuri Hospital. Hence, the state of a student or medical clerk was fluid, and the absence of a formalized examination system makes it difficult to interpret the sources with certainty. Shefer-Mossensohn concludes from her study of Ottoman sources that hospitals had a rather informal role in the education of Ottoman physicians (ibid., 143). 5.2. Family Education Although historians today overwhelmingly believe that medical training in particular was primarily provided within professional families, Arabic and Persian medieval and early modern sources do not seem to support

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this unequivocally. Especially the sources until the thirteenth century do not contain clear evidence for family training, whether in medicine or in the mathematical sciences. When Ibn al-Nadim, Ibn al-Qifti, or Ibn Abi Usaybiʿa mention teaching activities of famous scholars, these activities primarily relate to students from other families. Exceptions are the references to Hunayn b. Ishaq’s son Ishaq and nephew Hubaysh or Abu l-Wafa’s uncle as the scholar’s first teacher in the mathematical sciences. This is not to say that families of oculists, physicians, surgeons, or astrologers did not teach their offspring the family profession. It merely suggests that having studied outside the family seems to have held a higher value until at least the later twelfth century. The impression of the standing of education within a scholarly or professional family changes somewhat with evidence from those biographical dictionaries from the thirteenth century onwards that are overwhelmingly devoted to the class of the contemporary madrasa scholars, interspersed with information about rulers, military and administrative officials, and the occasional outsider. Here, family education is often more prominently displayed. Families of scholars are listed from grandfathers to grandsons, including uncles, sons, cousins, or nephews. But even in this type of historical literature family education is clearly overshadowed by the evidently most highly esteemed form of education through master-student and master-disciple relationships. This general picture applies to all the disciplines. For instance in al-Sakhawi’s dictionary, the relatively few family contributions to education in the four kinds of disciplines relevant to this book focus on the mathematical sciences, in particular arithmetic and the mathematical branch of law, that is the calculation rules for inheritance cases. Surprisingly, in the entries dealing with medical education either as a person’s primary field or as one among others, family participation in training is rarely mentioned. Obviously, family education in these areas was only of minor interest to the Mamluk historian, independently from whence the students came or where they learned. Two of the few examples related to the mathematical sciences and medicine concern Muhammad b. ʿAbd al-Rahim, coming from a provincial family of scholars, and Abu l-Wafa’ Muhammad b. Ismaʿil, coming from a family of physicians in Cairo. The first Muhammad served his relative Najm al-Din b. Hajji as a disciple in arithmetic, Arabic, and other, not

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specifically named, disciplines (al-Sakhawi n.d., vol. 8, 49). The second Muhammad studied medicine with his uncle Shihab al-Din Ahmad b. Khalil (flourished c. second third fifteenth century) and with Ibn alBunduqi (flourished c. second third fifteenth century). After his training, he became one of the deputies at the Mansuri Hospital (ibid., vol. 7, 135). His teacher Ibn al-Bunduqi also taught at the Mansuri Hospital (ibid., vol. 10, 67). Hence, it is not impossible that Abu l-Wafa’ received parts of his education with Ibn al-Bunduqi at the hospital. A confirmation that teaching within families could not stand alone, but had to be embedded into learning with teachers outside the family, is the case of Yahya b. Muhammad al-Sahrawi (fifteenth century) from Cairo. He was the grandson of one of the regular teachers of arithmetic and inheritance mathematics in the Mamluk capital. While he did study with a brother of his mother, al-Sakhawi lists several other teachers with whom he studied partly the same kinds of knowledge he had read about with his uncle and partly books from other disciplines. Among those other teachers also was al-Kafiyaji (ibid., vol. 10, 251). Family members appear more often when basic Islamic education is concerned, the learning of the Qur’an and hadith in particular. Teachers and students are predominantly male. But sometimes women appear in both functions (ibid., vol. 1, 64, 86, 89, 158, 491; vol. 5, 116; vol. 6, 17, 22, 51, 74, 116, 185; vol. 7, 56; vol. 8, 96). Male teachers come mostly from the closer branches of a family: grandfathers, fathers, uncles, brothers, and cousins (ibid., vol. 1, 5, 7, 50, 55, 87, 89, 121, 135, 140, 148; and passim). In some cases, they also participated in the advanced education of adolescents and young adults, in particular in law and Arabic. An important role of male relatives was travelling with younger family members to centres of education such as Cairo, Damascus, Tunis, or Shiraz. Under exceptional conditions such as the death of the parents, a grandmother might take her grandson on this educational journey (ibid., vol. 8, 127). This tendency to combine training in families with practices of learning with masters outside the house is also confirmed in the relatively rare biographical notes in scientific treatises. Among the seven commentators of Ibn Sina’s Canon of Medicine and the Epitome of the Canon attributed to Ibn al-Nafis between 1250 and 1500, for instance, only two declared having had early medical training with their father or their uncle. But all of

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them studied outside the family and read additional medical treatises and texts on other disciplines with other masters (Fancy forthcoming). In his youth Qutb al-Din al-Shirazi, one of these seven commentators, studied medicine with his father and his uncle, who both were practicing physicians. His father also was the head of a hospital in Shiraz, a position in which Qutb al-Din, not his uncle, followed him after his death (Chipmann 2013, 119). Although Qutb al-Din was still a young man and hence had little experience, the post of hospital director apparently was inheritable and descended in the direct line in Shiraz, as was the case with other hospitals elsewhere. Despite Qutb al-Din’s medical education within the family, in autobiographical statements in his commentary on the theoretical part of Ibn Sina’s Canon he was outspoken that this training had not enabled him to fully comprehend the great work nor sufficiently prepared him for writing his own commentary (Niazi 2014,  62–63). It was only after his diplomatic mission to Mamluk Cairo in 1282 had brought him into contact with the works of Ibn al-Nafis and three other Ayyubid and Mamluk commentators that he felt able to write a worthwhile commentary (Chipman 2013, 116; Niazi 2014, 64). Practices of combining in-family training with external learning are also found among families where several men of different generations became madrasa teachers who read in their classes works on the mathematical sciences or philosophy. An example is the Dashtaki family in Shiraz. Sadr alDin Muhammad b. Mansur al-Dashtaki (1425–1498), his father Mansur, his cousins Majd al-Din Habib Allah and Nizam al-Din Ahmad, and his son Ghiyath al-Din Mansur (1461/2–1546) all studied with at least one member of the family, but mostly hadith (Pourjavady 2011, 17). Sadr al-Din’s teachers in philosophy and logic, however, came from other illustrious scholarly families, among them students of al-Sayyid al-Sharif al-Jurjani, whom we already met in Chapter Four. After studying philosophy, logic, and perhaps the mathematical sciences with his father, Ghiyath al-Din created a philosophical geneaology showing the chain of transmission in philosophy down to his father, which has four interesting features. First, two of the historical links are anonymous. Second, these two links concern transmission of philosophy within a family. Third, the chain contains three famous Iranian scholars of the Mongol period, namely Nizam al-Din al-Nisaburi, Qutb al-Din al-Shirazi, and Nasir al-Din al-Tusi. All three studied and even commented on Ibn Sina’s philosophical writings, in particular his Pointers

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and Reminders. Finally, the chain links Sadr al-Din directly to the famous philosopher and physician Ibn Sina through two of his students. Thus Ibn Sina and his philosophy are placed on a comparable level with hadith and the Prophet (ibid., 18). The emotional and intellectual relationship between Sadr al-Din and Ghiyath al-Din was very close. In 1478/9, the father built a madrasa in Shiraz. In a rather unusual act of praise for an adolescent, Sadr al-Din named the new madrasa after his seventeen-year old son (ibid.). He acknowledged the son’s philosophical and theological ideas as worthy of being studied by including references to them into his own later writings (ibid., 21, 23–24). In many of his own writings the son called his father his master (ustadh). He studied most of the disciplines relevant to a scholarly career in his father’s Mansuriyya Madrasa (ibid., 25). He commented on one of his father’s works and wrote a brief biography of his life and intellectual achievements (ibid., 20). Apparently the more able of the two, he did not always follow his father’s line of thought. Sadr al-Din had been a staunch adherent of Ibn Sina’s philosophical teaching, rejecting the more recent trends of Shihab al-Din al-Suhrawardi’s and Muhyi l-Din Ibn ʿArabi’s doctrines. Ghiyath al-Din, in contrast, integrated ideas of these two scholars of the twelfth and thirteenth centuries into his ­overall adherence to Ibn Sina’s positions (ibid.). Sadr al-Din’s scientific writings dealt with gemstones and the rainbow, while Ghiyath al-Din began his career as an author one year after the madrasa’s opening with a text on planetary theory, apparently following the style of Qutb al-Din al-Shirazi (ibid.). Father and son did not merely learn with and from each other, but also taught some of the same students. Sadr al-Din focused on philosophy, while Ghiyath al-Din also taught astronomy (ibid., 26). Ghiyath al-Din obviously was also a believer in astrology, divination, and magic since he produced talismans for Shah Ismaʿil and his army against the Shah’s enemies, and advised Ismaʿil, when asked, not to reconstruct Nasir al-Din al-Tusi’s observatory in Maragha before the next auspicious reign of Saturn began thirty years later (ibid., 27). 5.3. Travel for the Sake of Knowledge Travel for the sake of knowledge is an important concept in Muslim education. Today, many Muslims quote the spurious hadith: Seek

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knowledge, even if in China. But even if this particular formulation was invented long after the Prophet’s death, travels to a teacher over hundreds of kilometres are known already from the ninth century. Abu Zayd al-Balkhi, for instance, one of al-Kindi’s students mentioned in Chapter Two, travelled from Central Asia to Baghdad for his education, after he had received his first training with his father and other teachers in the village of his birth near Balkh and in the city itself. Later he returned to Balkh and taught philosophy there, among other kinds of knowledge. His student Abu l-Hasan al-ʿAmiri (died in 992) travelled more than once between Nishapur, Rayy, Baghdad, and Bukhara in order to acquire patronage, to particpate in philosophical meetings at various courts, and to get away from wars and other insecurities of life (Kraemer 21992, 234– 38; Wakelnig 2006, 10–34). Another famous student of the philosophical sciences in the ninth and tenth centuries was Abu Nasr al-Farabi. Modern historians of philosophy doubt the medieval story according to which he travelled from Farab in Central Asia to Baghdad in order to study there with the leading Christian philosophers of the time. According to Griffel, they rather believe that al-Farabi grew up in Baghdad (Griffel 2016, 273). Evidence for this assumption is unknown to me. Searching later for patronage, alFarabi visited courts in Iran, northern Iraq, and Syria. The last period of his life he spent in Damascus. Many of the astrologers of the tenth century also moved from one court to the other, from one city to the next, crossing the wide expanses between eastern Iran and Iraq, but whether this included learning and teaching experiences is unclear. Travel for the sake of learning became an important practice in alAndalus in the tenth century (Samsò 2002, 297). Such travels continued until the fall of the last Islamicate state on the Iberian Peninsula, the Nasrid Emirate of Granada (1232–1492). The last description of such a journey comes from the middle of the fifteenth century. In the second third of that century a student of the mathematical sciences from a small town near Granada undertook fifteen years of travel through North Africa, Egypt, and the Arabian Peninsula, combining pilgrimage with study. His name was ʿAli b. Muhammad al-Qalasadi (1412–1486). He needed three years of this time for the outward voyage and journey with caravans. The remaining twelve years he spent learning in Tlemcen and Tunis, and teaching in Cairo. He reached

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Mecca in 1447 before returning to Almería, where his journey had begun in 1436 (Marín 2004). Al-Qalasadi began his education as a young boy in his hometown, where he studied mathematics together with learning the Qur’an by heart. He acquired knowledge in arithmetic, algebra, geometry, and astronomy. His teachers were scholars of the religious sciences. With two of them he read the mathematical works of Ibn al-Banna’, a religious scholar, famous for his works in the mathematical sciences, who lived and taught in Morocco. Al-Sakhawi mentions that Ibn al-Banna’’s treatises were read in places as far apart as Tlemcen, Tunis, Damascus, and Mecca (al-Sakhawi n.d., vol.  8,  96). Copies can be found today in libraries in Syria, Turkey, Iran, and India, as well as in Europe and the United States. In his hometown, al-Qalasadi read one text of Ibn al-Banna’, The Four Chapters on Arithmetic, twice with two different teachers. During his eight years in Tlemcen and four years in Tunis, al-Qalasadi read Ibn al-Banna’’s other book, Epitome of the Operations of Arithmetic, which was already familiar to him, at least two more times with local teachers. He did so by reading it in conjunction with other writings of Ibn al-Banna’ on arithmetic, elementary geometry, and algebra (Aballagh 1988; Djebbar 1990). In Tunis, he began reading a text on the astrolabe and a book on number theory by another North African scholar, Abu Bakr Muhammad b. ʿAbdallah al-Hassar (twelfth century). The result of these years of study in North Africa was al-Qalasadi’s own writings, primarily on arithmetic and the determination of inheritance shares. Al-Qalasadi already wrote his first arithmetical treatise, The Introduction to the Dust Letters, in Tlemcen. Dust letters are a name for numbers, which derives from two different practices. One practice consists in the attribution of numerical values to letters, for instance 1 to a, 2 to b, or 20 to k. This practice is already known from Antiquity in other Semitic languages and also in the Indoeuropean Greek. The other practice comes from the Indian subcontinent and was familiar to Muslim scholars by the tenth century at the latest. It consists of using a board covered with dust or sand on which caclulations were carried out by using either letters of the Arabic alphabet or the signs for the numbers 1 to 9 learned from Sanskrit astronomical/astrological texts through their translations into Arabic during the eighth century. The name “dust letters” as used in North Africa refers specifically to the North African forms of the Indian number signs.

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Five other writings by al-Qalasadi may have seen the light of the day in Tunis, since copies of them are extant today in the National Library of Tunisia. His most successful work, with thirty-seven copies still surviving, is again a treatise on the so-called dust letters. In Cairo, al-Qalasadi even gave one of his students an ijaza for his mathematical works, conferring permission to teach the texts (al-Suyuti 1927, 131). A rather lengthy summary of al-Qalasadi’s educational travel account can be found in al-Sakhawi’s biographical dictionary (al-Sakhawi n.d., vol. 6, 14–15; for additional information see Lamrabet 1994, 119–23). While al-Qalasadi himself reported explicitly and in some detail on his mathematical studies, al-Sakhawi focused his description more on the religious disciplines, providing only generalities about the traveller’s educational efforts in the domains of arithmetic, inheritance calculations, and geometry. On the other hand, al-Sakhawi’s biographical entry shows that logic as well as rhetoric and other philological fields were also a stable part of al-Qalasadi’s training. Moreover, al-Sakhawi reports that al-Qalasadi wrote not only on mathematical subjects, but also on grammar and successfully taught the rational sciences in general, in addition to his fields of specialization (al-Sakhawi n.d., vol. 6, 15). These are points that the depictions available today of al-Qalasadi’s oeuvre and scholarly life usually ignore in their exclusive focus on the mathematical sciences. The desire to study with the best and to become a famous scholar motivated many young men to travel in search of education far beyond their families’ homes or even beyond their lands of origin. When the young al-Jurjani decided that he needed to collect ijazat (permissions to teach texts), he first went to Herat (today in Afghanistan). From there, he travelled to Anatolia, where he studied in Konya and Qaraman. Contrary to legendary stories in primary and secondary sources, it was another student of his teacher in Qaraman who convinced al-Jurjani to continue travelling for the sake of knowledge. The two young men arrived in Cairo in 1371. Al-Jurjani studied and taught in the Mamluk capital for four years and acquired reputation and appreciation. His main teachers in Cairo were themselves foreigners who trained a number of young men who later became leading scholars in various Turkic societies in Anatolia (Nur Yildiz 2014, 268). After his studies in Cairo, al-Jurjani travelled to find a position and patronage. It took him two to three years to succeed. In 1377/8, the head of a small Persian dynasty ruling in Shiraz

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was ­campaigning near Astarabad against a relative. Al-Jurjani, helped by a local scholar, managed to win the ruler’s patronage and went with him to Shiraz, where he received a teaching post at the madrasa linked to the newly built hospital (van Ess 2009, 21–29). In 1387, al-Jurjani had to travel again, but this time against his will. Timur’s troops had conquered the town and commanded al-Jurjani together with other scholars to move to the Timurid capital in Samarkand, in return for which Timur’s troops were given the order not to loot the scholars’ houses. Although al-Jurjani seems to have detested the enforced move, returning to Shiraz in 1405 after Timur’s death, his time in Samarkand was profitable for his own career and reputation. There, he met and befriended Saʿd al-Din Masʿud b. ʿUmar al-Taftazani (1322– 1390), another important scholar of the Timurid dynasty, who had been teaching in Samarkand since 1385. Although the two men’s relationship was friendly, it was also highly competitive. Al-Jurjani and al-Taftazani held many public debates. Public debates were characteristic of intellectual engagement in numerous Islamicate societies. They were a form of distribution of knowledge to the interested public and a form of teaching and learning. Not all public debates were of the same depth and importance, though. Van Ess quotes with some irony and amusement the subject of one of them: “Love of the cat is a part of the Faith” (ibid.) A debate commanded by Timur, possibly on the merits of Suhrawardi’s illuminist philosophy versus rational kalam, was much more serious in character and meaning. The ruler wished to decide who was the better scholar and thus worthy of his privileged support. Knowledge was not merely about skills, understanding, and eloquence. It was service to the mighty. The Timurids in particular understood very well the importance of scholarship for their legitimacy, wordly success, and reputation after their death. This applied to many different disciplines such as philosophy and kalam in the case of al-Jurjani. In Samarkand, Ulugh Beg (ruled as governor of Samarkand 1409–1447, and as head of the Tirmurid dynasty 1447–1449) supported geometry, planetary theory, arithmetic, and astrology. The courts of Iskandar Sultan in Shiraz, Yazd, and Isfahan supported the study of kalam, alchemy, medicine, astrology, astronomy, geography, and the knowledge of magic letters and numbers. One of the students who travelled from Anatolia to Damascus and Cairo in order to acquire knowledge not yet available in his homeland

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was Hacı Paşa (died c. 1425) of Konya, who after his successful education at Mamluk madrasas became court physician, judge, and madrasa teacher under the Aydınid dynasty (1308–1426) in southwestern Anatolia. In Damascus, Hacı Paşa apparently studied one of al-Urmavi’s main works on logic with Qutb al-Din al-Razi al-Tahtani (died in 1365), the man with whom al-Jurjani had wanted to study. Then Hacı Paşa continued to Cairo where he studied kalam, law, logic, and medicine (Nur Yildiz 2014, 265, 268). While his teachers in the first three disciplines were influential migrants from Azerbayjan and Iran, his medical teacher remains a faceless figure due to a lack of biographical or other data. Nonetheless, after having taken classes with him, Hacı Paşa was appointed to the Mansuri Hospital. He acknowledged the intellectual influence of Cairene physicians in his later writings on medicine (ibid., 270). About 1370, Hacı Paşa arrived at the court of the Aydınid ruler in southwestern Anatolia. Nur Yildiz suggests that this journey was inspired by the lavish patronage this Turkic dynasty offered to scholars who had received their education in Arab lands. This extravagance reflected their status as political, cultural, and religious newcomers and hence their need to establish an Islamic infrastructure of buildings, institutions, and scholars (ibid., 271–72). Students from Cairo also travelled for the sake of knowledge despite the multicultural flair of the scholarly community in Cairo during the fourteenth and fifteenth centuries. In Cairo itself, in addition to Egyptian and Syrian scholars, they could find teachers from lands of the rising Ottoman dynasty, and Maghribi teachers like the famous historian Ibn Khaldun who taught, besides Maliki law, divination from geometrical figures consisting of points drawn in sand, as already pointed out in Chapter Four. Above all, they could find Iranian and Central Asian teachers of logic and philosophy. Nonetheless, some students felt that they had to go abroad for the study of specific disciplines, in particular to Iran (al-Sakhawi n.d., vol. 6, 82). After the fall of the Mamluk dynasty to the Ottoman army in 1516/7 and the incorporation of its territories into the empire, more and more students from Egypt and Syria began travelling to the new centre of power and learning – Istanbul, where after 1453 Sultan Mehmet Fatih had founded eight madrasas at the mosque built by and named after him – the Fatih Mosque (see Chapter Four). He also established teaching positions elsewhere, for instance at the Aya Sofya, which he converted from a church into a mosque.

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Following him, members of the courtly administration and subsequent sultans also built madrasas in the capital and other cities and towns. One of the first to receive a teaching position at the madrasas built within the complex of the Fatih Mosque and then at the Aya Sofya Mosque was ʿAli Qushji of Samarkand (Barker-Heiderzadeh 2016, 51–52). After the death of his scholarly Timurid patron and mentor Ulugh Beg in 1449, ʿAli Qushji had to travel in search of a new position and patron. He turned first to the Timurid capital Herat, where he lived with his family and students for several years (Fazlıoğlu 2007, 946–48). After the defeat of the Timurid ruler of Herat by Uzun Hasan (ruled 1453–1478), the head of the Ak Koyunlu Confederation, in 1469, ʿAli Qushji went to his court in Tabriz (ibid.). In 1472, Uzun Hasan’s nephew Yusuf Mirza was kidnapped by Mehmet’s son Mustafa. Mehmet and Uzun Hasan were often in conflict. The Ottoman sultan used this occasion to pressure the Turkmen ruler for a hefty ransom, asking explicitly for rare books and albums of calligraphy (Pinto 2011,  167). Pinto speculates that it might have been ʿAli Qushji who carried a precious geographical manuscript to Mehmet  II and stimulated Ottoman courtly interest in Arabic and Persian geographical literature and maps (ibid., 168–69). Once in Istanbul, ʿAli Qushji became a highly esteemed scholar at court and received a chair for teaching the mathematical sciences. His travels and those of his family had thus come to an end. His children intermarried with Ottoman scholars, carrying Timurid mathematical traditions and texts over to the Ottoman court and its madrasa system. The biographical dictionary of the sixteenth-century Ottoman historian Ahmad b. Mustafa Tashköprüzade (1495–1561) indicates that many scholars from Ottoman lands often travelled to Cairo, as well as to Shiraz and other Iranian cities, to complete their education (Tashköprüzade 1978). This reflects, on the one hand, their recognition of Mamluk and then Ottoman Cairo as an important centre of learning, and on the other, their acceptance of Iran as their cultural point of reference and of Iranian scholars as leading luminaries in the rational sciences and the exegesis of the Qur’an. Imber believes that there was a further reason for those educational travels by scholars from the quickly expanding Ottoman state – the lack of high-level madrasas at home and the Ottoman Turks’ feeling that they lacked familiarity with Islamic law and religious doctrines (Imber 2009, 212–14). Travelling for education in the first half of the

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fourteenth century meant “the transfer of Muslim law and culture” to Anatolia (ibid., 213). By around 1500 and more so after the conquest of the Mamluk territories, the Ottoman Empire became itself a centre of learning and hence an important destination for educational travel. Dynastic promotion and patronage created a system of expectations and obligations that structured and stimulated learning and teaching. It functioned as a norm-setting institution and attracted many foreign scholars who settled in Ottoman cities (ibid., 214). Codices of customary law written by or for the sultans contained passages aiming to regulate the educational system by prescribing career patterns as well as teaching texts (ibid., 215) (see Chapter Four). This close connection between education, career, and the Ottoman state set the madrasa system in the Ottoman territories apart from the educational systems in other Islamicate societies except for the Mughals in India (ibid.). Beginning with Akbar (ruled 1556–1605), the Mughal educational system was much more integrated into the political and legal demands of the ruler than had been the case in earlier societies (Speziale 2013, 166). Not everybody undertook many years of travel for the sake of knowledge. But many young men travelled from their provincial towns or villages to major centres of learning and teaching such as Cairo, Damascus, Istanbul, Samarkand, Herat, Tabriz, Maragha, Shiraz, or Isfahan, depending on the times, the ruling dynasties, and the reputation of individual teachers. For many of those who later became teachers themselves, these travels were the beginning of a final move to a city. But even students born in such an urban centre often travelled for the sake of learning, either while a disciple to a master or as a scholar. Often these two phases overlapped. Yet high-ranking scholars could serve a master for more than a decade, often until a master’s death, even when they already had a large crowd of followers themselves. Pilgrimage was another major incentive for travelling, in combination with the acquisition of knowledge. As a result, many scholars originally from Iran or Central Asia spent many years of their lives in Mecca, Medina, Jerusalem, Damascus, or Cairo teaching their knowledge to visitors and local students. Al-Sakhawi, for instance, mentions more than 400 students and teachers whose names contain parts that point to their or their families’ origin in Iranian and Central Asian cities (al-Sakhawi n.d., tables of content). Other foreigners who came to Mamluk cities with

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purposes that included learning or teaching are listed for India, Anatolia, Iraq, Yemen, Tunisia, Algeria, Morocco, and al-Andalus. Further reasons for travel, or better – flight, were wars, nomad incursions into urban centres, economic decline, or religious and other persecutions. In the twelfth and thirteenth centuries, Iranian scholars migrated to northern India, Anatolia, Syria, or Egypt. The pre-Mongol movements of scholars, Marlow believes, were the result of economic depressions (Marlow 2010, 279). One of the better-known scholars who had a longterm impact on the teaching of the rational sciences, including logic, at Mamluk, Ottoman, and Safavid madrasas was Siraj al-Din al-Urmavi (1198–1283). Before he migrated to Konya in about 1258, he had already travelled widely for the sake of knowledge and acquired appreciation and reputation among Abbasid and Ayyubid scholars and rulers in Baghdad and Cairo (ibid., 280). Al-Urmavi was one of the Iranian scholars linked to Fakhr al-Din al-Razi who spread this scholar’s critical views of Ibn Sina’s philosophy, as well as his support for a joint study of the sciences of transmission, the rational sciences, and the mathematical sciences, from Central Asia to the Middle East. Al-Urmavi’s writings on logic, philosophy, and kalam became standard teaching texts at madrasas in Egypt, Syria, and Anatolia (ibid., 282–83). The conquest and destruction of Central Asia, Iran, Iraq, parts of Anatolia, and parts of Syria by the Mongols in the first half of the thirteenth century drove further waves of scholars from those regions towards the Middle East. Another period of scholarly migration due to military, political, and religious upheavals occurred in the first half of the sixteenth century. After the emergence of the Shiʿi Safavid dynasty, Sunni scholars fled from Iran to the Ottoman Empire or to Muslim dynasties in India. Among them was ʿAbd al-ʿAli al-Birjandi, whose commentaries on several astronomical works by Nasir al-Din al-Tusi were widely read at Ottoman and Indian madrasas and apparently also in Safavid Iran. Religious and other persecutions took place also within the boundaries of a specific Islamicate society, for instance the Mamluk state. The leading expert on planetary theory, the production of calendars, and the use of astronomical tables in Aleppo in the early fifteenth century was one Ahmad b. Ibrahim. His calendars became famous even outside of Aleppo so that the governor and other officials sent for them. This brought him accusations of religious indifference, and he had to flee. He went to Safad in Palestine (al-Sakhawi n.d., vol. 1, 204–05).

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The travels of Christian and Jewish students or teachers are usually more difficult to trace. After about 1300 information about them is seldom provided in Arabic or Persian historical sources. Under the Ayyubid and Mongol dynasties, Jewish and Christian scholars of philosophy, the mathematical sciences, or medicine travelled widely between Syria, Iraq, and Iran, either looking for patrons or visiting famous scholars for debates or for sharing ideas and manuscripts. Moreover, visitors from Byzantium and from other parts of Europe came to some cities with peaceful intentions. Among them was the physician Gregor Chioniades (died in c. 1320), who travelled in 1295 from Constantinople via Trebizond to Tabriz in order to study astronomy with Muslim scholars (Nicolaidis 2011,  110). He translated into Greek various Persian astronomical texts by Shams al-Din al-Bukhari (late thirteenth/early fourteenth centuries) and by Nasir al-Din al-Tusi, together with extracts from earlier Arabic astronomical handbooks. His translations were used by Byzantine scholars of the fourteenth century, partly replacing Ptolemy’s Almagest (ibid., 111, 216). In the fourteenth century, a Jewish physician from Tabriz travelled to Cairo and settled there. Al-Sakhawi regrettably does not report why the doctor left Iran. The turmoil at the end of the Mongol dynasty in Tabriz and following decades of instability may have been an important reason for a Jew to move away. His son and grandson continued to work as physicians in Cairo, but as Muslims, after the migrant converted in his new hometown (al-Sakhawi n.d., vol.  6,  165–66). Two centuries later, Christian students from the Ottoman Empire, in particular from Greek families, began to leave the Islamicate world for the sake of study. They often went to Italy to study medicine and sometimes also philosophy. Jewish students, sometimes under assumed names, came especially to the University of Padua to study medicine there. Such travellers came from many different corners of Europe, including the Ottoman Empire (Morrison 2014, 36–37). 5.4. Postface As in the case of the madrasa and related types of teaching institutes, the forms of organization of teaching and learning in other kinds of institutions such as the hospital were fluid and underwent significant changes

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at times. The clientele of such an institution depended on ideas of how to rule, how to exercise charity, and how to interact with different kinds of communities. The hospital as a caretaking institution did not have to include a concept of education. In some Islamicate societies both functions were combined, while in many others education remained the responsibility of either the family or the medical practitioner. For many hospitals, however, we lack documentation and thus are unable to make any clear statement about how they were run and whom they served. Family education was comparably fluid. While families of the scholarly elites often provided their male (and sometimes their female) children with a broad range of elementary skills, advanced education was often practiced either in a combination of family and madrasa training or outside the family altogether. Ruling families and families of courtiers, administrators, and wealthy merchants continued to pay for tutors before the second group of families sent their sons off to the madrasa or to travel. Of the three educational institutions discussed in this chapter, travel for the sake of knowledge acquisition appears to have been the most stable over time and space. It began under the early Abbasids and was still functioning on the eve of modernity, thus covering more than a millenium. In the first centuries travelling for the sake of knowledge was a necessary tool for accessing the latest publications and the newest theories. In later centuries, these two important motives for travelling were supplemented by what I call the politics of numbers. Acquiring knowledge remained important, but it did not always have to be cutting edge. The acquisition of reputation through studying with a leading scholar by now dominated educational practices also in the mathematical sciences, medicine, and natural philosophy. In the seventeenth century, the landscape of teaching and learning began to change. The first students, coming from Christian and Jewish communities, travelled abroad, outside not only their own Islamicate societies, but the Islamicate world at large in order to acquire mainly medical education. The process speeded up in the early eighteenth century, when first the Ottoman dynasty and then the Mughals promoted educational reforms. During the nineteenth century, major steps to replace traditional educational structures were taken in several Muslim and Christian communities in North Africa, the Ottoman Empire, Qajar Iran, and – under the pressure of the British colonial empire – in South

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Asia. Teachers from various European countries were hired in much greater numbers than in the eighteenth century. Students were sent with stipends from ruling dynasties to study at universities, in particular in France, England, Germany, and Austria, or went on their own to get an education in Russia. New schools were set up for military, scientific, medical, and some time later also pedagogical, education on the basis of curricula from European technical schools or universities. These changes led to the translation of French, English, or German mathematical, ­scientific, medical, and military-technical textbooks into Arabic, Ottoman Turkish, or Persian. The limited nature of these educational reforms of the nineteenth and early twentieth centuries is one of the many reasons for today’s multiple conflicts in modern societies of the Islamicate world.

Chapter 6 TEACHING AND LEARNING METHODS

T

eaching and learning methods can be considered from different angles. Since no formalized curriculum was known until the early eighteenth century, the choice of disciplines to teach or study obviously depended on individuals – the teacher and the student. Whether provided in a dictionary or a chronicle by a historian or in a list of teachers compiled by a former student, the extant biographical information shows great variety. Some students chose to study specific mathematical disciplines only with particular teachers. Other students studied any kind of mathematical text with a generalist. From this we may conclude that in the fourteenth and fifteenth centuries at least there were two such broad categories of teachers in the mathematical sciences – specialists and generalists. But other cases of combined disciplines named in the biographies highlight the fluidity of such a division. Similar claims can be made for logic. Whether called hikma or falsafa, which possibly meant different things to teachers and students after 1200 as well as in different regions, philosophy was even more a matter of personal choice than the mathematical sciences. It appears more rarely in the lists of fields of knowledge taught or studied. The teaching of philosophy achieved greater prominence and stability in the early modern period in Safavid Iran, where a greater range of texts is named as teaching material. Hence, in addition to comparing lists of disciplines taught or studied, lists of texts named explicitly in biographical reports provide us some glimpses into the content and level of learning and teaching and thus may point to some teaching methods. A specific type of biographical literature which focuses on naming teachers and texts read, but reports also on travels, are the so-called teacher-dictionaries (muʿjam), catalogues (fihrist), and programmes (barnamaj). This class of texts shows what was considered important as markers of good education: people, texts, and travels in high numbers. Quantity often mattered more than depth.

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In contrast to this type of self-presentation, manuscripts showing traces of true teaching activities can modify this number-oriented picture for some cases. They can show that some teachers and their students valued variety, breadth, and at least some depth. The literature about an individual’s educational trajectory can equally surprise today’s reader. This literature shows that despite the often rote and elementary nature of learning in the science classes such an individual might have taken, a bright student sometimes broke the rules and dominated a class and a teacher by asking unexpected questions or giving quick answers. Such unexpected information is also a feature of the biographical dictionaries written by historians. They show that the standard set of disciplines is sometimes broken by fields that otherwise rarely show up, such as geography, botany, or knowledge about animals. Such notes can also declare that one or the other student left the classroom and directly explored nature, studying plants or animals on his own or with a teacher. Thus, given the peculiarities of the sources available for a history of teaching and learning the sciences in different Islamicate societies, these little deviations from the apparent rule suggest that learning and teaching in practice must have been much more variable than this literature makes us believe, in particular since non-textual sources have rarely survived, if at all, for the centuries before 1700. The many thousands of extant school texts from all the scientific disciplines provide us a further glimpse into learning and teaching methods. They reflect the lower importance of these fields of knowledge in the overall system of learning and teaching in all institutional settings. They also show that many students participated over the centuries in such classes and struggled, just as they do today, to understand their principles, rules, and methods. They did exercises, added notes, drew diagrams, or took another text as auxiliary material. Sometimes they signed their efforts. Thus, they allow us today to see their involvement in the surviving mixtures of school texts and students’ notes. Finally, there are descriptions of, and prescriptions for, the “correct” manner of being a student. Pedagogical writings are mostly directed towards the students of the religious disciplines and as a rule disregard most of the fields of knowledge traced in this book. They also focus more on the first years of learning with a teacher than on advanced students. Hence they provide more insight into the sociocultural conditions of learning, than on learning methods per se. They offer some u­ nderstanding

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of two of the most important features of the development in learning and teaching in Islamicate societies over the centuries. Originally, disciplinary learning in the sciences, medicine, and philosophy apparently took place through an ordered sequence of texts, as for instance al-Farabi reports about his training in Abbasid Baghdad. This approach to education was replaced by a sociocultural practice wherein two other methods gained prominence. One consisted in the repeated reading of the same elementary or middle-level introductory or survey texts with more than one teacher. The other preferred the selected reading of small parts of “canonical” texts across all disciplines. The goal of this kind of approach to learning clearly was to acquire necessary basic skills. But this was done in a culture obsessed with numbers on the level of people – the more teachers a student managed to “collect”, the higher his reputation when he later became a teacher himself. It is not fully clear why this culture of numbers took hold in the mathematical sciences. Moreover, I have not found evidence for similar practices in philosophy or medicine. In this chapter I will not survey these pedagogical recommendations for students of the religious disciplines, but limit myself to surveying the only known treatise on rules for how to become a productive geometer and some treatises on how to ensure quality control among physicians and other medical workers. In addition, I will discuss methods and reflections about how to verify claims and how to proceed in disputations, as well as some aspects of the format of later scholarly literature that dominated learning and teaching practices. 6.1. Meetings, Teachers, Goals A standard form of teaching larger groups of students was the majlis and the halqa. Both Arabic words describe a kind of meeting, where students (or colleagues, disciples, and friends) sat together, mostly in a semicircle around the teacher who often sat on a higher cushion than the others. Meetings of learning and teaching could take place between beginners as well as mature students and teachers, or between colleagues. Although each generalization runs the danger of counterexamples, a halqa usually took place in a mosque or a madrasa, while a majlis was held in a private house or a hospital. One of the possible counterexamples is al-Sakhawi’s

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ms. Oxford, Bodleian Library Elliot 149, f. 287b; Iskandar (Alexander) observing a learning discussion in a majlis, from the seventh part of the Haft Awrang (Seven Thrones) on Alexander’s wisdom by Jami (1412–1492), composed between 1468 and 1485; copied in the second half of the sixteenth century.

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remark that someone reported beautifully about geographical topics (names of countries, their state of affairs, and their people) in a majlis held by his teacher Ibn Hajar al-ʿAsqalani (1372–1449) (al-Sakhawi n.d., vol. 2, 132). In addition to teaching and learning, the word majlis denoted other kinds of meeting like an administrative meeting, a meeting of a ruler with his advisors or the populace, or a meeting for entertainment. As pointed out in Chapter Two, meetings for entertainment could include elements of teaching and learning testified to by historical as well as scientific literature from the Buyid dynasty. In the transition period to the inclusion of the sciences into madrasa teaching, a majlis seems to have had a more formal, institutional meaning than before. At least this may be suggested by formulations like the one in the following example: Shaykh Fakhr al-Din from Mardin (died in 1198) had “a general majlis for teaching” in Damascus (Ibn Abi Usaybiʿa 1965, 356). That this majlis was mainly dedicated to teaching medicine is implied by Ibn Abi Usaybiʿa’s subsequent comments. One of the many who studied ­medicine there with Fakhr al-Din and served him as a disciple was alDakhwar. He was the founder of the first medical madrasa in Damascus, as reported in Chapter Four, and a teacher of Ibn Abi Usaybiʿa and Ibn al-Nafis. Al-Dakhwar read with Fakhr al-Din “one of the books of Ibn Sina’s Canon of Medicine and corrected it with him” (ibid.). This little remark reveals some of the elements that characterized teaching since the twelfth century at the latest. Reading texts did not necessarily mean reading an entire book, as it had meant in the tenth century in the case of Euclid’s Elements for the Buyid prince, whose later name as a ruler was ʿAdud al-Dawla. The second half of Ibn Abi Usaybiʿa’s remark does not imply that the pair corrected Ibn Sina’s book with regard to its content, but that the teacher corrected the copy of the part of Ibn Sina’s Canon, which al-Dakhwar had written in his teacher’s majlis. The difficulties that such biographical entries can pose to the modern historian become visible when we read the same kind of information in Ibn Abi Usaybiʿa’s biography of al-Dakhwar. There we are told that al-Dakhwar occupied himself with Ibn Sina’s work under the guidance of Fakhr al-Din, who was engrossed in the method of reading this work (diraya) and verifying its meaning (tahqiq) (ibid., 667). The method of reading (diraya) mentioned in this entry was one of the two recognized standard methods of teaching and learning any text. The teacher who chose this method (diraya) did not stand in an

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u­ninterrupted chain of transmitters reaching back to the erstwhile author. That is why the more conservative scholars opposed this method and preferred its alternative – the method of transmission (riwaya). Here, the teacher was linked to the author of a text in a presumably valid, uninterrupted chain of oral transmission. The philosopher and physician of Jewish descent Abu l-Barakat al-Baghdadi (died in 1164/5) offered another argument for why the transmission method of teaching and learning was preferable. In his Book of What Has Been Established by Personal Reflection, he complains that there is no knowledge available in his time in comparison to the past. This literary topos allows him to justify the reading of books as a learning method, although studying with a teacher was many times better, “because the teacher can choose the appropriate subjects and wordings which fit his auditory” (Eichner 2009,  23). We will encounter a variant of this method of reading, applied to the mathematical sciences, in the case of an Ottoman scholar in the first half of the sixteenth century. The method of verifying (tahqiq) the meaning of a text was another important teaching method, applied in either of the two approaches of transmitting knowledge by reading (diraya) or by oral transmission (riwaya). I will return to it in the penultimate section of this chapter. Meetings with scholars also characterized the cultural activities of rulers in the post-classical period. Several Ayyubid rulers, among them Salah al-Din (ruled 1171–1193), the founder of the dynasty, and his nephews al-Muʿazzam (ruled 1218–1227) and al-Kamil (ruled 1218– 1238), conducted them in Cairo, Damascus, Aleppo, Hama, and other holdings. Siraj al-Din al-Urmavi, introduced as a scholarly traveller in Chapter Five, reports that every Friday evening al-Kamil invited scholars to discuss with him questions pertaining to the religious sciences, philosophy, poetry, and princely conduct (Marlow 2010, 289). Ibn Khallikan adds that the Ayyubid ruler was highly educated and posed difficult questions to the scholars participating in his evening meetings (ibid.). Regular classes with a madrasa teacher took place either at scheduled hours in the teacher’s house or at agreed upon hours in a student’s house, in a garden, or at the place of teaching, which could be a madrasa, a mosque, a tomb, a house for the reading of the Qur’an or hadith, or occasionally a library, or a hospital. In the city of Tlemcen, today in Algeria, a teacher of al-Qalasadi, the Andalusian specialist in arithmetical sciences

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whom we already met in Chapter Five, read the sciences of transmission in the winter months and the rational and mathematical sciences in the summer months (Marín 2004, 308–09). Otherwise, we have almost no information about the hours when certain classes were given. The regularity of learning and teaching activities has to be derived from the set of texts that appear in the biographical entries in different periods and regions. Since many young men apparently read or learned by heart the same texts, there must have been some understanding of what a boy and then an adolescent or young adult had to know when he wished to declare the period of his learning finished. But such an indirect pointer to regularity can be mostly seen in the religious sciences. Texts studied in the mathematical sciences, medicine, logic, and philosophy are not named as often as religious and philological works. Thus, it is more likely that the scientific disciplines (with the exception of logic) were studied more informally, in some cities perhaps only when one or more students asked for such instruction. This fits the overall impression that mathematical, medical, and philosophical texts were not studied by all students, but only by a comparatively small number. Moreover, even those young men who took mathematical, medical, or philosophical classes rarely read more than a few texts. The favoured disciplines were the legal branch of “inheritance science”, arithmetic, and logic. Algebra, geometry, astronomical fields, medicine, and philosophy are less often mentioned. When titles of books are given, they refer often to the more elementary end of the spectrum. This general rule does not apply, of course, to everybody in all Islamicate societies throughout the centuries. The informality of scientific education allowed for individual choices and thus a relatively great variety of learning experience. The goals of learning and teaching varied over time and, as just said, between individuals. My impression is that there were periods of shift and reorientation. This impression is anecdotal and perhaps has to remain so due to the character of the extant sources as described in the introduction to this chapter. Areas like medicine or astrology could be seen as leading to money-earning and official positions at courts or, as discussed in Chapter Five, at hospitals. But they often were available only to the elite few. Others had to earn their living as itinerant healers and diviners, as druggists in market shops, in the service of doctors, or as badly paid advisors, herbalists, or servants. Whether instrument makers

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underwent ­formal training in the mathematical sciences, at least on an elementary level, is not well known. Young men who wished to work later for a judge determining inheritance shares were a further group of students who pursued some mathematical knowledge. The need to determine the legal shares of all heirs correctly was one of the causes for the anchorage of the disciplines of arithmetic and algebra in the madrasa. The need to determine the intervals of daily prayer times and the prayer directions towards the Kaʿba in Mecca encouraged the formation of the discipline of timekeeping, which in societies west of Iran provided the basis for the teaching of astronomical and geometrical knowledge at the madrasa. Students who focused on these classes often spent their life later as timekeepers or muezzins at madrasas and mosques. In Iran, Central Asia, and also some parts of India, geometry and astronomy classes at madrasas were the result of the inclusion of planetary theory in the religious discipline of kalam after the thirteenth century. Beside such types of professionally oriented goals, learning and teaching aimed at providing general education enabling men to participate in intellectually diversified conversations at court, in evening meetings, or in public debates. The veneration of the teacher seems to have permeated all Islamicate societies and centuries until the modern period. According to Kraemer, a particularly important period for teaching and learning the sciences, medicine, the “occult” sciences, and philosophy with regard to reflections about the purposes, goals, and meaning of such educational activities, was the tenth century under the rule of the Buyid emirs. Aristotle’s letters and epistles to his princely student Alexander were an ancient body of texts that motivated philosophers, literati, physicians, and other erudite men to discussions about teachers, students, courtiers, and friends. In one of the numerous meetings of scholars around the philosopher Abu Sulayman al-Sijistani, nicknamed the Logician (died c.  1000), the friends discussed the question raised in those texts why Alexander esteemed his teacher Aristotle more than his father. The texts transmit three different answers allegedly given by Alexander, which motivated the participants in the meeting to offer their own thoughts. According to these variegated answers, a teacher provides perfection, helps to overcome the world of generation and corruption, abstains from satisfying his natural desires in order to elevate a student’s intelligence, gives a student purpose for his life, and

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liberates him from the fetters of earthly existence (Kraemer 1992,  114). This perspective on the function of a teacher and his impact on the life of a student indicates that the acquisition of factual knowledge in any of the sciences including philosophy was not what mattered most to these philosophically interested men of the tenth century. This orientation towards the elevation of the soul and the afterlife continued to dominate the rhetoric of teaching and learning in Islamicate societies until the modern period, expressed often in the introductions of scientific texts, the use of quotations from the Qur’an, the application of sayings of the Prophet or lines of poetry within such texts and in biographical entries. A person who did not master these elements of knowledge had not successfully completed his education. The properties of learned men that are most often praised in biographical dictionaries in the madrasa era continued to include otherworldly orientations. But they also include values that are undeniably linked to life on earth in concrete historical conditions. A  learned man had to bring benefit to his students and the public. He had to read useful texts to them, to show excellence in at least one domain of knowledge (but better to do so in several), and to outdo his colleagues by his mastery of finer points, valuable details, and subtleties. Breadth of learning was appreciated, but standard. Depth of learning was preferred, but found only among a small number of scholars. Extraordinary memory caused amazement, as did eloquence and the capability to solve problems. On the opposite end of the spectrum, biographers chastized men with harsh words for their failures, lack of knowledge, and misbehaviour. Neither praise nor reprimand necessarily had to be true. Biographers did not write dictionaries exclusively for registering the truth or to express scholarly census. On the one hand, they participated with their works in creating and destroying reputations, promoting friends, family, and teachers. On the other hand, they denounced enemies and members of intellectual (and other) factions to which the writer himself did not belong. 6.2. Reflections on Creativity and Professional Control Writings on the pedagogy of teaching or learning the sciences are very rare. Remarks on the value of specific disciplines can be found more often. In his Introduction to History, Ibn Khaldun dedicated Section 7

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of Chapter VI to the various kinds of sciences and their methods of instruction (Ibn Khaldun 1958, vol.  3,  426). He argues for the view that scientific instruction is a craft by stating that understanding and memorizing do not lead to skill in a science. Rather, a habit needs to be formed “which enables its possessor to comprehend all the basic principles of that particular science, to become acquainted with its problems, and to evolve the details of it from its principles. As long as such a habit has not been obtained, skill in a particular discipline is not forthcoming” (ibid.). He derives a further argument for his thesis from the claim that the technical terminology used by famous scholars differs from that of other scholars. Since such a feature is characteristic of the crafts, technical terminology cannot be regarded as a part of the sciences. His examples are kalam and the philological disciplines (ibid., vol. 3, 427). After complaining about the disappearance of good instruction in the sciences in Fez and elsewhere in North Africa after 1300 (which does not fully agree with what is known from other sources), Ibn Khaldun turns against memorizing as a method of learning and teaching: The easiest method of acquiring the scientific habit is through acquiring the ability to express oneself clearly in discussing and disputing scientific problems. This is what clarifies their import and makes them understandable. Some students spend most of their lives attending scholarly sessions. Still, one finds them silent. They do not talk and do not discuss matters. More than is necessary, they are concerned with memorizing. Thus, they do not obtain much of a habit in the practice of science and scientific instruction. Some of them think that they have obtained (the habit). But when they enter into a discussion or disputation, or do some teaching, their scientific habit is found to be defective. The only reason for their deficiency is (lack of ) instruction, together with the break in the tradition of scientific instruction (that affects them). Apart from that, their memorized knowledge may be more extensive than that of other scholars, because they are so much concerned with memorizing. They think that scientific habit is identical with memorized knowledge. But that is not so (ibid., vol. 3, 429–30).

Rosenthal’s translation of the Arabic words ʿilm (knowledge) and ʿilmi (adjective of ʿilm) as science and scientific may mislead the reader to think

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that Ibn Khaldun speaks here indeed about the mathematical sciences, medicine, or philosophy. But notions like discussion and disputation suggest that his focus is, as before, on kalam, other religious sciences, and perhaps logic. Reflections on how to teach the other, non-religious disciplines cannot be found in abundance. But occasionally, a scholar took up his pen and codified what he thought was important. One such exceptional text in the mathematical sciences is Ahmad b. Muhammad b. ʿAbd al-Jalil al-Sizji’s Book on Making Easy the Ways of Deriving Geometrical Theorems (al-Sijzī 1996). As mentioned in Chapter Two, al-Sijzi was an active and well-known scholar of the mathematical sciences during the tenth century. He also was a fairly conservative scholar. In the discussions about the value and structure of Euclid’s Elements and the permissibility of modifying and rewriting this important teaching manual, he took the stance that it was a perfect book and that any modification of its structure, logic, or content was unacceptable. His friend and correspondent Abu Sahl Wijan b.  Rustam al-Kuhi (second half of the tenth century) took the opposite position. According to his own mathematical practice, he held the Elements to be imperfect and in need of modification and completion. Al-Sijzi’s attitude towards the Elements resembles that of a protagonist in an anecdote told about one of the sons of Musa, already introduced in Chapter Two.  Ahmad, the middle of the three brothers, was sitting one day in front of his house thinking about some geometrical problems. Some mediocre scholar passed by, stopped, and asked whether Ahmad had read Euclid’s entire book. When Ahmad answered in the negative, the passer-by became upset, asking him: How do you dare try to be better than Euclid without even having read the Elements in their entirety?! Ahmad did not wish to engage in this dispute, but the other man dragged him to Caliph al-Ma’mun and complained about Ahmad’s lack of proper scholarly behaviour. Al-Ma’mun asked Ahmad whether it was true that he solved geometrical problems without having read all of the Elements. When he confirmed this, the Caliph counselled Ahmad to read the book in order to avoid further complaints. Doing mathematics without having read the authorities was obviously not the best way of learning and doing things. Despite his conservative attitude towards scholarly authorities, al-Sijzi was genuinely interested in improving teaching methods in geometry. He

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objects to the belief of people in his time that “there is no way of learning the rules for deriving (new propositions) even with much research, practice, study, and lessons in the elements of geometry unless a man has an innate natural talent which enables him to discover figures, because study and practice are insufficient” (ibid., unpaginated [9]). Although he explicitly says, when describing his intentions, that he is writing for advanced scholars who know geometry well, his treatise provides helpful counsel for any person interested in learning how to do things and how to produce new knowledge. The purpose of al-Sijzi’s treatise was “to enumerate, in this book of ours, the rules which will make it easy for the researcher who knows and masters them to derive whatever geometrical construction he wants”(ibid.). His summary of the ability, skills, and labour needed to become a good scholar of the mathematical sciences shows a sound understanding of student ranking and the tasks of a good teacher interested in helping students to master their courses and promoting their learning progress: There are people who have a natural aptitude and an excellent ability for deriving figures, but who do not have much knowledge, and who do not work hard to study these things. But there are also people who work hard, who study the elements and the methods, but who do not have an excellent natural ability. If a man has an inborn natural talent and if he works hard to study and practice, then he will be first-rate and outstanding. If he does not have a perfect ability, but if he works hard and studies, then he can also become outstanding by means of study. As for someone who has the ability but does not study the elements, and does not devote himself to the constructions of geometry, he will not benefit from it in any way (ibid., unpaginated [9–10]).

Al-Sijzi’s last sentence in this paragraph, dismissing a person who declares that all one needs for doing successfully geometry is innate capability, implies that he was engaged in a sharp conflict about learning and teaching geometry. Unfortunately, no other traces of this dispute are known to exist. After this justification of his treatise, al-Sizji first explains the rules in a general way. At the end of this part, he condenses his explanations into seven main methods for becoming a productive geometer:

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1. Cleverness and intelligence, and bearing in mind the conditions which the proper order (of the problem) makes necessary. 2. Profound mastery of the (relevant) theorems and preliminaries. 3. […] but you must combine with that (i.e. the preceding method) cleverness and guesswork and tricks. The pivotal factor in this art is the application of tricks, and not only (your own) intelligence, but also the thought of the experienced (mathematicians), the skilled and those who use tricks. 4. Information about the common features (of figures), their differences, and their special properties. In this particular approach, the special properties, the resemblance and the opposition are (considered by themselves) without enumeration of the theorems and preliminaries. 5. The use of transformation. 6. The use of analysis. 7. The use of tricks, such as Heron used (ibid., unpaginated [14]). Rules 1–3 are generalities. Rules 4 and 7 are general recommendations for a student about what to pay attention to when getting instructions about a geometrical problem. Rules 5 and 6 refer to specific geometrical methods for problem solving. The detailed elaborations of al-Sijzi’s seven rules show that they are based on philosophical concepts about the classification of scientific objects, mathematical experience of the solvability of problems, the geometrical methods of Antiquity, and methods in use in his generation (ibid., unpaginated [4–5]). The second part of al-Sijzi’s treatise contains examples for learning how to apply his rules. He emphasizes that speaking in an abstract and general way about the methods for producing new knowledge is “illusory and deceiving”, without giving a reason why he thinks so. His subsequent explanation of the proper way to teach skills and methods implies that he privileged learning by exercise and detailed explanation (ibid.). Several of his geometrical treatises do exactly that – presenting one example after the other with an explanation of the procedure to solve them. Hence he may not have merely written this treatise on the pedagogy of geometry, but may have applied his beliefs in classroom work, too. The medical texts on examinations of aspiring doctors written in Arabic between the ninth and the thirteenth centuries offer another

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p­ erspective on methods of teaching and learning. Following a lost Galenic text translated by Hunayn b.  Ishaq in the ninth century, they reflect a ­mixture of literary topoi, practical experience, and professional competition (Micheau 1993, 117). The first Syriac physician of the ninth century who wrote his own treatise on examinations was Yuhanna b.  Masawayh (died in 857), the court physician of several Abbasid caliphs and son of the allegedly illiterate medical worker at the hospital of Gundishapur mentioned in Chapter Five. But Ibn Masawayh’s treatise has not survived. Ibn Masawayh’s student Hunayn b.  Ishaq also wrote a tract on medical exams, which were still recommended by twelfthcentury ­writers (Prioreschi 2004, 380, fn 679). Another lost treatise on exams was written by Ishaq b. ʿAli al-Ruhawi of Edessa (today Şanlıurfa in Turkey). Parts of it are summarized in his treatise on the proper comportment of ­physicians, patients, and the public at large, which has survived the centuries in one copy. As for the qualification of medical personnel, al-Ruhawi differentiates between doctors or naturalists, who treated humans on the basis of Greek medical theory, and oculists, phlebotomists, and other healers. He stipulated that the healers had to know those parts of medical theory that concern human anatomy and therapeutic procedures. The naturalists, in contrast, needed to be familiar, comprehensively and profoundly, with the entire range of theoretical knowledge. In order to determine the quality of their knowledge they should be tested in the so-called Sixteen Galenic Books, briefly mentioned in Chapters Two and Five (Micheau 1993, 118). Abu Bakr al-Razi did not share al-Ruhawi’s preference for a check of theoretical knowledge only. He believed that theoretical knowledge and practical experience should be well balanced. This position reflects his personal views, but also the rising importance of hospitals for teaching and learning, as discussed in Chapter Five. Hence, al-Razi proposed asking specific questions about how to proceed in concrete cases of disease, for example the treatment of an abscess in bodily organs such as the liver and the kidneys or in the intestines without relying on surgery, which ancient medical writers had discouraged in such cases (ibid., 119). Various texts written for rulers, physicians, or market inspectors appeared during the Ayyubid period. Jalal al-Din al-Shayzari (second half of the twelfth century), a judge and physician from Aleppo, compiled in 1164 a manual for market inspectors telling them to require all

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p­ hysicians in town to swear the Hippocratic Oath, to test the ophthalmologists’ knowledge of Hunayn b.  Ishaq’s treatise on eye diseases, to control the knowledge of bonesetters on the basis of relevant chapters from the Medical Compendium in Seven Books by Paulus of Aegina (died in c. 690), and to check whether surgeons were familiar with at least one of Galen’s books, perhaps On Bones for Beginners (Prioreschi 2004, 380; Savage-Smith 1994). While it remains unclear whether any of these prescriptions for maintaining or restoring the qualification of different medical practitioners were ever applied for any extended period of time or even at all, the few extant ijazat (teaching licences) leave no doubt that reading and writing practices constituted an important range of methods in medical training (al-Sakhawi n.d., vol. 6, 285). Ibn al-Nafis, for instance, gave his mature Christian student Shams al-Dawla Abu l-Fadl b. Abi l-Hasan, called Ibn al-Quff (1232–1286), such an ijaza for reading and mastering his entire commentary on the book On the Nature of Man attributed to Hippocrates (ibid.; ms. Bethesda, National Library of Medicine, A69, f. 67b): [In the name of ] God, the Provider of Good Fortune. The wise, the learned, the excellent Shaykh Shams al-Dawlah Abu al-Fadl ibn al-Shaykh Abi al-Hasan al-Masihi, may God make long lasting his good fortune, studied with me this entire book of mine – that is, the commentary on the book by the Imam Hippocrates, which is to say his book known as ‘On the Nature of Man’–by which he demonstrated the clarity of his intellect and the correctness of his thought, may God grant him benefit and may he make use of it. Certified by the poor in need of God, ʿAli ibn Abi al-Hazm al-Qurashi [known as Ibn al-Nafis] the physician. Praise be to God for his perfection and prayers for the best of His prophets, Muhammad, and his family. And that is on the twentyninth of Jumada I [in the] year six hundred and sixty eight [= ad 25 January 1270] (ibid.).

6.3. Reading, Writing, Speaking, Seeing The main learning activities consisted of reading, writing, memorizing, and repeating learned, read, or written passages. Some teachers also allowed questions. Some students used question time for showing off or for offending a

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Ijaza of Ibn al-Nafis for Ibn al-Quff, ms. Bethesda, National Library of Medicine, A69, f. 67b.

teacher who was perceived as poor in performance. The main teaching activities mirrored these student experiences. A teacher either read a particular text or part of it out loud or listened to a student reading it. While a student read, the better teachers corrected reading or writing mistakes. After particularly difficult or obscure passages had been read, such teachers explained

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their meaning to the students. Bad teachers merely let a student read a text and neither corrected nor explained it. Repetitors re-read a text they were studying with a small group of students or prepared a teacher’s class by reading the planned passages before the next lecture. It is not clear when the second mode of supporting students was introduced. El-Rouayheb suggests it came into use in the early modern period (El-Rouayheb 2015, 126). Since being able to recite substantial parts of a text was a highly appreciated form of knowledge, learning entire chapters or even treatises by heart became widespread. This is highly visible in biographical dictionaries of the madrasa period. While originally this method was primarily applied to the Qur’an, collections of hadith, and other religious and philological works, over time references to learning mathematical, medical, logical, or philosophical texts by heart increased. Al-Sakhawi’s dictionary of famous men and women of the ninth century after the hijra (1397–1494) draws a complex picture of the learning and teaching culture in Cairo, Damascus, Aleppo, Jerusalem, Mecca, Alexandria, Damietta, and other towns and villages in Egypt, Syria, and the Arabian Peninsula. There was no binding curriculum that had to be studied. Students made their own choices. Nonetheless, certain trends can be discerned. Many, but not all, students regularly took classes on the mathematical sciences as well as logic. Among the mathematical disciplines the legal field of inheritance calculations clearly dominates. Some students only read texts in this branch discipline. More students understood that it was better to combine this legal subdiscipline with a study of arithmetical texts. Thus, these two fields of knowledge appear often together in the relevant entries of al-Sakhawi’s work (al-Sakhawi n.d., vol.  1,  25,  128,  225,  232; vol. 6, 58, 82, 162, 252, 262; vol. 8, 96, 108; vol. 9, 18). A second group of students was interested in the methods available for determining prayer times, the directions of prayer towards the Kaʿba, and the rise of the lunar crescent. They studied the science of timekeeping either as their only mathematical class or together with arithmetic, geometry, and occasionally planetary theory (ibid., vol. 1, 60, 205, 228, 300; vol. 8, 75; vol. 10, 46). Those students who were more interested in planetary theory than timekeeping combined it with geometry rather than any of the other mentioned fields (ibid., vol. 10, 189, 259). Then there were students who were especially interested in algebra. They combined it with reading texts on arithmetic and sometimes one or more of the other mathematical branch disciplines (ibid., vol.  1,  236,  282;

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vol. 6, 236, 248, 330; vol. 7, 5, 72). Finally, there were students who apparently simply loved mathematics. They studied texts from all the mathematical sciences (ibid., vol. 6, 112; vol. 8, 211; vol. 9, 19). This picture is reflected in the impressive number of teachers available, in Cairo in particular, for teaching texts on these different topics. Students could thus choose among them and indeed did so. Some teachers became more famous and sought out than others. Undeniably the most highly appreciated and qualified teacher of the mathematical sciences in this century was Ibn al-Majdi (ibid., vol.  1,  330–33; Charette 2007a). But there were others who also had a good reputation. The number and quality of these teachers obviously ensured that students could turn to Cairo throughout the entire century covered by al-Sakhawi, when they wished to read a mathematical text (al-Sakhawi n.d., to be found in all ten vols). Since none of these teachers, however, held a position for teaching the mathematical sciences, but rather for teaching law, some other religious science, or Arabic language, grammar, rhetoric, or other philological disciplines, many of them also taught several of these other disciplines. Logic and philosophy followed a similar pattern. Many students included logic in their educational profile. Philosophy was much less studied. But students in Cairo were still surprisingly often interested in reading a text on a philosophical topic (ibid., vol. 1, 287; vol. 6, 114; vol. 7, 6, 23, 56, 60, 99, 113, 145, 174, 261; vol. 8, 114; vol. 9, 2; 10, 49). It is, however, not clear what exactly they were interested in, since al-Sakhawi does not provide specific information. Extant manuscripts suggest that students in Mamluk Egypt and Syria read texts by Ibn Sina, including his classification of the sciences, his treatise on the definitions, his already repeatedly mentioned work Pointers and Reminders, and perhaps parts of his philosophical encyclopaedias The Book of Healing and The Book of Salvation. They may also have studied commentaries by Fakhr al-Din ­al-Razi, Nasir al-Din al-Tusi, and others, as they had been discussed in these territories under the Ayyubid dynasty. Other philosophical doctrines, most likely taught and read about in this period in Cairo, Damascus, and elsewhere in the Mamluk state, are those of Ibn ʿArabi and possibly parts of al-Suhrawardi’s philosophy of illumination. The disciplinary complex in which logic and philosophy were studied and taught was just as variable as that of the mathematical sciences. Most often they appear together with the philological sciences, which

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al-Sakhawi considered to be components of the rational sciences (ibid., vol. 1, 176, 287, 303; vol. 5, 114; vol. 6, 6, 23, 56, 60, 99, 113, 145, 174; vol. 7, 261; vol. 8, 114; vol. 9, 2). The combination with other rational sciences, in particular the “foundations of faith”, appears also quite often (ibid., vol. 1, 86–87, 116, 172, 218, 228, 303; vol. 2, 10, 154; vol. 7, 171– 72,  259–61 and passim). But even students who focused primarily on law occasionally took classes on logic (ibid., vol. 1, 116). At the centre of these studies stood treatises by Ibn Sina, Najm al-Din al-Katibi al-Qazvini, Qutb al-Din al-Razi al-Tahtani, al-Sayyid al-Sharif al-Jurjani, and al-Taftazani. We already heard about these scholars in Chapters Two to Five. I will briefly discuss some of their texts in Chapter Eight. The small number of study itineraries that al-Sakhawi describes for students in Marrakesh, Fez, Tlemcen, or Tunis ressemble the patterns for the Mamluk state. Logic and philosophy were taken together either with Arabic, rhetoric, and other philological sciences or with the “foundations of faith”, sometimes also with the “foundations of law”, that is with two of the religious rational sciences (ibid., vol. 1, 116, 268, 303). The study of logic and philosophy (hikma, occasionally also falsafa) was not only more broadly available in Arabic-speaking societies west of Iran than often believed. It was also pursued in the fifteenth century in Cairo by Hanbali jurists. This is remarkable since the Hanbalis usually are seen as representatives of a very conservative Islam, hostile to philosophy and kalam. The Hanbali scholar Muhammad b. Ahmad of Cairo, called al-Ghazuli (died c. 1454), for instance, studied logic, semantics, rhetoric, and philosophy (hikma) with Majd al-Din Ismaʿil, a scholar from Anatolia (ibid., vol. 7, 23). Medicine was studied by the people listed in al-Sakhawi’s dictionary either alone or in combination with law, hadith, the philological sciences, or kalam (ibid., vol. 1, 234, 248–49; vol. 2, 195, 225, 310; vol. 3, 131; vol. 4, 27, 200; vol. 5, 110; 6, 263 and passim). Other possible combinations highlighted for the Mamluk period concern the various mathematical disciplines (ibid., vol.  1,  232,  240; vol.  2,  66,  174; vol.  3,  131; vol. 6, 263; vol. 5, 108; vol. 7, 6 and passim). The study of medicine together with astrology, alchemy, sand divination, and the “science of the letters” is surprisingly rarely mentioned. The most detailed information in this regard that al-Sakhawi provides is for ʿIzz al-Din b. Jamaʿa, one of the leading scholars of Cairo in the early fifteenth century introduced already in Chapter Five (ibid., vol. 6, 172).

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Logic and philosophy in addition to medicine also occur, but not too often (ibid., vol. 1, 91, 240, 248–49; vol. 2, 66; vol. 4, 27; vol. 7, 6). This does not seem to correspond to extant medical treatises from the Mamluk territories, where knowledge of philosophy appears to be a regular component of medical education during the thirteenth and fourteenth centuries, at least for works that comment on Ibn Sina’s teachings. Excursions into the countryside for the study of plants and herbs are a rare form of learning in medicine in al-Sakhawi’s dictionary (ibid., vol. 1, 130, 285). Nor did Ibn Abi Usaybiʿa mention them very often for the Ayyubid period. Nonetheless, some of his contemporaries, himself included, practiced this method (Ibn Abi Usaybiʿa 1965, 649). The post of an herbalist or an advisor for herbs at the Mansuri Hospital in Cairo suggests that this special knowledge was acquired more often than is mentioned by the biographers. Another information that seems to confirm that the knowledge of plants and their medical properties was more often pursued than the biographical dictionaries report concerns the Maghrib. In the late twelfth and early thirteenth centuries, ʿAbdallah b. Salih al-Kutami, an apothecary and teacher, lived in Marrakesh. It is believed that the wellknown herbalist and medical scholar Ibn al-Baytar (1197-1248) fromMalaga was one of his students (Ullmann 2009, 64). Before arriving in the Maghrib, Ibn al-Baytar had studied in Seville. There, collecting plants had been part of his training. For the Ottoman sixteenth century, the collection of plants in a kind of herbarium is attested for an unnamed scholar in Aleppo, which Leonard Rauwolf (1535–1596) acquired (perhaps by illegal means) during his visit there (Brentjes 1999, 442). Several methods of teaching and learning were shared through all the disciplines. Memorization of entire texts, the choice of epitomes and commentaries as preferred types of texts, and the reading and copying only of parts of a book are the methods most often mentioned by al-Sakhawi (alSakhawi n.d., vol. 1, 57, 128; vol. 2, 67, 156–57, 164, 196, 286; vol. 5, 12 and passim). Al-Sakhawi gives the titles of books that were memorized in the disciplines without, however, trying to be comprehensive. He writes time and again that a certain book was read in a few chapters or parts only (ibid., vol. 1, 49, 57, 90, 128, 268; vol. 2, 164, 196, 286 and passim). At times, he differentiates between reading texts of several disciplines according to the approach of a specific teacher, reading with books (diraya),

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ms. Tehran, Danishgah, Kitabkhanah-i markazi, 1359, Theodosius of Bithynia, Spherics, edition by Nasir al-Din al-Tusi, flyleaf 7 (out of nine), f. 72a.

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and reading with verification (tahqiq) (ibid., vol. 1, 60). Furthermore, he informs us that some students read a text with a teacher, investigating it (ibid., vol. 1, 56; vol. 2, 5, 60). Further common methods were notetaking and – in the advanced stage of learning – the composition of new texts. Notes were added to a book either in the margins of a text or on so-called flyleaves, smaller and larger pieces of paper filled by more or less legible student hands. Flyleaves do not appear among the learning methods in al-Sakhawi’s dictionary, but authoring new works is always mentioned if appropriate. Two types of tasks were particularly cherished by advanced students and teachers alike – the writing of commentaries and glosses in a chain of authors and the versification of texts written by one’s master or some other author (ibid., vol. 1, 130, 230, 234; vol. 6, 284–85). Once a student felt satisfied with his overall education and wished to deepen a part of his knowledge, he became the disciple of a teacher. Nine, ten, or even twenty years of discipleship were not considered excessive, in particular in the religious sciences. Disciples again read texts with their masters, choosing a few disciplines for this closer and possibly deeper learning relationship. They are often described by al-Sakhawi in such a manner that it seems possible to assume that they remained disciples until they excelled in at least one of their chosen fields of study (ibid., vol. 1, 130, 236, 241, 269). Although many discipleships concern law or hadith, al-Sakhawi also mentions them for inheritance mathematics, arithmetic, timekeeping, medicine, “the etiquette of disputation”, logic, and even philosophy (hikma) (ibid., vol. 1, 30, 75, 82, 134; vol. 2, 37, 195, 225; vol. 5, 171, 178; vol. 6, 48, 114, 263, 323 and passim). For the seventeenth century, the study of logic is known in more detail for the Ottoman Empire and North Africa due to its investigation by ­el-Rouayheb (2015). 6.4. Tradition, Ingenuity, and Discursive Method Two Ottoman historians – Ahmad b.  Mustafa Tashköprüzade and Muhammad al-Amin al-Muhibbi (died in 1699) – describe two different approaches to learning or teaching a mathematical text. Tashköprüzade privileges a transmitter chain and the strict following of tradition. He even applies the concept of learning by oral transmission (riwaya), ­practiced in

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hadith, fiqh (law), and other sciences of transmission, to an elementary mathematical text. Al-Muhibbi was impressed by the ingenuity of one of his teachers who wanted his students to understand the stereometrical books of Euclid’s Elements and consequently built models of mathematical solids from wax. Thus, al-Muhibbi praises a teaching method that goes beyond the standard method of scholastic reading of a text without an uninterrupted transmitter chain (diraya). Written in the first half of the sixteenth century, Tashköprüzade’s biographical dictionary of Ottoman scholars highlights not only tradition, but the dynastic control of the scholars, the instability of scholarly appointments, and the bureaucratic regulation of teaching and legal posts. References to the fields of knowledge taught and to teaching literature, while still present, are fairly muted. The access to madrasa positions or qadiships and the religiosity and social behaviour of the scholars matter more than the specifics of their education. If one were to trust this Ottoman historian, the group of scholars was of exemplary behaviour: kind, respectful, patient, self-controlled, and often uninterested in earthly matters. Writing about 150 years later, al-Muhibbi points to widespread corruption among them. Offices and posts were up for sale and depended on relationships with the high and mighty, not on knowledge or proper behaviour. It is not reasonable to assume that things changed so profoundly within a century. Tashköprüzade’s irenic world of exemplary scholars owes as much to the writer’s official post in the Ottoman state as al-Muhibbi’s disillusioned picture does to his life in a province far away from the capital and the luminaries of Ottoman society. Changes for the worse were already underway in Tashköprüzade’s time. In an anonymous law codex, most likely addressing the educational institutions of the three Ottoman capitals Bursa, Edirne, and Istanbul, the sultan, informed by his learned advisors, complained: […] it has been heard that teaching and learning are in decay […] that the banners of science are broken […] and the colleges are empty of teaching and learning (Imber 2009, 215).

The authors of this anonymous declaration criticize two features of madrasa learning and teaching clearly visible already in Ayyubid and Mamluk times: reading only parts of books without going deeply into

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their substance; unsystematically studying a treatise here and there, but not a sequence of texts covering a whole field of knowledge (ibid.). In conclusion, the decree demands certification, systematic and substantial education, and at least a five-year span before entering the professional path to become a teacher or a judge. In the late seventeenth century, alMuhibbi obviously still did not see these changes materializing. In such an overall context of learning and teaching, Tashköprüzade’s conservative methods for learning a mathematical text seem to represent the learning goal prescribed in the royal decrees. In his biographical entry on Fath Allah al-Shirvani (1417–1486), Tashköprüzade described how he himself had learned Qadizade al-Rumi’s commentaries on Shams al-Din al-Samarkandi’s (died c.  1322) extracts from Books I and II of Euclid’s Elements and al-Jaghmini’s elementary introduction to planetary theory through a chain of teachers, among whom was also his father. Qadizade al-Rumi, introduced already in Chapter Four, was one of the leading scholars at Ulugh Beg’s court in Samarkand in the early fifteenth century, while Shams al-Din al-Samarkandi and al-Jaghmini, who also appeared in that chapter, lived under Mongol rule in the thirteenth century. After learning the transmitted and the rational sciences with al-Sayyid al-Sharif al-Jurjani (Chapters Four and Five) and the mathematical sciences with Qadizade al-Rumi, Fath Allah al-Shirvani settled in Kastamonu near the Black Sea. There, he became a teacher of Mulla Niksari (died in 1495), the maternal uncle of Tashköprüzade’s father. They read together a book by al-Taftazani, al-Jurjani’s commentary on an important work on kalam with a chapter on planetary theory, and the two mathematical commentaries of Qadizade al-Rumi, already mentioned. (Fath Allah) recited the works to (Mulla Niksari) in precisely the same manner as he had heard them from the commentator [(Qadizade)]. (Mulla Niksari) on his side recited the two works to my father and this in exactly the same manner as he had heard them from (Fath Allah). Finally I myself heard them from my father, who (taught) them to me in the transmitted style (Tashköprüzade 1978, 64).

Tashköprüzade’s brief entry on al-Shirvani is imprecise and leaves out important elements of his educational and professional life. From about 1435 to 1440, al-Shirvani studied a full five years in Samarkand with

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Qadizade al-Rumi, reading with him not only the two elementary works mentioned above, but also Nizam al-Din al-Nisaburi’s higher-level commentary on Nasir al-Din al-Tusi’s Memoir on Astronomy, as well as alTusi’s work on kalam, and texts on law. Before he came to Samarkand in late 1435, he had already read al-Jurjani’s commentary on al-Tusi’s Memoir on Astronomy with a Shiʿi teacher in Tus.  This seems to have marked his entrance into the study of higher-level astronomy. Late in his life, after becoming a prolific author and a successful teacher, al-Shirvani not only wrote glosses on Qadizade al-Rumi’s two commentaries (1473), but also a commentary on al-Tusi’s Memoir for advanced students (1475). This commentary reports on the level of learning and teaching at Ulugh Beg’s madrasa in Samarkand. Al-Tusi’s Memoir was read together with al-Nisaburi’s commentary under the guidance of Qadizade al-Rumi. Ulugh Beg is said to have visited the school twice or three times a week, participating in the students’ reading of the two texts. At points he regarded important to elucidate, the ruler interrupted the student and asked for explanations of difficulties. Then Ulugh Beg would offer his comments (Saliba 1994, 45–46, fn 51). The difficulties are called “subtle”. This term is often found in descriptions of learning, teaching, and the goals to be achieved. Al-Shirvani included in his commentary on al-Tusi’s Memoir an ijaza (licence to teach) from Qadizade al-Rumi for his teacher’s two commentaries as well as works on kalam and law (Trigg 2016, 365). Al-Shirvani’s commentary also shows something about his teaching methods. Going beyond the immediate elucidation of the textual and conceptual difficulties of al-Tusi’s text itself, he added further elaborations usually not found in these commentaries, but supposed at least partly to be known already to the students. Among these additions are a debate on Euclid’s Elements, a long discussion on optics with references to Ibn al-Haytham’s main work on this field, the Optics, and comments on mathematical geography (Fazlıoğlu 2007, 1055–1056; Trigg 2016, 365). Trigg interprets al-Shirvani’s extension of the standard mathematical and natural philosophical introduction found in al-Tusi’s Memoir and the treatises of its commentators (at least for the case of optics) as an effort to increase his students’ understanding of optical themes important to astronomers (ibid., 368–69). Al-Shirvani’s glosses (or: super-commentary) to Qadizade al-Rumi’s astronomical commentary repeat a c­ omposition

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method more often found directly in manuscripts of the basic text. He does not quote either of the two works by al-Jaghmini and Qadizade alRumi as done in full-scale commentaries, but simply refers to them and then proceeds with explaining his own ideas or views. Trigg sees this work thus in some parts as “a set of instructor’s notes for clarifying difficult passages or providing context and background to the concepts in the base text” (ibid., 371). Nonetheless, al-Shirvani did not have a continuous, stable professional career. In 1453, he left Kastamonu, then under the rule of the Isfandiyarid dynasty (ruled c.  1280–1461), after several years of teaching the mathematical sciences there. He joined the retinue of the Ottoman grand vizier Çandarlı Halıl Pasha (vizier 1431–1453), with whom he participated in the conquest of Constantinople. But he had made the wrong choice of patrons. Sultan Mehmet II harbored a deep enmity against the all-powerful grand vizier. Two days after the conquest of the Byzantine city, he executed Halıl Pasha. Unsurprisingly, al-Shirvani’s application to the sultan as a new patron failed. Al-Shirvani returned to his Isfandiyarid patron in Kastamonu, resuming his teaching responsibilities. In 1467, he undertook a pilgrimage to Mecca, teaching on the way in madrasas in Iraq. From Mecca he travelled to Cairo, where he became one of the city’s teachers. In about 1473 he was back in Anatolia. A few years later, al-Shirvani was apparently exhausted from working in what was then an Ottoman town and returned to Shirvan, where he lived until his death (ibid., 366–67). Tashköprüzade’s entry contains none of this information. His interest in, and understanding of, the mathematical sciences was undoubtedly very limited. A similar description of the teaching methods used in Ulugh Beg’s madrasa at Samarkand can be found in the letters written by Ghiyath al-Din al-Kashi from Samarkand to his father in Kashan. These letters also highlight the intense competition among the scholars at the Timurid court, their nastiness when they perceived someone as inferior or conceited, and the high self-regard that al-Kashi had of himself. He clearly considered Qadizade al-Rumi and Fath Allah al-Shirvani as far below him in competence, aptitude, and skill (Bagheri 1997). These letters are quite long and thus cannot be quoted here. But I recommend readers to read them, if they wish to get an impression of the atmosphere amongst the experts in the mathematical sciences at Samarkand and their learning and teaching methods (Kennedy 1960; Bagheri 1997).

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In contrast to Tashköprüzade, al-Muhibbi preferred the unusual teaching method used by a teacher of his teacher. He wrote: Mahmud al-Basir al-Salihi from Damascus  […], our excellent shaykh  […]. He read in Damascus with the most important of the teachers, among them our shaykh, the arch-scholar Ibrahim al-Fattal, and by him he was trained and (educated) in (various) disciplines. He read with him Arabic, rhetoric, and logic. He took the mathematical (sciences) from Shaykh Rajab b. Husayn and metaphysics from Munla Sharif al-Kurdi. […]  And I took from him logic, geometry, and kalam. While I took geometry, he used tricks for determining their figures (or: theorems) well by giving examples from wax to me. His professor, the mentioned Shaykh Rajab, had imitated them for him. He made them in a very precise manner. I was astonished by his visual representation as he had taken them from his professor. It was said: if the figure appears, which he had fabricated, then it corresponds with the figure, which is in the book (al-Muhibbi n.d., vol. 4, 330–31).

Mahmud al-Basir al-Salihi’s use of tricks in geometry classes may suggest that this method, recommended in the tenth century by al-Sijzi and referred to by ancient as well as medieval scholars, had survived the centuries as oral and gestural knowledge and spread from Iran and Iraq to Syria. But this is difficult to judge since explicit information on the methods used in classes on the mathematical sciences is difficult to find. Methods of visualization and “practice” also appear in brief accounts of classes on geometry in one of the reports on his teachers by an Andalusian scholar who travelled to North Africa for the sake of learning. With a teacher in Tlemcen (today in Algeria) this traveller studied Euclid’s Elements from Book I to the middle of Book X. His teacher explained the theorems to him by the method of visualization. The very same teacher also taught arithmetic and algebra as found in texts by Ibn al-Banna’ and Ibn al-Yasamin according to “visualization and practice” (al-Majari 1982, 137). Other forms of independent learning, teaching, and problem-solving are also occasionally reported in Arabic sources. The very influential theologian Muhammad b. Yusuf al-Sanusi (1428–1490) participated in classes on the mathematical sciences and the rules for inheritance divisions. Later, he served the teacher of these classes as a disciple. When confronted with a difficult geometrical problem, this scholar refused to

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take recourse to books. He rather insisted on using his own mind and finding the solution independently (Lamrabet 1994,  126). In addition to diagrams, models, and practical problem-solving exercises, which were used in classes on geometry, students of arithmetic were helped by multiplication tables, images for reckoning with fingers, tables, and visualized or versified procedures of multiplication, root extraction, and other arithmetical operations. The spread of didactic versification of numerous mathematical texts was another instrument helping students to memorize how to count, calculate, or differentiate between names of plane figures, solids, and celestial bodies. In the thirteenth century, a title of appreciation for scholars became used more often, al-muhaqqiq. It is the present participle of the second root of the Arabic verb haqqa, which can mean to make something come true, to implement, to actualize, to determine, to ascertain, to verify, to recognize the true nature, and more. Hence, one of the meanings of the participle was “the verifier”. The word describes a scholar who does tahqiq, but not taqlid; he does not merely follow a doctrine, a teacher, or a prescription blindly or without asking questions. Although the second methodological concept refers primarily to the religious sciences, the first one and thus the title itself probably originated within the sphere of philosophy. According to Gutas, the method of tahqiq, also called the method of analysis (tahsil), was central to Ibn Sina’s philosophical project (Gutas 1988, 201, 209, 214–17). Hence, it comes as no surprise that it is also found at the beginning of al-Ghazali’s explanation of logic in his survey of philosophy (MS  Munich, Cod. arab. 2567, unpaginated, digitized as picture 6). But we also met it in Ibn Abi Usaybiʿa’s enumeration of Fakhr al-Din al-Maridini’s methods applied in Damascus when teaching students of medicine. Fakhr al-Din al-Razi did not receive this title, at least during his lifetime. According to Wisnowsky, he considered himself nonetheless to be a muhaqqiq par excellence, because he developed a well-grounded methodology of commentary practice, which I will summarize in the next section (Wisnowsky 2013, 371). Scholars with a high reputation beyond the rational sciences also bore this title. Examples are Nasir al-Din al-Tusi, Qutb al-Din al-Shirazi, and Kamal al-Din al-Farisi. They used a similar rhetoric in their scientific works and were eager to pose questions, criticize their predecessors, and claim their individual scholarly superiority. Qutb al-Din al-Shirazi

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makes such statements more than once in his astronomical and astrological works (Niazi 2014, 120–21, 123). He writes that his books allow the reader “to distinguish the chaff from the kernel” (ibid., 121). He offers at least one of his books on planetary theory to all classes of students – beginners, intermediate, and advanced students– as well as colleagues. Thus we can consider this kind of rhetoric not only as part of elevating self-representation by a well-known scholar, but as having entered their teaching parlance. This might indicate that scholars of the time hoped that their students would learn how to distinguish between solid scientific knowledge and methods on the one hand, and mindless repetition of simple phrases on the other. In some of their texts, the term tahqiq is used in the sense of correcting transmitted texts or mistakes in a construction, a proof, or the act of filling a perceived lacuna. It thus stands in line with other technical terms used for such indispensable repair work in an age of handwritten texts and scientific debate. Ibn al-Akfani applied this title especially to a group of physicians, who combined experience and rational arguments or methods (Ibn al-Akfani 1989, 47). Wisnowsky studied the method of tahqiq as applied in philosophy after Ibn Sina’s works written in the late tenth and first third of the eleventh centuries. As already explained in Chapter Four, from the twelfth to the fourteenth centuries, Ibn Sina’s Pointers and Reminders stimulated much of the discussion on natural philosophy. Then, further texts, including kalam texts, were included in the debate and in sixteenth-century Iran (perhaps already in the Timurid period) Ibn Sina’s major encyclopaedia The Book of Healing was again studied. Tahqiq was applied in these debates in a broad range of functions and meanings. At one end stood the philological task of discussing the text’s authenticity that is answering the ancient question of whether a text proposed for reading was indeed compiled by the assumed author. The other end marked the task of questioning and verifying the author’s philosophical theses (Wisnowsky 2013, 354). The philological tahqiq included editorial work, lexicographical analysis, and the presentation of definitions for key terms of a text. The philosophical tahqiq encompassed the expansion or transformation of the work’s content by the delivery of new proofs of a specific thesis or by changing the order in a proof, replacing its perceived weak part by stronger forms, providing a completely new proof, or criticizing the work of earlier commentators (ibid., 355–56). The more courageous ­commentators

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went beyond the text under consideration and offered proposals for harmonizing and systematizing the author’s doctrines for a set of his texts or took his doctrines apart critically. The terrain covered between these two practices was marked by efforts to prove the text’s authenticy, to complete incomplete quotes, or to add paraphrases of quoted texts and reflect on their authors (ibid., 354–57). Since commentaries and their derivatives (super-commentaries or glosses) were often read in class, such methods and techniques of tahqiq most likely were an essential part of teaching through reading and elucidating texts, too. Besides the social function of transmitter chains, this set of writing practices and their spillover into classroom reading practices explain why teaching and learning at madrasas dealt less and less with ancient and medieval texts by “great authors” and more and more with the works of the commentators. The debates in the late twelfth and the middle of the thirteenth centuries about the method of tahqiq in Fakhr al-Din al-Razi’s and Nasir al-Din al-Tusi’s commentaries on Ibn Sina’s Pointers and Reminders and related commentaries, to be summarized in the following section, led during the fourteenth and fifteenth centuries to a shift in the meaning of tahqiq as well as the ascription of the title muhaqqiq. Wisnowsky concludes that by this time the method of tahqiq “had ceased to be understood as following Avicenna’s [= Ibn Sina] method, and come to be seen as holding Avicenna’s position” (ibid., 375). This more limited interpretation of tahqiq comes to the fore not only in Jalal al-Din al-Davani’s attribution of the title to a subgroup of kalam scholars, but also in his reduction of the method to matters of faith: O Thou who hast enabled us to verify (tah.qīq) the Islamic creed and shielded us from imitation (taqlīd) in the principles and corrolaries of theology […] I have not abandonded myself to the alleys of gathering quotes, as is often done by the disputatious (ahl al-jidāl), who are unable to take the highroad of proof (istidlāl). Rather, I have followed the plain truth even if it goes against what is commonly accepted (mashhūr), and I have held on to the exigencies of proof even if not bolstered by the statements of the majority (al-jumhūr) (quoted after el-Rouayheb 2015, 33).

The second part of this quote, where al-Davani praises himself as a great scholar, is an almost literal copy of a statement in Fakhr al-Din al-Razi’s introduction to his Eastern Investigations, where he also speaks about his

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move to the method of verification, here called analysis (tahsil) (Eichner 2009, 67). Since al-Razi’s explanations of his methodological approach is situated in his debate with Ibn Sina’s philosophy, al-Davani’s claim does not merely show his identification with his illustrious predecessor, but also alludes to this philosophical debate about how to analyse texts and how to comment on them, as well as to issues of teaching. By the fourteenth century at the latest, the concept and the method of tahqiq was familiar to some communities of North African scholars, as Ibn Khaldun’s Introduction to his work on history shows. In the fifteenth century, al-Sakhawi not only confirms that this method was used in teaching in Cairo, but even mentions negatively when an otherwise broadly educated scholar was not well versed in it (al-Sakhawi n.d., vol. 1, 101). In the seventeenth century, under the impact of Kurdish scholars and books written by scholars from Iran, it grew in importance among Ottoman madrasa teachers. According to el-Rouayheb, its application in the Ottoman scholarly realm showed certain pecularities not as clearly visible in other Islamicate societies. At the level of teaching methods, this concerns the combination of verification with “the etiquette of scholarly disputation” (adab al-bahth) (el-Rouayheb 2015, 60, 99). But al-Sakhawi’s dictionary already contains references to such a combined appearance, or at least the parallel application of philosophical and disputational training, for the last Mamluk century. There too, the impact of scholars from Iran was decisive (al-Sakhawi n.d., vol. 1, 82, 90). A further term used for “verification” by writers about juridical dialectics of the elventh and twelfth centuries and also employed by Shams al-Din al-Samarkandi and other scholars in the treatises about the science of disputation is tashih (making something correct) (Miller 1984,  90–91,  109–11,  187 and passim). But the relationship between the two terms and their implications for teaching methods have not been discussed by Miller or el-Rouayheb. 6.5. “The Etiquette of Scholarly Disputation” Over the centuries, various efforts had been made to improve the rules for scholarly debates. Inspired by ʿAbd al-Latif al-Baghdadi’s (1163–1231; see Chapter Eight) arguments, Fakhr al-Din al-Razi accused his colleagues in the religious sciences of attacking a person rather than a problem or a

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method when in a dispute. In the two religious disciplines of dialectics and law, authors formulated types of questions that could be posed between two participants in a scholarly discussion and certain rules of how to deal with them. A good survey of the methods delineated by writers on such issues until the early thirteenth century has been given by Miller in his unpublished thesis (Miller 1984). Important changes occurred during the thirteenth century, when on the basis of these two traditions the new discipline of investigation (ʿilm al-bahth), or the science of disputation (ʿilm al-munazara), and its etiquette (adab) were worked out (for a brief discussion of the terms, their meaning, and origins see ibid., 203–04). Miller sees one of the main changes in the acknowledgement that this new discipline now dealt with disputations which transcended mere questions and answers by allowing for objections and asking for proof (ibid., 182–83). Briefly stated, a discussant had the right to assume the position of the person who raised questions when addressing another scholar who became the disputant. In this function, he had to explain the rationale of his position. He could formulate a thesis, and his opponent was allowed to offer one or more objections for which evidence then needed to be ­presented (Ormsby 1984, 93). Further changes concern the perception of the nature of the debate, the definition of its technical key terms, and the rules for comportment in such a debate (Miller 1984, 184–95). Especially Central Asian scholars and their students promoted this new discipline of disputation. One of the most often read and commented upon treatises on these new rules was Shams al-Din al-Samarkandi’s Epistle on the Science of the Etiquette of Investigation. But he also discussed these topics in other works on logic, disputation, and kalam (for a survey of the technical and social rules discussed by al-Samarkandi and their derivation from Aristotelian logic, on the one hand, and from the two Islamic traditions of theological and juridical dialectics, on the other, see ibid., 207–11). In one of his logical treatises al-Samarkandi elucidates this intellectual background: It has been the custom of our predecessors to place a chapter on dialectics (jadal) in their logical works. But since the science of juristic dialectics (khilāf) of our times does not need it, I  have brought in its stead a canon for the art of disputation and its order, the proper formulation of speech [in disputation] and its rectification. The [art] is, with respect to establishing a thesis and explaining it, just like logic with respect to deliberation and

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thought; for, through it we are kept on the desired path and are saved from the recalcitrance of speech. I have set it out in two sections, the first on the ordering and etiquette of debate, the second, on error and its causes (quoted after Eichner 2009, 399; for a slightly different translation see Miller 1984, 200).

The rules formulated by al-Samarkandi and other authors shaped not only methods of disputation among senior scholars, but also teaching in the rational sciences. Question raising, presenting opposing positions, and analyzing different points from different perspectives were accepted as forms of debate in classrooms and in commentary and super-commentary writing. But even in the seventeenth century, not every Muslim scholar had yet experienced the application of this teaching method. El-Rouayheb reports the astonishment of a Moroccan pilgrim and traveller in matters of knowledge who listened in Medina to a Kurdish teacher: His lecture on a topic reminded one of discussion […] and parley […], for he would say “Perhaps this and that” and “It seems that it is this” and “Do you see that this can be understood like that?” And if he was questioned on even the slightest point he would not stop until the matter was established (el-Rouayheb 2015, 35).

The cross-disciplinary education and knowledge practice that the madrasa educational system stimulated and promoted also encouraged scholars to participate in such methodological debates even when they chose a career in astrology and the mathematical sciences. The Ottoman scholar Ahmed b.  Lütfüllah Mevlevi (died in 1702) showed particular interest and ability in that group of disciplines. In 1668, Sultan Mehmet IV (ruled1648–1687) appointed him head astrologer (müneccimbașı), a court position involving the preparation of horoscopes and eclipse warnings as well as the supervision of all imperial astrologers and timekeepers. After the sultan’s death, Ahmed was dismissed and exiled to Cairo. In 1690, he moved to Mecca, accepting the directorship of a local lodge of the Mevlevi Sufi order, to which he belonged. One year after his arrival in Mecca, Ahmed wrote a treatise on the etiquette of properly reading a text (adab al-mutalaʿa). He considered himself an innovative scholar, since in his view nobody before him had discussed this matter except for one scholar who had written a very brief set of recommendations

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for reading scholarly texts based on the etiquette of investigation (ibid., 99–100, 106). The author of this short text classified textual statements as being either a definition of some kind or a propositional claim. If it was the first, he recommended the reader to reflect through the following four questions on the scholarly concept of “definition”: Is the definition adequate? Is it circular? Does it use terms that are more familiar than the definiendum? Does it use figurative or unclear terms? (ibid., 107–08).

If the last question was answered affirmatively, the premises and the argument needed to be checked. The reader was also enjoined to consider the possibility of a counterargument for proving an opposing conclusion. If the passage under investigation was a propositional claim, the reader should reflect whether any dialectical objection could be raised against it. If that was the case, he needed to look for possible answers to such an objection. In order to enable himself to follow such steps for a specific text, the reader is told to apply some regularity to his reading practice. This meant that he should read the entire part of a text elucidating the problem under investigation from beginning to end with the aim of grasping its general meaning. Then he should stop and start reflecting according to the sequence of steps described before (ibid.). Ahmed b.  Lütfüllah went beyond these basic proposals. He knew very well that a beginning student had many difficulties when trying to understand a new text and had to be taught how to do this. He believed that there was a set of necessary skills, which needed to be acquired first, from what he called “the instrumental sciences”. This set of disciplines included for him syntax, logic, dialectic, semantics, and rhetoric (ibid., 109). Here we come to understand one of the probable reasons why so many scholars in the Mamluk period combined the study of logic with the philological sciences. Ahmed’s goal was to introduce students to a reading practice that was not “crudely literal” (zahiri) and “uncritical” (hashwi). These terms belong traditionally to religious and methodological struggles between the different law schools in Sunni Islam and their principles and methods. El-Rouayheb believes, however, that Ahmed meant them in a less specifically religious and more general sense of being able to read a text in such a manner that the intentions of its author and the meaning of his words can be discerned (ibid., 110).

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After having passed the beginner stage, the intermediate and then the advanced students needed to be taught how to derive meaning from scholarly writings. This skill would have been acquired when the student was capable of successfully undertaking the following four activities: (1) to obtain knowledge that he does not have but for which he is prepared; (2) to move beyond knowledge taken on trust and uncover the evidential basis for scholarly propositions; (3) to deepen his evidentiary knowledge by repeated perusal, thus obtaining a thorough familiarity with the evidence and “the ability to call to mind at will” (malakat al-istih.dār); and (4) to deepen this evidentiary and consolidated knowledge by strengthening it through refreshing his acquaintance with familiar texts or through exposure to new texts and alternative presentations and proofs (ibid.).

El-Rouayheb calls Ahmed’s method “deep reading”. He believes that it soon took root in Ottoman madrasas, in particular in logic and other rational sciences (ibid.). 6.6. Commentaries and Super-Commentaries While epitomes, paraphrases, and extracts describe the preferred kind of texts studied across all disciplines, commentaries and commentaries on commentaries and all sorts of glosses and super-glosses define the writing practices of the advanced students and scholars of all stages in the madrasa era. Modern historians have regarded this literature for most of the twentieth century as unproductive regurgitation of sterile knowledge. In the last decades, this view of the teaching literature has changed and some scholars now investigate such texts for their content, form, style, and intellectual contexts (Ahmed-Larkin 2013; Wisnowsky 2013). Many focus their work, however, on the search for innovative elements and are less interested in the function and meaning of these texts within processes of learning and teaching although there can be no doubt that this is their primary context. The edited volume of Ahmed and Larkin differs here not only by its inclusion of the sciences, medicine, and philosophy, but also by the series of questions it raises about several sociocultural features. This book does not allow for a more substantial engagement with their themes, but as a brief illustration of the direction of their research, I present here four of their questions:

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TEACHING AND LEARNING THE SCIENCES What need did (the commentary as a scholarly genre) fulfill? How did some commentaries become authoritative over others? How were commentaries deployed in various fields as vehicles of pedagogical exchange and cultural transmission? Do non-textual forces, e.g., pressures of patronage and sectarian identities, shape the topics selected by the author of a commentary? (AhmedLarkin 2013, 214).

A second sociocultural site of commentaries and super-commentaries was courtly patronage, which was closely intertwined institutionally and intellectually with the world of the madrasas, mosques, tombs, libraries, and hospitals, as pointed out in Chapters Three to Five. Fakhr al-Din al-Razi presented a method of composing commentaries and their subsequent derivations for texts on philosophical and other rational sciences. It consists of identifying important questions or problems in a text a teacher or an advanced student wished to comment on and specifying objects for his enquiry (Eichner 2009, 31). While the biographical dictionaries rarely venture into descriptions of such textual and argumentative methods, numerous elementary school texts on one rational discipline or another in the centuries after al-Razi discuss such “problems” and “objects”. Many later writers on kalam, logic, and philosophical matters used this approach either directly or with some modification. Moreover, al-Razi’s organization of philosophical knowledge in his work The Essence of Philosophy (hikma) shaped most of those later writings on kalam that dominated the teaching of the rational sciences at madrasas in several Islamicate societies (ibid., 34). Having been designed in an active dialogue with earlier systematic presentations of philosophy by Ibn Sina, his student Bahmanyar b. Marzuban (died in 1066), the critique of Ibn Sina by Abu Hamid al-Ghazali, and the already mentioned Abu l-Barakat al-Baghdadi, al-Razi’s book constituted one important avenue for the entrance of philosophical thinking and arguing into the teaching of the rational sciences, even if philosophy classes were not explicitly offered. Eichner believes that this process of including philosophy in the form of al-Razi’s Essence in later madrasa teaching was enabled through the scholars around Nasir al-Din al-Tusi at the observatory in Maragha (ibid.). Wisnowsky’s analysis of commentaries on Ibn Sina’s Pointers and Reminders offers another facet of Fakhr al-Din al-Razi’s importance for the development of methodology in commentary-writing and, through this,

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for methods of philosophical and theological debate and analysis taught in advanced classes. He shows that in replies to Central Asian scholars, some of whom had strong interests in the mathematical sciences and tried to dismantle Ibn Sina’s status as a scientist, Fakhr al-Din took as one point of his rejoinder to his opponents the weakness of their methods of criticism. Among other things, Fakhr al-Din rejected reliance on earlier authorities when criticizing a writer, insisting that such a critique was insufficient. Methodologically sound criticism presupposed the systematic study of the criticized author’s work, including, if necessary, the study of others of his works, and the comprehensive analysis of the work to be commented upon. Once this footwork had been done, the criticism levelled against one or more points in the work had to be justified, not merely stated (Wisnowsky 2013, 361–62). This justification included the necessity of considering and evaluating counterarguments against positions held by the commentator and the authorities on which he intended to rely (ibid., 363). The steps described so far show obvious similarities to the debates surrounding dialectics, juridical dialectics, and the slowly emerging theory of disputation. But Fakhr al-Din goes beyond them in his methodological demands. He declares that sound commentary and hence sound philosophical criticism necessitates the study of ancient philosophers and the fair representation of their doctrines in order to understand the intellectual context of a more recent philosopher (ibid., 364). Subsequent commentators of al-Razi’s own commentary on Ibn Sina’s Pointers and Reminders took up this methodological debate. Some of them, among them Nasir al-Din al-Tusi, levelled the same accusation of methodological insufficiency against al-Razi that he had brought against his own opponents. In short, while accepting much of al-Razi’s methodological teaching they contended that “the excellent commentator” had fallen short in applying them fairly, consistently, and comprehensively in his own commentaries (ibid., 370–71). Wisnowsky, however, believes that these differences reflect a different stance with respect to the method of tahqiq and its application to Ibn Sina. Nasir al-Din al-Tusi, he contents, rejected Fakhr al-Din’s concept as too far-reaching because it included the commentator’s right to dismantle a previous author’s theories and replace them with proofs for his positions (ibid., 357,  371–74). In Wisnowsky’s view, however, he preserved this right, when commenting on Fakhr al-Din al-Razi (ibid., 372–73).

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A different perspective on the structure of commentaries and supercommentaries is taken by Ahmed who, in his analysis of a text on logic written in the eighteenth century in India and the commentaries and super-commentaries it spawned, drew a close connection between teaching methods and the style of such teaching texts. He argues that the dense and often elliptic language of the basic text in such a chain was intentionally chosen to “allow space for philosophical elaboration, expansion, and controlled digression in the teaching sessions” (Ahmed 2013, 323). The same applies to later steps in the chain, because those texts too were meant to be used in the madrasa to stimulate questions, reflections, and debate. Hence, the often elementary school texts need to be read today as one part only of the class work. Other texts need to be drawn into the analysis in order to determine the points of possible debate and in order to comprehend the oral part of the teaching and learning exercise. The need for a more complex understanding of each single text in a chain of basic text, commentaries, super-commentaries, and glosses seems to be supported by mathematical texts too. In particular, their textual insertions and their flyleaves with multi-levelled exercises and quotes culled from two or more additional texts point to this ­interaction between reading and writing, teacher and students, basic text and texts for elucidation or for advanced explanation. Thus, although many of the extant school texts in the mathematical sciences are elementary with regard to the knowledge they offer, this does not necessarily mean that they were used in class always or mostly in a simplistic manner. A final methodological point to be briefly mentioned here is the emergence of different kinds of notebooks. This is a literary phenomenon that also crosses all disciplines. Some notebooks are dedicated to one discipline or one set of disciplines only. Most notebooks I have seen in my studies in manuscript collections, however, combine notes from different disciplines, often seemingly without any order. Such collections of little snippets of text are often, but not always, identified by titles and author names. In some cases those identifications clarify that the compiler read Apollonius’s Conics or some text, which quoted from the Conics, Ibn al-Haytham’s commentaries on Ptolemy or Euclid, or other ancient or medieval works of the classical period. It seems that such notebooks were the fruit of independent or additional reading by an advanced student,

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repetitor, or disciple. Other notebooks may have served for learning the right things to say in an evening meeting or during a courtly conversation, since they do not contain only notes about mathematical, philosophical, or religious knowledge, but also poetry, short biographical notes, or extracts from literary or historical prose. 6.7. Postface This survey on teaching and learning methods clearly cannot cover the whole spectrum of possibly applied methods and forms of engagement at different levels of education. But since there is only very limited research available with regard to this kind of questions, in particular for the mathematical and “occult” sciences and medicine, most of what I could report builds on recent studies on methods within the field of the rational sciences, and the discussions about proper rules for scholarly debates, together with commentary literature and its functions and structural properties. Two questions remain unanswered in principle. Given the undeniably strong interest among scholars in Islamicate societies in methodological matters, why did rote learning overtake many schools and continues to dominate them until the present day in modern Islamic states? Since the rules for scholarly ­engagement formulated by the scholars discussed in this survey as well as other writers contain many profound and sensible ideas, why was the new knowledge that was fostered by their application fairly limited?

Chapter 7 ENCYCLOPAEDIAS AND CLASSIFICATIONS OF THE SCIENCES

E

ncyclopaedias and classifications of the sciences served three main purposes. They helped to organize knowledge and its practitioners in disciplines, branches, and groups. They provided the basis for polyvalent learning on different conceptual and qualitative levels. Last, they constituted a broad platform for criticizing and altering hegemonic discourses and for offering new systematic expositions. Encyclopaedias have been discussed from different angles by modern researchers taking into account a broad range of knowledge fields, arts, and techniques discussed in Arabic, Persian, and Ottoman Turkish works. Classification texts, while equally often discussed, are easier to categorize since they are – as a rule – shorter, more succinct, and called by their authors – with different words – classification texts. This is not the case for encyclopaedias. They carry no unambiguous key word or words in their titles, which are often flowery and rhymed, a feature of many titles of religious, philological, medical, mathematical, philosophical, and “occult works” from perhaps about the early eleventh century onwards. Neither are they unequivocally identified by the scope of the content or the intentions of their authors. Some modern historians even think that there was no concept of a “true encyclopaedia” subscribed to by authors in Islamicate societies. Others consider the encyclopaedias of administrators in Mamluk Egypt as the heyday of encyclopaedism in the Islamicate world. The notion of encyclopaedia as a literary genre among writers in Arabic, Persian, or Ottoman Turkish is thus much more vague and less well ­defined than is the case with the classification literature. I have nonetheless decided to include both kinds of writings in this chapter, because those encyclopaedias that include the mathematical sciences, medicine, philosophy, and – at times – the “occult” sciences share principles of order and positions of content with specific schemes presented in treatises on the classification of the scholarly disciplines. And both types of writings were

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relevant in educational settings in private houses, with tutors, in courtly circles, or at madrasas, which is the primary raison d’être of this chapter. Van Ess (2006) offered reflections on the great variety of such works. I will survey some of them below. Endress formulated a more streamlined view of how encyclopaedias as well as classificatory writings should be understood. He portrays them as two different traditions shaping two new systems of knowledge organization by contributing to “the construction of identities in the schools of knowledge” (Endress 2006a, 104). Endress also is of the opinion that both kinds of knowledge organization, as well as the presentation and performance of the disciplines discussed in these two forms, arrived in the madrasa only very late (ibid., 116, 128–32). The examples briefly presented in this chapter question this depiction. They overlap, interact, and shape each other’s spaces, forms, and components. Some of these texts were read in madrasas at the very latest in the ­thirteenth century. Their questions and answers became standard introductory school material as numerous, mostly unpublished examples show. Encyclopaedias including the sciences discussed in this book appear in three formats: comprehensive, philosophical, and selective. Comprehensive encyclopaedias are those that include the three major types of disciplinary knowledge pursued in Islamicate societies before the rise of the madrasa: the religious sciences, the philological sciences, and “the sciences of the ancients”. The content of these three classes differed between authors and changed over time, a point I will briefly discuss below. Philosophical encyclopaedias cover all the sciences an author thought belonged to philosophy, but do not – as a rule – treat any field of knowledge outside it. The term “selective encyclopaedias” may be viewed as an oxymoron, but biographers and authors of such works often depicted them as summas of specific disciplines. This defines them as legitimate members of the group of texts discussed in this chapter. It also shows them to be the result of previous debates about the system of respectable and respected knowledge as knowledge to be learned and taught. I abstained from including one example from this category, but instead opted for an outsider to the two kinds of sources discussed in this chapter. I took this decision due to considerations of the available space and added value that the outsider brings to this chapter. This outsider is a treatise on the classification of knowledge looked upon from the aspect of methodology, not from the aspect of taxonomy.

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The comprehensive encyclopaedias included under the three main disciplinary categories most, if not all, of the branches belonging to each category. Examples for the religious sciences are hadith (the transmission of the sayings of the Prophet or his companions), qira’a (the recitation or reading of the Qur’an), Qur’anic exegesis, and fiqh (law). Grammar, inflection, rhetoric, semantics, and metric are members of the philological sciences. Philosophy, divided according to Aristotle into theoretical (metaphysics, physics, mathematics) and practical (politics, economics, ethics) philosophy, came together in the category of “the ancient sciences” with the “occult” sciences and a more diversified presentation of the mathematical sciences, which included, for instance, branches like optics, mechanics, automata, burning mirrors, algebra, and surveying, in addition to the fundamental disciplines of the quadrivium (number theory, geometry, astronomy, theoretical music). Such comprehensive encyclopaedias were mostly written between the tenth and the fourteenth centuries. Their primary language was Arabic. But a good number of encyclopaedias were also written in Persian. Comprehensive encyclopaedias in Ottoman Turkish do exist, but in much fewer numbers. The comprehensive encyclopaedias of philosophy include in principle all six disciplines of the Aristotelian scheme. Some works of this type include in addition so-called branch disciplines. Others exclude the mathematical sciences completely or occasionally even focus only on metaphysics and natural philosophy. The social and ethnic origins of writers of such comprehensive encyclopaedias differed markedly, as did their intended audiences. The first writers of such encyclopaedias were philosophers and administrators of the tenth century. After the fourteenth century, comprehensive encyclopaedias slowly disappeared and an undeniable change of taste can be observed. This change may have been in the making for some time. Instead of comprehensive works people now opted for selective surveys of knowledge. This new form of selective encyclopaedias consisted as a rule of seven, twelve, or a comparable small number of disciplines. Since most of the authors of these selective surveys of knowledge were by now madrasa teachers, it is possible that this preference for selection instead of comprehensiveness was linked to other changes in the literary organization of knowledge relevant to madrasa education. The one change that comes to mind in such a comparative reflection is the emergence of a new kind of summa emphasized in biographical

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dicitionaries and some historical chronicles of the thirteenth to the fifteenth centuries. While summas in previous centuries usually focused on one type of knowledge, say medicine, and some of its subdiscipline or topics, the historians now stressed as a novelty the combination in one book of two to four different disciplines, which might even be members of different categories of disciplinary knowledge. Examples of such combinations are books on the foundations of faith, logic, arithmetic, and (parts of ) law. A second relevant change concerns the new agreement on terminology and order with regard to the categories for organizing respectable and respected knowledge. Instead of the earlier classes, mostly called religious, philological, and ancient sciences, from the late twelfth century onwards scholars more and more accepted a division of knowledge into “transmitted, rational, and mathematical sciences”. Transmitted sciences, often translated as traditional sciences, comprised hadith, exegesis, reading and reciting the Qur’an, and law. These were types of knowledge that depended on transmitters and oral performances, even when the codification of these kinds of knowledge in written forms became increasingly acceptable from the tenth century onwards. The rational sciences were all those that depended on the application of human reason. This understanding united under one roof religious, philological, and philosophical disciplines such as kalam, the foundations of faith and law, grammar, semantics, rhetoric, logic, metaphysics or divine science, and natural philosophy. It also allowed for fields like alchemy, talismans, or magic to be incorporated in this category, although not all authors of treatises on the classification of the sciences shared this position. The mathematical sciences remained fairly stable. Depending on their epistemological positions, some late medieval or early modern writers added the “occult” sciences as a fourth category or reorganized parts of the rational sciences under the header of philosophical (hikmiyya) sciences. The belief of many modern historians and historians of science that the rational sciences were nothing but a new name for the ancient sciences and included the mathematical sciences does not agree with most of the medieval and early modern sources, although occasionally the borders between the categories are fuzzy. This applies above all to biographical dictionaries. There, the often short formulations can indeed suggest that the compiler of the dictionary grouped the mathematical sciences into

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the category of the rational sciences. Another difficulty with such general evaluations about the systematic arrangement of the fields of knowledge learned and taught in various Islamicate societies arises from the deviations between individual authors. Although many scholars, in particular from Egypt to India, worked with the categories described here, others, in particular those in al-Andalus and the Maghrib, used other first-level labels. The Andalusian scholar Ibn Hazm (d. 1064), for instance, grouped all domains of knowledge for all of humanity, not limiting himself to Islamicate societies only. He thought that all nations or communities (umma) possessed everywhere and at all times seven types of sciences: the science of their religious system, the science of their (historical) information, the science of their language, the science of the stars, medicine, ­philosophy, and the knowledge of the configuration (of the universe). But while listing these seven disciplines, Ibn Hazm only allowed the last four as known to all communities. In the first three, he claimed, only three communities excelled, without, however, naming them. In the following paragraph, moreover, he declares that any religious system except Islam was futile (Ibn Hazm n.d., vol. 4, 78). With regard to the world of Islam only, Ibn Hazm taught basically the same disciplinary groupings as described above for the pre-madrasa period in general form. However, the order of the individual disciplines deviates from his previously mentioned one and the content of some of the disciplines differs in interesting ways from the standard definitions by other authors. The science of the configuration of the universe is now the first subdiscipline of the science of the stars, philosophy has been replaced by logic with a theoretical and an empirical, sense-based part, and surveying is an outcome of the application of the science of numbers (ibid., 79). More regular is his first group, the religious sciences. This group embraces the sciences of the Qur’an (reading and interpretation), hadith (knowledge of texts and oral transmissions), fiqh (legal rules of the Qur’an and hadith, the legal consensus and differences among Muslims), and kalam (knowledge of the writings, arguments, proofs, and falsehoods) (ibid., 78–79). It is followed by two philological sciences (grammar, lexicology). Further philological and literary disciplines appear after medicine: poetry, rhetoric, and semantics. His depiction of the content of the discipline of (historical) information (khabr) is also of interest.

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This discipline usually stands for the collection of reports about the Bedouin tribes on the Arabian Peninsula. For Ibn Hazm, however, ancient, Christian, and Islamic universal histories were also legitimate subgroups. Hence, he modified the discipline’s structural set up, writing that the science of (historical) information could be arranged according to four aspects: kingdoms, periods, countries, and generations (ibid., 79). There are many more such individually formed classifications of knowledge, since these areas of knowledge were undoubtedly domains of debate about methodology, epistemology, religious beliefs, culture, ­education, and identity politics. I  will discuss a small number of them below as representatives of three main groups of authors: philosophers, administrators, and madrasa teachers. I have only chosen representatives that are connected in some way or the other to the overarching theme of this book – learning and teaching the sciences. Some of their authors make such connections explicit. In other cases, their professional occupation as madrasa teachers provides the background for their writings and the rationale of my choice. A third group of texts is considered by modern researchers to consist of teaching texts, manuals, or reference books. Christian, Jewish, and Muslim scholars could draw inspirations for classifications of the sciences and their elucidation in the form of encyclopaedic works from ancient literature translated into Arabic or Syriac during the eighth and ninth centuries. Hence, it is no surprise that the first exemplars of encyclopaedias and treatises sorting and organizing the new knowledge were written during the period of translation and appropriation of the content of the translated texts. In this sense, early on encyclopaedic and classificatory works had a clear teaching function in addition to their organizing and structuring purpose, which straddled the two realms of learning extant knowledge and producing new knowledge. A Muslim and a Christian scholar were among the first authors of these two interrelated kinds of text in Arabic – al-Kindi, introduced in Chapter Two, and Qusta b. Luqa, whom we also met occasionally before. In the tenth and early eleventh centuries, two giants arose among Muslims interested in philosophy – Abu Nasr al-Farabi and Ibn Sina, both mentioned repeatedly in previous chapters. They created their own systematic expositions of Neoplatonic Aristotelianism with numerous modifications and some profound changes. The reader who wishes to learn more about these two great philosophers can turn to a broad range

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of specialized and general modern books about them as well as about philosophy in the time of the Abbasid caliphate (for example, YoungLatham-Serjeant 1990, Montgomery 2006, Rudolph 2012, TaylorLópez-Farjeat 2016). Here, I will only survey their ideas about the system of knowledge as propagated in some of their works. Administrators and other court officials between the ninth and twelfth centuries, in particular in Baghdad and in northeastern Iran, contributed their perspectives on what members of their professional class should know about the knowledge system at large and its individual disciplines. I have chosen three of them and their works for discussing some of the specifics of their approaches – Ibn Farighun (tenth century), Abu ʿAbdallah al-Khwarazmi (died in 997), and Shahmardan b.  Abi l-Khayr (second half eleventh/first third twelfth centuries). In addition, there are a number of anonymous encyclopaedias and classifications of the sciences (Vesel 1986). Like Shahmardan’s encyclopaedia of the natural kingdoms, these anonymous texts occasionally cross the boundaries between the domains of the administrators and the scholarly courtiers. They indicate that knowledge and its evaluation was by no means as rigidly separated among the different professional and social spheres as historians often assumed in the twentieth century. With the integration of the mathematical sciences, medicine, logic, and philosophy into the madrasas, texts of the classification literature became one of the regularly read works, introducing students to the system of knowledge. The standard representative of this class of literature read at madrasas in Ayyubid and Mamluk Syria and Egypt was apparently Ibn Sina’s treatise On the Parts of the Rational Sciences. His philosophical encyclopaedias, The Book of Healing and The Book of Salvation, as well as texts by Fakhr al-Din al-Razi, Nasir al-Din al-Tusi, Qutb al-Din al-Shirazi, al-Sayyid al-Sharif al-Jurjani, and other scholars were also studied, in particular in Iran and Central Asia. The main aspect of classification texts and encyclopaedias that attracted the attention of most historians during the twentieth century was the juxtaposition of the religious sciences in tandem with the philological sciences against the ancient sciences. The position of the first, second, and third group as the first, second, and third part of encyclopaedias or treatises on the classification of the sciences induced most modern historians to interpret this organizational scheme as an expression of hierarchical values: the religious sciences mattered more than the ancient sciences and the philological

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sciences were the ancillaries of the religious sciences. Such a reading of this principle of order is not completely false; but it is certainly one-sided. The very presence of the mathematical, philosophical, medical, and “occult” sciences in this kind of literature expressed their acceptance as members of the system of knowledge, their legitimacy and usefulness. This perspective is confirmed by the successful integration of these disciplines into the scholarly world of the madrasa teachers and their students, and their continued presence at many courts, dynastic and otherwise, until the later nineteenth century. A good number of modern historians went beyond a hierarchical reading of such structures and interpreted the ranking of the first and the third group as an expression of a continued fight between religious scholars and philosophers over the preeminence of their beliefs and knowledge. This perspective continues to shape Endress’s view of encyclopaedias and classification treatises. He believes that “the development of classification and systematization mirrors the subsequent stages of conflict and integration between religious and rational studies” (Endress 2006a, 111). 7.1. Philosophical Perspectives and Works Classifications of the sciences by philosophers of the pre-madrasa period have drawn the attention of historians, philologists, Arabists, and historians of science since the eighteenth century at the latest, even when representatives of these fields entered their study at different moments. Hence, there is a substantive body of literature to be found for learning about views of the leading philosophers like al-Kindi, al-Farabi, or Ibn Sina on the system of knowledge. In addition to these luminaries, numerous other philosophers or philosophically interested authors, among them even an entire group of men – the so-called Brethren of Purity, struggled with the challenging task of formulating their views on what should be considered a systematically organized body of knowledge and how its elements should be ranked and related to each other. Some of these books indicate explicitly that such efforts were not merely exercises in philosophical reassurance, epistemological grounding, and methodical standing, but had religious and political goals. Four of the many works of Abu Yusuf Yaʿqub b. Ishaq al-Kindi touch upon matters related to the classification of the sciences. Two of them are

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specifically dedicated to them, namely The Book on the Quiddity of Science and Its Parts and The Book on the Parts of Human Science. A quote from the first work has been discovered in an eleventh-century text. It provides an idea of the principle of organization of the sciences as beginning from physics and ascending via mathematics to metaphysics (ibid., 110). The second work and a third, called Epistle on the Fact that One Only Comes to Philosophy through Mathematics, are lost. Our knowledge of alKindi’s thoughts derives thus mostly from The Epistle on the Number of Books by Aristotle and on What is Required to Study Philosophy ( Jolivet 1996, 1009). Al-Kindi was a Muslim philosopher interested in religious as well as philosophical questions and used methods from philosophy to work them out. This shows in his reflections on the system of knowledge. He clearly separates divine and human knowledge. Divine science, also called prophetic knowledge, derives directly from The One through revelation. Human science, also called the science of the philosophers, needs to be learned and worked for (ibid., 1010). As the third title mentioned above and briefly touched upon in Chapter Two indicates, al-Kindi shared Galen’s view according to which the student of philosophy should first take classes or read books on the mathematical sciences. Al-Kindi repeats this view in his text on the order or number of Aristotle’s books, where he shows his relative unconcern for a strict order. First he accepts the Neoplatonic order of the quadrivial sciences: number theory, geometry, astronomy, and composition. A paragraph later he sorts them as number theory, the science of composition, geometry, and the science of the stars, identifying the last with the science of the configuration of the universe (al-Kindi 1950, vol. 2, 369–70). The knowledge to be acquired first by a student of philosophy is what al-Kindi calls “the science of the substance and the attributes of the substance” (ibid., 370). He divides the attributes of the substance into simple and compound. The simple attributes are quantity and quality. The first answers the question whether substances are equal or not, while the second answers whether they are similar or not (ibid.). The compound attributes are an existing (thing) without matter (tin = clay) and one with matter (ibid., 370–71). This entails further classifying divisions, which are interesting in themselves but not for the theme of this chapter. After discussing the science of the substance, al-Kindi now sorts the mathematical sciences under the categories quantity and quality. Number

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theory, which he identifies in this round as the fundamental arithmetical operations of addition, substraction, multiplication, and division, and the science of composition, which deals with ratios between numbers (= positive integers > 1), fall under the category of quantity, while the science of surveying, which al-Kindi now identifies with handasa, that is geometry, and the science of the configuration of the universe fall under the category quality. The subject of geometry is the fixed quality and the subject of astronomy is the quality in movement (ibid., 377). Following these subdivisions, al-Kindi returns to the question of the order of the mathematical sciences. He now argues for the standard Neoplatonic sequence, claiming that without these four sciences the other kinds of knowledge, that is knowledge of quantity, quality, and substance, and hence philosophy, would not exist (ibid., 377–78). Finally, he recommends reading books on logic, followed by those on natural philosophy, then books on metaphysics, ethics, politics, and what remains, whether discussed in his epistle or not (ibid., 378). In this epistle, the recipient is anonymously addressed. But Jolivet interprets the philosopher’s interest in the classification of the sciences and comments on his scheme as specifically directed toward an educational purpose. In his view, al-Kindi is directing a student how to proceed by reflecting on his own experiences as a beginner ( Jolivet 1996, vol. 3, 1010–1011). Endress has a different take on al-Kindi’s classifications and the encyclopaedic nature of his various teaching texts, discussed in Chapter Two, together with those that represent al-Kindi’s own learning efforts. In particular, he reads the text on the number of Aristotle’s books as taking up Neoplatonic propaedeutic explanations of a course of philosophy and the ancient obligation to reflect on the sequence, content, function, meaning, and author of the course’s individual books (Endress 2006a, 110–11). Al-Kindi, Endress argues, chose this approach as one component in his effort to present “a specific legitimization of philosophy with regard to the revealed law and the Muslim teaching of religious and legal hermeneutic: notwithstanding the universal and absolute validity of rational knowledge, revelation is necessary for imparting this knowledge to all mankind” (ibid., 111). Qusta b. Luqa wrote a very brief treatise without title, which takes a different approach to the classification of knowledge than that appearing in al-Kindi’s extant writings. Nonetheless, the conceptual, terminological, and phraseological relationship between Qusta’s and al-Kindi’s texts as

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well as to several works translated for him is evident (Daiber 1990, 100). Qusta’s approach comes – like that of al-Kindi – from Neoplatonic philosophical literature. Daiber believes that Qusta was familiar with the commentaries of Ammonius, an important teacher in Alexandria, either in their Greek original or in Syriac adaptations (ibid., 101). Qusta is unique in starting his description of the disciplinary subdivisions of philosophy not with the sciences directly, but with knowledge or cognition, which he divides into what cannot be expanded and what can be widened. The first category belongs to the realm of the plants or the animals; the second is human knowledge, which grows through the application of logic. Human knowledge is then classified as embracing four arts or techniques. First comes the art of language with four subdivisions (argumentation, rhetoric, poetry, grammar). The second is the art of doing things manually with tools such as carpentry, building, or goldwork. The third consists of the practical art conducted without tools except hands and bodies, such as wrestling, dancing, or singing (ibid., 102–05). The difference between the two practical arts rests in the work’s continued existence or its disappearance when its cause is removed. The work of a carpenter, for instance, remains after he has finished his work. The dance stops when the dancer rests. The fourth art shares the properties of all three preceding it. Examples are the physician, the scribe, the surveyor, and the calculator. They all acquire their knowledge through speaking, observing, and working with instruments and/or their hands (ibid., 104–05). Philosophy is separate from these four arts, because it unites knowledge and action. It strives to know the truth of all things and acts to improve and purify the soul. Its goal is to make man similar to God (ibid., 106–07). After this classification of knowledge and its disciplines leading to philosophy as its highest and most complete representation, Qusta b. Luqa offers the reader a sequence of definitions of this highest form of knowledge and an explanation of the meaning of the Greek word philosophia (ibid., 106–09). Qusta’s approach was not very successful among his contemporaries and successors, although certain of its elements resurfaced in modified form with other authors. An example is Qusta’s emphasis on action, be it with the hands and the body or with the hands and instruments. Al-Farabi shares this respect for the material, the instrumental, and the artisanal with Qusta b. Luqa without picking these preferences up from Qusta’s work ( Jolivet 1996, 1012–1013).

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Compared to Qusta’s approach, al-Farabi’s treatise on the Enumeration of the Sciences is more conventional. This text is the first that we know of by a Muslim philosopher that offers an integration of religious, philological, and philosophical disciplines (Akasoy-Fidora 2016, 107). In the treatise’s introduction, al-Farabi mentions only five principal sciences, namely the science of language, logic, the mathematical sciences, natural philosophy, and political science. In the text itself, however, he intercalated between natural philosophy and political science a sixth science – metaphysics. Here he introduces kalam as secondary to a universal demonstrative science, namely metaphysics, and the religious discipline of law on a similar footing to ethics. The philological sciences are paired with logic (Endress 2006a, 117). One central component of al-Farabi’s educational program is his emphasis on demonstrations. In his chapter on logic, he insists on the demonstrative skills, because they provide “the rules to examine demonstrative statements, the rules of things with which philosophy is concerned and everything that leads its operations to perfect accomplishment” ( Jolivet 1996, 1012). In the order of instruction, it ranks fourth, since three kinds of reasonings and expressions need to be known in preparation for it. It is followed by four other skills of speech, which all depend on the complete mastership of demonstrative skills (ibid.). Another element of training made explicit by al-Farabi concerns the knowledge needed by craftsmen. It is the last element of the last mathematical discipline in his scheme. Al-Farabi calls this discipline hiyal (tricks), which the English translator of Jolivet’s French paper renders ingeniously as industrious techniques (ibid., 1013). These techniques contain arithmetical procedures, including algebra, and three sets of procedures called handasiyya (geometrical): the art of making constructions, the processes for measuring the different sorts of bodies, to fabricate astronomical and musical instruments, arcs, arms; to fabricate optical instruments, mirrors and to use these for different purposes (such as construction of “burning mirrors”); to fabricate “marvellous vessels” (hydraulic mechanisms), and instruments of various techniques (ibid.).

These techniques and the knowledge that they embody are “the sciences (that) furnish the principles which are appplied in the skilled craft trades

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(construction, carpentry,  etc.)” (ibid.). The similarities to Qusta’s little treatise are undeniable, as is the survival of these and other ideas of alFarabi in later encyclopaedias and classifications. Some of the examples below certainly offer similar views, although we do not know their intellectual genealogies with precision. Ibn Sina was an intellectual child of al-Farabi and managed to outshine him, although al-Farabi was admired as the second teacher (after Aristotle) among many Muslim, Christian, and Jewish scholars. One of the treatises in which Ibn Sina discusses his ideas about the classification of the sciences is titled Epistle on the Parts of the Rational (or: Intellectual) Sciences. It is undated, but historians assume that it was one of his early writings (Lizzini 2007, 236). The great attention that this short text attracted among modern researchers is the result of their focus on diachronic studies which link the activities of scholars in Islamicate societies directly with those of Late Antiquity and their belief that such texts reflect some kind of curriculum (ibid., 236–37). According to this historiographical program, the study of classificatory treatises allows us to uncover the continued impact of ancient Greek knowledge on the intellectual history of Islamicate societies and the trajectory of the changes which this ancient knowledge underwent or, in the eyes of some modern researchers, even suffered (ibid., 237). As the few examples indicate which I selected for this chapter, it is much more important to study such treatises for their embeddedness in the debates among scholars in Islamicate societies than for their undeniable link with Aristotelian and Neoplatonic classifications. The former opens one of the many available avenues to grasp the world in which such scholars lived, their engagement with knowledge and its challenges, and their conflicts with their colleagues and compatriots among the elites and the population at large. The latter constrains the study of the intellectual history of Islamicate societies not only to a history of ideas, but does so in a very selective manner. The damages that such a reductionist approach to Islamicate intellectual history has caused during the last two centuries have been indicated at various places in this book and cannot be lamented enough. The examples briefly discussed in this chapter confirm that there was no such thing as a curriculum of study in the sense this word is understood in the context of medieval European universities, whether in the

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pre-madrasa period or in the madrasa period up to 1700. Scholars clearly agreed on a number of texts to be taught and methods used in teaching or studying. But this did not lead to any kind of formalized plan of study containing subject matters, books, the year of study. Endowers of madrasas did not prescribe the teachers they hired specific subject matters, books, in which year of study to teach a specific text, or the time when classes in a particular discipline should be held. Classification texts reflect the approaches and perspectives of their authors and the choices they made with regard to earlier such texts and the views of their authors. But there is no study so far that proves a direct link between any of those treatises and a concrete educational path of either a single teacher or a single student, let alone a more regular educational pattern in one city and in a specific period. Neither is there a convincing methodological reflection on what and how to generalize such individual positions in a meaningful manner that includes the specificities of the contexts of each individual case on a middle level of abstraction, instead of jumping directly to the macro-level of Islam, Arabic or Persian sciences, and similar such terms. These are the main reasons that I abstain in this chapter from trying to write a survey of encyclopaedic and classificatory literature in Islamicate societies, but prefer to present the roles of such texts in teaching and learning through a few specific examples for three groups of authors. Ibn Sina’s Epistle on the Parts of the Rational (or: Intellectual) Sciences focuses on philosophy and presents it in its Aristotelian scheme. Theoretical philosophy is introduced with its lowest part – natural philosophy, followed by the mathematical sciences as the intermediary discipline, and crowned by metaphysics or divine science. Practical philosophy serves to achieve the Good and consists of ethics, economics, and politics ( Jolivet 1996, 1019). The specific feature of Ibn Sina’s classification is the adoption of a bipartite system of fundamental and branch disciplines. Natural philosophy thus embraces seven branches: medicine, astrology, physiognomy, oneiromancy, the science of talismans, theurgy, and alchemy. This division with its elements reappears in encyclopaedias and classification treatises by later authors, whether administrators or madrasa teachers, as some of the examples below will show. The branch disciplines of the mathematical sciences are Indian arithmetic, i.e. the decimal positional systems and its rules of the four basic

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operations together with the extraction of square and cubic roots, algebra, the arts of surveying, industrious techniques, the moving of heavy loads, heavy bodies and balances, the five classical “machines’, optics and mirrors, hydraulics, astronomical tables and calendars, and strange musical instruments like the organ (ibid., 1020, with some modifications). Endress suggests that the young Ibn Sina appropriated this scheme and its elements from his teacher Abu Sahl ʿIsa b. Yahya al-Masihi, whom we met in Chapter Two as one of al-Biruni’s collaborators (Endress 2006a, 119). He sees the philosopher’s oeuvre, however, as containing two far-reaching revisions of this model. The first stage of revision is inscribed in Ibn Sina’s philosophical summa, The Book of Healing, which was written approximately between 1020 and 1024. The second stage is found in a today hotly debated text written about ten years before Ibn Sina’s death – The Philosophy of the Easterners (ibid., 119–20). The Book of Healing by and large follows the Aristotelian division of philosophy including the Neoplatonic division of the mathematical sciences. It begins with logic, followed by natural philosophy, and metaphysics in two parts – the first part on the universals and the principles of the sciences and the second part on divine science dealing with the essence, emanation, and activitiy of the First Cause, followed by the discussion of revelation and the return of the soul to its origin (ibid., 119). The books that The Book of Healing mostly emulates are the classics of ancient scientific literature. In this sense it is less complete than the little treatise on the parts of the sciences, since many of the branch sciences did not make it into The Book of Healing. But Ibn Sina wrote other works on some of the branch sciences, including his medical encyclopaedia, the Canon of Medicine. It is not so much the plan of organizing knowledge that is new in The Book of Healing as major parts of its doctrinal content, which is beyond the scope of this book. A new element in his approach to classification compared with his predecessors is his use of metaphysical criteria for the division of the philosophical disciplines. The theoretical ones are those that deal with things “whose existence is not by our choice and action,” which is the case for the practical disciplines (Akasoy-Fidora 2016, 108). One of the discussions in The Book of Healing, which contributes a new reflection on themes related to the organization of knowledge and its disciplines, is found in the part dealing with epistemology. Rizvi

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c­onsiders this theory of knowledge the philosopher’s “second most influential idea” (http://www.iep.utm.edu/avicenna/#H6). He summarized its subject as follows: The human intellect at birth is rather like a tabula rasa, a pure potentiality that is actualized through education and comes to know. Knowledge is attained through empirical familiarity with objects in this world from which one abstracts universal concepts. It is developed through a syllogistic method of reasoning; observations lead to prepositional statements, which when compounded lead to further abstract concepts. The intellect itself possesses levels of development from the material intellect (al-ʿaql al-hayulani), that potentiality that can acquire knowledge, to the active intellect (al-ʿaql al-faʿil), the state of the human intellect at conjunction with the perfect source of knowledge (http://www. iep.utm.edu/avicenna/#H6).

The question of the truth-value of propositions or experiences is situated within a debate about the tools of formal inferences and the role of the active intellect. The tools of formal inferences guarantee that a statement is logically correct. The active intellect allows access to the true knowledge of things, since it is transcendent and the place of residence of all the essences of things and all knowledge. It illuminates the human intellect through conjuction, if this particular intellect is actualized, i.e., properly educated (Rizvi http://www.iep.utm.edu/avicenna/#H6; see also Lizzini 2016). A part of this discussion is Ibn Sina’s exposition of the theory of demonstration. He discusses issues related to the classification of the sciences for instance in Section 7 of Chapter 2. In this chapter, he elucidates the differences and commonalities between the sciences through a discourse of separation (Ibn Sina 1375/1956, d). It is written in a systematic, well-formalized style proceeding from a general single category to a division and from each division down to the next level of partition. Ibn Sina explains that sciences can differ due to their different subject matters, but also when dealing with the same subject matter. These two groups are further divided in several sublevels with two or more subgroups. These further subdivisions explain, for instance, that number theory and geometry differ completely with regard to their subject matter and that medicine and morals have something in common (the study of the powers of the human soul), while studying different

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subject matters (the human body; the rational soul and its practical powers). Sciences can be similar in respect to principles, subjects, and problems ( Jolivet 1996, 1017–18). Although number theory and geometry pursue fully different subject matters they share some principles, for instance the Euclidean axioms of Book I. Another subclass of sharing is that of natural philosophy and medicine with regard to problems, because the two share the study of bodies, but natural philosophy does that in a more general manner than medicine (ibid., 1018). Ibn Sina develops both themes – the differences and the commonalities – in greater depth in further subdivisions of relationships (ibid., 1017–18). His reflections had little to no impact on the groupings traced here in the chosen examples, except perhaps that of al-Jurjani. But the scheme developed by Ibn Sina in The Book of Demonstrations invites us to investigate the sense in which this approach to the classification of the sciences motivated other authors to take up some of his ideas. Other parts of The Book of Demonstration discuss other aspects of relevance to the classification of the sciences and their foundations following Aristotle’s Posterior Analytics, but also going beyond it in innovative ways (Akasoy-Fidora 2016, 109–10). In addition to and derived from The Book of Healing, Ibn Sina wrote two shorter encyclopaedic texts on philosophy – one in Arabic (The Book of Salvation), the other in Persian (The Epistle of Knowledge). The Persian version was written at the behest of the Kakuyid ruler ʿAla’ al-Dawla Muhammad (ruled 1008–1044), whom Ibn Sina served as a vizier. Van Ess considers this work as the only philosophical collection coming close to the modern concept of an encyclopaedia, since it alone was written for a lay person and presented all the important doctrines of the philosophical disciplines in short form (van Ess 2006, 9). Many manuscripts of both works only contain the chapters on logic, natural philosophy, and metaphysics. The mathematical sciences are often absent. This is partially the result of Ibn Sina’s outsourcing of this chapter to his student and later secretary Abu ʿUbayd al-Juzjani (died after 1037). But it may also reflect the process of separation between the mathematical sciences and the other theoretical sciences of philosophy, which in a certain sense is a kind of Neoplatonic feature and comes to the fore in the apparently dominant view among madrasa scholars that considers the mathematical sciences as a third group of sciences independent of the rational ones.

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Ibn Sina continued to tackle the issues of knowledge, certainty, and systematicity until late in his life, as The Philosophy of the Easterners, written in the years 1027–1029, shows. In the introduction to this work, he grouped universals and “divine science” as different parts of theoretical science. This constituted a fourfold instead of the Aristotelian threefold division of theoretical philosophy: natural philosophy, the mathematical sciences, “divine science”, and the science of the universals. Endress argues that this scheme “became the general framework for the integration of Islamic theology into the system of the theoretical sciences” (Endress 2006a, 119–20). Griffel’s view of Fakhr al-Din Razi’s contributions to the classification of the sciences (presented below in the section on the madrasa teachers) contradicts this evaluation to some degree, because he argues that Ibn Sina did not complete this process of dividing metaphysics into two different domains of knowledge (Griffel 2011). 7.2. Administrators and Their Encyclopaedias and Knowledge ­Systems Among administrators as authors of encyclopaedias we encounter one of Abu Zayd al-Balkhi’s students and thus an educational “grandson” of al-Kindi. His appellation is not precisely known, since its written form is ambiguous. His father may have been called Farighun or Fariʿun or Furaiʿun. As his son, the author of The Summaries of the Sciences is called Ibn Farighun (or one of the two other forms of spelling). He was born in the early tenth century and died after 955, the year when he dedicated his work to a local ruler in a town north of the Amudarya. It is possible that he himself was a member of another small local dynasty who paid tribute to the Samanids ruling from Bukhara. We may thus read his classification of the sciences as a mixture between the philosophical teachings of al-Kindi and his successors and the views of the local gentry who held important positions in the administration of northeastern Iran. Endress, however, thinks that “the secretaries of the caliphal vizierate and the provincial administration of the Iranian East” followed wholesale “the school of al-Kindī, a school uniting encyclopaedic scope and professional scientific competence with the Platonic ethics of knowledge” (ibid., 111). Endress’s inclination to perceive the mathematical sciences as “applied sciences” representing “professional scientific competence” is

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too modern to fit the conditions of the Abbasid caliphate and its many different regions. It remains unclear in what sense al-Kindi’s or al-Balkhi’s knowledge of the mathematical sciences was professional, as opposed to their knowledge of natural philosophy, metaphysics, the “occult” disciplines, or the rules of educated comportment. The two philosophical disciplines open the way to thinking and a happy life. The last discipline permitted what in British parlance would be called gentlemanly conduct, and was a preferred intellectual occupation of Abu Zayd al-Balkhi. The “occult” disciplines are not discussed by Endress, but belong in al-Kindi’s writings either to theoretical philosophy or to the practical arts. The mathematical disciplines pursued by al-Kindi are based on the standard teaching texts of Late Antiquity (Mansfeld 1996, 1998). The few texts that do not fall under this category deal with what is called recreational mathematics. Recreational mathematics offers problems, methods, and techniques with the goal to surprise, to entertain, and to sharpen the memory. One of the particular characteristics of Ibn Farighun’s work is his use of a tree structure for visualizing the organization of his categories and the structure of the sciences. This pictorial approach is placed between two longer explanations of two separate fields of knowledge – Arabic grammar at the beginning and the “occult” sciences at the end. Biesterfeldt understands Ibn Farighun’s placement of language at the beginning of his classification as a declaration that without language no knowledge and no education is possible (Biesterfeldt 2012, 168). In contrast, the appearance of the “occult” sciences at the end of the work is explicitly legitimized by the medieval administrator. He doubted that they were indeed worthy of the appelation “science” and emphasized that many people considered them fraudulent, deceitful, and money-grabbing (ibid.). The integration of the other fields of knowledge between these two parts of beginning and end clearly reflects the secretarial interests of the author and perhaps also of his princely patron. The first array covers fields of knowledge needed by the administrator, for example tax collection, administrative services in the military, postal secret services, legal obligations, diplomatic letter writing, calligraphy, and accounting, followed by historical knowledge and ethical behavior with regard to superiors and inferiors. Then philosophical and religious types of knowledge are described, but again in forms adapted to the profession of the administrator and his courtly context.

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These are presented in four separate arrays, beginning with ethics and princely virtues, followed by policy and the art of war, then kalam and religious deontology, and finally sources of knowledge together with forms and methods of transmitting knowledge and philosophy (ibid.). The explanatory details found for each single discipline within these five arrays are closely related to ideas taught by al-Kindi, for instance in his possible teaching synopsis Epistle on the Number of Aristotle’s Books, as well as to the specific interest in belles-lettres of Ibn Farighun’s teacher Abu Zayd al-Balkhi. This anchoring of Ibn Farighun in the philosophical and some of the religious debates of the ninth and tenth centuries is highlighted, among other passages, by his identification of functions, subject matters, methods, or goals of philosophical and religious fields of knowledge. Metaphysics is not merely the highest of all sciences that studies in this position the causes of all things and the power of the Creator respectively, but is a kind of mirror image of kalam in its methods and themes (ibid., 169). This issue of the relationship between the philosophical and some or all of the religious sciences, vigorously debated during Ibn Farighun’s lifetime, remained an intellectual challenge for some of the best scholars in Islamicate societies throughout the centuries. As we know today – contrary to earlier claims and beliefs – the answers given differ profoundly. If the application of the adjective Islamic to any of the ­non-religious disciplines makes sense, it is to philosophy as it emerges from these debates. Hence, what we can observe over time in some regions of the Islamicate world is not only the emergence of the new scholarly persona, which can be called somewhat simplifying the jurist-physician as discussed in Chapter Five, but also that of the mutakallim-philosopher, a religious scholar who specializes in kalam with philosophically grounded and informed questions, methods, arguments, and systematic procedures. In addition to this “theologian-philosopher”, Endress sees the formation of a further scholarly persona among the madrasa teachers and researchers of philosophy: the jurist-philosopher (Endress 2006a, 127–28). Abu ʿAbdallah al-Khwarazmi lived for some time in Nishapur in northeastern Iran, but also served as a secretary at the Samanid court in Bukhara. His work of interest here, for which he is well known, is called The Keys to the Sciences. These keys are primarily technical terms, but also structures and definitions. The work has, like the one by Ibn Farighun, a courtly recipient. In this case, it was a Samanid vizier, the head of the

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Samanid administration. Al-Khwarazmi explicitly addresses his colleagues as the audience for whom he outlines the knowledge system of his time and summarizes administrative practices and their procedures. As a prose text more elaborate than Ibn Farighun’s tree-like schemes, al-Khwarazmi combines the genre of classifying the sciences with the description of their content in a summary fashion as found in encyclopaedias. Al-Khwarazmi’s approach is to take a middle ground between two extremes: things that are well known to the average educated person and things that are obscure. This middle ground he explicitly divides into two major classes: the religious sciences of Islam with their philological ancillary of Arabic and the sciences of all foreigners, Greeks and other nations (Rosenthal 1994, 54). The first class contains six disciplines: law, kalam, grammar, the secretarial arts, poetry and prosody, and history. The second class includes a broad range of philosophical disciplines. Both classes receive a fairly balanced number of pages and are thus, when we subtract the introduction, put on an equal footing. Al-Khwarazmi justifies his approach by criticizing textbooks for their lack of clarity concerning the technical terminology used in the sciences. Focusing on textbooks of grammar and language, he admonishes their authors for all too often forgetting to talk about this kind of terms (Bosworth 1963, 100). In his view, secretaries apparently know enough about Qur’an exegesis and hadith, since he does not include these two religious sciences in his first class, one of the major differences between his depiction of the universe of knowledge and those of later madrasa teachers. His second class can be seen as the truly interesting part of his encyclopaedia, since if taken at face value it encouraged the Samanid vizier and his administrators to acquire basic knowledge of a broad range of scientific disciplines. Although mainly following the Aristotelian division into theoretical and practical philosophical sciences, al-Khwarazmi enumerates first the discipline, which investigates things with form and matter, calling it the knowledge of nature or natural (things). Then he turns to the highest theoretical science, which deals with things beyond those with form and matter, calling it divine science and explaining that in Greek it is called theology. This is a reference to the Neoplatonic treatise Theology ascribed in Arabic sources to Aristotle. The third theoretical discipline deals with things, which exist in matter: quantities, configurations, movements, and the like. Al-Khwarazmi calls its content the doctrinal

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sciences or the sciences that are taught, which is a literal translation of the Greek term mathematical sciences. He also informs his readers that there was a different name for this discipline, namely the sciences that were or had to be exercised, another Arabic translation of the same Greek term. Although he does not comment on these terms, they highlight one of the problems that a beginning student of philosophy had to overcome: the multiplicity of a terminology that came from a different language and had been translated to the best ability of the translators of the eighth and ninth centuries, but often in a rather literal sense which was alien to the Arabic or Persian speaker. The practical sciences are ethics, economics, and politics. However, al-Khwarazmi refuses to discuss them further, since he claims that these three disciplines are well known, not merely among the elites, but also among the ordinary people (al-Khwarazmi n.d., 58). The theoretical sciences allegedly are less familiar to the people in Yazd and hence al-Khwarazmi continues to classify them and then to elucidate their disciplinary content. Like other writers of this period, al-Khwarazmi teaches his readers a mixture of Neoplatonic and Aristotelian arrangements, terms, and definitions and informs them about the correspondences between transliterated Greek names and Persian or Arabic terms. The latter resembles the approach of the Brethren of Purity who also explain that arithmatiqi is number theory, jumatriya the science of handasa, or astrunumiya knowledge about the stars. The knowledge of nature embraces many more disciplines than the mathematical sciences. Al-Khwarazmi places under this rubric medicine, meteorology, the knowledge of minerals, plants, and animals, and the knowledge of all things of the sublunar world to which alchemy belongs, because it investigates minerals (ibid.). The remainder of al-Khwarazmi’s second class, comprising in one of its printed versions 51 pages, teaches fundamental concepts, their meaning, and some of their applications. A few examples have to suffice here. The first philosophical term is matter, here called hayula according to the Arabic transliteration of the Syriac rendering of the Greek hyle. It is explained that each body is the carrier of its form. As an example, wood is presented as the matter for a bed and a door, silver for a seal and an anklet, and gold for a dinar and a bangle. Other terms for matter are madda, ʿunsur (more often meaning element), and tin (clay) (ibid., 59). Among the numerous other philosophical terms that follow, khalaʿ (vacuum) is

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perhaps one of the most interesting, since al-Khwarazmi informs his readers that most of the philosophers deny its existence in the universe and beyond, allowing thus for some who acknowledge it (ibid.). Logic, which follows the discussion of philosophical terms, is explained on the basis of Porphyry’s Isagoge and the Aristotelian Organon (ibid., 61–66). Medicine provides in eight sections a short course on anatomy, diseases and their remedies, foodstuffs, simple and compound remedies, remedies with similar names, weights used by physicians, and theoretical elements of humoral pathology (ibid., 66–80). In the parts dealing with the four fundamental mathematical sciences, al-Khwarazmi teaches through the explanation of the terms the basics of these four disciplines. Number theory follows the work of Nicomachus of Gerasa. Proportions are dealt with in a mixture of Euclidean and Nicomachean definitions. Arithmetical systems combine rules taught for the Indian decimal positional system as well as oral methods of calculation and the sexagesimal system used in astronomy and astrology. Incommensurable and inexpressable magnitudes are concepts taken from Book X of Euclid’s Elements. The principles of axiomatic-deductive geometry and the figures of plane and solid geometry come from Books I–IV and XI–XIII of the same book. Trigonometrical terms, the structure of the universe including constellations, the additional planets of the head and the tail of the eclipse dragon, and astrological rules are partly of ancient Greek and partly of a mixed origin that includes Indian beliefs in the special planet Rahu responsible for eclipses and Rahu’s transformation into a dragon, possibly undertaken by Zoroastrians in Iran or maybe by Manichaeans. Scientific and musical instruments, musical scales, and rhythms combine ancient Greek with medieval Arabic and Persian material (ibid., 80–103). Afterwards, al-Khwarazmi surveys one branch science which he calls tricks. There, he talks about instruments to move big loads easily, war machines, hydraulics, mechanical tricks, and the instruments of surveyors and other practitioners (ibid., 104–06). The final chapter on alchemy also begins with surveying instruments. Then ­al-Khwarazmi turns to the names of gemstones, metals, and minerals. The last section presents names of alchemical procedures (ibid., 107–10). This tour de force enables the work’s reader to understand conversations between different kinds of experts, whether at a court, in a classroom, or in a shop. It situates this broad range of basic knowledge in an epistemologically grounded sphere of educated entertainment,

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administrative practice, and skilled business. The terminological and textual details show that al-Khwarazmi had read broadly when preparing his book. The only scholar whom he quotes explicitly is the Arabic grammarian and compiler of the first known Arabic dictionary al-Khalil al-Farahidi (died in c. 786). But there is no doubt that he read Euclid’s Elements, Nicomachus’ Introduction to Number Theory, some text about Heron’s Mechanics, al-Farabi’s Enumeration of the Sciences, something of Ibn Sina’s philosophical writings, most likely some parts of the Epistles of the Brethren of Purity, probably texts from the so-called Jabir b. Hayyan corpus, and also a good number of other books or treatises. Both features, the broad preparation of the author and the substantive offer to the reader to learn, make al-Khwarazmi’s Keys to the Sciences an outstanding teaching manual for the non-scholarly student. Between 1113 and 1120, Shahmardan b. Abi l-Khayr wrote his encyclopaedia The Book of Entertainment for ʿAla’ (al-Din). As secretary of finances, he too worked at a court in Yazd. His encyclopaedia’s recipient was another member of the Kakuyid dynasty mentioned above. It deals with knowledge and sayings about nature and its parts. Shahmardan presents it as a translation of an earlier version written in Arabic, which is, however, lost. Written a century after Ibn Sina’s Persian encylopaedia, Shahmardan wrote in a much simpler Persian language, criticizing Ibn Sina’s style as too complicated for the student interested in nature and its wonders. Shahmardan had a well-known scholar of the mathematical sciences as his teacher (Vesel 1986, 27). Hence, that he wrote a specialized encyclopaedia on astronomy and astrology The Garden of the Astrologers does not come as a surprise. Vesel believes that Shahmardan copied parts from his Garden of the Astrologers into his Book of Entertainment (ibid., 28). Shahmardan’s Book of Entertainment consists of two parts. The first part describes the characteristics and properties of men, animals, plants, and minerals. The second part treats the usefulness of methods of calculation, the universe, and a number of individual topics (recipes, manual crafts, procedures of production). Theoretical themes from natural philosophy and the mathematical sciences can be found in both parts, but they appear in the first sections of the second part in concentrated manner (ibid., 28–29). The structure and content of his encyclopaedia defines Shahmardan as a popularizer of scientific and philosophical knowledge, who – like al-Khwarazmi – considered alchemy as a form of knowledge useful in the practical arts.

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Two other Persian encyclopaedias were written in dialogue with this work – one about sixty-five years (1185) after the Book of Entertainment, the other a further eighty-five years later (1270). Both were meant to educate and edify as Shahmardan intended to do with his own book. The attention to practical matters and daily life visible in Shahmardan’s text becomes ever more pronounced in these two followers. The first three chapters of the second successor, for instance, retain the theoretical philosophical sciences, including astrology, but the following eight chapters are dedicated to issues of health, poisons and antidotes, sexual relationships, gemstones and their properties, physiognomy, wonders of nature, men and the three kingdoms of nature, agriculture, miracles of prophets and saints, talismans, and the virtues of reading the Qur’an (ibid., 31–32). The author, Shams al-Din Dunaysiri (thirteenth century), did not add a new level in teaching the theoretical sciences to a broader population, but taught how to deal with the standard problems of daily life, adding at the end of his work some instructions for living properly as a Muslim. 7.3. Madrasa Teachers as Writers of Summas and Divisions Religious scholars had started early on to formulate their own views about what knowledge should be taught and learned. The many processes of dispersing and interrelating the disciplines they cherished with those of the philosophers, while not free of tensions and resistance, led to integrated systems where both sides acknowledged parts of the others’ preferences as respectable, necessary, and useful. Since the nineteenth century, these processes have often been misunderstood, simplified, and overloaded with modern values by scholars, to a degree that many people in Islamicate countries during the modern period accepted these trivializations as an everlasting dichotomy, an enduring rejection of the philosophical sciences by the so-called religious orthodoxy, or even the complete death of philosophy after 1198. Although historians of philosophy in Islamicate societies before modernity have redrawn this black-and-white picture in more colours and nuances, there is still a long way to go before the public across the globe today understands the profound falsity of the older narrative. This book cannot deal in a substantive manner with these historiographical issues. But I wish to open this section on encyclopaedias and classifications of

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the sciences by madrasa teachers with an encyclopaedia by a top-rank religious scholar whose work represents a decisive phase in these processes of encounters, rejections, and amalgamation. His main places of activity were princely courts and private houses in Iran, Central Asia, and Afghanistan. But he also studied at one madrasa and taught at three others. The last of them was specifically built for him in Herat by a sultan of the Ghurid dynasty (ruled as a Muslim dynasty from 1011 to 1215). The scholar’s name – Fakhr al-Din al-Razi – has been mentioned repeatedly in previous chapters as someone who profoundly shaped the relationship between the religious and the philosophical sciences as well as the methods of discourse, writing, and teaching at madrasas. Fakhr al-Din, born in the middle of the twelfth century in Rayy, today a suburb of Tehran, began his education under the tutelage of his father. After his father’s death, he travelled to Khurasan where he studied with famous teachers in Nishapur. Nishapur had early on opened its arms to Ibn Sina’s philosophy. No wonder then, that Fakhr al-Din encountered several of his texts in this very city. They encouraged him to study philosophy seriously. Disagreeing with important aspects of Ibn Sina’s teachings, Fakhr al-Din wrote commentaries on three of Ibn Sina’s works. One, often mentioned in Chapters Four and Six, is Pointers and Reminders. The two others are The Philosophy of the Easterners and Sources of Philosophy (Friemuth 2008). Often very critical of Ibn Sina’s doctrines and methods, Fakhr al-Din appropriated many of them, as explained for the case of commentary writing and teaching methods in Chapter Six. One of the classificatory changes that Fakhr al-Din introduced in his specialized encyclopaedia on philosophy and logic concerned the threefold partition of theoretical philosophy. He deviates here clearly from the dominant Aristotelian scheme, which is found so often among other writers, independently of whether they were philosophers, administrators, or madrasa teachers. For Fakhr al-Din, the three parts of theoretical philosophy are (1) the study of the things that are common (to all beings); (2) the study of substances and accidents; and (3) “divine science” (or in modernized parlance: philosophical theology). Building on the ideas of Ibn Sina and the authorial practices of Bahmanyar b. Marzuban (introduced in Chapter Six) and al-Lawkari (died between 1109 and 1123), allegedly a student of Bahmanyar, Fakhr al-Din also divided metaphysics into two separate disciplines: (1) metaphysics proper as a discipline that

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studies “the existent insofar it is existent” and (2) the knowledge of the Creator and the First Cause, i.e. “divine science” (Griffel 2011, 343). Furthermore, Fakhr al-Din compiled two versions of a comprehensive encyclopaedia – one in Arabic, the other in Persian. Most known manuscripts contain a Persian version. Different recensions present forty, fifty, or sixty disciplines. Three titles are transmitted in the manuscripts – the Summa of the Sciences, The Book of the Sixty Sciences, and The Garden of Lights and the Truth of Secrets. According to the preface, Fakhr al-Din wrote the encyclopaedia in 1179 for the sultan of Khwarazm, ʿAla’ alDin Tekesh (ruled 1172–1200). Having difficulties with the local mutakallimun, Fakhr al-Din had decided to move on. But before leaving, he wished to write a comprehensive survey of all the disciplines he had studied and was familiar with. In the explanation of his goals, we find the classification of the two main sets of disciplines taught in his time at madrasas – the rational and the transmitted sciences: “(I wished to) compose a book which combines all the possible rational and traditional sciences considering them from the angle of their principles as well as their applications” (Vesel 1986, 35). Fakhr al-Din named scholars at Tekesh’s court as the intended beneficiaries of his efforts at gathering for them “all the sciences of his age in order to establish a repertoire” (van Ess 2006,  11). His encyclopaedia was thus as much a certificate of his own education and erudition as it was meant as a teaching compendium and reference book for people at court, who were obviously insufficiently educated in al-Razi’s eyes. Like other comprehensive encyclopaedias, Fakhr al-Din’s Summa of the Sciences follows a bi-partite plan. The first group encompasses the sciences of the Muslims, the second the philosophical sciences. The second class shows idiosyncracies, which cannot be found in other encyclopaedias of this type. It begins with logic, followed by natural philosophy, the mathematical sciences, and metaphysics. This order might represent Fakhr al-Din’s didactic concept that students should start with learning the tools of the philosophical sciences provided by logic and then climb up the ladder of the theoretical sciences from the lowest to the highest. After metaphysics, Fakhr al-Din does not proceed immediately to the practical philosophical disciplines, but inserts first a chapter on religious sects. The three practical philosophical disciplines are followed by non-philosophical kinds of knowledge, which should have

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been included among the religious disciplines (life after death; prayers) or history (comportment of kings). The final chapter treats chess (Vesel 1986, 36–37). The presence of various “occult” disciplines under the headers natural philosophy and mathematical sciences reflects Fakhr al-Din’s personal interests. Oneiromancy, physiognomy, alchemy, and talismans are presented as disciplines of natural philosophy. Astrology, sand divination, and even exorcism appear as mathematical sciences (ibid., 37). After having finished this work, Fakhr al-Din left for Herat, which then was in the possession of the Ghurid dynasty. Late in his life, he returned for some time to Khwarazm where he became the teacher of Tekesh’s son Muhammad. Many of Fakhr al-Din Razi’s works shaped intellectual debates among madrasa teachers in both the transmitted and the rational sciences. Several of his works, including his commentary on Ibn Sina’s Pointers and Reminders, became standard works of madrasa teaching at least in Iran, Central Asia, northern India, Iraq, Syria, Egypt, and Anatolia. Some 130 years after Fakhr al-Din had passed away, another madrasa teacher wrote a multi-volume Persian encyclopaedia in a courtly context. This teacher was Muhammad b. Mahmud Amuli. He taught at the third Mongol capital in Iran – Sultaniyya – during the reigns of the last two Ilkhanid rulers Öljaytu (ruled 1304–1316) and Abu Saʿid (ruled 1316– 1335). When Abu Saʿid died at the age of thirty, he had no offspring nor had he chosen a successor. The fight among the Mongol claimants to the throne was bloody, protracted, and led to the final destruction of Ilkhanid rule in Iran. Amuli fled from Sultaniyya to Shiraz, to the court of the Inju dynasty, a Shiʿi family of Mongol descent that had only established its suzerainty over Shiraz and Isfahan in 1335. Dedicating his work to the Injuid prince Shaykh Abu Ishaq (ruled c. from 1343–1357), Amuli too wished to offer his princely reader a ­sur­vey of the entire disciplinary knowledge of his time. Returning somehow to the more standard classification of the sciences in the two groups of the sciences of the moderns and the sciences of the ancients, his approach to sorting and presenting disciplinary knowledge also possesses a personal flair. He opens his treatment of the first class with a discussion of belles-lettres and the rules of comportment, turning only then to the religious sciences. Before he discusses history, he inserts a chapter on Sufi teachings. The philosophical sciences are divided between fundamental sciences and branches. Here, Amuli combines older traditions already found among ancient

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and pre-madrasa authors with developments in the religious sciences of Islamicate societies. Not only does he separate the four fundamental mathematical sciences from twelve branch sciences, he applies the same scheme to the theoretical disciplines of philosophy. This approach inspires him to begin the part on the philosophical sciences not with the theoretical disciplines of philosophy, but with the three practical disciplines. The theoretical disciplines follow under the header foundations of philosophy. There, Amuli placed logic, first philosophy, metaphysics, and natural philosophy. The four fundamental mathematical sciences are taken out and follow in a separate chapter. But here too, Amuli does not follow the standard Neoplatonic plan, but presents first geometry and astronomy, placing number theory directly before music, which deals with proportions. The disciplines, which Fakhr al-Din had placed under the heading of natural philosophy, appear in Amuli’s work with some alterations as the branch disciplines of natural philosophy. Amuli’s separation between natural philosophy proper and its branch disciplines seems to be inspired by Ibn Sina. Astrology and exorcism are now presented as branches of natural philosophy. The group of the mathematical branch disciplines shows other interesting aspects. Not only do optics, mechanics, instruments of war, the configuration of the stars, and sand divination appear there, but geography, the science of the configuration (of the universe) (that is, planetary theory), the Middle Books, the astrolabe, calendars, and magic squares are also all placed here (Vesel 1986, 39–40). Other mathematical disciplines like algebra, systems of calculation, or surveying appear there too. Amuli’s encyclopaedia became widespread in Iran. It shows that not all madrasa teachers agreed to follow Fakhr al-Din wholeheartedly. It reveals that Amuli and his followers prefered an extension of the traditional system by new additions to a complete overhaul of the system. The classification of the sciences of a third madrasa teacher, which I will survey now, was referred to repeatedly in Chapters Four and Five as an important source for information about teaching material and the content of madrasa teaching in the mathematical sciences, medicine, and natural philosophy. Its author is the Cairene herbalist, physician, and madrasa teacher Ibn al-Akfani. Ibn al-Akfani declares as his goal in composing the treatise to teach through the classification of the sciences and the explanation of their content and literature how to achieve the primary purpose of learning – the acquisition of true knowledge and its

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verification in order to firmly believe in The True (One), i.e., God, and to do good deeds (Ibn al-Akfani 1989, 452). In addition to this fundamental goal of learning and teaching through the listing of the types of the sciences and their differences, Ibn al-Akfani ­pursues seven subordinated purposes with his treatise. First, he wishes to arouse the desire of the pure soul for human perfection. Second, he hopes that the learner will profit from his encounters with knowledge. Third, the student should learn about each discipline on its own terms and its ranking in comparison to all the other sciences. This will also allow him to assess any scholar’s standing in the system of knowledge, as well as how the d­ iscipline will be useful to the student in the life to come and to his comportment. Fourth, Ibn al-Akfani wishes to teach his readers to make comparisons between the disciplines and enable them to recognize which ones are virtuous and noble, which ones are certain and reliable, and which ones are feeble and trivial. Fifth, students of his book will learn, Ibn al-Akfani claims, to discover – by knowing the subject matter of a discipline, its goals, problems, and rank – who is an impostor, but hides his pretension. Sixth, the reader who wants to become a polymath can learn by way of the common (things) the scope, which he intends (to acquire). Seventh, he hopes that such a person can achieve a rank and status c­ omparable to that of the scholars (ibid., 13). In accordance to these goals, Ibn al-Akfani introduces his discussions of the disciplines of knowledge with three sections on the dignity of knowledge and scholars, on teaching and learning and their conditions, and on what belongs to the sciences. In the third of these sections he states that the philosophical sciences are the first, but in the actual list he begins with belles-lettres and the rules of comportment (adab), which usually are treated as part of the philological sciences. Ibn al-Akfani’s approach shows several parallels to Amuli’s encyclopaedia, which he certainly did not know and would not have been able to read. He differentiates all disciplines according to their status as fundamental or branch sciences. Both are members in a relationship. The former he sees as universal and the latter as particular with regard to each other. Medicine, for instance, is a branch science and particular in relationship to natural philosophy, which is fundamental and universal. Medicine studies the human body, while natural philosophy studies the body as such. Ibn al-Akfani also agrees with Amuli in regrouping the

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mathematical sciences as geometry, the configuration (of the universe), number theory, and music. Ibn al-Akfani’s focus in classifying the disciplines is on the universal sciences since they are independent from the branch sciences and thus can be sorted according to their subject matter, principles, problems, and goals. The principles are conceptualizations and instances of assent. They constrain each kind of science in particular ways (ibid., 14–22). Conceptualization and assent are standard terms in philosophy and logic as taught in Islamicate societies. Different authors, however, define them differently as we will hear below from al-Sayyid al-Sharif al-Jurjani. For Ibn al-Akfani, conceptualizations are definitions, while the meaning of instances of assent differ between the disciplines. In some disciplines, they are understood as proofs and in others as axioms. The madrasa teacher and physician Ibn al-Akfani follows the philosophers, in particular Ibn Sina, in his approach as Amuli did too. His views offer another counterexample against the belief of modern historians that the philosophical sciences only flourished in the Persianate world and then in the Ottoman Empire, but not in Syria and Egypt under the Ayyubids and Mamluks. After these general reflections, Ibn al-Akfani presents a list of sixty disciplines. This list unites religious, philological, philosophical, and mathematical sciences without any further formal hierarchical organization and subordination (ibid., 22–67). Some depictions of the fundamental sciences also include sequences of branch disciplines. The books and authors named in this list indicate that the fourteenth-century madrasa teacher Ibn al-Akfani was very well read, if not in all sciences, then at least in texts about them. The summaries of the content of the individual disciplines presented by Ibn al-Akfani demonstrate that he did more than merely read treatises on sciences, authors, and books. He also read at the very least summaries of the disciplines’ subject matters. Among the philosophers we find not only Aristotle and Ibn Sina, but also Ibn Rushd and his epitomes of Aristotle’s books. Ibn al-Akfani describes them as useful. Among the scholars of the mathematical sciences and astrology, which Ibn al-Akfani classifies like Ibn Sina and Amuli as a branch discipline of natural philosophy, we find a good number of scholars of the pre-madrasa period, which may suggest a non-negligible presence of such works in Mamluk Cairo. Examples are Kushyar b.  Labban (tenth century), Ibn Hibinta (tenth century), Abu Maʿshar, al-Sijzi, and al-Biruni.

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The latter three we already met in Chapter Two. Other authors known to Ibn al-Akfani lived in the thirteenth century and worked either at the Ayyubid or the Ilkhanid courts (ibid., 49, 57–58). As in philosophy, Ibn al-Akfani also knows several scholars and their works from al-Andalus (ibid., 55,  57). This reflects the closer connections between Egypt, North Africa, and al-Andalus in general and the arrival of refugees from the Iberian Peninsula in Egypt beginning in the late twelfth century. A complete list of the authors mentioned by Ibn al-Akfani can be found in Witkam (ibid., 243–50). After this classification of the disciplines Ibn al-Akfani discusses philosophical terminology in a final chapter. Ibn al-Akfani’s text is not only rich with regard to the names of authors and books, but also with regard to branch disciplines. His work shares many of them with Amuli’s encyclopaedia, but contains also names not found there, for example burning mirrors and the science of timekeeping. Several later, in particular Ottoman, authors of encyclopaedias or treatises relied on Ibn al-Akfani’s work when classifying the sciences (ibid., 252–54). At least one student in the fifteenth century studied Ibn alAkfani’s text with a teacher. It is unknown, however, whether students of other disciplines, for example medicine, the science of timekeeping, the foundations of faith, or exegesis, used his book as a propaedeutic text and a recommendation of what to read. A fourth madrasa teacher who took a different approach to the issue of classification than the other authors discussed in this chapter is alSayyid al-Sharif al-Jurjani, whom we already met in Chapter Five, travelling from Iran via Anatolia and Syria to Cairo in search of excellent teachers. Instead of classifying individual disciplines, he wrote a critique of major approaches to the classification of knowledge. Thus, his text differs radically from those of Fakhr al-Din al-Razi and al-Amuli discussed above. As for the classification of the disciplines, it also differs from that by Ibn al-Akfani, as al-Jurjani does not classify the sciences. Al-Jurjani’s epistle shares nonetheless one element with all of them – it is inspired by concepts and doctrines of the philosophers, in particular Ibn Sina. Al-Jurjani chose two methodological concepts to provide order to the realm of knowledge, which we already encountered in Ibn al-Akfani’s booklet. Yet while the latter uses them as plural forms, conceptualizations (tasawwurat) and instances of assent (tasdiqat), al-Jurjani speaks of them in the singular as conceptualization and assent. The background to their

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emergence are debates about the content and function of logic and its relationship to linguistics on the one hand and logic’s relationship to epistemology on the other (Black 1998, 709). Conceptualization is the production of a mental notion. A  simple example is the notion of frog. Such a mental notion can include propositions, for instance the claim that frogs are green. But it does not include the endorsement of such a statement. Asserting the proposition that all frogs are green is called assent. I owe this example to Peter Adamson with whom I discussed the issues of translation and meaning of the Arabic terms. A  more formal explanation is given by Forcada in his paper on Ibn Bajja’s (introduced in Chapter One) understanding of the two terms: “Conceptualization amounts to the definition of an object of knowledge, and assent to the recognition, via some kind of reasoning, that this definition is true” (Forcada 2014, 103). Ibn Bajja was an important Andalusian philosopher who was deeply indepted to al-Farabi’s teachings, who was the first Muslim philosopher to compose a profound explanation of these concepts and their functions in a theory of knowledge. Al-Jurjani’s discussion of the two concepts thus stands in a long chain of predecessors interested in epistemology. In his treatise, called On the Divison of Knowledge, he grouped some of his predecessors and their works according to their definitions of the two concepts. The first group he loosely calls “the ancients and the modern muhaqqiqun”, while he dedicates the fourth group specifically to two works of Ibn Sina (Pointers and Reminders, The Book of Healing) and one text of Nasir al-Din al-Tusi (The Purification of the Belief). Fakhr al-Din al-Razi and his followers represent the second position. The third one is held by two other madrasa teachers who taught for many years at madrasas under the Ayyubids or Mamluks in Syria and Egypt – Afdal al-Din al-Khunaji and Shams al-Din al-Isfahani (died in 1348). Both were important contributors to logic, the first more so than the second. A good survey of al-Jurjani’s intellectual relationships to other philosophers, logicians, mutakallimun, and authors of encyoplaedias and classifications of the sciences can be found in Endress’s study of Ibn Sina’s texts taught and learned at madrasas (Endress 2006b, 420). Al-Jurjani’s criteria for his grouping are the use of ­conceptualization and assent to classify knowledge and to determine the relationship between assent and judgment. He believes (falsely so) that the p­ hilosophers do

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not divide knowledge into these two categories and consider de facto assent the same as judgment. The exception to this rule is Ibn Sina, to whom al-Jurjani ascribes the view that assent is conceptualization with judgment. Fakhr al-Din al-Razi holds that assent is a composite quiddity and judgment one of its components. Conceptualization, in contrast, is a simple or non-composite entity in al-Razi’s view. Al-Tusi’s position oscillates between that of the philosophers and a modification of al-Razi’s positions. Al-Jurjani describes al-Khunaji’s and al-Isfahani’s opinions as dividing knowledge into conceptualization and assent. If knowledge is pure conceptualization, then no judgment is needed. If it is assent, then judgment is attached to it. The differences between the four stances result from the ways that the relations between conceptualization, assent, and judgment are seen (Özturan 2015, 100–04, 109). The long-term education of madrasa students in logic and philosophy clearly shows in al-Jurjani’s approach to the issue of classification. He bases his critique of his predecessors on defining in good scholastic manner what a proper division is and which properties the divided parts have to have. The divided entity and its divisions must be in a relationship of general inclusiveness. The parts need to be opposites. The divided entity should be common to all its subgroups (ibid., 105). Al-Jurjani’s goal is to establish a classification that is appropriate to its goals and matches methods with subdivisions. An example of the latter is the case of Ibn Sina’s view that pure conceptualization are definitions and conceptualization with judgment are proofs (ibid., 110). Al-Jurjani finds that the positions of groups 1 and 4 are either flawless or appropriate, but insufficient as far as the matching of methods and subdivisions is concerned. The divisions proposed by groups 3 and 4 contain faults, because al-Jurjani considers judgments as a part, not an attachment of knowledge and as an action (ibid., 110). His main critique is directed against the positions held by group 2 which he rejects as mistaken due to their violation of formal conditions and conflicts between the division and its goals. He considers the relations defined by Fakhr alDin between conceptualization, assent, and judgment and their matching with methods as either faulty or superfluous (ibid., 111–12). Thus, while most of the other works surveyed in this chapter teach the structure of disciplinary knowledge and its terminological and factual content according to its parts, al-Jurjani’s treatise teaches a methodology of classifying knowledge in relationship to epistemology and logic.

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7.4. Postface This chapter tried above all to provide a few glimpses into works that are not textbooks or texts written with the primary intention of being used for learning and teaching, but had a broader range of functions and purposes. However, offering encouragement and proposals for the improvement of education or compiling summaries of respectable and respected knowledge were parts of their authors’ goals and intentions. I have abstained from trying to produce a bird eye’s view. Too many even of the summarized works have not been properly analyzed and contextualized. Moreover, I  do not believe in the possibility of producing a single meaningful history of all encyclopaedias and classification treatises, not even if they are limited to the types of text discussed in this chapter. I rather suspect that differences among such works correspond to different groups of people, problems, and contexts and thus deserve to be narrated independently. Nor do I believe any longer in the supposed two-sided fight between what has been called Islamic orthodoxy and philosophy, which the philosophers allegedly lost in the eyes of twentieth-century historians and seem to be winning in the eyes of historians writing in the twenty-first century. We need new categories and new ways to approach the relationship between different scholars and their beliefs and doctrines. Such historiographical challenges are too big for a book on the history of education in the mathematical sciences, medicine, natural philosophy, and the “occult” sciences. What is, however, indisputable to me is that Endress’s grand – and in several respects very impressive – depiction of a history of encyclopaedias and classification treatises as a single history in Islam needs to be substantially overhauled, or shelved if this turns out not to be possible.

Chapter 8 TEACHING LITERATURE AND ITS TEMPORAL GEOGRAPHIES

In this final chapter, I  will present material about the texts that were taught at madrasas, mosques, tombs, shrines, special houses for timekeepers (müvekkithane), or hospitals, starting in the twelfth century. As in many other instances in this book, the information I can offer is impressionistic. With the exception of the Ottoman Empire, there are no studies that try to provide a comprehensive survey of all texts studied in any city or region in a specific period and then rank them according to frequency and impact (textbooks, commentaries, supercommentaries, glosses, marginal notes, quotes in notebooks or elsewhere). I  will use biographical dictionaries, historical chronicles, and manuscripts as my sources. I will focus on the mathematical sciences, because this is the discipline I know best, but I will also include some data on the other disciplines treated in this book. As in other chapters, a substantial part of the information about teaching literature comes from biographical dictionaries and manuscripts and their catalogues. Ibn al-Akfani’s data about epitomes, books of middle length, and extensive works provide further, albeit limited, insights into the teaching literature of his time. The reports by premodern scholars do not cover the breadth given by the manuscripts. They limit themselves to what we could call standard or canonical literature, encompassing the texts studied and taught most often. The living reality was, however, more diverse. Many epitomes or synopses of twenty-odd folios are anonymous. Many author names are unidentifiable to us. The people behind them rarely or never appear in historical chronicles, biographical dictionaries, or classification treatises. Writing in the madrasa period was thus an important element of learning and teaching, perhaps because more famous books were too expensive and because writing had become a central marker of scholarly identity.

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ms. Oxford, Pococke 369, f. 183b. Ptolemy’s Almagest in the edition of Nasir al-Din al-Tusi. Copied in 799/1396 from a copy in the hand of Shams al-Din Muhammad, a son of Mu’ayyad al-Din al-ʿUrdi from Ayyubid Damascus, one of the main astrologers in Maragha and a colleague of al-Tusi.

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It is often taken for granted that the main ancient teaching texts, almost all of which had been translated into Arabic by the end of the ninth century, were a stable component of teaching over the centuries in all or at least most Islamicate societies. This idea, which generalizes observations of manuscripts, overstates the presence of Euclid’s Elements and the Middle Books, or Ptolemy’s Almagest in teaching or learning activities. In the first section of this chapter I have hence laboured to provide some impressions of what is known so far about the fate of this teaching material in West Asia and partly also in North Africa. In addition to alAndalus, which I generally ignored in this book due to my lack of competence for this part of the Islamicate world, in this chapter I have also excluded South Asia and Central Asia. In the case of Central Asia, I have made an exception and included the reign of Ulugh Beg, first as governor and later as head of the Timurid dynasty, during the first half of the fifteenth century, because he and his scholarly entourage have received ample historical research. When measured in terms of the numbers of extant mathematical manuscripts, it is clear that the teaching and learning of most mathematical disciplines did not take place via ancient textbooks, synopses, or epitomes, but through specialized textbooks of different formats, newly composed by madrasa teachers for a local or regional student body. Education’s primary orientation toward the local population is clearly expressed in the entries of scholars included in biographical dictionaries, as well as in the languages and content of many such texts. Persian or Ottoman Turkish as languages of teaching material in the mathematical sciences, medicine, or natural philosophy do not appear in regions where the local population spoke Arabic. But they are carriers of instruction, often side by side with Arabic, in territories where Persian was the main language of culture, as in Timurid Central Asia or Mughal India, or where Ottoman Turkish was the main administrative language, as in the Balkans and in the Greek provinces. The emergence of this very variegated body of teaching literature reflects a second major trend in the spread and direction of scientific education. Although urban centres remain the main loci of teaching and  learning, including the sciences discussed in this book, the legal, institutional, and material properties of the educational landscapes in Islamicate societies favoured their spread and extension to provincial

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towns, border locations like fortresses, and even villages. The mobility of teaching and learning as discussed in Chapter Five was certainly one important factor in this process of expanding socialization of education. In the same time, mobility was the result of the unevenness of this process and the unequalness of quality provided in rural areas. Nineteenth- and twentieth-century wooden slates with writing, counting, and calculating exercises show the rudimentary nature of knowledge provided in such village schools by local religious scholars or saints. On the other hand, the rural households of wealthy landowners apparently continued the educational practices of the pre-madrasa period described in Chapter Two and may have been, for example, the reason for manuscript copies of Euclid’s Elements produced in a few villages of Safavid Iran during the seventeenth century (Brentjes 2010). The types of teaching material discussed in Chapter Two, namely manuals, synopses, aide-memoires, epitomes, paraphrases, commentaries, or short epistles on specific issues, continued to be in use during the madrasa period. Glosses, superglosses, versifications, notebooks, and flyleaves appeared as either new or more widely spread formats. These new formats are already visible in manuscripts extant from the twelfth and early thirteenth centuries, but they proliferated in the fourteenth and fifteenth centuries. Increasingly, the author of a text refashioned it in several derivative forms as a paraphrase, a commentary, or a didactic poem. Two Mamluk authors who liked to simplify or modify their own ­treatises repeatedly were Ibn al-Ha’im and Sibt al-Maridani (or: Maridini) (1423–1501). Students, on the other hand, were proud to versify the ­writings of their teachers. In this chapter, I discuss teaching bestsellers as well as the standard forms of organization of teaching material beginning with the mathematical sciences, divided into ancient texts, geometry, arithmetic, algebra, and related disciplines, and followed by medicine, logic, and natural philosophy. I show that the available data on manuscripts and their temporal geographies prove the existence of distinct regions of teaching and learning for the mathematical sciences, where different textbooks and other forms of teaching material dominated the scene. Several such distinct regions of scientific activities are known from studies of the astronomical and astrological handbooks produced in alAndalus and North Africa (Samsò 1992, 2007, 2008), in Egypt and Syria

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(King 1986, 1993, 2004), and in Iran (Saliba 1994, 1997; Ragep 1993). The same statement applies to agricultural, astronomical, and astrological works in Yemen (King 1983; Varisco 1997; Schmidl 2007). Hence, it is not surprising that a similar regionally specific distribution of literature and content can be found in teaching material for North Africa, Egypt, Syria, and Iran. The limited survey that I present in this chapter shows that such a regionalization took also place in geometry, arithmetic, and algebra. The teaching material in the Ottoman Empire combined textual sources on geometry from four different regions, in particular the Timurid and Mamluk territories with some additions from North Africa and the Safavid realm. A  different picture prevails for arithmetic and algebra, where a single text from Safavid Iran dominated Ottoman madrasas in the seventeenth and eighteenth centuries. Madrasas in Muslim regions of India shared much of their teaching material with two different regions – Iran and Mamluk Egypt and Syria. The presence of Persian mathematical textbooks in Indian madrasas resulted from the migration of Iranian scholars to the subcontinent, above all from the fifteenth to the eighteenth centuries, although some scholars from Iran also came to India in earlier times. The impact of Arabic mathematical treatises, in contrast, was the result of educational journeys of students from India to Cairo and Damascus and pilgrimages to Mecca and Medina. 8.1. Euclid’s Elements and the Middle Books As already explained in Chapter Two, in the classical period, basic education in the four fundamental mathematical sciences probably followed mainly ancient teaching traditions. The few extant manuscripts of this period, as well as historical sources, testify to the adoption of Euclid’s Elements and a collection of texts on spherical geometry, elementary astronomy, and geography, sometimes called in ancient sources the Little Astronomer, under the new name of Middle Books (al-kutub al-mutawassitat) as standard teaching material. The collection of the Middle Books underwent a process of enrichment and modification beginning in the ninth century and continuing at the very least until the fourteenth century. A few more ancient mathe­ matical texts and several Arabic, plus one or two Persian, ­mathematical

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ms. Tehran, Majlis-i Shura-yi Milli, Kitabkhanah, 5143, unpaginated, ff. 4b-5a; Nasir al-Din al-Tusi’s edition of Euclid’s Elements, Book I, theorems 1–5; Persian translation by Qutb al-Din al-Shirazi; copied in 1586 by Ahmad b. ʿAli.

works were added to the collection. The Middle Books have thus a clearer geometrical character than the ancient collections of the Little Astronomer (Mansfeld 1998, 16–20). Since the Middle Books formed, despite all variations, a collective unit in many manuscripts, I will discuss them in this section as a whole (Kheirandish 2000, 131–44). The Elements became the leading and most comprehensive textbook of geometry in the madrasa period too, although our precise knowledge about their presence in specific cities and schools is extremely limited. The second place of fame may perhaps go to the Middle Books, when we

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look at the number of extant manuscripts and their geographical and temporal distribution. The manuscripts show, however, a much greater variability than the Elements. While the Elements were often copied as a whole, the Middle Books appear in three main formats. One format can be regarded as a kind of standard collection with texts by Theodosius of Bithynia, Autolycus of Pitane, Hypsicles of Alexandria, Menelaus of Alexandria, Aristarchus of Samos, Euclid, Archimedes, Thabit b. Qurra, the Banu Musa, and Nasir al-Din al-Tusi. A second format is offered in collections that go beyond the standard one by adding texts by al-Kindi, Abu Sahl al-Kuhi, or some other author from the classical period. This second format also appears sometimes as combinations of texts from the Middle Books with the Elements or the Almagest. The third format is represented in collections with a smaller number of texts than the standard one. I will provide their titles and discuss some examples in what follows. The extant copies of the Elements, which do not contain all fifteen books of the Late Antique version of the Elements, often lack parts due to material damage. They mostly lost either the beginnings or the ends. Sometimes also parts between beginning and end can be missing. Most of the manuscripts known to me do not show, however, any sign that their incompleteness was the result of conscious teaching or learning decisions. The first copies of mathematical texts produced during the twelfth century at the Nizamiyya Madrasas in Baghdad and Mosul suggest that the texts of the Middle Books were among the first taught in the early phase of mathematical education at madrasas. The flexibility of the content of the Middle Books indicates that not all their ancient and medieval texts were always studied together. The distribution of marginal notes beyond scribal corrections points in the same direction. A  similar observation applies to the Elements. Very few of the copies that I know contain marginal notes in all of the fifteen books. In particular, copies of the translations made during the late eighth and the ninth centuries seem to have been placed primarily in libraries without ever being used in class. In one case, however, a statement after the colophon at the end of Book XV contradicts such an interpretation. It says that some student had read the Elements until the end of Book IX with Ahmad b. al-Sarraj (flourished first half fourteenth century), an inventor and maker of astronomical instruments and proficient teacher of the mathematical sciences. According to the note, Ibn al-Sarraj corrected the content of the Elements during his

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classes based on his intelligence (ms. Oxford, Bodleian Library, Thurston 11, f.  212b). Hence, the (almost) complete absence of comments in a text does not necessarily testify to its lonely, silent existence on a library shelf. The picture offered by copies of Nasir al-Din al-Tusi’s edition of the Elements differs profoundly. Many of these copies contain, in addition to scribal corrections of copying mistakes, student and teacher notes. These notes differ, of course, in their depth and extent from copy to copy. In addition, students and other copyists often copied notes by earlier readers of a manuscript. The notes are rarely fully signed or are not signed at all. If they show marks at the end, these are abbreviations, which only the user of such a copy may have been able to explain or a modern codicologist can identify. The marks indicate that often several students left their notes in a copy of the Elements, thus providing later readers with considerable explanatory and paratextual information. Without claiming too much, the most humble set of notes encompasses, at the beginning of Book I, one or more brief references to one or more authors, mostly Nasir al-Din al-Tusi, but occasionally also to Ibn al-Haytham, Qutb al-Din al-Shirazi, al-Sayyid al-Sharif al-Jurjani, and other scholars. Some of these notes indicate that classical texts were still studied here or there in the fourteenth and later centuries. This feature of learning and teaching geometry is not accessible through biographical dictionaries, which usually mention only the most widely studied standard titles. After such brief biographical or bibliographical notes on the first folios of Book I, marginal notes begin to explain concepts, terminology, phrases, or a particular step in a construction or a proof. This basic content of marginal notes to the Elements confirms that students indeed practiced the reading and writing practices of commentators, surveyed in Chapter Six, in the annotations to this fundamental mathematical text. This also supports my assumption that the methods of commentary and super-commentary writing by advanced students and teachers were presented orally in lower-level classes. More complex and longer notes offer alternative proofs and case studies copied from other editions, comparisons with older copies of the Elements put on the market by other editors, and discussions of longer parts of various constructions or proofs. Alternative proofs and case studies were seen by scholars of the thirteenth century as the true duty of a commentator on the Elements, while earlier editions lacking case

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studies were denounced. Checking other copies and collecting information about earlier commentators is an often repeated practice across manuscripts of the Middle Books. Serious students of mathematical texts obviously believed that the reliability of their mathematical knowledge depended on textual correctness and an understanding of the nature of the differences between different versions. The notes of the highest level that I have encountered in copies of the Elements produced after the thirteenth century consist of systematic comments on an entire proof, documentations of comparative readings of several versions of the text, including the ninth-century translations and eleventh- as well as thirteenth-century editions, and fresh alternative proofs exercised possibly in class. A minority of copies of Nasir al-Din al-Tusi’s edition of the Elements contain such marginal notes throughout all books or in the first six books and the last six books, leaving out the arithmetical books VII–IX. The Elements and the Middle Books introduced students to concepts such as definitions, axioms, postulates, direct and indirect proofs, constructions, or theorems, that is, they were exposed to an axiomaticdeductive structure of a mathematical science. They learned about plane, spherical, and stereometric geometry, ratios and proportions, number theory, different kinds of magnitudes, and several methods used in geometry, among them analysis and synthesis. Furthermore, they received basic astronomical information about the risings and settings of planets and stars, distances between planets and their sizes, the determination of longitudes and latitudes on Earth, the celestial equator, the ecliptic, solar declination, and other astronomically relevant magnitudes. In Nasir al-Din al-Tusi’s editions of these texts, they also acquired knowledge in optics, about ninth- or tenth-century translations and editions and their mutual relations, and about leading scholars of the mathematical sciences in the classical period. There seems to be no standardized version of the Middle Books that was regularly taught, at least in a particular city or region for some period of time. But on average, manuscripts, which contain the editions made by Nasir al-Din al-Tusi, include the following list of works either ­completely or partially: three Euclidean texts (Data; Phenomena; Optics); three treatises by Theodosius (Spherics; On Habitations; On Days and Nights); three texts by Archimedes (On the Measurement of the Circle; On Sphere and

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Cylinder; Lemmats); two works by Autolycus (Moving Sphere; On Risings and Settings); one book by Menelaus (On Spherical Figures); one text by Aristarchus (On the Two Luminous Bodies); two works by Thabit b. Qurra (On the Given [Things]; On Compound Ratios); one book by Nasir al-Din al-Tusi (On the Sector Theorem). The presence of a larger range of ancient texts in the Middle Books is perhaps indicated by reading notes such as the one about the Data attributing the teaching of this work to ʿAli b. Ahmad al-Nasawi (died c. 1075) (ms. Tehran, Sipahsalar 559). Older collections present, instead of al-Tusi’s treatise on the sector theorem, Thabit b. Qurra’s text on this topic and a commentary on it by the just mentioned tenth-century scholar al-Nasawi. They also include the edition of Autolycus’ Risings and Settings by Thabit b. Qurra, an edition of Menelaus’s Spherical Figures by ʿAli b. Abi Bakr al-Harawi (died in 1215), and texts by the Banu Musa, Abu Sahl al-Kuhi, and Sharaf al-Din al-Tusi (1135–1213) (ms. Istanbul, Topkapı Sarayı, Ahmet III, 3464). These differences highlight the lively history of the Middle Books. Despite a recognizable trend towards some standardization, individual scholars apparently always had the freedom to compile their own collections. One example is the impressively rich v­ ersion of the Middle Books compiled and copied by the Ottoman official Mustafa b. Salih Sidqi. In addition to the standard texts of such a collection and some of the additional mathematical texts just listed, he appended to them about thirty advanced geometrical and astronomical works by ­leading scholars of the classical period and further texts from post-classical authors (mss. Cairo, Dar al-Kutub, 40 and 41). His goal was to improve his own mathematical training. Smaller sets include the Archimedean works alone or the texts by Theodosius and Autolycus. Sometimes single texts were bound together with treatises on non-mathematical themes (an example is ms. Mashhad, Astan-i Quds, Majmuʿa 944). Such separations may indicate individual interests of teachers, students, or collectors. But there are also ­manuscripts, which go considerably beyond the collections described above. They add treatises on topics of other mathematical disciplines such as a­ rithmetic, timekeeping, algebra, or magic squares. Codicological features suggest that such combinations might not reflect patterns of learning and teaching, but rather indicate decisions of librarians, owners, or sellers of manuscripts, who bound copies made by different scribes ­together in one volume. Ms. Istanbul, Topkapı Sarayı, Ahmet III, 3464 provides one such example.

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The volume’s seventeen texts were written by at least six different copyists. The colophons of five texts have dates for the years 1219, 1228, 1233, and 1290. Two of them also provide the towns of their production in eastern Anatolia – Arzinjan and Sivas. One of the four named scribes was Muhammad b. Abi Bakr Muhammad, whom we met already in Chapter Two as the copyist who declared, or transmitted a declaration, that Thabit b. Qurra’s book On Compound Ratios had been composed for students. His possible link to Mosul indicates the movement of the Middle Books between Iran, northern Iraq, and eastern Anatolia in the second or third quarter of the thirteenth century. A  botanical glossary added after alNasawi’s Commentary on the Sector Theorem documents the texts’ arrival in Arzinjan, where they might have come into the possession of a physician. From there they moved westwards to Sivas. The distribution of these ancient teaching texts across the Islamicate world is not well studied. We know of many exemplars of the Elements and a smaller, but still substantive, number of copies of the Middle Books, but have little information about their temporal geographies. In addition, as I will point out in the next section, data on the study of geometry is comparatively rare for medieval and early modern North Africa and the Mamluk territories. The few times al-Sakhawi specifies geometrical texts studied in Cairo and elsewhere in the Mamluk realm, for instance, he notes the Elements, al-Samarkandi’s summary of Books I and II, and Qadizade al-Rumi’s commentary on this treatise (Brentjes 2008,  324–25). Equally, in North Africa, the Elements were used and well known during the fourteenth and fifteenth centuries (Lamrabet 1994, 79, 114–15). The most often and most densely commented, and thus most likely taught, parts of the Middle Books, at least in the eastern parts of the Islamicate world, are Theodosius’s Spherics, Autolycus’s Moving Sphere, Euclid’s Data, Archimedes’ Measurement of the Circle, and his On Sphere and Cylinder (see, for instance, ms. Tehran, Majlis-i Shura-yi Milli, 4569). Occasionally, manuscripts of Archimedes’ books also contain ancient and medieval commentaries like those by Eutocius of Ascalon (first half fifth century) or one on the partition of the sphere in a given ratio by Abu Sahl al-Kuhi. Through them, some of their readers learned higher levels of geometry, including methods from Apollonius’ Conics, and added their notes to them in the margins (ms. Tehran, Majlis-i Shura-yi Milli,

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ms. Tehran, Danishgah, Kitabkhanah-i markazi, 1359, cover page of Theodosius’s Spherics in the edition produced by Nasir al-Din al-Tusi in Shaʿban 663/June 1265

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Kitabkhanah, 22513). It is, however, almost never possible to determine whether these readers were autodidacts or undertook their higher studies with a teacher. During the sixteenth and the seventeenth centuries, an upsurge of interest in Nasir al-Din al-Tusi’s editions of ancient mathematical teaching texts occurred in Safavid Iran. Even his edition of Apollonius’ Conics was again taught, perhaps by Baha’ al-Din al-ʿAmili. One of Baha’ al-Din’s brightest students, the later court astrologer Muhammad Baqir b. Zayn al-ʿAbidin (died after 1637) of Yazd, copied and commented on this work in the first half of the seventeenth century. King emphasizes that Muhammad Baqir was one of the rare scholars known to us who did not merely teach madrasa students, but was also an instrument maker (King 1999, 131). Other information gleaned from single manuscripts opens up the possibility that teaching choices made by scholars of the Ilkhanid period were taken up and repeated by individual teachers and their students in Timurid Iran and in the Ottoman Empire. One example of such a longterm teaching and learning tradition is the combination of Nasir al-Din al-Tusi’s edition of the Elements with commentaries on various of its parts by scholars of ninth-century Abbasid Baghdad and tenth-­century Buyid cities in Iran in an Ottoman manuscript from October 1729 (ms. Munich, Bayerische Staatsbibliothek, Cod. arab. 2697). This set of closely interrelated texts is complemented by texts or individual theorems by one of the sons of Nasir al-Din al-Tusi, one of Nasir al-Din’s students, and a student of another of his students. This seems to support my understanding of the entire manuscript as an Ilkhanid teaching collection with later Timurid and Ottoman additions. The goal of the Ilkhanid collection most clearly was to achieve fluency in Euclid’s books, including their more difficult parts, situated in the tradition of learning and commenting on them, as it had formed since the ninth century. Other learning goals apparently consisted of creating familiarity with basic concepts of geometry and the beginnings of epistemology and of training in techniques of proofs and case analysis. This rather intense study of elementary geometry was accompanied by excursions into often taught kalam texts like ʿAdud al-Din al-Iji’s Stations of the Science of Kalam and al-Sayyid al-Sharif al-Jurjani’s critical commentary on this work. They appear as notes on free pages or as references in marginal notes.

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Intercalated between the Elements and the texts related to them or following this sequence are single theorems on particular geometrical problems and constructions. There are also extracts from astronomical treatises, or astronomical chapters of kalam works, comments, and two complete treatises, one on geometry, the other on astronomical instruments. Among the short pieces we find a brief comment on the positions of Venus and Mercury by someone who seems to have worked for al-Biruni, introduced in Chapter Two, and single theorems or problems by one tenth-century scholar, two further Ilkhanid scholars, and one Mamluk timekeeper and madrasa teacher. The last set of such short extracts comprises three astronomical determinations of the Prophet Muhammad’s birth by two astrologers of the late eighth and ninth centuries and one historian. These pieces either teach specific mathematical skills or introduce particular astronomical topics. The two complete texts joined to the sequence of the Elements and related commentaries are a treatise on the determination of plane and spherical figures by the Banu Musa, whom we already met in Chapter Two, and the Commentary on Observational Instruments by the Timurid scholar Ghiyath al-Din al-Kashi. The text by the Banu Musa could also be found in the Middle Books. It thus comes as no big surprise to find it here in the context of discussions on the Elements. Al-Kashi wrote his commentary on observational instruments in 1415 at the command of the Timurid ruler Iskandar Sultan. Its presence in this manuscript was, however, most likely the decision of the Ottoman enthusiast who copied the material in 1729. The marginal notes provide further insights into learning and ­teaching habits among Ilkhanid and Ottoman students and teachers of geometry, although it is not always clear how the individual comments are related. As described for philosophy in Chapter Six, there was a strong a­ ntiquarian interest among those who read Tusi’s edition of the Elements. In nume­ rous instances, they compared Tusi’s formulations with copies of the ninth-century translations attributed to al-Hajjaj b. Yusuf b. Matar (flourished in the later eighth century and the first third of the ninth century) and to Ishaq b. Hunayn and Thabit b. Qurra (both scholars were introduced in Chapter Two). But this comparison did not satisfy the needs of linguistic and possibly technical proficiency. The users of this manuscript also included editions by Ibn Sina, Athir al-Din al-Abhari, and Nizam al-

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Din al-Nisaburi. They read Qutb al-Din al-Shirazi’s Arabic comments on Tusi’s edition as well as his Persian translation of this version. This is an impressively broad exercise of reading as a tool for analyzing and understanding this basic text of geometrical education. The marginal notes also confirm the other level of multiple textual interpretation, which greets the reader already on the first folio – the relationship between geometrical knowledge and the study of school texts on kalam. Other features of the marginal notes reflect the efforts of their writers to follow the instructions of their teachers in class by adding references to individual theorems of the Elements in later proofs, if they were not already registered, and by adding explanations of parts of a theorem or entire alternative constructions or proofs. Since these notes are found in all fifteen books of the Elements and in some of the related commentaries, the teaching of geometry exercised through this particular manuscript was undoubtedly very intense and probably quite successful in training geometrical skills along some of the lines proposed by al-Sijzi in his treatise on how to become a productive geometer, which I presented in Chapter Six. 8.2. Other School Texts for Geometry A set of two texts closely related to the Elements, but much more limited in scope, became perhaps even more prominent as teaching texts. This pair consists of Shams al-Din al-Samarkandi’s The Fundamental Theorems and Qadizade al-Rumi’s commentary on al-Samarkandi’s work. The context in which al-Samarkandi wrote his short treatise on thirty-five postulates and theorems of Books I and II of the Elements is not well known. Qadizade, however, undeniably wrote his commentary as part of his work as a teacher at the madrasa built by Ulugh Beg in Samarkand. These two texts became introductory reading material in the Ottoman Empire (from where numerous copies are extant), North Africa, and possibly India. For Iran, the currently available data do not speak of their wide distribution, although they were studied for instance in Shiraz in the fifteenth century. In addition to these two short treatises, numerous low-level texts taught the names and properties of plane figures like triangles, regular

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and irregular quadrangles, circular figures, and compound figures. These little surveys were often composed as a set of rules, illustrated by diagrams or sketches, and free of theorems, constructions, or proofs. They were offered as independent texts or as a chapter or two in similarly elementary general texts dedicated primarily to arithmetic and algebra, like the Essence of Arithmetic by the leading Safavid religious scholar of the second half of the sixteenth and the first quarter of the seventeenth centuries, Baha’ al-Din al-ʿAmili, which I will discuss in the following section. In the Maghrib and in Mamluk Egypt, titles of texts on geometry are not very often transmitted in biographical dictionaries. Manuscript catalogues do not show a greater number of independent geometrical writings by madrasa scholars for those regions. One of the scholars whose work deviates from this general perspective was Ibn al-Banna’, whom we already met in Chapters Four and Five. He wrote two books on theoretical geometry, two on practical geometry (surveying), and one mixed work (Lamrabet 1994, 82). But they were – as far as I could see – ignored by his successors, who ardently studied, commented on, or versified his works on arithmetic, algebra, or number theory (ibid.) In his survey on Maghribi mathematics, Lamrabet underlines the fact that scholars applied geometrical methods only under exceptional circumstances, for instance to prove algebraic properties (ibid., 110, 112). But this does not mean that no geometry was taught. Learning geometry certainly took place within astronomical and astrological studies. The reading of texts on timekeeping and instruments, often authored by Mamluk scholars, as well as astronomical handbooks composed by scholars from al-Andalus and the Maghrib presuppose such training (ibid.). This general silence about geometrical teaching texts used in North Africa is also upheld in Ibn Khaldun’s Introduction (to History). In his discussion of geometry and its branches, he only rarely mentions specific titles beyond the Elements, its abridgements or commentaries, or texts of the Middle Books. But he remembers a nice saying by his teachers on the discipline’s value: Our teachers used to say that one’s application to geometry does to the mind what soap does to a garment. It washes off stains and cleanses it of grease and dirt. The reason for this is that geometry is well arranged and orderly, as we have mentioned (Ibn Khaldun 1958, vol. 3, 131).

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8.3. Arithmetic, Algebra, and Number Theory In the three mathematical disciplines of arithmetic, algebra, and number theory, the differences across time and territory are even larger than in the case of geometry. As already pointed out in Chapter Four, in North Africa texts by Ibn al-Banna’ were prominent from the thirteenth century onwards. Almost every student seriously interested in arithmetic and algebra read and commented on his Epitome on Arithmetic (Lamrabet 1994). This text was also read by the sons of some North African dynasties. Other texts on arithmetic and algebra fairly widespread among madrasa teachers in North Africa were those mentioned in the educational voyage of al-Qalasadi in Chapter Five: texts by al-Hassar and Ibn al-Yasamin plus treatises written by al-Qalasadi himself (ibid.). Number theory and combinatorics were read on the basis of Euclid’s Books VII to IX and works by local authors, at the very least between the twelfth and the fourteenth centuries. In the Mamluk realm, works by Ibn al-Majdi and Shihab al-Din, called Ibn al-Ha’im, dominated the study of arithmetic and algebra, complemented by Ibn al-Banna’’s Epitome, Ibn al-Yasamin’s poems, and Nizam al-Din al-Nisaburi’s Treatise for Shams al-Din [ʿAbd al-Latif ] on Arithmetic. This reflects a combination of local traditions with methods and problems preferred in the west of North Africa and in Iran. What that meant in specific terms is not well researched. Number theory was rarely taught. But some traces of it, like arithmetical series or the Pythagorean theorem for even or odd numbers, can be found in some of Ibn al-Majdi’s treatises. Another text on arithmetic often read in Cairo, but also studied at Syrian and Ottoman madrasas, was Shams al-Din al-Sakhawi’s Epitome on the Science of Arithmetic (Osmanlı Matematik Literatürü Tarihi 1999, vol. 1, 43–46). Al-Sakhawi, the author of the biographical dictionary explored so often for this book, had studied with Ibn al-Majdi and Ibn al-Ha’im. Ibn al-Akfani’s information on the literature for beginners, middlelevel, and advanced students often focuses on material from the classical period, which is not mentioned in the biographical dictionaries of the Ayyubid or Mamluk dynasties either for Syria or for Egypt. It is possible that these titles do not reflect learning and teaching habits in Ibn al-Akfani’s lifetime in Cairo, or even in the two centuries before him.

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The  ­situation differs when he mentions names and/or titles that are contemporary to him or appear in the various dictionaries. An example is Ibn Fallus (died in 1239), a scholar of the Ayyubid period from Damascus. He taught different branches of arithmetic, algebra, geometry, and medicine at madrasas in Cairo and Damascus. Ibn al-Akfani names Ibn Fallus’ treatises on oral computation and algebra as introductory texts (Ibn al-Akfani 1989, 60–61). Moreover, Ibn al-Akfani’s survey only covers texts in Arabic. But the teaching of arithmetic, algebra, and surveying in Iran, Central Asia, and India took place overwhelmingly in Persian. This is at least my impression from manuscript collections. Since there is no census for the distribution of copies of Persian arithmetical and algebraic texts and since many texts are anonymous and untitled, I am not able to determine leading teaching texts among them. A similar process becomes visible for the Ottoman Empire during the sixteenth century, when a slowly increasing number of elementary school texts using Ottoman Turkish as their medium of communication appeared. But until the eighteenth century at least, a student at an Ottoman madrasa could expect to be taught arithmetic, algebra, and surveying most often in Arabic or Persian. Reading mathematical texts in the Anatolian parts of the empire, but less so in its Arabic, Greek, and Slavic regions, was thus often also an exercise in linguistic culture. The texts most often copied at and linked to madrasas were ʿAli Qushji’s Persian and Arabic treatises on elementary arithmetic (38 copies in Turkish libraries, 32 in Iranian libraries, 3 in India, 31 each in Iraq, Syria, and Egypt, 5 or 6 in Europe), Arabic commentaries on works by Ibn al-Ha’im, and above all commentaries on Baha’ al-Din’s Essence of Arithmetic, which I will discuss below (Osmanlı Matematik Literatürü Tarihi 1999, vol. 1, 93–95, 98–99, 112–18, 124– 26, 131–32, 136–41, 143–45, 155–61 and passim). Turkish descriptions of the literature studied in the arithmetical branch disciplines are often based on Tashköprüzade’s biographical collection and classification of the sciences. Almost all the booktitles named there are copied, sometimes with mistakes, from Ibn al-Akfani’s respective chapters and thus provide no insight into the situation at Ottoman madrasas in the first half of the sixteenth century (see İzgi 1997, vol. 1, 194–96). In Ilkhanid and Timurid Iran, classroom work on arithmetic and algebra also relied primarily on books written by local scholars. The most

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widely documented school texts were written by Ilkhanid and Timurid scholars. At the top of this list in terms of numbers were the texts by alNisaburi and al-Kashi. All of these texts originated in a courtly context and were dedicated to Ilkhanid or Timurid rulers or viziers. This implies a low threshold of socio-cultural boundaries with regard to the acquisition of arithmetical and algebraic skills at courts and madrasas. Moreover, in contrast to Egypt and North Africa, the textual basis for learning and teaching these two mathematical disciplines was more variegated. How this difference is reflected in the content of what was learned and taught is not yet known. In addition to such locally produced treatises, a few teaching texts also arrived in those regions from the west and gained respect and appreciation. One of those foreign materials was a text written by ʿImad al-Din ʿAbdallah b. Muhammad al-Khaddam, a thirteenth-century scholar from Baghdad. It quickly became accepted at madrasas in Iran, Central Asia, and some parts of India. Its success may have been based on its broad range of topics. It contains chapters on arithmetic, business calculations, surveying, specific weights, algebra, and a number of examples (Matvievskaya-Tllashev 1981, 26–28). Al-Kashi followed the same approach in his very successful Key of Arithmetic (or: of Calculators). The broader content of elementary teaching material in Iraq, Iran, Central Asia, and India seems to be another difference to teaching material compiled by Mamluk scholars in Syria and Egypt. In Mamluk texts, arithmetic and algebra were more often clearly separated from geometry. A shift in the texts preferred for education in arithmetic and algebra occurred in the seventeenth century. Baha’ al-Din al-ʿAmili’s textbook The Essence of Arithmetic superseded most of the older texts between India and Egypt, becoming the most often taught introductory source for arithmetic, algebra, and surveying in the Ottoman, Safavid, and Mughal Empires. A major reason for its success probably was the fact that it too covered a broad range of topics. It presented in a succinct manner all branches of the mathematical sciences (except astronomy) that were useful for the routine work of judges and their staff, administrators, and surveyors. Astronomy was taught separately through other elementary texts, to be discussed in the following section. Two other cultural conditions contributed to the success of this particular textbook despite the overwhelmingly inimical relationships

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between the Safavid dynasty and its main neighbours. The itineraries of Baha’ al-Din’s Essence of Arithmetic through the Ottoman Empire, for example, did not follow the geographies that linked the Ottoman with the Safavid realm. There was no continuous move from Isfahan westwards through major Anatolian cities with schools until Istanbul was reached. Manuscripts rather suggest that the text was brought first to the Ottoman capital, before it reached schools in provincial towns. This impression is by necessity incomplete, because too many intermediary witnesses are unknown or lost. But this currently known geography of the text seems to indicate that the scholars who carried the text westwards followed the socio-cultural patterns of the Ottoman scholarly and administrative career system with Istanbul at its heart. Only when they could not establish themselves in the capital, did they move elsewhere. In Iran, number theory was more often written about than in Egypt and North Africa. Encyclopaedias by Iranian and Central Asian scholars like Ibn Sina, Qutb al-Din al-Shirazi, or Muhammad b. Mahmud al-Amuli (whom we met in Chapter Seven) contain chapters on this topic. Written more specifically for courtly patrons, copies could also be found in madrasa libraries where sometimes someone wrote notes in their margins. It is, however, not clear whether these notes reflect individual autodidactic readings or classroom work. A fairly elaborate text on arithmetic and algebra, which also contained sections on number theoretical problems, was composed by Muhammad Baqir b. Zayn al-ʿAbidin of Yazd, whom I introduced above. His Sources of Arithmetic was well appreciated locally and repeatedly read and copied, even translated into Persian (Matvievskaya-Rozenfel’d 1985, vol. 2, 590). As in Iran, number theory attracted Ottoman teachers who wrote treatises on different topics traditionally learned in this discipline – odd and even numbers and further subclasses, amicable numbers and perfect numbers, or magic squares. These themes were also linked to the so-called “occult sciences”. They offered the basic knowledge required for producing talismans or creating magic squares. Sultans and their high-ranking officers, for instance, used shirts with magic squares, Qur’anic verses, magic letters, and other devices. These devices were applied to underwear used when going to war. Although readers may not expect this, the amount of mathematical knowledge needed for mastering these themes was not

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negligible. Important scholars of the mathematical sciences, among them for instance Thabit b.  Qurra and Ibn al-Haytham, had contributed to developing construction methods: One of the most impressive achievements in Islamic mathematics is the development of general methods for constructing magic squares. A magic square of order n is a square divided into n2 cells in which different natural numbers (mostly the n2 first naturals) must be arranged in such a way that the same sum appears in each of the rows, columns, and two main diagonals. If, in addition to this basic property, the square remains magic when the borders are successively removed, we speak of a “bordered square.” If the sum in any pair of complementary diagonals (i.e., pairs of parallel diagonals lying on each side of a main diagonal and having together n cells) shows the constant sum, the square is called “pandiagonal.” Squares are usually divided into three categories: odd order squares (n = 2k + 1, k natural), evenly even squares (n = 4k), and evenly odd squares (n = 4k + 2). There are general methods for constructing squares of any order from one of these three categories (Sesiano 1997, 536–38).

8.4. Astronomy and Astrology Astronomy appears in the sources under various names. In the classical phase, it was called either astrunumiya or the science of the stars. Astrunumiya is the transliteration of the Greek term astronomia, mediated through Syriac translations. Science of the stars is a literal translation of the Greek astrologia. Overtime, astrunumiya lost its prominence, although the word did not completely disappear from the sources. The content and use of the expression science of the stars shifted from astronomy to astrology. By the tenth century at the latest, but probably beginning already earlier, a renaming and thus a reorganization of themes and methods set in. Some historians believe that this process resulted from the conflicts over astrology. On the one hand, astrological claims violated the strict interpretation of Islamic monotheism subscribed to in some scholarly and

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political circles. On the other hand, astrologers and their discipline were ridiculed, because all too often their predictions did not come true. The reorganization of astronomical and astrological knowledge is thus seen as a process of separation between these two spheres. The new discipline of “pure” astronomy was named the science of the configuration (of the universe). Its focus was directed to ­modelling the movements of the planets and the Sun. Its literary codification assumed two levels. One level provided surveys, rules, diagrams, and examples. It worked without proofs and was called the simple level. The other level constructed expositions in the axiomatic and deductive style of ancient mathematics and anchored teachings according to Aristotelian epistemology in the higher sciences of natural philosophy and geometry. Not all writers of texts on the science of the configuration, however, subscribed to this outlook and its differentiations. Many authors saw no problem in presenting astrological matters in their treatises about planetary movements, distances, and sizes. Even the term itself was used with variations. Pre-modern historians such as Ibn al-Akfani or al-Sakhawi did not see the term as covering all of astronomy. They believed that the composition of astronomical handbooks, the compilation of calendars, the discussion of instruments or observations, and in particular the new science of timekeeping, which was formulated and specifically named in the late thirteenth century, all represented further branches of astronomy with some independence from each other (Ibn al-Akfani 1989, 57–59; al-Sakhawi n.d. vol. 2, 62; vol. 10, 89, 259). Others even identified the science of the configuration with the science of timekeeping, a move that does not seem to be supported in those manuscripts of both fields investigated so far. My impression is that the separation of disciplinary branches by attributing special names for identification is more a differentiation between types of literature – and thus a reflection of learning and teaching patterns as they emerged over time at madrasas in different regional settings – than an epistemologically grounded process of diversification. Ibn al-Akfani presents astronomy as consisting of six branches: the science of the configuration (of the universe); the science of handbooks and calendars; the science of prayer times; the science of the quality of observations; the science of the (projection) of the sphere on a plane; and the science of shadow instruments (Ibn al-Akfani 1989, 57–59). The books presented for the first discipline are differentiated according to whether they used

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geometrical proofs or only diagrams. Some of the first group, like al-Abhari’s edition of the Almagest and al-Biruni’s Canon for al-Masʿud, were known among Timurid and Mamluk scholars. But it is unclear whether both were indeed used in schools. Interestingly, for the second group Ibn al-Akfani lists exclusively books by Ilkhanid authors: al-Tusi’s Memoir as an introduction; al-ʿUrdi’s Commentary on the Almagest as a middle-level text, and Qutb al-Din al-Shirazi’s The Limit of Perception as an extended work. There can be no doubt that the first and the third book were used in teaching in Iran and Central Asia. Mamluk and Ottoman scholars taught the Memoir, even if less often than the dominant elementary introduction by al-Jaghmini, which Ibn al-Akfani does not mention. Some of them also knew al-Shirazi’s The Limit of Perception as well as the Royal Gift by the same author. We can assume that some students with more ambitious goals took classes on these books, but since there is no research on their distribution and their marginal notes available, it is impossible at present to estimate how often, where, and when they were studied. For the domain of timekeeping, Ibn al-Akfani’s data reflects the early phase of its institutionalization in Cairo. Thus, it is not surprising that he names only two works, one by Abu ʿAli al-Marrakushi, the other anonymous. Ibn al-Akfani’s choice of al-Marrakushi’s work marks him as a very competent judge. Charette believes that Abu ʿAli al-Marrakushi wrote his book, with the title Collection of the Principles and Objectives in the Science of Timekeeping, in Cairo between 1276 and 1282 at a time when the first timekeepers were installed fulfilling a practical need of society (Charette 2007b, 739–40). The Collection is a very substantial work. The extant copies often cover between 250 and 350 folios with many tables and diagrams. It begins with a long introduction to the necessary principles and methods of geometry, before it deals with the main problems of timekeeping and the instruments suited for their solution. Its final chapter offers questions and answers to students. Al-Marrakushi thus succeeded in writing a comprehensive teaching manual. At the same time, he produced one of the rare synthetical works existing in the mathematical sciences. It presents timekeeping problems and practices in a systematic manner, based on the work of predecessors, but adding the author’s own perspective and original ideas (ibid.). The following centuries saw a blossoming of books and treasises on timekeeping problems. Large tables with up to 415,000 entries were

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c­ alculated for a number of astronomical parameters, and auxiliary functions to ease the solution of all standard problems of spherical astronomy and for all terrestrial problems of spherical trigonometry for any latitude were invented. The table of 415,000 entries was compiled in the first half of the fourteenth century. It is the largest known table compiled before the nineteenth century (Charette 2007c, 819). Since no groups of calcula­ tors like those in nineteenth-century Germany, for instance, are known for fourteenth-century Egypt, the table’s production remains an enigma, unless its author, Najm al-Din al-Misri (flourished c. 1300–1350), spent all of his life calculating for long hours. But since he also managed to write a book about one hundred different kinds of astronomical instruments, he might have had the support of students or paid calculators. In addition to such tables and descriptions of instruments, many works were written as introductions and aide-memoires for the education of timekeepers and muezzins. The most influential and often studied works deal with the directions of prayer, prayer times, the construction of astrolabes, astrolabic and sine quadrants, unusual variants of quadrants, sundials, stereographic projections, and the visibility of the crescent moon. Their authors were Ibn al-Majdi and Sibt al-Maridani (or: Maridini) (Charette 2007a, 561–62; Matvievskaya-Rozenfel’d 1985, vol. 2, 514–22). Sibt al-Maridani taught timekeeping, arithmetic, algebra, and the rules of inheritance law at the Azhar mosque, where he also worked as a timekeeper (al-Sakhawi n.d., vol. 1, 25; vol. 2, 65, 213; vol. 4, 48, 57; vol. 5, 166; vol. 6, 262, 271, 325; vol. 8, 108, 138; vol. 9, 7, 18, 35; vol. 10, 94, 104, 242). One of his most often read astronomical texts deals with the sine quadrant. It teaches students how to measure angles for astronomical and terrestrial applications such as the hour angle of a star, the width of a river, the depth of a well, or the height of a tower. In Iran and Central Asia texts on timekeeping apparently arrived only in the nineteenth century. At least this is what entries in manuscripts, which were given as religious endowments to the library of the Imam Riza Shrine at Mashhad, suggest. Manuscript libraries in India, in contrast, imply that Indian students in Cairo brought such teaching literature home with them in the early modern period. Other important works of teaching literature in the astronomical branches studied in Iran, Central Asia, India, and the Ottoman Empire

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were Nasir al-Din al-Tusi’s and ʿAbd al-Ali al-Birjandi’s treatises on calendars and astrolabes, al-Tusi’s Memoir and various commentaries and supercommentaries on it, al-Jaghmini’s introduction to astronomy, and the astronomical handbooks by al-Tusi and Ulugh Beg.  With this kind of literature, the later professional experts were able to produce the yearly calendar for the court, to predict eclipses, and to measure geographical latitudes, solar altitudes, and other astronomical magnitudes. Al-Jaghmini’s introduction and some other elementary texts on planetary theory and instruments were also copied in the early modern period as far to the east as Kashgar, suggesting that some teaching and learning of these matters according to these traditions was undertaken under the (Mongol) Chaghatai Khans (ruled c.  1514–1572) and their local Muslim successors, despite the endless wars that ravaged this region between about 1400 and 1760. 8.5. Medicine Medical teaching literature encompassed books that were studied in many Islamicate societies over many centuries and texts that were taught on a regional level. This differentiation seems to be stronger than in the case of the mathematical sciences or philosophy. But there is no numerical data available to support my impression. Reasons for the stronger local character of medical teaching are probably manifold. Healers had to talk to patients in their local languages. Arabic as a spoken language did not move far to the east, except for tribes and trading communities in port cities. Hence, teaching exclusively in Arabic in regions where other languages dominated may not have been very helpful. Persian and Ottoman Turkish became important teaching languages for medicine. At the latest after 1700, Urdu, Hindi, and Pashto made their appearance in South Asia in medical literature too. Two further reasons for a greater diversification of medical teaching books across the various regions between the Atlantic and the Gulf of Bengal were in all likelihood the numerical relationship between Muslim and non-Muslim inhabitants in the individual states, and the presence or absence of other cultures of healing. In India, where Muslims often remained a minority, Ayurveda healing traditions had a visible impact on Muslim medical practices beyond those that had already been i­ ntegrated

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during the eighth and ninth centuries thanks to the translation of Sanskrit texts into Arabic. Trilingual medical dictionaries are known from the sixteenth, seventeenth, and eighteenth centuries. Their languages were Arabic, Persian, and Sanskrit or another language of the subcontinent. Through such dictionaries Indian medical knowledge from non-Muslim communities was integrated into Persian medical literature. Folk practices, on the other hand, apparently remained outside this formal teaching of medicine at madrasas. But it may well have been part of teaching through apprenticeship. Special developments set in after the expulsion of the non-Christian populations of the Iberian Peninsula at the end of the fifteenth century. Their physicians and druggists brought translations of Latin medical texts to the eastern Mediterranean. The influx of this kind of literature in Latin, Spanish, or Italian increased once more during the second half of sixteenth and the first quarter of the seventeenth centuries, when people of Jewish and Muslim descent, who had been forced to convert to Christianity, were driven out of Spain. The transfer of medical knowledge was also promoted during the seventeenth century and later through Ottoman Greek subjects who studied in Padua and perhaps at other universities. The medical teaching texts, which crossed many boundaries and societies in North Africa and Asia between the Red Sea and eastern India, were Ibn Sina’s Canon of Medicine and a cluster of texts derived from it as compendia, commentaries, and epitomes. Ibn al-Nafis’ commentary on Ibn Sina’s Canon of Medicine, the text called Digest on the Canon attributed to Ibn al-Nafis, and several commentaries and supercommentaries on the Digest were among the medical teaching texts studied in the Mamluk realm, the Ottoman Empire, and northern India over several centuries. The importance of the Digest for teaching and debate is confirmed by manuscripts in various libraries, among them commentaries written in Iran, Anatolia, Egypt, and Syria or by the copy of Ibn al-Nafis’s Digest finished in 1348 in a madrasa of Sivas in eastern Anatolia (Fancy 2013a; ms. London, British Library, Or. 5659). Fancy, however, doubts the work’s attribution to Ibn al-Nafis, because this orthodox text contradicts the scholar’s own, modified psychology and physiology. It also deviates from Ibn al-Nafis’s usually critical depiction of conflicts among physicians as well as between medical experts and philosophers (Fancy 2013a, 114–19).

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Often, Qutb al-Din al-Shirazi’s commentary and al-Jaghmini’s compendium are also mentioned or registered in biographical dictionaries or manuscript catalogues from Egypt to India. Beyond this set of texts written by or related to Ibn Sina, a few texts by or attributed to Hippocrates (Aphorisms, Oath, Prognostics) and com­ mentaries on them by physicians from different religious communi­ ties were shared from the Atlantic to the Gulf of Bengal. Books by Galen, Hunayn b. Ishaq, Abu Bakr al-Razi, ʿAli b.  ʿAbbas al-Majusi, and other famous physicians from Baghdad, Rayy, Damascus, Cairo, Córdoba, and cities west of Iran were often studied in societies along the Mediterranean and in Iraq and parts of Iran, but do not seem to have found the same acclaim in South Asia. There, works by physicians from Iran had greater distribution, partly due to the later spread of Islamicate societies on the subcontinent and partly through the presence of Iranian doctors in India over the centuries. Manuscripts from Islamicate societies in India show that from about the fourteenth century, many of their texts were composed in Persian. This fact indicates that they were written for the elites, who since the Ghaznavids had opted for Persian as the cultural language of the court. Indeed, a good number of them are dedicated to rulers. Some are also presented as texts written for the education of the author’s children and his students or for students in general. Examples are two Mughal texts written in the sixteenth and the early eighteenth centuries. Akbar’s (ruled 1556–1605) court poet and historian Nami, in ordinary life called Mir Muhammad b.  Masʿum Shah (second half sixteenth century), whose family came from Bakhar in Sind (today part of Pakistan), compiled a treatise on medical simples “for the convenience of students” (Catalogue of Arabic & Persian Manuscripts, vol. 11, 21). His work consists of twenty-six chapters, arranged according to diseases. Muhammad Akbar Arzani (died 1722) wrote The Balance of Medicine with a teaching purpose in mind. In three chapters he informs the reader about basic concepts of natural philosophy such as the four elements and their qualities, simple and compound medicinals, and the symptoms of diseases and their treatment (ibid., 33). Nami’s information about his sources indicates one of the more widely read medical texts in Iran, Central Asia, and India – the pharmacological book Wonderful Selections. Its author was ʿAli b. Husayn alAnsari (1330–1403), the son of a physician and druggist from Isfahan

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in late Mongol and Timurid Iran. The Treasure of the Khwarazm Shah is a second frequently read medical work in Persian, a compendium of Ibn Sina’s Canon of Medicine. Its author was the highly appreciated doctor, philosopher, and scholar of kalam, Zayn al-Din Ismaʿil b. al-Husayn alJurjani (1040–1136). He composed it around 1110/1 for the then ruling Khwarazm Shah Muhammad (ruled 1098–1127). Ismaʿil’s intention was ambitious and didactic at the same time. He wished his name to survive the centuries and “to remove the want and inconveniece of physicians and others, which they felt in the absence of a comprehensive medical work” (ibid., 3–4). He succeeded in both goals. Following Ibn Sina, whose intellectual grandson in medicine he was, the book explains in ten volumes natural philosophy as the basis of medical theory, anatomy, physiology, hygiene, diagnosis and prognosis, fevers, diseases from head to toe, surgery, skin diseases, poisons and antidotes, and simple and compound medicinals (ibid., 4). A third book that was also read further to the west in the Mamluk realm and at Ottoman madrasas was al-Jaghmini’s synopsis of Ibn Sina’s Canon of Medicine (ibid., 9). In India it was studied in its Persian translation, while in the west the Arabic version prevailed. Medical teaching literature from India, in contrast, did not reach the Ottoman Empire or North Africa, as far as I can tell. Even in Iran such texts came into libraries mostly or perhaps only through religious endowments after the death of the owner of such a text. Most often such donations were made to the Shrine of Imam Riza in Mashhad. It is thus not very likely that they circulated at Iranian madrasas. But the Persian materials that had travelled to India also moved westwards. Ottoman manuscript collections and Ottoman biographical dictionaries testify to their arrival in Anatolia. In the Ottoman Empire too, Persian was the language of high culture and a companion language in the sciences, medicine, and philosophy. The study of Arabic translations of ancient medical texts by or attributed to Hippocrates and Galen was, as we have already seen in Chapters Four and Five, fairly widespread in Iraq, Syria, and Egypt until the early sixteenth century at the very least. Beyond the texts mentioned there, commentaries on ancient texts include Hippocrates’ Prognostics, Epidemics, and On the Nature of Man (Savage-Smith 2011,  18,  31). One of the authors of such commentaries was al-Dakhwar, the Ayyubid physician in Damascus discussed in Chapters Four and Five. One of his students wrote

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the copy today extant at the Bodleian Library (ibid., 29–30). Ibn al-Nafis, the author of other such commentaries, may also have written them for his classes. A  marginal note in a copy of an eleventh-century commentary on Hunayn b. Ishaq’s Problems of Medicine for Students (already discussed in Chapter Five) shows that one of its readers was familiar with the Synopses of the Alexandrinians (or: The Alexandrian Epitomes), a teaching collection of Galenic medical texts from Alexandria (ibid., 146; see also Walbridge 2014). This is not surprising, since the Synopses are documented in other commentaries on Hunayn’s text as teaching material, too (ibid., 147). Another note in the commentary on Hunayn’s treatise is an ijaza (teaching licence) given by a thirteenth-century physician from Damascus, thus confirming the use of this commentary in the training of a student (Savage-Smith 1996, 942). Other texts used in addition to the cluster around Ibn Sina’s Canon and the translations of ancient texts by Hippocrates, Galen, and occasionally also Rufus of Ephesos and Paulus of Aegina, came from the classical period of Islamicate societies. They include works by Hunayn b. Ishaq, Thabit b. Qurra, ʿAli b.  ʿAbbas al-Majusi, Abu Bakr al-Razi, Abu Sahl al-Masihi, Ibn Tilmidh, and other physicians (see, for instance, for Cairo al-Sakhawi n.d., vol. 6, 284–85, 323; vol. 7, 6; 7, 273; vol. 8, 150). The geographical and temporal distribution of these texts seems to have differed. But this judgment is based on a study of a few manuscript catalogues from Europe, India, and Iran and is thus to be used with caution. Notes or ownership marks in copies of those texts indicate that the prescriptions of market inspectors of the Ayyubid dynasty, mentioned in Chapter Five, were not always considered binding. Perhaps in 1390, a person who had moved from the Arabian Peninsula to Nablus copied Abu Bakr al-Razi’s Book for al-Mansur for his own use. One of his relatives added two recipes to it after reading this copy. This relative was a surgeon (Savage-Smith 2011, 157–58). Surgeons were not required to study such higher-level works on human medicine. Another reader in the Mamluk state studied al-Razi’s work in c.  1478, although without adding whether he did so alone or with a teacher (ibid., 160). A further argument for the role of the medical texts preserved at the Bodleian Library as study material is the fact that many of them were copied by practicing physicians or other medical practitioners. A  comparison with other manuscript holdings will show whether this is a typical feature of medical manuscripts or the

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accidental result of the access of seventeenth-century English, Dutch, or German buyers of Arabic and other manuscripts to such works. Generally, madrasa students also read medical and other texts by Muslim, Christian, Jewish, and polytheistic authors. This applies also to Ayyubid Damascus and Mamluk Cairo despite the polemical discourse of physicians such as al-Dakhwar and sultans such as Qalawun. Among the medical literature studied at madrasas in Cairo in addition to ancient authors, were, for instance, texts by Ibn Jazla (died in 1100), Muhammad b. ʿAbd al-Latif al-Khujandi (d. 1157), Najib al-Din al-Samarkandi (died in 1222), Ibn al-Baytar, and ʿAfif al-Din Abu Saʿid al-Isra’ili (fifteenth century) (al-Sakhawi n.d., vol. 6, 285; vol. 7, 7; vol. 9, 150; vol. 10, 128). A student who learned five of these texts by heart and, if alSakhawi did not make a mistake here, surprisingly also his own medical treatise on symptoms and causes, was the Hanbali jurist and ­practicing physician Kamal al-Din Muhammad b. Muhammad, called Ibn Saghir (died in 1486) of Cairo (ibid., vol. 9, 150). Manuscript collections document an interest in a broader scale of ancient works than mentioned in biographical dictionaries. This generally applies to all disciplines discussed in this book. The problem with many manuscripts, however, is that they often betray no traces of their contexts of production, distribution, usage, or even time. Unless they were signed or stamped by a well-known teacher, bear signed marginal notes, or refer to a madrasa or another teaching context, it is difficult to decide whether they were produced as replacements for worm-eaten or water-stained previous exemplars or indeed used for teaching or at least for autodidactic learning. Examples are the Galenic works in Arabic as well as treatises attributed to Galen that are found in the Bodleian Library. None of them bear information about their use as textbooks or as sources for private learning (Savage-Smith 2011, 72–114). Nonetheless, the existence of a broader range of texts dated to later centuries allows one to assume that there was some literature that was read in addition to and beyond classroom work. Perhaps manuscripts with marginal notes beyond simple textual corrections belonged to the phase of discipleship. This teaching tradition, combined with the focus summarized above on Ibn Sina’s Canon and numerous compendia, epitomes, commentaries, and supercommentaries, continued in a similar manner in the Ottoman Empire, but with some modification. For instance, t­ reatises

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by or ascribed to Galen seem to have attracted less attention than in other, earlier Turkic societies (İzgi 1997, vol.  2,  44–63,  68–70). As in other Islamicate societies, several books by Abu Bakr al-Razi were part of the teaching program. In the Ottoman Empire, they were studied at least until the seventeenth century (ibid., 66–68). The translation of scientific works into Ottoman Turkish can be regarded as an indication of interest in specific works, although this does not always have to signify their use in classroom work. Rarely studied and historiographically undervalued translations of Arabic and Persian scientific texts into Ottoman Turkish were undertaken in impressive quantity. Medical books are well represented in this cross-cultural enterprise. Classical authors of such translated works are, for instance, ʿAli b.  ʿAbbas al-Majusi, Abu Bakr al-Razi, Abu Sahl al-Masihi, Ibn Sina, Zayn al-Din al-Jurjani, and other important authors, like the Andalusian doctor and author of a famous book on anatomy Abu l-Qasim al-Zahrawi (died in 1036) or the Christian physician Ibn Jazla (ibid., 46–48,  57,  64–66,  68,  70,  74,  77,  79). But not only classical works were included in this translation enterprise. Important pharmacological and medical books by authors of later centuries were also transferred into Ottoman Turkish. One example is the widely copied materia medica of the Andalusian author Ibn al-Baytar, who, after travelling through North Africa, Anatolia, and Syria, settled in Ayyubid Cairo. Another example is the Memoir on the Science of Medicine by the physician Da’ud b.  ʿUmar (died in 1599), who had come to Ottoman Cairo from Antioch (ibid., 63–66). Before the process of translation into Ottoman Turkish had started, a small number of Arabic medical books were also translated into Persian. Their addressees were mostly Ottoman rulers (ibid., 46–47, 75). Occasionally, manuscripts contain reports about individual learning activities. Once collected, they may correct and modify the picture, which I tried to paint here on the basis of biographical dictionaries and manuscript catalogues. One example of such a personal account is found in a manuscript of the Bodleian Library’s Thurston Collection. William Thurston was a merchant of London, who wrote reports to the East India Company together with other merchants in 1640 from Basra and in 1645/6 from Agra (Baladouni-Makepeace 1998, 38–39, 42). But only five of the manuscripts bearing his name

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today were actually given by him to the library. The origin of the other forty manuscripts of the Thurston Collection is unknown (SavageSmith 2011, 11, 31). One of the manuscripts of unclear origin is ms. Thurston 10. It contains an eleventh-century commentary on the Aphorisms attributed to Hippocrates. The medical practitioner Nasir al-Din Muhammad b.  Ibrahim, known as Ibn al-Turays (died after 1359 or 1458/9 [?]), called both this treatise and a text (probably his commentary on Hippocrates’ Prognostics) by the Ayyubid doctor alDakhwar (whom we met in Chapters Four and Five) “the most noble books of the medical arts” (ibid., 10). He also informs us that he studied further books, among them another text by an eleventh-century author and The Book of Causes and Symptoms by Najib al-Din Samarkandi, a physician from Samarkand mentioned earlier in this chapter. Najib alDin lived until 1222 in Herat, when he died as a result of the Mongol conquest of the city. The commentaries and abbreviations of several ancient medical works held by the Bodleian Library at Oxford contain ownership entries and other notes which document the circulation of these manuscripts among Christian physicians and clerics of northern Syria, Lebanon, and southern Anatolia during the fifteenth and sixteenth centuries (ibid., 11, 14, 31). Another manuscript, this time a copy of Ibn al-Nafis’ Commentary on Hippocrates’ Aphorisms, contains a note from a Melchite Christian (a member of the Greek Orthodox Church) called Yusuf b. Jurjis (died in 1656?) who stated in April or May 1637 that he had studied this commentary. After Yusuf ’s death, Niqula b. Yusuf, possibly Yusuf ’s son, became the new owner of the manuscript (ibid., 22–23). Christian physicians did not only acquire Arabic commentaries and abbreviations of ancient medical texts. They also copied or bought medical texts composed by Christian, Jewish, and Muslim authors since the Abbasid dynasty. Hunayn b. Ishaq’s Problems of Medicine for Students, for instance, went through the hands of two Christian physicians in the sixteenth and early seventeenth centuries (ibid., 139). A commentary on this work by an eleventh-century author and another one by Ibn Tilmidh (see Chapter Five) were also transmitted in Christian families (ibid., 146, 149). Jewish physicians also learned their profession for many centuries through such Arabic texts written either in Arabic or in Hebrew letters.

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8.6. Logic and Natural Philosophy Logic was early integrated into the study of religious disciplines. Ibn Khaldun ascribes an important role in this process to Abu Hamid alGhazali (Ibn Khaldun 1958, vol. 3, 52). But the turn to the tools of logic seems to have begun before him. Although sharp-tongued opponents repeatedly wrote against logic, this discipline became well established in the educational activities at madrasas, mosques, and in private study circles in many Islamicate societies between al-Andalus and India. Due to these voices, modern historians and scholars of Islam of the twentieth century believed that logic had only a marginal impact on the intellectual histories of Islamicate societies. Even more severe were the judgments of modern scholars in the case of philosophy. They did not only see it as a widely stigmatized and marginalized field of knowledge, but as an area that completely disappeared after the death of Ibn Rushd in 1198. Only in the last few decades have opinions begun to change. The study of Aristotelian natural philosophy among some groups of religious scholars already occurred during the second half of the ninth and the tenth centuries. Some brief statements in letters from the eighth century show that individual religious scholars read the ancient philosopher even then. As summarily described in Chapters Four and Six, there were multiple reasons for the inclusion of philosophical concepts, methods, entire doctrines, arguments, and questions into the discipline of kalam and the two disciplines of the foundations of matters of faith and law across time and space. These processes of adoption and adaptation took place in different formats in various Islamicate societies, some of which are better researched than others. As I have argued in Chapter Four, the material presented by the Mamluk scholar Shams al-Din al-Sakhawi shows that philosophical literature and themes were part of the educational activities in Cairo and other Mamluk cities of his time, even if he did not name very many specific texts. Among those he named were standard texts also read in Islamicate societies east of the Mamluk state, such as Ibn Sina’s philosophical encyclopaedias or Nasir al-Din Tusi’s commentary on Ibn Sina’s Pointers and Reminders (al-Sakhawi n.d., vol. 2, 196). Al-Sakhawi’s dictionary also confirms the

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study of philosophy with madrasa teachers in North African cities of the fifteenth century. Ibn al-Akfani’s and Ibn Khaldun’s books leave no doubt that each of the two authors was familiar with philosophical literature and major topics. The presence of philosophical studies is also well attested for Iran and Central Asia after the death of Ibn Rushd. More recent research by Ahmed and el-Rouayheb indicates the presence of philosophical or logical studies in Mughal India and the Ottoman Empire (Ahmed 2013; el-Rouayheb 2015). From the early ninth to the early eleventh centuries, the main teaching material for learning about natural philosophy and logic was taken from translations of Greek or Syriac texts by Aristotle and his ancient commentators and critics. This at least is the impression that Abu Nasr alFarabi’s description of his years of study with Christian philosophers in Baghdad creates. The accounts of Buyid scholars and Abu Sahl al-Masihi’s classification of the sciences support this interpretation. Ibn Sina’s autobiography adds al-Farabi’s Metaphysics as a key text for accessing Aristotle’s work. Al-Kindi’s and Thabit b.  Qurra’s epistles, letters, and paraphrases document their reading of Aristotle’s Physics, Meteorology, On the Heavens, On Generation and Corruption, and other Aristotelian texts. Whether they also taught them as a whole, is difficult to evaluate. But they certainly taught ideas, questions, concepts, and methods taken from these works. Aristotle’s natural philosophical works never disappeared completely from the book market and libraries in different Islamicate societies. They were studied in the twelfth century in al-Andalus and Baghdad, in the thirteenth century in Damascus, and in the seventeenth century in Isfahan. For the twelfth and early thirteenth centuries, the early period of scientific studies at madrasas, it is difficult to extract concrete titles from the standard biographical sources used for this book. It is obvious that numerous physicians and astrologers in Iraq, Syria, and Egypt were deeply immersed in philosophical reading and that some of them also read logic. Names of teachers are provided, but titles of the texts ­studied remain the exception. Such exceptions are for instance found with regard to Fakhr al-Din al-Maridini, Kamal al-Din b.  Yunus, and ʿAbd alLatif al-Baghdadi. Fakhr al-Din studied philosophy with the ­physician Najm al-Din Ahmad b.  al-Sari, who is often portrayed as a scholar of the ­mathematical sciences only. He read with Ibn al-Tilmidh the

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chapter on logic of The Book of Salvation, an epitome of Ibn Sina’s Book of Healing produced by his student ʿAbd al-Wahid al-Juzjani. This epitome is characterized by Ibn Abi Usaybiʿa as having been of middle length (Ibn Abi Usaybiʿa 1965,  356). Kamal al-Din b.  Yunus wrote his own synopsis of philosophy, which he taught to his students (ibid., 365–66). ʿAbd al-Latif al-Baghdadi was a grammarian, jurist, philosopher, hadith and kalam scholar, and physician from Baghdad, who travelled widely in search of a good teacher of philosophy in Iraq, Syria, and Egypt, and in search of patronage in Anatolia. He taught public sessions on medicine and other topics in Jerusalem, Damascus, and Cairo. He complained bitterly about the dominance of Ibn Sina’s works among those interested in philosophy, while he himself wished to return to Aristotle’s and Plato’s books in Arabic translation and their interpretation by al-Kindi and al-Farabi. Ibn al-Akfani and Shams al-Din al-Sakhawi do not provide much information about teaching texts for the study of natural philosophy. Although Ibn al-Akfani points to the Aristotelian corpus and in a general manner to Ibn Sina’s oeuvre, his formulations sound – as in many other cases – rather like copies from earlier books, perhaps from one of the Ayyubid or early Mamluk biographical dictionaries, than like a description of Mamluk learning and teaching realities (Ibn al-Akfani 1989, 45–46). For logic, the situation differs. Ibn al-Akfani again points – with some error – to Aristotle’s writing. But he also discusses some of the relevant texts by classical authors such as al-Farabi and Ibn Rushd and provides titles for his standard classification of short, middle, and extended works. These three classes encompass exclusively works by scholars of the twelfth and thirteenth centuries. He names Najm al-Din al-Katibi (introduced in Chapter Four), Siraj al-Din al-Urmavi (introduced in Chapter Five), Shams al-Din al-Samarkandi (introduced in Chapter Five), and Nasir alDin al-Tusi as authors of epitomes. The titles of books of middle length again come from leading scholars who worked in Ilkhanid Iran and Ayyubid Syria and Egypt: Najm al-Din al-Katibi, al-Afdal al-Khunaji (introduced in Chapter Four), and Ibn Wasil (1208–1298). The latter was a well-known scholar of the mathematical sciences, logic, and history. Like al-Urmavi, he served the Ayyubid rulers as ambassador to the Hohenstaufen kings of Sicily, chosen in particular for his scientific and philosophical knowledge.

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While works by al-Katibi and al-Khunaji were indeed used as teaching texts in Iran, Syria, Egypt, Anatolia, or North Africa, I have not come across evidence for the specific titles given by Ibn al-Akfani as school texts nor for Ibn Wasil’s writings on logic. But since the Mamluk physician mentions for the titles by Najm al-Din al-Katibi and al-Afdal al-Khunaji an extended commentary (al-Katibi) and glosses (al-Khunaji), these two texts certainly moved in the scholastic sphere of learning and teaching. Perhaps the most creative of these writers of textbooks on logic was alKhunaji, who took Ibn Sina’s positions on this discipline as his starting point, but visibly went beyond him by introducing new questions and problems, thus setting “the agenda for most other thirteenth- and fourteenth-century works in logic” (Schmidtke 2013, 204–05; for some of al-Khunaji’s innovations see el-Rouayheb 2009). Among the extended books on logic, Ibn al-Akfani names Ibn Sina’s books on logic from his Book of Healing and The Great Logic by Fakhr alDin al-Razi. He emphasizes that texts on logic often appear in volumes united with natural philosophy and “divine science” (metaphysics). Since in his classification, logic precedes the philosophical disciplines, he points to these comprehensive manuals in this section. The titles he names now clarify the coexistence of Islamic peripatic philosophy, mainly provided by texts dealing with Ibn Sina’s philosophical teachings, Shihab al-Din Suhrawardi’s illuminist philosophy of a more strongly Platonist bend, and “philosophical theology”, here represented by a major work of Fakhr al-Din al-Razi (Ibn al-Akfani 1989, 27–29; Endreß 2001, 11 and passim). This is one of the many indicators for the amalgamation of logic as well as of parts of philosophy with the rational religious disciplines, a process that Endress called the emergence of a “school philosophy” and – adapting Klein-Franke – the transformation of the religious disciplines into sciences through the application of philosophy (ibid., 11). The authors named by Ibn al-Akfani represent most of the leading participants in the philosophical debates of the twelfth and thirteenth centuries and their scholastic codification: Abu l-Barakat al-Baghdadi, Fakhr al-Din al-Razi, Siraj al-Din al-Urmavi, Nasir al-Din al-Tusi, Athir al-Din al-Abhari, the Jewish philosopher Ibn Kammuna, and Najm al-Din al-Katibi (Ibn al-Akfani 1989, Arabic text, 29). Even if not all of their works were regularly taught at madrasas and mosques or studied privately, Ibn al-Akfani shows himself in tune with contemporary intellectual life without covering all major authors.

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The study of logic shortly before and during Ibn al-Akfani’s lifetime also followed other authorities. Among the authors that were studied most we find in addition to Ibn Sina, the tenth-century philosopher alFarabi, a student of Fakhr al-Din al-Razi, and the scholar of kalam and jurist ʿAllama al-Hilli (died in 1325), who had studied in Maragha the mathematical sciences and Ibn Sina’s philosophy with Nasir al-Din alTusi and logic with Najm al-Din al-Katibi. One of al-Hilli’s students was Qutb al-Din al-Razi, whose commentary on al-Katibi’s handbook on logic became very popular in the following period (ibid.). Shams al-Din al-Sakhawi’s depiction of the teaching literature in philosophy and logic one century later does not differ greatly from that given by Ibn al-Akfani. He repeatedly mentions that teachers of the religious rational sciences, like al-Kafiyaji, as well as those who taught the mathematical sciences in addition to law, like Ibn al-Majdi, taught philosophy, called either falsafa or hikma. But he does not list specific titles used in their classes. In contrast, he provides a clear range of books on logic that were studied and taught in Cairo and other cities: Ibn Sina’s logical epistles; Athir al-Din al-Abhari’s Introduction to Logic modelled on Porphyry’s Introduction to the Categories; Siraj al-Din al-Urmavi’s The Rising Times of the Light, a substantial manual; Najm al-Din al-Katibi’s epistle Shamsiyya on the Rules of Logic and commentaries or glosses on it by Qutb al-Din al-Razi, al-Sayyid al-Sharif al-Jurjani, Saʿd al-Din al-Taftazani, and others together with supercommentaries on the texts of these later authors; and al-Taftazani’s Embracement of Logic and Kalam (al-Sakhawi n.d., vol. 6, 7, 15, 82, 187, 190, 262; vol. 7, 7, 58, 113, 116 and passim). These texts were also studied in the Jewish communities of Cairo and probably of Damascus and Aleppo, as the example of David b. Joshua Maimonides (flourished c. 1335–1410), the leader of the Cairene Jewish community and descendant of Maimonides, demonstrates (Schmidtke 2013). Despite some variations, the logical works mentioned by al-Sakhawi seem to have been the minimal number of canonical school texts during the fourteenth and fifteenth centuries in the educational centres of Egypt, Syria, the Arabian Peninsula, Iran, and Central Asia. Due to the travels of students from Anatolia to acquire advanced education in Cairo and to a lesser degree in Iran, and the migration of mainly Iranian scholars to various Turkic principalities in that region during these two centuries, these texts were also incorporated in the developing madrasa system of the small Turkic states and the rising Ottoman Empire, which swallowed them.

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Other texts on logic, introduced by Iranian migrants to Damascus and Cairo, were also named more than once in the biographical sources as teaching literature. They were chapters in a genre of works that seems to have risen to prominence as a result of the various processes of integrating different kinds of knowledge with each other. This development was supported by the multidisciplinarity fostered and demanded by the legal and structural set-up of the madrasas as institutions primarily devoted to legal teaching. Works that dedicated their chapters to more than one discipline were often described as bringing together or uniting knowledge (jamʿ). An example is Afdal al-Din al-Khunaji’s combination of law with logic, arithmetic, and inheritance arithmetic. This text, called The Summa, was taught in Cairo and Damascus, but also moved into the schools of North Africa, for instance in Tunis and Tlemcen, and Anatolia (el-Rouayheb 2015, 137–38). Although no systematic survey of the texts used for teaching is available yet for this long timespan and huge territory, some general positions are shared among most current scholars of intellectual history in Islamicate societies. Ibn Sina’s philosophical encyclopaedias The Book of Healing, The Book of Salvation, and Pointers and Reminders, plus several of his shorter works like The Parts of the Rational Sciences or The Definitions, shaped philosophical learning and teaching in many Islamicate societies. Important carriers of this bulk of knowledge were his own students and their students’ students, followed by Fakhr al-Din al-Razi and his students, and Nasir al-Din al-Tusi and some of his colleagues and students. All of these texts contained chapters or statements on logic as well as natural philosophical themes. Another group of texts that was widely used for learning and teaching about philosophy were the philosophical manuals of the thirteenth century, above all the already repeatedly mentioned textbooks by Athir al-Din al-Abhari and Najm al-Din al-Katibi. Encyclopaedic literature like the works discussed in Chapter Seven also often presented natural philosophy among their disciplines. The same applies to various kinds of texts that deal with the division and order of the knowledge system. Although apparently only a few such encyclopaedias were studied at madrasas or mosques, the classification literature was well known among madrasa scholars. Extant manuscripts confirm the use of such texts for teaching.

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A major “explosion” of philosophical teaching occurred, as already shown in Chapter Four, after the middle of the fifteenth century, but in particular during the late sixteenth and all of the seventeenth centuries. Two different “returns to the sources” took place, one in Shiraz – to Ibn Sina’s Book of Healing – and the other in Isfahan – primarily to Aristotle, Alexander of Aphrodisias, Proclus, al-Kindi, al-Farabi, Ibn Bajja, and Ibn Rushd, mostly focusing on metaphysics and psychology. The collections of philosophical “libraries” in one-volume-manuscripts define one of the literary and teaching trends of this period. Endress analyzed two such collections (Endreß 2001). But their content is too rich to be presented here in detail. Suffice it to say that natural philosophy is present in both collections. Regrettably, modern researchers rarely analyze late treatises on natural philosophy. A different kind of a library in one volume was produced for the Safavid shahs of the second half of the seventeenth century at the command of their grand viziers. A further copy was made for the Safavid governor of Azerbayjan. The library’s texts combine all fields of knowledge from Shiʿi law, kalam, and doctrine through metrics, grammar, philosophy, medicine, astrology, geography, and the standard mathematical sciences geometry, planetary theory, and arithmetic. But they also include branches like optics, magic squares, mechanics, d­ irections of prayer, and different kinds of divination. Furthermore, the collection offers texts on natural philosophy, number theory, music, and literature (prose and poetry). Altogether, the table of content comprises 152 titles of more or less brief entries. The three known manuscripts of this library are richly illustrated with tables, dia­ grams, constellations, colours, calligraphy, and beautiful title decorations. Their appearance is worthy of a courtly library. The library’s natural philosophical content is visualized in tables on the four elements, qualities, and other fourfold relationships, diagrams on the eye and vision where medicine and natural philosophy overlap, and short texts about the movements of bodies and the structure of the universe, where astronomy and natural philosophy connect. Some important scholars whose texts are included in this collection in an abbreviated form or who are mentioned in it are Pythagoras, Plato, Aristotle, Hippocrates, Euclid, Ptolemy, al-Farabi, Ibn Sina, Fakhr al-Din Razi, Nasir al-Din al-Tusi, and Qutb al-Din al-Shirazi. The collection reflects the intellectual trends among madrasa scholars

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during the seventeenth century, but the content of its texts and tables is elementary and didactic. The shahs and their governor will not have been able to compete with their madrasa scholars in an evening meeting. But at least they learned the rudiments of each of the disciplines, as well as the names of their most famous authors or texts (ms. Cambridge Mass., Harvard University, Sackler Museum 1984.463). 8.7. Postface With this chapter the journey through a millennium of learning and teaching the sciences in Islamicate societies has come to an end. It was an erratic process, broken by many gaps and interrupted by too many questions I could not answer or perhaps not even ask. But I hope that some major features of the forms in and through which learning and teaching occurred in the sciences have become clear – private learning through tutors, madrasa learning, autodidactic training, hospital education, family teaching, travelling for the sake of learning, and various forms and methods of classroom work and teaching literature. Many foreign names of people and books were presented, while the knowledge that was offered and acquired could only be summarized, and contexts could be touched upon only in passing. I hope that the tables and maps will help readers to navigate in these strange and foreign educational territories.

APPENDICES

Table 1: Islamicate Dynasties Prominently Mentioned in this Book Name

Time

Region/s

Centres

Umayyad caliphs

661–750

Iberian Peninsula to Khurasan

Damascus, Harran

Abbasid caliphs

750–1258

North Africa to Central Asia

Baghdad, Samarra

Samanid amirs

819–1005

Central Asia, parts of Iran

Bukhara, Samarkand

Fatimid caliphs

909–1171

North Africa to Syria and Yemen

Mahdiyya, Cairo

Buyid amirs

932–1062

Iran, Iraq

Shiraz, Rayy, Isfahan, Baghdad

Ghaznavid sultans

977–1186

eastern Iran, Afghanistan

Ghazna, Lahore

Great Saljuq sultans

1034–1194

Central Asia, Iran, Iraq, Anatolia and Syria

Merv, Isfahan

Ayyubid maliks

1171–1260

Egypt, Syria, Yemen

Cairo, Damascus, Aleppo, Hama

Mongol Ilkhans

1256–1335

Iran, Iraq, Anatolia

Maragha, Tabriz, Sultaniyya

Mamluk sultans

1260–1517

Egypt, Syria, Hijaz, Yemen, Cilicia

Cairo, Damascus

Ottoman padishahs

c. 1290–1922

Anatolia, Aegean islands, Greece, Thrace, the Balkans, Syria, Egypt, Hijaz, Iraq, Podolia, etc.

Bursa, Edirne, Istanbul

Timurid sultans

1370–1505

Central Asia, parts of Iran, Afghanistan

Samarkand, Herat, Shiraz, Isfahan

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Qara Qoyunlu (Black Sheep) Confederation

1375–1486

Azerbayjan, Armenia, Iraq

Tabriz

Aq Qoyunlu (White Sheep) Confederation

1378–1508

Azerbayjan, eastern Anatolia, northern Iraq, western Iran, later also northeastern Iran

Diyar Bakr, Tabriz

Safavid shahs

c. 1501–1722

Iran

Tabriz, Qazvin, Isfahan

Mughal padishahs

1526–1540, 1555– 1857

Afghanistan, Pakistan, northern to central India

Delhi, Agra, Lahore, Fatihpur Sikri, Shahjahanabad

Table 2: Ancient Scholars Name

Time

Location/s

Alexander

flourished c. 200 Aphrodisias

philosophy

Apollonius

lived from c. 262-c. 190 bce

geometry

Pergamon

Disciplines

Archimedes

died in 212 bce

Syracuse

geometry, mechanics

Aristarchus

flourished from c. 310-c. 230 bce

Samos

astronomy

Aristotle

lived c. 384–22 bce

Stagira, Athens, Lesbos, Macedonia, Euboea

philosophy

Autolycus

lived c. 360c. 290 bce

Pitane

geometry

Dioscorides

first century

Asia Minor, Rome

pharmacology

Dorotheus

first century

Alexandria (?), Sidon (?)

astrology

Euclid

third century bce

Alexandria

geometry, number theory, astronomy, optics, ­mechanics

APPENDICES

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Eutocius

lived c. 480–540 Ascalon

geometry

Galen

lived c. 129–200 Pergamon, Rome or 215

medicine, logic, philosophy

Heron

first century (?)

Alexandria

mechanics, geometry

Hippocrates

lived c. 460c. 370 bce

Kos

medicine

Hypsicles

lived c. 190c. 120 bce

Alexandria

geometry, astronomy

Menelaus

first century

Alexandria

geometry, astronomy, mechanics

Nicomachus

second century

Gerasa

number theory, philosophy, numerology

Pappus

second half fourth century

Alexandria

geometry, astronomy, mechanics

Paulus

died in c. 690

Aegina

medicine

Philoponos, John

490–570

Alexandria

philosophy

Plato

died in 348/7 bce

Athens

philosophy

Polemon

died c. 270/69 bce

Athens

philosophy, philology, theology

Porphyry

died between 301–05

Tyrus, Rome

logic, philosophy, astrology

Proclus

412–85

Athens

philosophy

Ptolemy

second century

Alexandria

astronomy, astrology, natural philosophy, geography

Pythagoras

6th century bce

Samos, southern Italy

religion

Rufus

died before 140

Ephesus

medicine

Theodosius

lived from c. 160-c. 100 bce

Bithynia

geometry, astronomy, geography

Theon

lived from c. 335-c. 405

Alexandria

geometry, astronomy

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Table 3: Scholars from Islamicate Societies Name

Time

Location/s Disciplines

Dynasties

al-Abhari, Athir al-Din

died in 1265 Irbil, Mosul, Baghdad, Sivas, Shabestar

philosophy, logic, mathematical sciences, kalam

Artuqid (ruled 1098–1408), Atabegs of Irbil (ruled 1132–1232), Ilkhanid, Rum Saljuq (ruled 1077–1307)

Abraham ben Maimonides

1186–1237

Cairo, Damascus

medicine, Jewish religious disciplines

Mamluk

Abu Maʿshar

died in 886

Merv, Baghdad

hadith, astrology, mathematical sciences, natural philosophy

Abbasid

Abu l-Wafa’

948–98

Buzjan, Baghdad

mathematical sciences

Buyid

Ahmad b. Ibrahim

fifteenth century

Aleppo, Safad

astrology, calendars

Mamluk

Ahmad b. Khalil, Shihab al-Din

flourished c. second third fifteenth century

Cairo

medicine

Mamluk

Ahmad b. alSarraj

first half fourteenth century

Damascus

timekeeping, geometry, arithmetic, instruments

Mamluk

al-ʿAmili, Baha’ al-Din

1547– 1621/2

Jabal al-ʿAmil, Qazvin, Isfahan

law, Sufism, hadith, kalam, philosophy, mathematical sciences, medicine

Safavid

al-ʿAmiri, Abu l-Hasan

died in 992

Nishapur, Rayy, Baghdad, Bukhara

kalam, philosophy

Abbasid, Buyid

APPENDICES al-Amuli, Muhammad b. Mahmud

died in c. 1352

al-Ansari, ʿAli 1330–1403 b. Husayn

267

Amul, Sultaniyya, Shiraz

religious Ilkhanid, Inju sciences, history, (ruled c. 1325– encyclopaedia 1353)

Isfahan

medicine, pharmacy

Ilkhanid, Inju, Timurid

Arzani, Muhammad Akbar

died in 1722 India

religious disciMughal plines, medicine

al-ʿAsqalani, Ibn Hajar, Ahmad b. ʿAli

1372–1449

Cairo, Mecca, Zabid, Damascus, Jerusalem

law, hadith, history

al-Baghdadi, ʿAbd al-Latif

1163–1231

Baghdad, Damascus, Jerusalem

religious disciAbbasid, Ayyubid plines, grammar, philosophy

al-Baghdadi, died in Abu l-Barakat 1164/5

Balad, Baghdad

medicine, philo- Abbasid sophy

flourished al-Baghdadi, c. 1194 Muhammad b. ʿAbdallah b. al-Mahall (?)

Baghdad

arithmetic

Abbasid

Mamluk

Bahmanyar, Abu l-Hasan

died in 1066 Hamadan, Isfahan

philosophy, logic

Abbasid, Buyid

al-Balkhi, Abu Zayd

died in 932

Balkh, Baghdad

hadith, Qur’an exegesis, logic, philosophy, mapmaking

Abbasid, Saffarid (ruled 861–1003), Samanid

Banu Musa: Muhammad, Ahmad, alHasan

ninth century

Merv, Baghdad

mathematical sciences

Abbasid

Bar Hebraeus (= Bar ʿEbroyo)

1225/6– 1286

Malatya, Antioch, Maragha, Tabriz

Abbasid, ­Ilkhanid theology, bible exegesis, history, logic, philosophy, mathematical sciences, geography

Bar Shakko, Jacob Severus

died in 1241 Mar Mattai near Mosul or Tikrit, Mosul

theology, Syriac Abbasid grammar, logic, dialectics, philosophy

268

TEACHING AND LEARNING THE SCIENCES

al-Birjandi, ʿAbd al-ʿAli

died in 1527 Birjand, Qazvin, Istanbul

religious sciences, mathematical sciences

Safavid, Ottoman

al-Biruni, died after Abu l-Rayhan 1048

Kath, Gurgan, Rayy, Gurganj, Ghazna

Buyid, Ziyarid mathematical sciences, history, (ruled 931-c. 1090), astrology Ma’munid (ruled 995–1017), Ghaznavid

al-Bukhari, Shams al-Din

late ­thirteenth early fourteenth centuries

Tabriz

mathematical sciences

Ilkhanid

al-Dakhwar, Muhadhdhab al-Din ʿAbd al-Rahim b. ʿAli

1169/70– 1230/1

Damascus, Cairo

medicine

Ayyubid

al-Dashtaki, Sadr al-Din

1425–1498

Shiraz

philosophy, kalam, logic

Timurid

al-Dashtaki, Ghiyath alDin

1461/2– 1542

Shiraz

philosophy, kalam, logic, medicine, mathematical sciences, astrology

Timurid, Safavid

Da’ud b. ʿUmar

died in 1599 Antioch, Cairo

medicine, philosophy

Ottoman

al-Davani, Jalal al-Din

1426–1501

Kazirun, Shiraz, Tabriz

kalam, law, exegesis, logic, ethics, philosophy, mysticism

Timurid, Aq Koyunlu

David b. Joshua Maimonides

flourished c. 1335– 1410

Cairo

Jewish theology, Mamluk kalam, logic

al-Dunaysiri, ʿImad al-Din

1209–1287

Dunaysir, Damascus

medicine

Artuqid, Ayyubid, Mamluk

al-Dunaysiri, Shams al-Din

thirteenth century

Dunaysir

administration (?)

Artuqid

APPENDICES

269

al-Farabi, Abu died in Nasr c. 950

Rayy, Baghdad, Aleppo, Damascus

philosophy, mathematical sciences

Abbasid, Buyid, Hamdanid (ruled 890–1004)

al-Fattal, Ibrahim

seventeenth century

Damascus

philological sciences, logic

Ottoman

al-Farghani, Muhammad b. Kathir

died after 961

Baghdad

astronomy

Abbasid

al-Ghazali, Abu Hamid

1055–1111

Tus, Nishapur, Baghdad

religious disciplines, Sufism, logic, philosophy

Abbasid, Saljuq

al-Ghazuli, Muhammad b. Ahmad

died c. in 1454

Cairo

law, hadith, grammar, logic, semantics, rhetoric, philosophy

Mamluk

Gilani, Muhammad Tabib

sixteenth/ seventeenth centuries

Golconda

medicine

Qutb Shah (ruled 1518–1687)

al-Habashi, Bilal

fifteenth century

Aleppo

law, Sufism, alchemy

Mamluk

Habib b. Bahriz

late eighthearly ninth centuries

Harran, Mosul, Hazza, Baghdad

religious disciplines, translations, mathematical sciences

Abbasid

Hacı Paşa

died in c. 1425

Konya, Damascus, Cairo, Ayasuluk

medicine, logic, law, philosophy

Aydınid (ruled 1308–1426)

al-Hajjaj b. Yusuf b. Matar

flourished Baghdad between 786 and 833

mathematical sciences, translator; perhaps army pioneer

Abbasid

mathematical sciences

Zangid, Ayyubid

al-Harawi, ʿAli died in 1215 Mosul, b. Abi Bakr Aleppo

270

TEACHING AND LEARNING THE SCIENCES

al-Hassar, Abu Bakr Muhammad b. ʿAbdallah

twelfth century

al-Hilli, Najm al-Din ʿAlama

Sabta (?)

arithmetic, algebra, inheritance calculation

Almohad (ruled 1121–1269)

died in 1277 Hilla, Maragha

kalam, logic, philosophy

Abbasid, Ilkhanid

Hunayn b. Ishaq

died in 867

medicine, translator

Abbasid

Ibn Abi ­l-Bayan

died in 1236 Cairo

medicine

Ayyubid

Ibn Abi Hulayqa

1223–1308

Cairo

medicine

Ayyubid, Mamluk

Ibn Abi Sadiq died after 1068

Nishapur

medicine

Ghaznavid, Saljuq

Ibn Abi Usaybiʿa

1203–1270

Damascus, Cairo, al-Karak, Sarkhad

medicine, historian

Ayyubid, Mamluk

Ibn Aflah, Jabir

first half twelfth century

Seville (?)

astronomy, geometry, trigonometry

Almoravid (ruled 1040–1147)

Ibn al-Akfani

died in 1348 Sinjar, Cairo

Mamluk medicine, pharmacology, botany, religious sciences

Ibn ʿArabi, Muhyi l-Din

1165–1240

Sufism, mystic philosophy

Ayyubid

imam, alchemy

Almohad

philosophy, astronomy, medicine, music, poetry, logic, natural philosophy

Almoravid

al-Hira, Baghdad, Alexandria

Konya, Damascus

Ibn Arfaʿ Ra’s, died in 1197 Fez Abu l-Hasan (= al-Jayyani al-Andalusi) Ibn Bajja

died in 1138/9

Zaragossa, Seville, Fez

APPENDICES

271

Ibn al-Banna’

1256–1321

Marrakesh, Aghmat

law, inheritance Marinid (ruled 1244–1465) calculation, arithmetic, algebra, astronomy, astrology, Sufism

Ibn al-Baytar, Diya’ al-Din Abu Muhammad

1197–1248

Malaga, Marrakesh, Bejaia, Tunis, Tripoli, Barqa, Cairo, Damascus

medicine, pharmacy, botany

Almohad, Ayyubid

Ibn al-Bunduqi

flourished c. second third fifteenth century

Cairo

medicine

Mamluk

Ibn Fallus

died in 1239 Damascus, (?) Cairo

law, mathematical sciences, medicine

Ayyubid

Ibn Farighun

tenth century

Balkh (?)

administration

Ibn al-Fuwati

1244–1323

Baghdad, Maragha

history, librarian Ilkhanid

Ibn al-Ha’im

died in 1412 Cairo, Jerusalem

Ibn al-Haytham

died after 1040

Basra, Cairo mathematical Fatimid sciences, philosophy, kalam (?)

Ibn Hibinta

tenth century

Baghdad

Ibn al-ʿIraq, lived Kath, Abu Nasr c. 960–1036 Gurgan, Mansur b. ʿAli Gurganj, Ghazna

law, inheritance calculation, algebra, arithmetic

Mamluk

mathematical sciences, astrology

Abbasid

mathematical sciences

Afrighid (ruled ?-995), Ziyarid, Ma’munid, Ghaznavid

272

TEACHING AND LEARNING THE SCIENCES

Ibn al-Jamaʿa, 1348–1416 ʿIzz al-Din

Cairo

Mamluk law, hadith, kalam, Arabic, medicine, astrology, rhetoric, logic, divination, philosophy

Ibn Jazla, Abu died in 1100 Baghdad ʿAli

medicine

Abbasid

Ibn al-Lubudi, Najm al-Din

1210-after 1267

vizier,­ mathematical sciences

Ayyubid, Mamluk

Ibn Kammuna

died in 1284 Baghdad

Jewish religious thought, exegesis, logic, philosophy, natural philosophy

Ilkhanid

Ibn Khaldun

1332–1406

law, history, geomancy

Hafsid, Marinid, Mamluk

Ibn Mutran

died in 1191 Damascus

medicine

Fatimid, Zangid, Ayyubid

Ibn al-Majdi

1366–1447

Cairo

Mamluk law, philology, inheritance calculation, timekeeping, mathematical sciences, philosophy, astrology, divination

Ibn al-Nadim

died in 995 or 998

Baghdad

stationer, philosophy

Abbasid, Buyid

Ibn al-Nafis

1213–1288

Damascus, Cairo

medicine, religious sciences

Mamluk

Ibn al-Qifti

1172–1248

Qift, Aleppo

vizier, history

Ayyubid

Ibn al-Quff, Shams alDawla Abu l-Fadl b. Abi l-Hasan

1232–1286

al-Karak, Sarkhad, Cairo

medicine, surgery

Mamluk

Hims (today Homs), Aleppo

Tunis, Fes Cairo

APPENDICES

273

Ibn Rushd

died in 1198 Córdoba, Fes

law, medicine, philosophy, mathematical sciences

Almohad

Ibn Saghir family

eleventhfifteenth centuries

Cairo

medicine

Mamluk

Ibn Saghir, ʿAla’ al-Din ʿUmar b. Muhammad

died in 1462 Cairo

medicine

Mamluk

died in 1486 Cairo Ibn Saghir, Kamal al-Din Muhammad b. Muhammad

medicine, law

Mamluk

Ibn al-Sari, Najm al-Din Ahmad

died in 1154 Baghdad, Mosul, Damascus

medicine, mathematical sciences

Abbasid, Artuqid, Saljuq

Ibn Sina

died in 1037 Bukhara, Isfahan, Rayy, Hamadhan

philosophy, medicine

Samanid, Buyid

Ibn Taymiyya

1263–1328

Damascus

law, hadith, kalam

Mamluk

Ibn al-Tilmidh, Amin al-Dawla

1073–1165

Baghdad

medicine, pharmacy, poetry, calligraphy

Abbasid

Ibn Turka, Saʿin al-Din

lettrism, law, died in 1432 Isfahan, Samarkand, philosophy, Sufism Baghdad, Cairo, Yazd, Tabriz, Mazandaran, Natanz, Herat

Timurid

Ibn alUkhuwwa

died in 1329 Cairo

law, market inspector

Mamluk

Ibn Wasil

1208–1298

history, logic, mathematical sciences

Ayyubid

Damascus, Sarkhad

274

TEACHING AND LEARNING THE SCIENCES

Ibn al-Yasamin

died in 1204 Seville

poetry, law, ­mathematical sciences

Almohad

Ibn Yunus, Kamal al-Din

1226–1286

Mosul, Baghdad

law, kalam, logic, philosophy, music, mathematical sciences, Jewish and Christian scriptures

Atabegs of Mosul, Ayyubid, Mamluk

Gaza, Cairo

law, alchemy, astrology, botany, lettrism, Sufism

Mamluk

1339–1413 Ibn Zuqqaʿa (= Ibrahim b. Muhammad al-Nawfili) Ibrahim b. Hilal b. Ibrahim, Abu Ishaq

died in 994

Baghdad

history, administration, geometry, arithmetic

Abbasid, Buyid

Ibrahim b. Sinan b. Thabit b. Qurra

908–46

Baghdad

medicine, mathematical sciences

Abbasid, Buyid

al-ʿIji, ʿAdud al-Din

died in 1355 Shiraz

kalam

Inju

al-Isfahani, Shams al-Din

died in 1348 Mecca, Cairo

kalam, foundations of faith, logic, philosophy

Mamluk

Ishaq b. Hunayn

died in 911

Baghdad

medicine, translator

Abbasid

al-Isra’ili, ʿAfif fifteenth al-Din Abu century Saʿid

Cairo

medicine

Mamluk

Jabir b. Hayyan

Kufa (?)

alchemy, philosophy

Umayyad, Abbasid

eighth ­century (?)

APPENDICES

275

al-Jaghmini, first half Mahmud thirteenth b. Muhammad century

flourished in Khwarazm

medicine, astronomy

precisely where he lived is unknown; the region was ruled by two different Mongol dynasties

Jami, Nur al-Din ʿAbd al-Rahman

1412–1492

Jam, Herat, Samarkand

poetry, Sufism, philosophy, logic, mathematical sciences

Timurid

al-Jildaki, ʿIzz al-Din Aydamir

died in 1342 Jaldak near Mashhad, Damascus, Cairo

alchemy, magic, botany, mineralogy, medicine, natural philosophy

Ilkhanid, Mamluk

al-Jurjani, Zayn al-Din Ismaʿil b. alHusayn

1040–1136

Nishapur, Khwarazm, Merv

medicine, pharmacy, kalam, philosophy

Great Saljuq, Khwarazm Shah

al-Jurjani, al-Sayyid alSharif

1339–1413

Taju near Astarabad, Herat, Karaman, Damascus, Cairo, Gurgan, Shiraz, Samarkand

kalam, logic, philosophy, mathematical sciences, philology

Kart (ruled 1245– 1389), Karamanid (ruled 1250–1487), Mamluk, Muzaffarid (ruled 1314– 1393), Timurid

al-Juwayni, Sharaf al-Din

died in 1286 Baghdad

law, history

Ilkhanid

al-Juzjani, ʿAbd al-Wahid

died after 1037

al-Kafiyaji, Muhammad b. Sulayman al-Rumi

died in 1474 environment of Manisa, Cairo

Bukhara, philosophy, Gurgan, mathematical Rayy, Shiraz sciences foundations of faith and law, grammar, logic, conics, burning mirrors, spherics, astronomy, historiography, mysticism

Samanid, Buyid

Saruhan (Turkmen) dynasty (c. 1300– 1410), Mamluk

276

TEACHING AND LEARNING THE SCIENCES

al-Kashi, Ghiyath alDin Jamshid

died in 1429 Kashan, Isfahan, Samarkand

medicine, mathe­ Timurid matical sciences, astrology

al-Kaskari, Yaʿqub

first half tenth ­century

medicine, logic

Abbasid, Buyid

al-Katibi al-Qazvini, Najm al-Din

died in 1276 Qazvin, Juvayn, Maragha

logic, kalam, philosophy

Ilkhanid

timekeeping, astrology

Mamluk

Baghdad

mathematical sciences, natural philosophy

Abbasid, ­Ilkhanid

Khafri, Shams d. 1550 al-Din

Khafr (?), near Shiraz, Shiraz

religious, mathematical, and “occult” sciences

Safavid

al-Khalil b. Ahmad al-Farahidi

died in c. 786

Basra

grammar, lexicography

Abbasid

Khaydarabadi, Fadl-i Haqq

died in 1861 Hyderabad, Delhi

kalam, logic, philosophy

British Raj (1858–1947)

al-Khazin, Abu Jaʿfar

died Samarkand, between Rayy 961 and 971

mathematical sciences

Samanid, Buyid

al-Khazini, ʿAbd al-Rahman

died after 1125

Merv

mathematical sciences

Great Saljuq

al-Khujandi, Muhammad b. ʿAbd alLatif

died in 1157/8

Isfahan

medicine, law

Great Saljuq

Baghdad

al-Kawmrishi, died in 1335 Kawm alRish, Cairo Ahmad b. Ghulam Allah al-Khaddam, ʿImad al-Din, ʿAbdallah b. Muhammad

born in 1245

APPENDICES

277 Ayyubid

al-Khunaji (or: Khunji), Afdal al-Din

1194–1248

Khuna (?) near Zanjan, Cairo

foundations of faith and law, kalam, logic, philosophy, law, inheritance calculation

al-Khwarazmi, Muhammad b. Musa

first half ninth century

Baghdad

Abbasid algebra, arithmetic, surveying, geography, astronomy, astrology, inheritance calculation

al-Khwarazmi, Abu ʿAbdallah

died in 997

Yazd

administration

Samanid

al-Kindi, Abu Yusuf Yaʿqub b. Ishaq

c. 800-after 870

Basra, Baghdad

philosophy, mathematical sciences, astrology, divination, medicine, etc.

Abbasid

al-Kuhi, Abu Sahl Wijan b. Rustam

tenth century

Rayy, Baghdad (?)

mathematical sciences

Abbasid, Buyid

Kushyar b. Labban

tenth century

Rayy

mathematical sciences, astrology

Abbasid, Buyid

Kutami, ʿAbdallah b. Salih

late twelfth early thirteenth centuries

Marrakesh

pharmacy, herbalist

Almohad

al-Lawkari, Abu l-ʿAbbas Fadl b. Muhammad

died between 1109 and 1123

Lawkar (near Merv), Nishapur

philosophy

Saljuq

al-Majusi, died in 994 ʿAli b. ʿAbbas

Ahwaz, Baghdad

medicine

Abbasid, Buyid

al-Maghribi, Ibn Abi Shukr

Damascus, Maragha

astrology, ­mathematical sciences

Ayyubid, ­Ilkhanid

lived c. 1220– 1283

278

TEACHING AND LEARNING THE SCIENCES

Maimonides

died in 1204 Córdoba, Cairo

Almohad, medicine, philosophy, mathe- Ayyubid matical sciences, Jewish religious disciplines

al-Maqrizi, Taqi al-Din Ahmad b. ʿAli

1364–1442

Cairo, Damascus

law, hadith, history, geometry, astrolabe, divination, market inspector, imam

Mamluk

al-Marrakushi, Abu ʿAli Hasan

second half thirteenth century

Marrakesh (?), Cairo

mathematical sciences, instrument maker

Mamluk

al-Maridini, Fakhr al-Din

died in 1198 Mardin, Damascus

medicine, mathematical sciences, Sufism

Artuqid, ­Ayyubid

al-Masihi, Abu Sahl ʿIsa b. Yahya

died in 1012 Samarkand, Gurgan

medicine

Samanid, Ziyarid

Dayr Qunna, Baghdad

religious sciences, philosophy

Abbasid

Mevlevi, Ahmed b. Lütfüllah

died in 1702 Istanbul, Cairo, Mecca

astrology, astronomy, mathematical sciences, Sufism

Ottoman

Mir Damad, Muhammad Baqir Astarabadi

died in 1631/2

kalam, logic, philosophy, law

Safavid

Misri, Najm al-Din

flourished Cairo c. 1300–1350

timekeeping

Mamluk

al-Mubashshir b. Fatik, Abu l-Wafa’

eleventh century

Cairo, Damascus

belles-lettres, historian, studied mathematical sciences, medicine, philosophy

Fatimid

Muhammad Baqir b. Zayn al-ʿAbidin

died after 1637

Yazd, Isfahan

mathematical sciences, astrology

Safavid

Matta tenth cenb. Yunus, Abu tury Bishr

Gurgan, Mashhad, Isfahan, Najaf

APPENDICES

279

Muhammad b. ʿAbd alRahim, Abu l-Baqa’

fifteenth century

?

Arabic, arithme- Mamluk tic, law

Muhammad b. ʿAbd alWahhab

fifteenth century

Cairo

law, medicine

Mamluk

Muhammad b. Abi Bakr Muhammad

thirteenth century

Mosul

mathematical sciences, copyist

Zangid

Muhammad b. Ismaʿil, Abu l-Wafa’

born after1426

Cairo

medicine

Mamluk

al-Muhassin b. Ibrahim b. Thabit

died in 1010 Baghdad (?) mathematical sciences

Abbasid, Buyid

al-Muhibbi, Muhammad al-Amin

died in 1699 Damascus, Bursa, Istanbul

law, history, ­mathematical sciences

Ottoman

Mulla Niksari died in 1495 Kastamonu

mathematical sciences

Isfandiyarid, Ottoman

Mulla Sadra

died in 1640 Shiraz, Isfahan, Basra

kalam, law, philosophy, exegesis, mysticism

Safavid

Munla Sharif al-Kurdi

seventeenth century

kalam, “divine science”, logic

Ottoman

arithmetic

Mamluk

poetry, history, medicine, “general”, governor

Mughal

law, kalam, dialectics, logic, philosophy, algebra

Saljuq, Delhi sultans, Ilkhanid

Damascus

Najm al-Din b. al-Hajj Nami (pen-name; given name: Muhammad b. Masʿum)

second half sixteenth century

Bakhar, Quetta, Lahore (?)

al-Nasafi, Burhan alDin

born Nasaf, c. 1233, died Samarkand, after 1277 Delhi, Baghdad

280

TEACHING AND LEARNING THE SCIENCES

al-Nasawi, ʿAli b. Ahmad

died in c. 1075

Nasa (?), Rayy, Simnan

falconer, soldier, Buyid mathematical sciences, medicine, pharmacology, philosophy

Nasir al-Din Muhammad b. Ibrahim, known as Ibn al-Turays

died after 1359 or 1458/9 (?)

?

medicine

Mamluk

al-Nawa’i, Muhyi l-Din

1233–1277

Nawa, Damascus

law, hadith, kalam, history

Ayyubid, Mamluk

al-Nawbakhti, died in 923 Abu Sahl

Baghdad (?) kalam

Abbasid

al-Nayrizi, Abu l-ʿAbbas

died c. 922

Baghdad (?) astronomy, geometry

Abbasid

Niqula b. Yusuf

seventeenth century

?

medicine

Ottoman

al-Nisaburi, Nizam al-Din

died in 1328 Maragha or 1330

kalam, Qur’an exegesis, mathematical sciences

Ilkhanid

Nuʿaym b. Muhammad b. Musa

ninth century

geometry

Abbasid

al-Nuʿaymi, ʿAbd alQadir

died in 1521 Damascus

history

Mamluk, Ottoman

Philoxenus Nemrod (Patriarch Ignatius IV)

died in 1292 Maragha

theology, exegesis

Ilkhanid

Qadizade al-Rumi

died after 1440

Bursa, Samarkand

mathematical sciences, law, letter magic

Ottoman, Timurid

al-Qalasadi, ʿAli b. Muhammad

1412–1486

Basta, Tlemcen, Tunis, Cairo, Mecca, Almería, Granada

arithmetic, ­inheritance calculation, logic, astronomy

Nasrid, Marinid, Mamluk

Baghdad

APPENDICES Arles, ­Avignon, Salonica, Rome

281

translation, mathematical sciences, medicine

Qalonymus ben Qalonymus

1268-after 1328

al-Qushji, ʿAli

died in 1474 Samarkand, Kirman, Herat, Tabriz, Istanbul

kalam, mathematical sciences

Timurid, Aq Koyunlu, Ottoman

al-Rahbi, Radi al-Din

1140–1234

Damascus

medicine

Fatimid, Zangid, Ayyubid

Rajab b. Husayn

seventeenth century

Damascus

kalam, “divine science”

Ottoman

al-Razi, Abu Bakr

lived 865c. 925

Rayy, Baghdad

medicine, philosophy

Abbasid, Buyid

al-Razi, Fakhr died in 1210 Rayy, Gural-Din ganj, Herat, Firuzkuh

kalam, Qur’an exegesis, philology, philosophy, astrology, astronomy, alchemy (?), mineralogy, physiognomy

Great Saljuq, Khwarazmshah (ruled c. 1077– 1231), Ghurid (ruled before 879–1215)

al-Ruhawi, Ishaq b. ʿAli

died in the late 890s

Edessa

medicine

Abbasid

al-Rumi, Majd al-Din Ismaʿil

fifteenth century

Cairo

logic, semantics, rhetoric, philosophy

Mamluk

al-Sahrawi, Yahya b. Muhammad

1429-after 1465

Cairo

arithmetic, inheritance calculation, law

Mamluk

Saʿid b. ­al-Hasan

died in 1072

al-Sakhawi, Shams al-Din

1428–1497

Cairo, Damascus, Jerusalem, Mecca, Medina

religious sciences, historian, ­arithmetic

Mamluk

al-Salihi, Mahmud alBasir

seventeenth century

Damascus

mathematical sciences

Ottoman

medicine

282

TEACHING AND LEARNING THE SCIENCES

al-Samarkandi, Najib al-Din

died in 1222 Samarkand, Herat

medicine

al-Samarkandi, Shams al-Din

died in c. 1322

Samarkand

logic, kalam, mathematical sciences, disputation

Ilkhanid

Sanad b. ʿAli

ninth century

Baghdad

mathematical sciences, astrology

Abbasid

al-Sanusi, Muhammad b. Yusuf

1428–1490

Tlemcen

law, hadith, kalam, logic, mathematical sciences

Zayyanid (ruled 1235–1556)

al-Sarakhsi, Ahmad b. alTayyib

lived c. 833 Sarakhs, or 837–99, Baghdad when he was executed

mathematical Abbasid sciences, astrology, philosophy

Sayf al-Din al-Amidi

1156–1233

foundations of faith, law, logic, philosophy

Artuqid, Abbasid, Ayyubid

astrology, natural philosophy

Samanid

Shahrazur

kalam, philosophy, medicine, Sufism

Ilkhanid

Cairo

arithmetic, algebra, balances

Mamluk

?

geometry

Abbasid, Buyid

Amid, Baghdad, Hama, Cairo, Damascus

Rayy, KhuShahmardan flourished b. Abi l-Khayr second half rasan eleventh century-first third twelfth century al-Shahrazuri, Shams al-Din

died between 1288 and 1304

al-Shamuli, fifteenth ʿAbd al-Majid century (?) al-Shanni, Muhammad b. Ahmad, Abu ʿAbdallah

flourished in the last third tenth century

APPENDICES

283

al-Shayzari, Jalal al-Din

second half twelfth century

Aleppo

medicine, law

al-Shirazi, Qutb al-Din

1236–1311

Shiraz, Maragha, Tabriz, Sivas

Ilkhanid, Rummedicine, Saljuq (ruled mathematical sciences, philo- 1077–1308) sophy, hadith, Qur’an exegesis, Sufism

al-Shirvani, Fath Allah

1417–1486

law, philology, Shirvan, logic, mathemaTus, Samarkand, tical sciences Kastamonu, Istanbul, Mecca, Damascus, Cairo

Timurid, Isfandiyarid (ruled 1292–1461), Ottoman, Mamluk

Damascus, Cairo

timekeeping, arithmetic, inheritance calculation, algebra

Mamluk

administrator, mathematical sciences

Ottoman

Sistan, Baghdad

logic, philosophy, adab, history

Abbasid, Buyid, Saffarid

Sistan, Khurasan, Rayy (?)

geometry, astro- Abbasid, Buyid, nomy, astrology, other minor dynasgeography ties in Iran

1423–1501 Sibt alMaridini, Muhammad b. Muhammad Sidqi, Mustafa b. Salih

died in 1769 Istanbul

died in al-Sijisc. 1000 tani, Abu Sulayman, the Logician al-Sijzi, Ahmad b. Muhammad b. ʿAbd al-Jalil

tenth century

Simeon of Qalʿa Rumayta

died in 1289 Maragha, Tabriz

Sinan b. Thabit

Baghdad

Zangid, Ayyubid

medicine

Ilkhanid

medicine, mathematical sciences

Abbasid

284

TEACHING AND LEARNING THE SCIENCES

al-Sufi, ʿAbd al-Rahman

903–86

Rayy

mathematical sciences

Buyid

al-Suhrawardi, Shihab al-Din

1154-executed in 1191

Suhraward, Maragha, Isfahan, Baghdad, Anatolia, Aleppo

kalam, philosophy

Ayyubid

al-Taftazani, Saʿd al-Din

1322–1390

Taftazan, Samarkand

Timurid kalam, law, Qur’an exegesis, logic

al-Tahtani, Qutb al-Din al-Razi

died in 1365 Rayy, Amul, kalam, logic, Damascus philosophy

Ilkhanid, Mamluk

Taj al-Din son thirteenth of Simeon century

Maragha, Tabriz

medicine

Ilkhanid

Tashköprüzade, Ahmad b. Mustafa

1495–1561

Bursa, Istanbul

religious sciences, history

Ottoman

Thabit b. Qurra

died in 901

Kafartutha, Harran, Baghdad

mathematical sciences, medicine, philosophy, talismans, magic squares, Sabian religious knowledge

Abbasid

Thabit b. Sinan

died in 973/4

Baghdad

mathematical sciences, medicine

Abbasid, Buyid

al-Tusi, Nasir al-Din

1201–1274

Alamut, Maragha, Tabriz, Baghdad

Shiʿi law, kalam, Ismaʿili, Ilkhanid logic, philosophy, mathematical sciences, astrology, mineralogy, divination

Tus, Mosul, Aleppo

mathematical sciences, astrology

al-Tusi, Sharaf c. 1135– al-Din 1213/4

Saljuq, Zangid

APPENDICES

285

Ulugh Beg

1394–1449

Samarkand

Timurid prince, mathematical sciences, philosophy (?)

Timurid

al-ʿUrdi, Mu’ayyad al-Din

died in c. 1266

Damascus, Maragha

astrology, mathematical sciences, instrument maker

Ayyubid, ­Ilkhanid

thirteenth al-ʿUrdi, Shams al-Din, century Muhammad b. Mu’ayyad al-Din

Maragha

copyist, mathematical sciences

Ilkhanid

al-Urmavi, Siraj al-Din

1198–1283

Cairo, Konya

law, logic, philo- Ayyubid, Rum sophy Saljuq

Yahya b. ʿAdi

894–974

Baghdad

philosophy, theology

Abbasid, Buyid

Yuhanna b. Masawayh

died in 857

Gundishapur, Baghdad

medicine

Abbasid

Yusuf b. Jurjis

died in 1656 ? (?)

medicine

Ottoman

al-Zahrawi, Abu l-Qasim

died in 1036 al-Zahra, Córdoba

medicine

Umayyad, Ta’ifa (1031-1092)

286

TEACHING AND LEARNING THE SCIENCES

Table 4: Muslim Rulers Name

Time

Dynasty

Capital

al-Mansur

756–75

Abbasid

Baghdad

al-Mahdi

775–86

Abbasid

Baghdad

Harun al-Rashid

786–809

Abbasid

Baghdad

al-Ma’mun

813–33

Abbasid

Merv, Baghdad

al-Muʿtasim bi-Llah

833–42

Abbasid

Baghdad, Samarra

al-Mustaʿin bi-Llah, Ahmad

862–66

Abbasid

Samarra, Baghdad

al-Muʿtadid bi-Llah

892–902

Abbasid

Baghdad

al-Muqtadir bi-Llah

908–32

Abbasid

Baghdad

Rukn al-Dawla

935–76

Buyid

Rayy, Isfahan

ʿAdud al-Dawla

949–83

Buyid

Isfahan, Shiraz, Baghdad

Qabus b. Vushmgir

977–81, 997–1012

Ziyarid

Isfahan, Rayy, Gurgan

ʿAli b. Ma’mun

997–1009

Ma’munid

Gurganj

Abu l-ʿAbbas Ma’mun

1009–1017

Ma’munid

Gurganj

Abu l-Harith Muhammad b. ʿAli

1017

Ma’munid

Gurganj

Mahmud

997–1030

Ghaznavid

Ghazna

ʿAla’ al-Dawla Muhammad

1008–1044

Kakuyid

Yazd

Masʿud I

1030–1040

Ghaznavid

Ghazna

Muhammad

1098–1127

Khwarazmshah Gurgan

Alp Arslan

1063–1072

Saljuq

Merv

Malikshah

1072–1092

Saljuq

Isfahan

Nur al-Din Zangi

1146–1174

Zangid

Mosul, Aleppo, Damascus

Salah al-Din

1171–1193

Ayyubid

Damascus, Cairo

APPENDICES

287

ʿAla’ al-Din Tekesh

1172–1200

Khwarazmshah Gurganj

al-ʿAdil

1200–1218

Ayyubid

Damascus

al-Malik al-Kamil

1218–1238

Ayyubid

Cairo

al-Muʿazzam ʿIsa

1218–1227

Ayyubid

Damascus

al-Ashraf Musa

1229–1237

Ayyubid

Damascus

al-Mustansir bi-Llah

1226–1242

Abbasid

Baghdad

Nasir al-Din Yusuf

1250–1260

Ayyubid

Damascus, Aleppo

al-Mansur Sayf al-Din Qalawun

1279–1290

Mamluk

Cairo

Öljaytu

1304–1316

Ilkhanid

Tabriz

Abu Saʿid

1316–1335

Ilkhanid

Sultaniyya

Shaykh Abu Ishaq

c. 1343–1357

Injuid

Shiraz

Iskandar Sultan

1403–1415

Timurid

Shiraz, Yazd, Isfahan

al-Ashraf Barsbay

1422–1438

Mamluk

Cairo

Uzun Hasan

1453–1478

Aq Qoyunlu

Tabriz

Mehmet II Fatih

1444–1446, 1451– 1481

Ottoman

Amasya, Manisa, Edirne, Istanbul

Bayezid II

1481–1512

Ottoman

Istanbul

Süleyman Kanuni

1520–1566

Ottoman

Istanbul

Akbar

1556–1605

Mughal

Agra, Fatihpur Sikri, Lahore

Muhammad Quli

1580–1612

Qutb Shahi

Golconda

Mehmet IV

1648–1687

Ottoman

Istanbul

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INDEX

Abbasid/s 11, 17, 18, 19, 21, 24, 33, 35-39, 42-43, 45, 57-58, 84, 91-92, 98-99, 108, 114-116, 126, 143, 145, 149, 160, 193, 205, 235, 254, 263, 266-269, 271-273, 275-285 al-Abhari, Athir al-Din 80, 89, 104, 236, 258, 260, 266 edition of the Almagest 89, 245 Gift of Philosophy (Wisdom) 101 Introduction to Logic 259 Abraham ben Maimonides 122, 266 Abu Bakr al-Razi see al-Razi, Abu Bakr Abu Ma‘shar 43, 46-47, 217, 266 The Great Introduction 46 Abu Sa‘id 214, 287 Abu l-Wafa’ (al-Buzjani) 42, 56-59, 132, 266 adab 178 adab al-bahth 177 adab al-mutala‘a 179 al-‘Adil 92, 287 administrator/s 6, 12, 34, 68, 73, 76, 92-93, 97, 116, 125-126, 145, 187, 189, 192-193, 200, 204-205, 207, 212, 241, 282 ‘Adud al-Dawla 39, 115, 151, 286 Aegean islands 263 Aegina 161, 251, 265 Afghanistan 43, 57, 138, 212, 263-264 Africa 81, 94 North 10, 11, 26-27, 30, 67, 72, 81, 83-84, 89, 97, 101, 110, 114, 136-137, 145, 156, 168, 173, 177, 218, 225-227, 233, 237-239, 241-242, 248, 250, 253, 256, 258, 260, 263 sub-Saharan 10 Aghmat 271 Agra 253, 264, 287 ahl al-jidāl 176

Ahmad b. Ibrahim 143 b. Khalil, Shihab al-Din 133, 266 b. al-Mu‘tasim bi-Llah = Caliph al-Musta‘in bi-Llah 39, 286 b. al-Sarraj 229, 266 Ahwaz 277 Akbar 30, 87, 142, 249, 287 akşe 74 ‘Ala’ al-Dawla Muhammad 203, 286 Alamut 284 alchemy 6, 10, 12, 18, 75, 106-110, 139, 165, 190, 200, 208-210, 214, 269-270, 273-274, 280 Aleppo 33, 89, 110, 143, 152, 160, 163, 166, 259, 263, 268-269, 271, 283-287 Alexander = Iskandar 33, 150, 154 Alexander of Aphrodisias 99-100, 261, 264 On the First Cause 100 On the Principles of the Universe after Aristotle 100 Alexandria 5, 9, 37-38, 123, 163, 197, 229, 251, 264-265, 270 The Alexandrian Epitomes see Synopses of the Alexandrinians algebra 6, 10, 23, 61, 66, 70, 81-85, 87-88, 90, 97, 105, 137, 153-154, 163, 173, 189, 198, 201, 215, 226-227, 232, 238-242, 246, 269-270, 276, 278, 281 Algeria 143, 152, 173 ‘Ali b. ‘Abbas al-Majusi see al-Majusi b. Abi Bakr al-Harawi see al-Harawi ibn Abi al-Hazm al-Qurashi see Ibn al-Nafis b. Ahmad al-Nasawi see al-Nasawi b. Hasan 82 b. Husayn al-Ansari see al-Ansari

306 INDEX b. Ma’mun 57, 286 b. Muhammad al-Qalasadi see al-Qalasadi Qushji see al-Qushji son in law of Muhammad 18 Almería 83, 137, 280 Alp Arslan 67, 286 Amid = Diyar Bakr 282 al-Amidi, Sayf al-Din 93, 282 al-‘Amili, Baha’ al-Din 235, 242, 266 Essence of Arithmetic 85, 238, 240-242 al-‘Amiri, Abu l-Hasan 136, 266 Amudarya 204 Amul 67, 267, 284 al-Amuli, Muhammad b. Mahmud 108, 214, 242, 267 Anatolia 10, 24, 26-27, 67, 70, 80-81, 84-85, 94-95, 97, 101-102, 114, 127-128, 138-140, 142-143, 165, 172, 214, 218, 233, 240, 242, 248, 250, 253-254, 257-260, 263-264, 284 anatomy 91, 126, 160, 209, 250, 253 al-Andalus 10, 26, 33, 72, 83, 97, 110, 114, 136, 143, 191, 218, 225-226, 238, 255-256 Andalusian 85, 89, 99, 111, 152, 173, 191, 219, 253 al-Ansari, ‘Ali b. Husayn 249, 263, 267 Wonderful Selections 249 Antioch 38, 104, 253, 267-268 Aphrodisias 99-100, 261, 264 Apollonius 23, 40-42, 55, 81, 86, 184, 233, 235, 264 Conics 40-42, 81, 86, 184, 233, 235 Cutting Lines in Ratios 55 apprentice/s 66, 113, 129, 131 apprenticeship 11, 122, 248 al-‘ aql al-fa‘il 202 al-hayulani 202 Arabic 9, 17-19, 33-40, 44-50, 54, 57-58, 64, 72, 73, 75, 78, 83, 92, 95, 97, 99-102, 115, 131-133, 137, 141, 144,

146, 149, 156, 159, 164-165, 173-174, 187, 189, 192, 200, 203, 205, 207-210, 213, 219, 225, 227, 237, 240, 247-250, 252-254, 257-258, 271, 277 Graeco-Arabic 96 Judeao-Arabic 120 Archimedes 23, 40, 66, 229, 231, 233, 264 Lemmas 40, 232 Measurement of the Circle 40, 231, 233 On Sphere and Cylinder 40, 231-233 Aristarchus 40, 229, 232, 264 Distances of the Planets and Their Sizes 40 On the Two Luminous Bodies 232 Aristotle 23, 31, 33, 44-45, 52-53, 61, 66, 99-100, 104-105, 154, 189, 195-196, 199, 203, 207, 217, 256-257, 261, 264 First Analytics 52 On Generation and Corruption 61, 256 On the Heavens 61, 100, 256 Metaphysics 53 Meteorology 61, 256 Physics 45, 256 Posterior Analytics 203 Aristotelian 19, 38, 43, 59, 60, 100, 106-107, 178, 189, 192, 199-201, 204, 207-209, 212, 244, 255-257 non-Aristotelian 106 pre-Aristotelian 26 arithmetic 6, 23, 33, 38, 56, 64, 70, 78, 81-83, 85, 87-88, 90, 95, 97, 105, 132-133, 137-139, 152-154, 163, 168, 173-174, 190, 200, 226, 231-232, 238-242, 246, 260-261, 266, 269-270, 273, 276-277, 279-281 arithmetical 49, 61, 88, 128, 174, 196, 198, 209, 231, 239-241 inheritance 260 Arles 279 Armenia 264 Armenian 18 Arzani, Muhammad Akbar 249, 267 The Balance of Medicine 249

INDEX 307 Arzinjan 233 Ascalon 233, 265 al-Ashraf Barsbay 89, 285 al-Ashraf Musa 92-93, 127, 285 Asia 248 Central 10-11, 18, 21, 23-24, 26-27, 36-37, 42, 56, 67, 81, 84, 89, 94, 110, 114, 128, 136, 140, 142-143, 154, 178, 183, 193, 212, 214, 225, 240-242, 245-246, 249, 256, 259, 263 Minor 264 South 10-11, 72, 129-130, 145-146, 225, 247, 249 South East 10 West 225 al-‘Asqalani, Ahmad b. ‘Ali, Ibn Hajar 151, 267 assent 217-220 Astarabad = Gorgan 129-130, 139, 275 astrolabe/s 66, 84-85, 88, 109, 137, 215, 246-247, 276 astrology 6, 10, 19, 27, 43, 50, 53, 56, 61, 64, 75, 77, 80, 93, 101, 106, 108110, 135, 139, 153, 165, 179, 200, 209, 210-211, 214-215, 217, 243, 261, 265-268, 270-271, 273, 275-277, 280-283 see also science of the stars astrologer/s 19, 24, 26, 39, 36, 65-66, 132, 136, 224, 236, 244, 256 court 50, 80, 85, 89, 235 head 179 imperial 179 astrological 28, 61, 64, 85, 88, 175, 209, 227, 243 handbook/s 18, 144, 226 knowledge 244 studies 238 tables 88 texts 92, 109, 137 astronomy 6, 10, 39, 40, 43, 53, 56, 62, 64, 66, 70, 80-81, 83-85, 87-88, 100, 135, 137, 139, 144, 154, 171, 189, 195-196,

209-210, 215, 241, 243-244, 247, 261, 264-265, 269-270, 274-280, 282 astrunumiya 208, 243 elementary 227 pure 244 spherical 246 astronomical 12, 26, 58-59, 64, 85, 87-90, 106, 111, 143, 154, 171, 175, 227, 231-232, 236, 246 handbook/s 18, 53, 110, 144, 226, 244, 247 instrument/s 58, 198, 229, 236, 246 knowledge 154, 244 learning 85 manuscript/s 36, 86 observation/s 19, 37, 58 parameter/s 72, 246 studies 238 tables 88, 97, 143, 201 teaching manual/s 84 texts 24, 26, 54, 58, 77, 93, 137, 144, 246 Ptolemaic 61 theoretical 72, 93, 97, 111 Athens 9, 264-265 Atlantic 247, 249 Austria 146 author/s 9, 13-14, 19, 21, 23, 34, 47, 52, 59-60, 72, 75, 78, 81, 83-86, 90, 96, 101, 104, 115, 128, 135, 152, 168-169, 171, 175-176, 178-180, 182-184, 187-192, 194, 196-197, 200, 203-205, 207, 210-211, 215, 217-219, 221, 223, 229-230, 232, 239, 244-246, 249-251, 253-254, 256-259, 262 alchemical 110 ancient 24, 252 Andalusian 253 Christian 252, 254 classical 253, 257 Greek 104 Hellenistic 61 Ilkhanid 245

308 INDEX Indian 61, 130 Iranian 61 Jewish 252, 254 Late Antique 61 Mamluk 226 Muslim 24, 27, 61, 252, 254 pre-madrasa 215 polytheistic 252 post-classical 232 Syriac 104 autodidact/s 11, 34, 235 autodidactic 262 education 80 learning 119, 252 readings 242 studies 44 Autolycus 38-40, 229, 232, 264 The Moving Sphere 39, 232-233 Risings and Settings 40, 78, 232 automata 189 Avignon 281 axiom/s 209, 217, 231, 244 axiomatic 49, 209 Ayasuluk 269 Azerbayjan 140, 261, 264 Baghdad 5, 9, 11, 26, 35-39, 42-43, 49, 53, 56-58, 67, 70, 77-78, 91, 105-106, 114-115, 119, 123, 129, 136, 143, 149, 152, 177, 182, 193, 229, 235, 241, 249, 256-258, 263, 266-287 al-Baghdadi, ‘Abd al-Latif 177, 256-257, 267 al-Baghdadi, Abu l-Barakat 152, 182, 258, 267 Book of What Has Been Established by Personal Reflection 152 al-Baghdadi, Muhammad b. ‘Abdallah b. al-Mahall (?) 78 Baha’ al-Din see al-‘Amili Bahmanyar b. Marzuban, Abu l-Hasan 182, 212, 267 Bakhar 249 Balad 267 Balkans 225, 263

Balkh 43, 67, 136, 267, 271 al-Balkhi, Abu Zayd 42-43, 136, 204-206, 267 Banu Musa 40, 229, 232, 236, 267 Ahmad 267 al-Hasan 267 Muhammad b. Musa 49-50, 267 Bar Hebraeus 102, 104-105, 267 Bar Shakko, Jacob Severus 102-104, 267 Book of Dialogues 104 barnamaj 147 Barqa 271 Basra 42, 253, 271, 276-277, 279 Basta 280 Bayezid II 94, 287 Bejaia 271 Berber 27, 83 bestseller/s teaching 12, 111, 228 bimaristan 85, 115, 123-125 Birjand 268 al-Birjandi, ‘Abd al-‘Ali 84, 143, 247, 268 treatise on calendars 247 al-Biruni, Abu l-Rayhan 42, 56-66, 80, 85, 90, 201, 217, 236, 245, 268 Book on India 64-65 Book of the Stars = The Book on the Understanding of the Principles of the Art of the Stars 60-63 The Mas‘udi Canon 90 Questions to Ibn Sina 59-61 Bithynia 38, 77, 167, 229, 265 bodies 45, 105-107, 124, 197-198, 203, 261 celestial 19, 88, 174 compound 105, 107 composite 106 elementary 106 heavenly 64 heavy 10, 90-91, 201 human 9 meltable 106 natural 19, 106-107 simple 105, 107 bone-setters 125, 161

INDEX 309 bone-setting 91 botany 12, 148, 269, 270, 273-274 Bukhara 34, 59, 136, 204, 206, 263, 266, 273, 275 al-Bukhari, Shams al-Din 144, 268 burning mirrors 10, 43, 97, 189, 198, 218, 275 Bursa 129, 169, 263, 279-280, 284 business calculation/s 241 Buyid/s 33, 36, 39, 56, 58, 67, 114-115, 151, 154, 235, 256, 263, 266-269, 272-277, 279-286 Buzjan 58, 266 Buzurgmihr 34 Byzantium 19, 49, 116, 144 Cairo 9, 11, 26-27, 68, 73, 81, 83, 86, 89-90, 94, 108, 110-111, 114, 121-124, 127-129, 132-133, 136, 138-144, 152, 163-166, 172, 177, 179, 218, 227, 232-233, 239-240, 245-246, 249, 251-252, 255, 257, 259-260, 263, 266-283, 285-287, 289 Ayyubid 253 Mamluk 97, 134, 217, 252 Ottoman 141, 253 calendar/s 84-85, 88, 143, 201, 215, 244, 247 Çandarlı Halıl Pasha 172 Chagatai Khans 247 challenge/s 5, 13, 23, 27, 41, 47, 51, 59-60, 111, 127, 199 conceptual 13 historiographical 221 intellectual 206 material 13 chair/s 97 mathematical sciences 141 medicine 24, 91 Chennai 50 China 24, 136 Christian/s 9, 11, 18-19, 24, 35-36, 38, 43, 71, 94-95, 99, 104-106, 115-117, 122-123, 126, 136, 144-145, 161, 192, 199, 252-254, 256, 273

Catholic 24 Greek 42 Syriac 24, 37, 43 church/es 102, 140 Church of the East 44, 115-116, 123 Greek Orthodox Church 254 Syriac Orthodox Church 104 Cilicia 263 classroom 10, 12, 44, 47, 51, 53, 100, 148, 159, 176, 179, 209, 240, 242, 252-253, 262 concept/s 31, 33-34, 62, 70, 84, 105, 117, 135, 145,168, 172, 174, 177, 180, 183, 187, 202-203, 208-209, 213, 218-219, 230-231, 235, 249, 255-256 mathematical 45 medical 33 philosophical 23, 159 natural 101, 106 pre-Islamic 23 conceptualization/s 217-220 conics 275 Conics see Apollonius content 5-7, 13-14, 27, 40, 45, 49, 54, 65-66, 67, 90-91, 102, 106, 121, 123, 142, 147, 151, 157, 175, 181, 187-188, 191-192, 196, 201, 207-208, 210, 215, 217, 219-220, 225, 227, 229-230, 241, 243, 261-262 context/s 13, 18, 36, 66, 100, 106, 117, 125, 170, 172, 181, 183, 199, 200, 205, 214, 221, 236-237, 241, 252, 262 contextual 17 contextualize 5, 12, 17, 221 Coptic 35-36 Córdoba 249, 273, 278, 285 craft/s 11-12, 56, 65, 156, 198, 210 craftsman/men 49, 55-56, 59, 65, 108, 156, 198 craftsmanship 90 culture/s 17, 19, 21, 142, 149, 192, 211, 225, 250 healing 247 Indian 64 intellectual 17, 65

310 INDEX knowledge hybrid 19 multifaceted 21 learning 86, 163 linguistic 240 political 17 social 17 teaching 86, 163 curriculum 147, 163, 199 al-Dakhwar, ‘Abd al-Rahim b. ‘Ali, Muhadhdhab al-Din 92-93, 122-123, 126-127, 151, 250, 252, 254, 268 Damascus 9, 11, 26-27, 78, 89, 92-93, 104, 121-123, 126-129, 133, 136-137, 139-140, 142, 151-152, 163-164, 173-174, 227, 240, 249-251, 256-257, 259-260, 263, 266-272, 274, 276-285 Ayyubid 92, 127, 224, 252 Damietta 163 al-Dashtaki, Ahmad, Nizam al-Din 134 al-Dashtaki, Habib Allah, Majd al-Din 134 al-Dashtaki, Mansur, Ghiyath al-Din 98, 134, 268 al-Dashtaki, Mansur 134 al-Dashtaki, Muhammad b. Mansur, Sadr al-Din 30, 99, 134, 268 data 77, 81, 140, 223, 226, 233, 237, 245 Data see Euclid or Thabit b. Qurra Da’ud b. ‘Umar 253, 268 Memoir on the Science of Medicine 253 al-Davani, Jalal al-Din 99, 176-177, 268 David b. Joshua Maimonides 259, 268 Dayr Qunna 36 debate/s 17, 19, 21, 34, 54, 98, 107, 114, 144, 171, 175-179, 183-184, 188, 192, 199, 201-202, 206, 219, 248 intellectual 106, 214 legal 105 philosophical 31, 177, 183, 258 public 139, 154 rational 50 religious 19, 206 scholarly 50, 177, 185

scientific 175 theological 183 deductive 49, 209, 231, 244 deep reading 181 definition/s 51-54, 61, 164, 176, 178, 180, 191, 197, 206, 208-209, 217, 219-220, 231 philosophical 100 Delhi 87, 105, 107, 129, 264, 276, 279 Dioscorides 78-79, 264 De Materia medica 31, 78-79 diraya 151-152, 166, 169 discipline/s 10-14, 27, 31, 34, 43, 64, 66-69, 71-73, 75, 77, 82, 84, 86-87, 93, 95-97, 108-110, 132-135, 139-140, 147-149, 153-156, 163-164, 166, 168, 173, 178-181, 184, 187-194, 197-198, 200-201, 205-209, 211-218, 223, 226, 238, 242, 244, 252, 255, 258, 260, 262, 264, 266-269, 276 astronomical 12, 26 branch 87, 163, 189, 200, 215, 217-218 arithmetical 240 mathematical 163, 217 courtly 19 divinatory 97, 108 ghariba, occult 10, 37, 68, 71, 72, 107, 205, 213 remarkable 107 strange 107 fundamental 200 quadrivium 189 historical 10 literary 10, 191 mathematical 5, 10, 12, 34, 44, 65-66, 77, 81, 83, 105, 147, 163, 165, 198, 205, 215, 225, 232, 239, 241 medical 34 non-religious 5, 67-68, 70, 72, 91, 157, 206 philological 10, 75, 96-97, 156, 164, 191 philosophical 10, 34, 44, 87, 103, 190, 198, 201, 203, 205, 207, 258

INDEX 311 practical 201 philosophy 75, 213, 215 rational 182, 258 religious 10, 66-67, 69, 73, 75, 96-97, 108-109, 130-131, 138, 148-149, 154, 178, 198, 214, 255, 258 scholarly 12,187 scientific 9-14, 35, 53, 71, 77, 86, 148, 153, 207 secular 71, 96 theoretical 76, 101, 207, 215 of transmission 75 divination 6, 10, 43, 75, 107, 109, 135, 140, 261, 271, 276, 283 sand 80, 108-110, 165, 214-215 diwan 80 Diyar Bakr 264 doctrine/s 17, 23, 26, 52, 76, 105, 174, 176, 183, 218, 221, 255, 261 Aristotelian 107 astrological 61 Ibn ‘Arabi 135 Ibn Sina 212 of the intellect 106 philosophical 21, 98-100, 164, 203 religious 141 Shi‘i 30 scientific 35 Indian 65 about the soul 91, 106 Sufi 105 al-Suhrawardi 99, 135 Dorotheus 46 doubt/s 23, 34, 38, 66, 110, 126, 136, 161, 181, 205, 210, 245, 248, 256 Dunaysir 268 al-Dunaysiri, Imad al-Din 92-93, 268 al-Dunaysiri, Shams al-Din 211, 268 Dutch 252 Earth 19, 45-46, 88, 106-107, 155, 231 earthy (element) 62 earthquake/s 43, 106 ecliptic 19, 88, 231

economics 189, 200, 208 Edessa 36, 160, 281 Edirne 94, 129, 169, 263, 287 education 10, 12, 14, 27, 36, 43, 49, 55, 57-58, 67, 69, 72-74, 83, 89, 93, 95, 102, 105, 111, 113, 125-126, 130-133, 136-138, 140-142, 145-147, 149, 155, 168-169, 170, 185, 192, 202, 205, 212-213, 220-221, 225-227, 241, 246, 249 advanced 5, 12, 14, 27, 33, 57, 68-69, 71, 73, 76, 111, 130, 133, 145, 259 autodidactic 80 cross-disciplinary 179 family 6, 125, 131-132, 145 general 97, 154 geometrical 237 Greek 36 hospital 262 Islamic 133 madrasa 73, 91, 189 mathematical 89, 102, 229 medical 11, 56, 91, 93-94, 124, 130-132, 134, 145, 166 Mughal 87 Muslim 128, 135 philosophical 95, 102, 106, 127 princely 108 private 11 professional 49 religious 93 school 80 scientific 54, 153 self 80 theological 104 theoretical 12 travelling/travels for 111, 114 Egypt 10-11, 18, 24, 36, 42, 67, 69-70, 72, 84, 90, 92-93, 97-98, 100, 102, 108, 114, 128-129, 136, 140, 143, 163, 191, 217-219, 226-227, 239-242, 246, 248-250, 256-259, 263 ancient 26 Ayyubid 257 Egyptian 89, 97, 140

312 INDEX Mamluk 72, 81, 94, 102, 110, 164, 187, 193, 214, 227, 238 element/s 45-46, 52, 61-62, 65, 87-88, 91, 94, 100, 106-107, 151, 155, 158, 170, 181, 194, 197, 200-201, 209, 249, 261 Elements see Euclid encyclopaedia /s 6, 21, 66, 100-101, 175, 187-189, 192-194, 199-200, 203-204, 207, 210-216, 218, 221, 242, 255, 266 The Book of Healing (Ibn Sina) 100, 164, 175 The Book of Salvation (ibn Sina) 164 comprehensive 188-189, 213 medical 201 philosophical 164, 188, 193, 260 selective 188-189 encyclopaedic 12-13, 116, 192, 196, 200, 203-204, 260 England 146 English 94, 146, 198, 252 ephemerides 110 Ephesus 251 epistle/s 11, 43-44, 46, 48.49, 51, 61, 100, 154, 196, 218, 226, 256, 259 logical 259 Epistles of the Brethren of Purity (Ikhwan al-Safa’) 210 The Epistle on Definitions (Ibn Sina) 102 The Epistle of the Essence of Arithmetic for Shams [al-Din] (al-Nisaburi) 85 The Epistle on the Fact That One Comes Only to Philosophy Through Mathematics (al- Kindi) 195 The Epistle of Knowledge (Ibn Sina) 203 The Epistle on the Number of Books by Aristotle and What is Required to Study Philosophy (al-Kindi) 195, 206 The Epistle on the Parts of the Rational (or: Intellectual) Sciences (Ibn Sina) 199-200 The Epistle on the Science of the Etiquette of Investigation (al-Samarkandi) 178

ethics 189, 196, 198, 200, 204, 206, 208, 268 Euboea 264 Euclid 6, 23, 27, 30, 35, 38-40, 42, 45, 47, 49, 51-54, 61, 66, 78, 80-81, 86, 102, 104, 151, 157, 169-171, 173, 184, 209-210, 225-229, 233, 235, 239, 261, 264 Data 40, 231-233 Elements 6, 23, 27, 30, 35, 38-39, 42, 45, 47, 51-54, 61, 66, 80-81, 86, 102, 151, 157, 169-171, 173, 209-210, 225-231, 233, 235-238 Optics 39, 49, 231 Phenomena 39, 78, 231 Euclidean 203, 209, 231 Euphrates 36 Europe 137, 144, 240, 251 eastern 94 Latin 66 Ottoman 10 southern 85 western 24 European 146, 199 Eutocius of Ascalon 233, 265 exegesis 73, 75, 141, 189-190, 207, 218, 267-268, 271, 278-282 exorcism 214-215 experience/s 10, 27, 58, 65, 134, 136, 153, 159-160, 162, 175, 196, 202 experienced 159, 179 falsafa = philosophy 97, 147, 165, 259 falsafiyyat = philosophical sciences 96 Fatima 18 Fakhr al-Din al-Razi see al-Razi, Fakhr al-Din al-Farabi, Abu Nasr 27, 36, 98-100, 136, 149, 192, 194, 197-199, 210, 219, 256-257, 259, 261, 269 Enumeration of the Sciences 198 The Great Logic 258 Metaphysics 256 al-Farghani, Muhammad b. Kathir 66, 269 Fath Allah 87

INDEX 313 Fatihpur Sikri 264, 285 al-Fattal, Ibrahim 173, 269 fatwa 70 Fez 83, 156, 165, 270, 272 fihrist 147 fiqh 169, 189, 191 Firuzkuh 281 form/s 19, 21, 33, 38-39, 56, 61-62, 65, 69, 72, 87, 89, 107, 113-114, 126, 139, 144, 175, 181-182, 185, 188-192, 197, 203-208, 210, 218, 226, 261-262 African 137 circular 107 of debate 179 dialogical 47 of divination 75, 109 of education 132 medical 11 private 11 educational 14, 113 geometrical 45 of independent learning, teaching, and problem-solving 173 of institutionalized learning 14, 70 knowledge 94, 163, 197 divinatory 31 transfer 55 of learning 166 of learning and teaching 13, 23-24, 65, 86, 139 private 12 of Neoplatonic philosophy 30 of teaching 33-34, 108, 149 formal 11, 44-45, 70, 110, 131, 151, 154, 202, 217, 219-220, 248 foundation/s 19, 67, 70, 73,94, 109, 117, 203 of faith 12, 70, 73, 75, 97, 165, 190, 218, 258, 273, 275-276, 281 of law 12, 70, 73, 75, 165, 190, 258, 275-276, 281 of philosophy 215 philosophical natural 127

of religion 70, 73 of schools 12 France 146 French 146, 198 Galen 23, 38, 44, 52, 96, 127, 161, 195, 249-253, 265 The Art of Medicine 122 On Bones for Beginners 122, 161 On the Pulse for Beginners 122 On the Sects for Beginners 122 Sixteen Texts of Galen 122, 160 Therapeutics to Glaucon 122 Galenic 52, 124, 160, 251-252 Gaza 274 geography 74, 107, 139, 148, 171, 215, 272, 242, 261, 265, 267, 276, 282 geometry 10, 23, 33, 40, 43, 45, 50, 53-56, 61-62, 66, 70, 83, 85, 87-88, 95-97, 100, 105-106, 137-139, 153154, 157-159, 163, 173-174, 189, 195-196, 202-203, 215, 217, 226-228, 230-231, 233, 235-241, 244-245, 261, 264-266, 273, 276, 278-279, 281-282 axiomatic-deductive 209 elementary 137, 235 plane 42, 61, 209, 231 practical 238 solid 42, 61, 209 spherical 42, 72, 227, 231 of the sphere 61 stereometric 231 textbook of 36 theoretical 238 Gerasa 38, 44, 209, 265 Gerard of Cremona 39, 54 Germany 146, 246 German 146, 252 al-Ghazali, Abu Hamid 174, 182, 255, 268 Ghazna 57, 61, 64, 263, 267, 271, 284 Ghaznavid 57, 90, 249, 263, 267, 269, 271, 284 al-Ghazuli, Muhammad b. Ahmad 165, 268

314 INDEX Ghurid 212, 214, 280 Gilani, Muhammad Tabib 130, 268 Golconda 31, 130, 268, 285 Granada 136, 279 Greece 263 Greek/s 9, 18-19, 40, 45, 49, 54, 58, 104, 137, 144, 197, 207-209, 243, 248 authorities 23 city states 19 education 36 knowledge 199 Orthodox Church 254 philosophers 26, 99, 104 philosophy 27 physician/s 104 provinces 225 regions 240 sources 35 texts/s 27, 39-40, 43, 53-54, 64, 116, 122, 256 astronomical 9 mathematical 9, 38, 46, 78 medical 35, 38, 46 philosophical 9, 35, 38, 46 scientific 35, 46 teaching 27 theologian/s 104 theory medical 160 treatise/s 61 Gregor Chioniades 144 Gulf of Bengal 247, 249 Gundishapur 115, 117, 160, 285 Gurgan = Jurjan 57, 267, 271, 274, 277, 286 Gurganj 56, 267, 271, 281, 286-287 al-Habashi, Bilal 110, 269 Habib 44-47 Habib b. Bahriz 44, 269 Hacı Paşa 140, 269 hadith 37, 75, 94-96, 133-135, 163, 165, 168-169, 189-191, 207, 257, 266-268, 271-272, 276, 278, 280-281

see house/s [of (reading) hadith] al-Hajjaj b. Yusuf b. Matar 236, 269 halqa 149 Hama 152, 263, 267, 281 Hamadhan = Hamadan 267, 272 handasa 196, 208 handbook/s 123 astrological 226 astrological-astronomical 18 astronomical 53, 110, 144, 226, 238, 244, 247 on logic 259 medical 18 pharmaceutical 123 haqqa 174 al-Harawi, ‘Ali b. Abi Bakr 232, 269 Harran 38, 44, 49, 263, 269, 284 Harun al-Rashid 286 Hasan 18, 61, 68, 267 hashwi 180 al-Hassar, Muhammad b. ‘Abdallah, Abu Bakr 137, 239, 270 The Explanation = The Explanation and Memorization of the Art of Working with the Dust (Numbers) 78 Hazza 44, 269 heavens 9, 19, 49 Herat 67, 100, 138, 141-142, 212, 214, 254, 263, 273, 275, 281-282 herbalist/s 125, 153, 166, 215 Hermes 46 Heron 159, 265 Mechanics 45, 210 Hijaz 83, 263 hijra 163 hikma = philosophy, wisdom 97, 147, 165, 168, 182, 259 Hilla 270 al-Hilli, ‘Allama, Najm al-Din 259, 270 Hims = Homs 272 Hindi 247 Hippocrates 38, 52, 93, 96, 98, 161, 249-150, 250-251, 254, 261, 265 Aphorisms 122, 126-127, 249, 254

INDEX 315 Epidemics 122 On the Nature of Man 161, 250 The Oath 122, 249 Prognostics 122, 249, 254 al-Hira 270 historiography 9, 102, 275 historiographical 12-13, 17, 129, 199, 211, 221, 253 hospital/s 6, 12, 21, 24, 36, 56, 69, 92-94, 97, 102, 113-117, 119, 121-126, 128-130, 133-134, 139, 144-145, 149, 152-153, 160, 182, 223, 262 ‘Adudi 115, 119, 121, 123 Gundishapur 160 Hafsa Sultan 94 Haseki 94 Ilkhanid 128 Mansuri 94, 97, 121, 123-124, 126, 128, 133, 140, 166 Qalawun 121, 124-126 Mehmet Fatih 94 Muqtadir 119 Nasiri 123 Nuri 93, 121-123, 125, 128, 131 Ottoman 114-115, 126 practice 117 Süleyman Kanuni 94 house/s 11, 14, 62, 67, 71, 92, 100, 115, 139 for caretaking 115 hadith 23-24, 67, 71, 152 of lay teachers 11 of the Qur’an 23-24, 67, 71, 152 of the rich 11 for medicine 115 private 100, 188, 212 religious 14 student’s (house) 152 of teachers/teacher’s (house) 71, 152 for timekeepers 70, 223 Hubaysh b. al-Hasan al-‘Asam 117-118, 132 Book of Problems = Problems of Medicine for Students 117-118, 251, 254

Hunayn b. Ishaq 53, 117, 132, 160-161, 249, 251, 270 Problems of Medicine for Students = Book of Problems 117-118, 251, 254 Husayn 18 Hyderabad 129-130, 275 Hypsicles = Inqila’us 38, 40, 229, 265 Ascencions 40 Ibn Abi l-Bayan 123, 270 Ibn Abi Hulayqa 125, 270 Ibn Abi Sadiq 127, 270 Ibn Abi Shukr al-Maghribi see al-Maghribi Ibn Abi Usaybi‘a 43, 93, 95, 115, 117, 121-124, 131-132, 151, 166, 174, 257, 270 Ibn Aflah, Jabir 89, 270 Ibn al-Akfani 89-90, 128, 175, 215-218, 223, 239-240, 244-245, 256-259, 270 Ibn al-‘Amid 39 Ibn ‘Arabi, Muhyi l-Din 26, 135, 270 Ibn Arfa‘Ra’s, Abu l-Hasan 110, 270 Ibn Bajja 98-99, 219, 261, 270 Ibn al-Banna’ 83, 137, 173, 238-239, 271 Epitome of Arithmetic 239 Epitome of the Operations of Arithmetic 137 The Four Chapters on Arithmetic 137 Ibn al-Baytar, Diya’ al-Din, Abu Muhammad 166, 252-253, 271 book on materia medica 253 Ibn al-Bunduqi 133, 271 Ibn Fallus 240, 271 Ibn Farighun 193, 204-207, 271 The Summaries of the Sciences 204 Ibn al-Fuwati 105, 271 Ibn al-Ha’im 81, 83, 226, 239-240, 271 Ibn al-Haytham 42, 171, 184, 230, 243, 271 Optics 171, 184 Ibn Hibinta 217, 271 Ibn al-‘Iraq, Abu Nasr Mansur 42, 56-58, 271 Ibn al-Jama‘a, ‘Izz al-Din 97, 165, 272

316 INDEX Ibn al-Jarrah 126 Ibn Jazla, Abu ‘Ali 252-253, 272 Ibn al-Lubudi, Najm al-Din 80, 272 Ibn Kammuna 102, 272 Ibn Khaldun 109-110, 140, 155-157, 177, 255-256, 272 Introduction (to History) 177, 238 Ibn Khallikan 152 Ibn al-Majdi 81-83, 164, 239, 246, 259, 272 Treatise on the drawing of hour lines on three kinds of sundials = Guide to the Right Path for the Perplexed in Drawing the Circle of Projection 82 Ibn Mutran 123, 272 Ibn al-Nadim 43-44, 49, 51, 55, 119, 132, 272 Catalogue = Fihrist 119 Ibn al-Nafis 123-127, 133-134, 151, 161-162, 248, 251, 254, 272 commentaries on Ibn Sina’s Canon of Medicine 126 Hippocrates’ Aphorisms 126-127, 254 Digest on the Canon 248 Epitome of Ibn Sina’s Canon 127, 133 Ibn al-Qifti 50, 91, 121, 132, 272 Ibn al-Quff, Abu l-Fadl b. Abi l-Hasan, Shams al-Dawla 161-162, 272 Ibn Rushd 98-99, 217, 255-257, 261, 273 Ibn Saghir, ‘Umar b. Muhammad, ‘Ala’ al-Din 97, 273 Ibn Saghir, Muhammad b. Muhammad, Kamal al-Din 97, 252, 273 Ibn al-Sari, Ahmad, Najm al-Din 78, 256, 273 Ibn Sina 21, 26, 30, 34, 42, 57, 59-61, 66, 70, 72, 80, 96, 98-102, 104-106, 130, 134-135, 143, 151, 164-166, 174-177, 182-183, 192, 194, 199-204, 210, 212, 214-215, 217-220, 236, 242, 249, 253, 255-259, 261, 273 The Book of Demonstrations 203 The Book of Healing 100, 102, 104-105, 175, 193, 201, 219, 257-258, 260-261

The Book of Salvation 100, 193, 260 Canon of Medicine 95, 102-103, 117, 119, 123, 126-127, 130, 133-134, 151, 248- 252 The Epistle on Definitions 102, 260 The Epistle of Knowledge 203 On the Parts of the Rational (or: Intellectual) Sciences 193, 199-200, 260 The Philosophy of the Easterners 201, 204, 212 Pointers and Reminders 30, 93, 100-102, 104-105, 127, 134-135, 164, 175176, 182-183, 212, 214, 219, 255, 260 The Sources of Philosophy 102, 212 Ibn Taymiyya 95, 273 Ibn al-Tilmidh, Amin al-Dawla 123, 251, 254, 256, 273 commentaries on The Canon of Medicine by Ibn Sina 123 The Completion of the Alexandrian Epitomes 123 The Comprehensive Book of Medicine by al-Razi 123 Great Dispensatory 123 Ibn al-Turays, Muhammad b. Ibrahim, Nasir al-Din 254, 280 Ibn Turka, Sa‘in al-Din 108, 273 Ibn al-Ukhuwwa 95, 273 Ibn Wasil 257-258, 273 Ibn al-Yasamin 83, 173, 239, 274 Ibn Yunus, Kamal al-Din 103-104, 257, 274 Ibn Zuqqa‘a = Ibrahim b. Muhammad al-Nawfili 109, 274 Ibrahim b. Hilal b. Ibrahim, Abu Ishaq 50, 274 Ibrahim b. Sinan b. Thabit b. Qurra 42, 55, 274 Analysis and Synthesis 55 Selected Problems 55 Tangent Circles 55

INDEX 317 ijaza/t 69-70, 138, 161-162, 171, 251 al-‘Iji, ‘Adud al-Din 235, 274 The Stations of the Science of Kalam 235 Ilkhan/s 24, 263 Ilkhanid 26, 84-85, 102, 104-106, 111, 114, 128, 214, 218, 235-236, 240-241, 245, 257, 266-268, 270-272, 275277, 279-280, 282-285, 287 ‘ilm 10, 156 al-bahth 178 al-munazara 178 ‘ilmi 156 ‘ilmiyye 70 ‘ulum 10 see also discipline/s and science/s imtihan 69-70 India 10, 19, 27, 30, 64-65, 67, 81, 83-87, 89, 91, 94, 101, 107, 109, 114, 128, 130, 137, 142-143, 154, 184, 191, 227, 237, 240-241, 246-247, 249-251, 255, 264, 267 eastern 248 Mughal 31, 87, 225, 256 northern 64, 143, 214, 248 western 31 Indian 19, 61, 64-65, 86-87, 95, 130, 137, 143, 200, 209, 246, 248 innovation/s 10, 12, 34, 258 institution/s 5-6, 11-14, 23, 71-72, 94, 113-114, 116, 140, 144-145, 260 advanced education 12, 71 of learning and teaching 11-12, 31, 129 educational 23, 71, 77, 111, 145, 169 medical learning 129 norm-setting 142 Ottoman 131 religious 70-71 Shi‘i 72 specialized 24 Sunni 71 institutional 23, 33, 75, 148, 151, 182, 225 institutionalization 107, 245 institutionalize 11, 14, 70-71

instruction 36, 50, 61, 72, 128, 153, 156, 159, 198, 211, 225, 237 oral 11 scientific 156 instrument/s 9, 17, 33, 55, 57, 65, 72-73, 88, 93, 174, 197-198, 209, 215, 238, 244-247, 266 astronomical 58, 229, 236, 246 musical 201, 209 observational 236 optical 198 scientific 37, 209 surveying 209 instrument maker/s 33, 153, 235, 276, 283 instrument making 56, 65 introduction/s 9-10, 17, 45-46, 52, 54, 61, 153, 155, 176, 198, 204, 207, 245-246 of/to astronomy 88, 247 for beginners 12 disciplinary 12 elementary 89, 170, 245 mathematical 171 to medicine 93, 117 to natural philosophy 101 natural philosophical 171 philosophical 47 to philosophy 101 of Persian 87 Introduction to the Categories (Porphyry) 38, 259 The Introduction to the Dust Letters (al-Qalasadi) 137 Introduction to History (Ibn Khaldun) 155, 177, 238 Introduction to Logic (Athir al-Din al-Abhari) 259 Introduction to Number Theory (Nicomachus of Gerasa) 38, 44-45, 210 The Great Introduction (Abu Ma‘shar) 46 Iran 10-11, 24, 26-27, 30, 34, 36-37, 40, 42, 58, 67, 70, 72, 78, 80-81, 83-85, 89,

318 INDEX 91, 94, 100-102, 104, 108-109, 114, 127-128, 136-137, 140-144, 154, 165, 173, 175, 177, 209, 212, 214-215, 218, 227, 233, 235, 237, 239-242, 246, 248-249, 251, 256, 258-259, 263-264, 283 central 114 eastern 21, 58, 136, 263 Ilkhanid 240, 257 Mongol 95, 250 northeastern 43, 129, 193, 204, 206, 264 northwestern 24, 89 post-Mongol 129 Qajar 145 Safavid 31, 98, 109, 129-130, 143, 147, 226-227, 235 Sasanian 19 southern 114 Timurid 235, 250 western 114-115, 264 Iranian 26, 43, 61, 86-87, 102, 130, 134, 140-143, 204, 227, 240, 242, 245, 249- 250, 259-260 Iraq 10-11, 24, 26, 34, 42, 67, 70, 78, 80, 84, 100, 102, 105, 110, 114, 126-128, 136, 143-144, 172-173, 214, 240-241, 249-250, 256-257, 263-264 northern 72, 128-129, 136, 233 Irbil 266 Isfahan 9, 67, 81, 86, 98-100, 129, 139, 142, 214, 242, 249, 256, 261, 263-264, 266-267, 273, 276, 278-279, 284, 286-287 al-Isfahani, Shams al-Din 219-220, 274 Isfandiyarid 172, 279, 283 Ishaq b. ‘Ali al-Ruhawi see al-Ruhawi Ishaq b. Hunayn, Abu Ya‘qub 39-40, 53, 236, 274 Iskandar Sultan 81, 108, 139, 236, 287 Isma‘il 135 Isma‘ili 24, 34, 284 al-Isra’ili, ‘Afif al-Din, Abu Sa‘id 252, 274

Istanbul 9, 50-51, 74, 94, 129, 131, 140-142, 169, 232, 242, 263, 268, 278279, 281, 283-284, 287, 289 istidlāl 176 Jabal al-‘Amil 266 Jabir b. Hayyan 108, 210, 274 jadal 178 al-Jaghmini, Mahmud b. Muhammad, Sharaf al-Din 84, 88-90, 170, 172, 245, 247, 249-250, 275 Epitome on Plain Theoretical Astronomy 84, 89 Jaldak 275 Jam 275 jam‘ 260 Jami, ‘Abd al-Rahman, Nur al-Din 150, 275 Haft Awrang = Seven Thrones 150 Jerusalem 81, 101, 142, 163, 257, 267, 271, 281 Jew/s 24, 94, 126, 144 Jewish 9, 11, 24, 26, 35, 37, 71, 95, 97, 102, 104, 122-123, 126, 144-145, 152, 192, 199, 248, 252, 254, 258-259, 266, 268, 272, 274, 278 Karaite 97 al-Jildaki, Aydamir, ‘Izz al-Din 110, 275 jumatriya 208 al-jumhūr 176 jurist-philosopher 206 jurist-physician 94-97, 206 al-Jurjani, Isma‘il b. al-Husayn, Zayn al-Din 250, 253, 275 The Treasure of the Khwarazm Shah 250 al-Jurjani, al-Sayyid al-Sharif 90, 102, 134, 138-140, 165, 170-171, 193, 203, 217-220, 230, 235, 259, 275 On the Division of Knowledge 219 Juvayn 275 al-Juwayni, Sharaf al-Din 105, 275 al-Juzjani, ‘Abd al-Wahid, Abu ‘Ubayd 203, 257, 275

INDEX 319 Ka‘ba 154, 163 Kafartutha 283 al-Kafiyaji, Muhammad b. Sulayman al-Rumi, Muhyi l-Din 70, 89, 97, 133, 259, 275 Kaiseri 128 Kakuyid 203, 210, 286 kalam 23, 30, 70, 75, 80, 97, 99, 101, 105, 107, 139-140, 143, 154, 156-157, 165, 170-171, 173, 175-176, 178, 182, 190-191, 198, 206-207, 235-237, 250, 255, 257, 259, 261, 266, 268-283 al-Karak 270, 272 Karaman 275 Kashan 48, 172, 276 al-Kashi, Jamshid, Ghiyath al-Din 85, 172, 236, 241, 276 Commentary on Observational Instruments 236 Key of Arithmetic or Key of the Calculators 85, 241 al-Kaskari, Ya‘qub 56, 116, 276 Kastamonu 170, 172, 279, 283 Kath 56, 268, 271 al-Katibi al-Qazvini, Najm al-Din 101, 165, 257-260, 276 Shamsiyya on the Rules of Logic 259 Wisdom of the Source 101 Kawm al-Rish 110, 276 al-Kawmrishi, Ahmad b. Ghulam Allah 109, 276 Kazirun 268 khabr 191 al-Khaddam, ‘Abdallah b. Muhammad, ‘Imad al-Din 241, 276 al-Khafri, Shams al-Din 85, 276 al-Khalil b. Ahmad al-Farahidi see al-Farahidi Khaydarabadi, Fadl-i Haqq 107, 276 The Fortunate Gift 107 al-Khazin, Abu Ja‘far 39, 42, 276 al-Khazini, ‘Abd al-Rahman 56, 80, 276

khilāf 178 al-Khujandi, Muhammad b. ‘Abd al-Latif 252, 276 Khuna 277 al-Khunaji, Afdal al-Din 101, 219-202, 257-258, 260, 277 The Summa 101, 260 Khurasan 110, 212, 263, 282-283 al-Khurasani, Ahmad b. Muhammad 48 Khwarazm 56-57, 61, 213-214, 275 al-Khwarazmi, Abu ‘Abdallah 193, 206-210, 277 Keys to the Sciences 210 al-Khwarazmi, Muhammad b. Musa 66, 277 Khwarazmshah/s 56-57, 250, 275, 281, 286-287 al-Kindi, Ya‘qub b. Ishaq, Abu Yusuf 39, 42-47, 49-52, 58, 98-99, 108, 136, 192, 194-197, 204-206, 229, 256-257, 261, 277 The Book on the Parts of Human Science 195 The Book on the Quiddity of Science and its Parts 195 The Divisions of Human Learning 44 That the Elements and the Outermost Body are Spherical in Form 45 The Encouragement for Learning Philosophy 44 The Epistle on the Number of Books by Aristotle ... 195, 206 Epistle on Rain and Moisture 44 The Essence of Science and Its Division 44 Optics 49 Questions Asked about the Benefit of Mathematics 44 Scientific Evaluation 44 On the Subject that Philosophy Cannot be Acquired Except through the Knowledge of the Mathematical (Sciences) = Epistle on the Fact that One Only Comes to Philosophy through Mathematics 44, 195

320 INDEX Kirman 281 knowledge 24, 33-37, 42-43, 46, 49, 56, 58-59, 61, 64-66, 70-73, 75-76, 85-86, 93-96, 100, 105-109, 111, 113-114, 116-117, 119, 121, 125, 128, 133, 135-140, 142-143, 145, 147-148, 152, 155, 160-161, 163, 166, 168-170, 179, 181, 184, 187-191, 193-199, 201-202, 204-207, 210-211, 213, 216, 218-220, 226, 228, 255, 260-262 alchemical 110 anatomical 126 ancient 43, 199 Aristotelian 107 astronomical 154, 244 astrological 244 basic 207, 209, 242 classification 66, 188, 192, 196-197, 216 of the Creator 213 disciplinary 98, 188, 190, 214, 220 divinatory 31 divine 195 empirical 10 evidentiary 181 factual 155 geometrical 154, 237 gestural 173 Greek 199 historical 205 human 195, 197 hybrid 19 Indian 19 of instruments 65 insufficient 36 mathematical 83, 88, 154, 231, 242 medical 38, 94, 116, 125, 248 Indian 248 memorized 156 of nature 207-208, 210 new 158-159, 185, 192 oral 173 philosophical 37-38, 42, 182, 210, 257 practical 93, 127

professional 37 prophetic 195 rational 196 religious 33, 110, 185 Sabian 283 respected 188, 190, 221 scientific 11, 64, 175, 210, 257 special 166 specialized 34 about the stars 208 sterile 181 superficial 98 technical 85 theory of 202, 217 theoretical 160 true 202, 215 Konya 118, 128, 138, 140, 143, 269-270, 285 Kos 265 Kufa 18, 274 al-Kuhi, Wijan b. Rustam, Abu Sahl 80, 157, 229, 232-233, 277 Kushyar b. Labban 217, 277 al-Kutami, ‘Abdallah b. Salih 166, 277 al-kutub al-mutawassitat see Middle Books Lahore 263-264, 279, 287 Lawkar 277 al-Lawkari, Fadl b. Muhammad, Abu l-‘Abbas 212, 277 Lesbos 264 letter/s 10-11, 27, 44-48, 52, 59, 61, 74, 117, 172, 255-256 Arabic 254 Aristotle’s letters 154 diplomatic 205 dust 137-138 Hebrew 254 magic 27, 139, 242 science of = letter science = letter magic 108-109, 165, 279 library/ies 9, 24, 34, 36, 40-41, 47, 50, 60, 63, 69-71, 78-79, 84, 86, 89-92, 94, 99-100, 103, 111, 114, 118, 120, 122,

INDEX 321 125, 131, 137-138, 150, 152, 161-162, 182, 229-230, 240, 242, 246, 248, 250-254, 256, 261, 289 librarian/s 91, 105, 232, 270 Little Astronomer 40, 227-228 logic 6, 11, 23-24, 27, 39, 44, 52-53, 56, 65, 70-73, 75, 84, 87, 93, 95-98, 100-101, 105-106, 134, 138, 140, 143, 147, 153, 157, 163-166, 168, 173-174, 178, 180-182, 184, 190-191, 193, 196-198, 201, 203, 209, 212-213, 215, 217, 219-220, 226, 255-260, 265-283 Aristotelian 38, 178 logical 18, 65, 102, 128, 163, 178, 202, 256, 259 logician/s 154, 219, 282 The Great Logic see al-Farabi Introduction to Logic see al-Abhari Introduction see Porphyry The Rising Times of the Light see al-Urmavi Shamsiyya on the Rules of Logic see al-Katibi Embracement of Logic and Kalam see al-Taftazani Lubna 33 Macedonia 264 madrasa/s 6, 11, 13-15, 23-24, 30, 66-74, 76-101, 103-108, 109-111, 113, 124-125, 128-135, 139-145, 149, 151-152, 154-155, 163, 169, 171-172, 176-177, 179, 181-182, 184, 188-189, 191-194, 200, 203-204, 206-207, 211-215, 217-220, 223, 225-229, 235-242, 244, 248, 250, 252, 255-256, 258-262 Gazanfer Aga 74 Mansuriyya 135 Mustansiriyya 91 Nizamiyya 23, 67, 70, 77-79, 105, 229, 260 Old Zahiriyya 89 Sultan al-Hasan 68

Maghrib 114, 166, 191, 238 Maghribi 111, 140, 238 al-Maghribi, Ibn Abi Shukr 80, 104, 277 al-Mahdi 286 Mahdiyya 263 Mahmud Ghaznavid 57, 286 see al-Jaghmini see al-Salihi Maimonides 123, 278 Majd al-Din Isma‘il see al-Rumi majlis 149-151, 228, 233, 289 al-Majusi, ‘Ali b. ‘Abbas 116, 249, 251, 253, 277 The Complete Art of Medicine = The Royal Book 116-117 māl, pl. amwāl 83-84 Malaga 166, 271 malakat al-istihdār 181 Malatya 104, 267 al-Malik al-Kamil 287 Malikshah 67, 286 Mamluk/s 24, 27, 6972-73, 75-76, 81, 83-84, 89-90, 94-95, 98, 102, 108-111, 114, 121, 124-128, 130, 132-134, 138, 140-143, 164-166, 169, 177, 180, 187, 193, 217, 219, 226-227, 233, 236, 238-239, 241, 245, 248, 250-252, 255, 258, 263, 266-276, 278-284, 287 Ma’mun, Abu l-‘Abbas 57, 286 al-Ma’mun 286 Manisa 94, 275, 287 al-Mansur 286 al-Mansur Sayf al-Din Qalawun see Qalawun see al-Dashtaki see Ibn al-‘Iraq al-Maqrizi, Ahmad b. ‘Ali, Taqi al-Din 109, 277 Mar Mattai 36, 103-104, 267 Maragha 24, 26, 89, 104-105, 135, 142, 182, 224, 259, 263, 267, 270-271, 276-277, 280, 283-285 Mardin 151, 278

322 INDEX al-Maridini, Fakhr al-Din 174, 256, 278 Marrakesh 83, 165-166, 271, 278 al-Marrakushi, Hasan, Abu ‘Ali 245, 278 Collection of the Principles and Objectives in the Science of Timekeeping 245 Maryam 33 Masawayh, Abu Yuhanna 117 Mashhad 100, 232, 246, 250, 275, 278, 289 mashhūr 176 mashsha’i = peripatetic 101 al-Masihi, ‘Isa b. Yahya, Abu Sahl 57, 59, 100, 201, 251, 253, 256, 278 Mas‘ud I 90, 286 al-Mas‘umi, Abu Sa‘id Ahmad b. ‘Ali 59-60 mathematics 10, 44, 51, 65, 80, 101, 130, 133, 137, 157, 164, 168, 189, 195, 205, 238, 243-244 Matta b. Yunus, Abu Bishr 36, 278 Mazandaran 273 Mecca 9, 73, 88-90, 97, 101, 105, 114, 137, 142, 154, 163, 172, 179, 227, 267, 274, 278, 280-281, 283 mechanics 43, 80, 90, 189, 215, 261, 264-265 Mechanics see Hero medicine 5-6, 10-12, 17-19, 23-24, 27, 30-31, 34, 36-38, 43, 50, 52-53, 58, 65-73, 75-77, 87, 91-98, 101, 110, 114-117, 119, 122-125, 127-132, 134, 139-140, 144-145, 149, 151, 153-154, 157, 165-166, 168, 174, 181, 185, 187, 190-191, 193, 200-203, 208-209, 215-216, 218, 221, 225-226, 240, 247-253, 257, 261, 265-285, 289 theoretical 126 The Balance of Medicine see Muhammad Akbar Arzani Canon of Medicine see Ibn Sina Problems of Medicine for Students see Hubaysh and Hunayn b. Ishaq

Medina 114, 142, 179, 227, 281 Mehmet II Fatih 73, 94, 131, 140-141, 172, 287 Mehmet IV 179, 287 Menelaus 40, 78, 229, 232, 265 On the Sector Figure 40 Spherics = On Spherical Figures 78, 80, 232 Merv 263, 266-267, 275-277, 286 Mesopotamia 26, 49 metaphysics 10, 53, 70, 72, 75, 95, 98, 101, 105, 173, 189-109, 195-196, 198, 200-201, 203-206, 212-213, 215, 258, 261 see also divine science Metaphysics see Aristotle or al-Farabi method/s 6, 10, 12-13, 23, 26, 40, 42, 52, 55, 66, 86-88, 90, 111, 119, 148-149, 151-152, 158-159, 163, 166, 173, 178, 180-182, 205-206, 212, 220, 233, 239, 243, 245, 256, 262 analysis 174 ancient 55 analysis and synthesis 55, 231 argumentative 182 arithmetical 88 of calculation 66, 210 composition 172 construction 108, 243 of criticism 183 of debate philosophical 183 theological 183 diraya 151-152, 166, 169 disciplinary 13 of discourse 212 discursive 168 disputation 179 excursion/s 166 geometrical 45, 159, 238 of instruction 156 learning 147-148, 151, 156, 160, 166, 168, 170, 172, 185

INDEX 323 mathematical 75 medical 161 oral 209 philosophical 23, 61, 195, 255 pre-Islamic 23 rational 175 of reading 151-152 deep 181 of reasoning 202 riwaya 152, 168 scientific 65, 175 standard 169 stereographic projection 80 tahqiq 151-152, 168, 174-177, 183 tahsil 174, 177 taqlid 174, 176 teaching 13, 86, 147-148, 151, 156-157, 160, 166, 169, 171-173, 177, 179, 184- 185, 200, 212 therapeutic 122 traditional 64 transmission 152 of verification or verifying 152, 168, 177 visualization 173 of writing 212 commentary 212, 230 methodology 46, 174, 182, 188, 192, 220 methodical 194 methodological 35, 54, 99, 174, 177, 179-180, 183-185, 200, 218 Mevlevi, Ahmed b. Lütfüllah 179, 278 Middle Books 6, 39-40, 42, 45, 51, 66, 78, 80-81, 86, 97, 215, 225, 227-229, 231-233, 236, 238 Middle East 10, 18, 24, 101, 143 Mir Damad, Muhammad Baqir, Astarabadi 98, 100, 278 Mir Muhammad Mu’min 130 Mir Muhammad b. Mas‘um Shah 249, 279 mirror/s 198, 201 burning 10, 43, 97, 189, 198, 218, 275 image 206

al-Misri, Najm al-Din 246, 278 model/s 85, 169, 174, 201 non-Ptolemaic 23, 26 planetary 84-85, 89, 111 modelling 88, 244 Mongol/s 5, 24, 27, 50, 67, 72, 80-81, 84, 89, 91, 95, 100, 102, 104, 114, 119, 124, 128-129, 134, 143-144, 170, 214, 247, 250, 254, 263, 275 Morocco 137, 143 mosque/s 11, 13-14, 23-24, 70-71, 73, 88, 94, 111, 113, 130-131, 140, 149, 152, 154, 182, 223, 255, 258, 260 Aya Sofya 140-141 Azhar 246 Fatih 140-141 Ibn Tulun 94 Sultan al-Hasan 68 Sultan Süleyman 131 Mosul 36, 44, 67, 70, 77, 103-104, 229, 233, 266-267, 269, 273-274, 279, 284, 286 al-Mu‘azzam ‘Isa 152, 287 mu‘jam 147 Mubashshir b. Fatik, Abu l-Wafa’ 42, 278 mudarris/un 68, 71-72 Mughal 30-31, 72, 85-87, 109, 111, 142,145, 225, 241, 249, 256, 264, 267, 278, 285 Muhammad 18, 37, 96, 161, 236, 285 ‘Ala’ al-Dawla see ‘Ala’ al-Dawla Muhammad b. Abi Bakr b. Muhammad 51-52, 78, 233, 279 b. ‘Abdallah al-Hassar, Abu Bakr see al-Hassar b. ‘Abdallah b. al-Mahall (?) al-Baghdadi see al-Baghdadi b. ‘Abd al-Latif al-Khujandi see al-Khujandi b. ‘Abd al-Rahim, Abu l-Baqa’ 132 b. ‘Abd al-Wahhab 98, 279 b. Ahmad al-Ghazuli see al-Ghazuli

324 INDEX b. Ahmad b. Michael 118 b. Ahmad al-Shanni see al-Shanni b. ‘Ali, Abu l-Harith 57, 286 al-Amin al-Muhibbi see al-Muhibbi Baqir b. Zayn al-‘Abidin 235, 242 Sources of Arithmetic 242 b. Ibrahim see Ibn al-Turays b. Isma‘il, Abu l-Wafa’ 132, 279 b. Jahm [al-Barmaki] 48 b. Kathir al-Farghani see al-Farghani b. Mahmud al-Amuli see al-Amuli b. Mansur see al-Dashtaki b. Mas‘um 279 b. Muhammad see Ibn Saghir b. Musa see Banu Musa b. Musa al-Khwarazmi see al-Khwarazmi Khwarazmshah 250 Quli 130, 286 b. Sulayman al-Rumi see al-Kafiyaji Tabib Gilani see Gilani b. Tekesh 214 b. Yusuf al-Sanusi see al-Sanusi, Muhammad b. Yusuf muhaqqiq/un 174, 176, 219 al-Muhassin b. Ibrahim b. Thabit 50, 52, 279 al-Muhibbi, Muhammad al-Amin 109, 168, 279 mülazemet 70 mülazim 70 Mulla Niksari 170, 279 Mulla Sadra 98, 100, 279 al-Munajjim, ‘Ali b. Yahya 50 müneccimbașı 179 Munla Sharif al-Kurdi 173, 279 al-Muqtadir bi-Llah 55, 286 see hospital music 53, 215, 217, 261, 270, 273 theoretical 10, 43, 52, 100, 189 musical 198, 201, 209 Muslim/s 11, 18, 24

Mustafa 141 Mustafa Sidqi 80 al-Musta‘in bi-Llah 39, 286 see Ahmad al-Mustansir bi-Llah 91, 287 see madrasa al-Mu‘tadid bi-Llah 50, 286 mutakallim/un 105, 107, 213, 219 mutakallim-philosopher 206 al-Mu‘tasim bi-Llah 39, 286 muwaqqit 72 müvekkithane 223 Nablus 251 Najaf 278 Najm al-Din b. al-Hajj 132 Nami (pen-name) see Mir Muhammad b. Mas‘um Shah Nasa 280 Nasaf 279 al-Nasafi, Burhan al-Din 105- 107, 110, 279 Commentary on the Foundation of Intellectual Perspicacity 105 al-Nasawi, ‘Ali b. Ahmad 232-233, 280 Commentary on the Sector Theorem 233 Nasir al-Din Yusuf 89, 287 see al-Tusi see Ibn al-Turays Natanz 273 al-Nawa’i, Muhyi al-Din 98, 280 al-Nawbakhti, Abu Sahl 50, 280 al-Nawfili, Ibrahim b. Muhammad see Ibn Zuqqa‘a al-Nayrizi, Abu l-‘Abbas 280 Commentary on the Almagest 90 Neoplatonic see philosophy and Plato Necessary Existent 23 Nicomachus of Gerasa 209, 265 Introduction to Arithmetic = Introduction to Number Theory 38, 44-45, 47, 210 Niqula b. Yusuf 254, 280

INDEX 325 al-Nisaburi, Nizam al-Din 84, 134, 236-237, 241, 280 commentary on al-Tusi’s Memoir on Astronomy 171 The Epistle on Arithmetic for Shams [al-Din] = Treatise for Shams al-Din [Abd al-Latif ] on Arithmetic 85, 239 Nishapur 67, 70, 127, 136, 206, 212, 266, 269-270, 275, 277 Nisibis 35 Nizam al-Mulk 67 North Africa see Africa Nu‘aym b. Muhammad b. Musa 50-51, 280 al-Nu‘aymi, ‘Abd al-Qadir 92-93, 280 number theory 6, 10, 43, 47, 52, 61, 95, 100, 105, 137, 189, 195, 202-203, 208-209, 215, 217, 231, 238-239, 242, 261, 264-265 Nur al-Din Zangi 93, 121-122, 286 observation/s 58-59, 202, 225, 229, 244 astronomical 19, 37, 58 empirical 59 observational instruments 236 oculist/s 125, 128, 132, 160 Öljaytu 214, 287 oneiromancy 200, 214 ophthalmologist/s 95, 115, 125, 161 ophthalmological 128 ophthalmology 91 optics 10, 43, 48-49, 97, 171, 189, 201, 215, 231, 261, 264 Optics see Euclid, Ibn al-Haytham or al-Kindi orb/s 46, 88 celestial 106 lunar 19 Ottoman 10, 27, 30-31, 69-70,72-74, 80-81, 83-85, 89, 91, 94-95, 109, 111, 114-115, 126, 129-131, 140-146, 152, 166, 168-169, 172, 177, 179, 181, 187,

189, 217-218, 223, 225, 227, 232, 235-237, 239-242, 245-248, 250, 252-253, 256, 259, 263, 268-269, 278-281, 283-285, 287 Padua 144, 248 Pakistan 249, 264 Patriarch Ignatius IV see Philoxenus Nemrod patronage 14, 21, 34, 93, 114-116, 136, 138-140, 142, 182, 257 courtly 19, 117, 182 urban 19 Pappus of Alexandria 40, 265 Pashto 247 Paulus of Aegina 251, 265 Medical Compendium in Seven Books 161 Pax Mongolica 24 Peninsula Arabian 83, 136, 163, 192, 251, 259 Iberian 94, 136, 218, 248, 263 Pergamon 9, 264-265 Persian 9, 38, 40, 62, 64, 67, 80, 87, 101, 115, 131, 138, 141, 144, 146, 187, 189, 200, 203, 208-211, 213-214, 217, 225, 227-228, 237, 240, 242, 247-250, 253 Middle 18-19, 34 New 21, 35, 57 Phenomena see Euclid phenomena 46 meteorological 45, 104 Philoponos, John 99, 265 philosopher/s 21, 26, 30, 33, 35-36, 38-39, 44-47, 91, 95-96, 99, 102, 104, 107-108, 119, 121, 135-136, 152, 154, 183, 189, 192, 194-196, 198, 201-202, 206, 209, 211-212, 217-221, 248, 250, 255-259 philosopher-physician/s 95-96 philosophy 5, 17-18, 21, 23-24, 26-27, 30-31, 33-34, 36-39, 43-44, 48, 50, 58, 64-65-68, 75-77, 80, 93, 95, 97-98,

326 INDEX 100-101, 104-106, 110, 127-128, 134-136, 139-140, 143-144, 147, 149, 152-155, 157, 164-166, 168, 174-175, 177, 181-182, 187-189, 191-193, 195-198, 200-201, 203, 206, 208, 210-212, 215, 217-218, 220-221, 236, 247, 250, 255-261, 264-285 Greek 27 of light = illuminist = of illumination 26, 30, 99,139, 164, 258 natural 6, 10-12, 19, 24, 30, 36-37, 43-44, 49, 53, 56, 65, 69-72, 75, 77, 84, 95- 96, 98, 100-101, 104-107, 145, 175, 189-190, 196, 198, 200-201, 203-205, 210, 213- 217, 221, 225-226, 244, 249-250, 255-258, 260-261, 265-266, 270, 272, 275-276, 282 Aristotelian 19 Neoplatonic 30 peripatetic 258 practical 75, 200-201, 203 theoretical 200, 204-205, 212 Philoxenus Nemrod 280 physician/s 11, 19, 34, 36-38, 43-44, 53, 55-56, 68-69, 78, 80, 86, 91-93, 95, 97-98, 102, 104, 115-117, 119, 121-129, 131-132, 134-135, 144, 152, 154, 160-161, 175, 197, 206, 209, 2015, 217, 233, 248-254, 256, 257 Ayyubid 92, 127, 250 Christian 11, 24, 115, 117, 122, 126, 253-254 court 117, 140, 160 head 93, 122, 125 Jewish 24, 71, 122, 126, 144, 254 Mamluk 127, 258 Muslim 122, 126 Ottoman 131 Shi‘i 24 Sunni 24 Syriac 160 Syrian 127 physiognomy 200, 211, 214, 281 physiognomic 33

Pitane 38, 229, 264 planet/s 46-47, 62, 88, 209, 215, 231, 244 additional 19 planetary 23, 26, 72, 84-85, 88-90, 107, 109, 111, 135, 139, 143, 154, 163, 170, 209, 215, 244, 247, 261 Plato 31, 99, 257, 261, 265 Platonic 204 Platonist 258 Neoplatonic 19, 30, 43, 99-100, 105, 192, 195-197, 199, 201, 203, 207-208, 215, 273 Podolia 263 Polemon 99-100, 265 politics 111, 189, 196, 200, 208 identity 192 of numbers 145 religious 87 Timurid 109 Porphyry 265 Introduction = Isagoge 38, 209, 259 post/s 23, 68, 70, 134, 139, 166, 169 postulate/s 54, 231, 237 parallel 40 practice/s learning 11 teaching 11 prayer 67, 161, 214 direction/s 21, 73, 88, 154, 163, 246, 261 time/s 21, 73, 154, 163, 244, 246 Prime Mover 23 Proclus 99, 261, 265 Ptolemy 23, 46, 50, 184, 261, 265 Almagest 38-40, 45, 62, 66, 80-81, 86, 144, 224-225, 229 Commentary on the Almagest see al-Nayrizi Commentary on the Almagest see al-‘Urdi, Mu’ayyad al-Din edition of the Almagest see al-Abhari Tetrabiblos 52 Pythagoras 261

INDEX 327 al-Qabbani 90 Qabus b. Vushmgir 57, 59, 286 Qadizade al-Rumi 84, 170-172, 233, 237, 280 commentaries on The Epitome of Plain Theoretical Astronomy The Fundamental Theorems 237 al-Qalasadi, ‘Ali b. Muhammad 83, 136-138, 152, 239, 280 The Introduction to the Dust Letters 137 Qalawun, al-Mansur, Sayf al-Din 94, 121, 124-126, 256, 287 Qalonymus ben Qalonymus 44, 281 Qaraman 138 Qazvin 100, 165, 264, 266, 268, 276 Qenneshre 35-36 Qift 272 qibla 88 direction/s of prayer = prayer direction/s 88, 154, 163, 246, 261 qira’a 189 Quetta 279 Qur’an 37, 58, 67-68, 75, 133, 137, 141, 155, 163, 189-191, 207, 211, 267, 274, 280-281, 283-284 house of (reading) 23-24, 67, 71, 152 al-Qushji, ‘Ali 84-85, 141, 240, 281 Qutb al-Din al-Razi al-Tahtani see al-Razi, Qutb al-Din Qutb al-Din al-Shirazi see al-Shirazi, Qutb al-Din

Book for al-Mansur 251 Comprehensive Book on Medicine = Hawi = Jami‘ 93, 123, 126-127 al-Razi, Muhammad b. ‘Umar, Fakhr al-Din 23, 95, 101,108, 121, 127, 143, 164, 174, 176-177, 182-183, 193, 212-213, 218-220, 258-260, 281 The Book of the Sixty Sciences 213 commentaries on the theoretical part of Ibn Sina’s Canon of Medicine = Commentary of the Kulliyat of the Qanun 119, 121 The Philosophy of the Easterners 212 Pointers and Reminders 181-182, 212, 214 Sources of Philosophy 212 Eastern Investigations 176 The Essence of Philosophy 182 The Garden of Lights and the Truth of Secrets 213 The Summa of the Sciences 213 al-Razi al-Tahtani, Qutb al-Din 140, 165, 259, 284 Rayhana 33, 60-62, 64 ridicule 21, 244 riwaya 152, 168 Rome 9, 38, 264, 265, 281 Roman Empire 19 Rufus 161, 251, 265 On the Ailment of Melancholy 116 al-Ruhawi, Ishaq b. ‘Ali 117, 160, 281 The Education of the Physician 117 Rukn al-Dawla 39, 286 al-Rumi, Isma‘il, Majd al-Din 165, 281

al-Rahbi, Radi al-Din 123, 281 Rajab b. Husayn 173, 281 Rayy 39, 56, 114-115, 119, 129, 136, 212, 249, 263, 266, 268-269, 273, 275-277, 280-284, 286 Rauwolf, Leonard 166 al-Razi, Muhammad b. Zakariyya’, Abu Bakr 93, 96, 119-120, 123, 126-127, 160, 249, 251, 253, 281

Sabta 269 Sabur b. Sahl 116, 123 Dispensatory 116 Safad 143 Safavid 30-31, 72, 81, 83-86, 98-100, 109, 111, 129-130, 143, 147, 226-227, 235, 238, 241-242, 261, 264, 266-268, 277-278 al-Sahrawi, Yahya b. Muhammad 133, 281

328 INDEX Sa‘id b. al-Hasan 117 Stimulating a Yearning for Medicine 117 al-Sakhawi, Shams al-Din 69-70, 81-82, 90, 96-98, 100, 109-110, 132-133, 137-138, 142, 144, 149, 163-166, 168, 177, 233, 239, 252, 255, 257, 259, 281 dictionary of famous men and women of the ninth century after the hijra 163 Epitome on the Science of Arithmetic 239 Salah al-Din 152, 286 salary/ies 23, 68, 74, 91, 93, 125 al-Salihi, Mahmud al-Basir 173, 281 Saljuq/s 67, 70, 127, 269-270, 273, 277, 279, 283-284, 286 Great 23, 263, 275-276, 281 Rum 266, 281, 283, 285 Salonica 281 Samanid/s 34, 39, 204, 206-207, 263, 267, 273, 275-278, 282 Samarkand 9, 27, 39, 81, 139, 141-142, 170-172, 237, 254, 263, 273, 275-276, 278-285 al-Samarkandi, Najib al-Din 252, 254, 282 The Book of Causes and Symptoms 254 al-Samarkandi, Shams al-Din 170, 177-179, 233, 237, 257, 282 The Epistle on the Science of the Etiquette of Investigation 178 The Fundamental Theorems 237 Samarra 263, 286 Samos 229, 264-265 Sanad b. ‘Ali 50, 282 Sanjar al-Shuja‘i, ‘Alam al-Din 125 Sanskrit 18-19, 34, 64, 248 al-Sanusi, Muhammad b. Yusuf 173, 282 Sarakhs 282 al-Sarakhsi, Ahmad b. al-Tayyib 43, 282 Sarkhad 270, 272-273 Saruhan 89, 97, 275 Sasanian 19, 33-34, 115-116

Sayf al-Din al-Amidi see al-Amidi scholar/s 7, 11-12, 14, 19, 21, 24, 26, 33-34, 36-37, 39-42, 45-47, 49-50, 54, 56-59, 65, 70, 72, 74, 76-78, 80-81, 85, 89-90, 96-97, 101-102, 104-111, 125, 127-129, 132, 135, 137-145, 152, 155-158, 165-166, 169-170, 172-182, 185, 190-191, 193, 199-200, 206, 210-213, 216-218, 221, 223, 225, 227, 230-233, 235-236, 238, 240-243, 248, 250, 255-257, 259-260-261, 266 Abbasid 143 Anatolian 26, 165 ancient 264 Andalusian 89, 173, 191 Ayyubid 143 Buyid 256 Byzantine 144 Central Asian 110, 178, 183, 242 Christian 9, 37, 43, 106, 109, 144, 192, 199 Egyptian 140 foreign 142 Hanbali 110, 165 Ilkhanid 85, 236 Iranian 102, 134, 143, 227, 242, 259 Jewish 9, 144, 192, 199 Kurdish 177 legal 26, 98, 109-110 madrasa 98, 132, 203, 238, 260-262 Mamluk 90, 109, 238, 241-242, 245, 255 medical 166 medieval 24, 54, 173 mediocre 157 Muslim 9, 19, 26, 36, 95, 102-103, 138, 144, 179, 192, 199 of non-Arab origins 19 North African 137, 177 Ottoman 89, 141, 152, 169, 179, 245 religious 21, 26, 50, 87, 93, 95, 102, 127, 194, 206, 211-212, 226, 238, 255 Safavid 84, 99, 238

INDEX 329 Shi‘i 26, 85, 87 Sunni 26, 101, 121, 143 Syriac 37, 102 Syrian 140 Timurid 236, 245 Turkish 89, 115 scholarly 6, 11-12, 24, 34, 37, 39, 43, 47, 50, 55, 57, 64, 66, 70, 73, 95, 104, 108, 110-111, 128, 132, 134-135, 138, 140-141, 143, 145, 149, 152, 155-157, 169, 177- 178, 180-182, 185, 187, 193-194, 206, 210, 223, 225, 242-243 scholarship 30, 140 school/s 5-6, 9-14, 21, 23, 31, 36, 45, 58, 67, 73, 76-77, 92, 105, 111, 130, 146, 171, 185, 188, 204, 228, 242, 245, 260 legal 21, 71, 91 mathematical 19 medical 9, 19, 92 ancient 31 of Nisibis 35 philosophical 9, 19 religious 23 law 23, 69, 180 Shafi‘i 67 Sunni 23, 94 technical 146 village 226 schoolbook/s 14, 84 science/s 5-6, 9-10, 13-15, 17-19, 23, 27, 37, 46, 61-62, 65, 69, 77, 86, 100, 106, 109, 111, 113, 124, 127-128, 148-149, 151, 154-156, 164, 169, 177, 181, 185, 187-188, 190-208, 211, 213-219, 225, 240, 244, 250, 256, 258, 262 ancient 17, 24, 75, 190, 193 of the ancients 75, 188-189, 214 applied 204 Arabic 75, 200 arithmetical 152 branch 86, 201, 209, 214-217 of composition 195-196

of the configuration of the universe 191, 195-196, 215, 244 of disputation 178 divine 75, 101, 105-106, 190, 195, 200-201, 204, 207, 212-213, 258, 279, 281 doctrinal 207-208 fundamental 214, 216-217, 227 of handbooks and calendars 244 human 195 Indian 64 inheritance 153 instrumental 180 of investigation 178 of juristic dialectics 178 of language 191, 198 legal 10, 12 of magic letters and numbers = of letters 27, 108-109, 165 mathematical 10-12, 17-19, 23-24, 27, 30-31, 33-34, 36-40, 44, 49, 53, 55-58, 64-70, 72-73, 76-78, 80-81, 83-84, 86-87, 91, 97, 101, 104, 106, 108, 110, 131-132, 134, 136-138, 141, 143-145, 147, 149, 152-153, 157-158, 160, 163-164, 170, 172-173, 179, 183-185, 187, 189-190, 193-196, 198, 200-201, 203-205, 208-210, 213-215, 217, 221, 223, 225-227, 229, 231, 241, 243, 245, 247, 256-257, 259, 261, 266-285 medical 108, 194 of medicine 124 of the moderns 75, 214 natural 105-106 new 19 occult 10, 12, 17-19, 23, 27, 31, 36, 69, 77, 101, 154, 185, 187, 189190, 194, 205, 221, 242, 276 practical 208 Persian 200 philological 96, 104, 164-165, 180, 188-191, 193-194, 198, 216, 269

330 INDEX philosophical = of philosophy or wisdom = science of the philosophers 37, 71, 75, 96, 104, 130, 136, 190, 194-195, 203, 207, 211-217 political 198 of prayer times 244 quadrivial 195 of the quality of observations 244 rational 73, 75, 87, 101, 131, 138, 141, 143, 153, 165, 170, 174, 179, 181-182, 185, 190-191, 203, 213-214, 259 religious 31, 95, 97-98, 130, 137, 152-153, 157, 164-165, 168, 174, 177, 188-189, 191, 193, 206-207, 214-215, 217, 259, 267-268, 270, 272, 278, 281, 284 of shadow instruments 244 of (the projection) of the sphere on a plane 244 of the stars 191, 195, 243 of the substances 195 surveying 196 of talismans 200 theoretical 204, 207-208, 211, 213 of timekeeping 10, 26, 72, 81, 89, 218, 244 transmitted = of transmission 75, 101, 130, 143, 153, 169, 190, 213-214 universal/s 204, 217 demonstrative 198 of weight/heavy bodies 10 Seven Sleepers of Ephesos 38 Seville 83, 166, 270, 274 Shabestar 266 shagerd 131 Shahjahanabad 264 Shahmardan b. Abi l-Khayr 193, 210211, 282 The Book of Entertainment 210-211 The Garden of Astrologers 210 Shahrazur 282 al-Shahrazuri, Shams al-Din 102, 282

al-Shamuli, ‘Abd al-Majid 90, 282 al-Shanni, Muhammad b. Ahmad, Abu ‘Abdallah 41, 80, 282 Shaykh Abu Ishaq 214, 287 shaykh 124, 151, 161, 173 shaykh al-islam 85 al-Shayzari, Jalal al-Din 160, 283 Shihab al-Din see Ahmad b. Khalil Shi‘i 23-24, 26, 30, 67, 71-72, 80, 85, 87, 99, 128, 130, 143, 171, 214, 261, 284 Shiraz 9, 11, 30, 72, 80-81, 85-87, 98, 100, 133-135, 138-139, 141-142, 214, 237, 261, 263, 267-268, 274-276, 279, 283, 286-287 al-Shirazi, Qutb al-Din 80, 85, 89-90, 102, 111, 134-135, 174, 193, 228, 230, 237, 242, 245, 249, 261, 283 The End of Perception on the Science of the Celestial Orbs = The Limit of Perception 90 Persian translation of the Elements 228 Royal Gift 89, 249 Shirvan 172, 283 al-Shirvani, Fath Allah 170-172, 283 Sibt al-Maridini, Muhammad b. Muhammad 81, 83, 228, 246, 283 Sidon 264 Sidqi, Mustafa b. Salih 80, 232, 283 al-Sijistani, Abu Sulayman, the Logician 154, 283 al-Sijzi, Ahmad b. Muhammad b. ‘Abd al-Jalil 80, 157-159, 173, 217, 237, 283 Book on Making Easy the Ways of Deriving Geometrical Theorems 157 Simeon of Qal‘at Rumayta 104, 283 Simnan 280 Sinan b. Thabit 50, 55-56, 283 Sind 249 Sinjar 128, 270 Sistan 283 Sivas 9, 233, 248, 266, 283 Slavic 240 square/s 62, 66, 83, 88, 201, 243

INDEX 331 magic 10, 108, 215, 232, 242-243, 261, 283 Stagira 264 stipend/s 23, 68, 92, 113, 129, 140 student/s 5, 10-11,13-14, 21, 23, 27, 33, 37, 40, 42-44, 46-47, 49-52, 55, 57-59, 61, 64-66, 68-70, 73-76, 78, 81-84, 86, 88, 90, 92-93, 95-102, 104-105, 110-111, 113-114, 116-119, 121-125, 129-136, 138-142, 145-149, 152-156, 158-166, 168-169, 171, 174-175, 178, 180-182, 184, 193-196, 200, 203-204, 208, 210, 212-213, 216, 218, 225-227, 229-233, 235, 239-240, 245-246, 249-252, 257, 259-260 Arabic 50 Christian 35, 70, 144, 161 Hindu 87 Ilkhanid 236 Indian 246 Jewish 71, 144 madrasa 114, 131, 220, 251 medical 96 Muslim 35-36, 38, 104-105, 125 Ottoman 236 princely 45, 154 Shi‘i 71 Syriac 36, 50, 104 al-Sufi, ‘Abd al-Rahman 39, 77, 284 Sufi 27, 70-71, 105, 109-110, 128, 179, 214 Sufism 23, 26, 110, 266, 268-270, 272-274, 277, 281 Suhraward 284 al-Suhrawardi, Shihab al-Din 26, 30, 99, 101-102, 135, 139, 164, 258, 284 Süleyman Kanuni = Süleyman the Magnificent 94, 131, 285 Sultaniyya 214, 263, 267, 287 summa/s 6, 117, 188-190, 201, 211 Sunni 23-24, 26, 30, 67, 71-72, 85, 94, 99, 101, 121, 128, 143, 180 surgeon/s 115, 125, 128, 132, 161, 251

Synopses of the Alexandrinians = Alexandrian Epitomes 251 Syracuse 264 Syria 10-11, 24, 36, 38, 67, 69, 70, 72, 78, 80-81, 84, 89-90, 92, 94, 98, 100, 128-129, 136-137, 140, 143, 144, 163-164, 173, 214, 217-219, 226-227, 239-241, 248, 250, 253, 256-259, 263 Ayyubid 193, 257 Mamluk 81, 102, 108, 110, 114, 193 northern 254 Syrian 89, 97, 127, 140, 239 Syriac 18, 24, 35-36, 45, 49-50, 54, 58, 102, 104, 192, 197, 208, 256, 267 Aramaic dialect 18 Christian/s 24, 37, 42-43 Greco-Syriac 38 monk/s 103 philosopher/s 35-36, 104 physician 160 scholar/s 102 student/s 36, 104 translation/s 9, 243 surveying 85, 87, 105, 149, 189, 191, 196, 201, 209, 215, 238, 240-241, 277 system/s 74, 148, 200, 204, 211, 215, 242 arithmetical 209 of calculation 10, 61, 215 decimal positional 19, 200, 209 educational 75, 87, 142, 179 examination 131 knowledge 6, 19, 188, 193-195, 204, 207, 216, 260 madrasa 101, 141-142, 179, 259 modern Western 10 religious 191 sexagesimal 209 Tabriz 40, 100, 104, 128-129, 141-142, 144, 263-264, 267-268, 273, 281, 283-284, 287 Taftazan 284

332 INDEX al-Taftazani, Sa‘d al-Din 139, 165, 170, 259, 284 Embracement of Logic and Kalam 259 tahqiq = taḥqīq 151-152, 168, 174-177, 183 tahsil = tạḥṣīl 174, 177 al-Tahtani, Qutb al-Din al-Razi see al-Razi al-Tahtani, Qutb al-Din Taj al-Din, son of Simeon 104, 284 Taju 275 taqlid = taqlīd 174, 176 talisman/s 106, 108, 110, 135, 190, 214, 242, 283 talismanic 31 tasdiq/at 218 Tashköprüzade, Ahmad b. Mustafa 141, 168-170, 172-173, 240, 284 tasawwur 218 teacher/s 5-6, 10-11, 13-15, 21, 24, 33-34, 36-42, 44, 47-49, 51, 57-59, 64-66, 68-76, 80-683, 85-85, 88-94, 96-98, 100-101, 103-106, 108-109, 111, 113-114, 121-125, 129-134, 136-138, 140, 142, 144, 146-149, 151-152, 154-155, 158, 161-164, 166, 168-174, 177, 179, 182, 184, 189, 192, 194, 197-199, 200-201, 204, 206-207, 210-212, 214-215, 217-219, 225-226, 229-230, 232, 235-239, 242, 251-252, 256-257, 259 Tekesh, ‘Ala’ al-Din 287 text/s 9, 12-14, 17-19, 23-24, 26, 33-35, 38-40, 42, 44-55, 58-59, 65-66, 69-70, 72, 77-78, 80-90, 93, 96, 98-102, 104-108, 110, 122-123, 125-127, 134-135, 137-138, 141, 147-149, 151-155, 157, 160, 162-166, 168-173, 175-182, 184, 187-188, 192-193, 195, 198-201, 205, 207, 210-212, 217-219, 221, 223, 225-227, 229-233, 235-242, 244, 246-252, 254 - 262 agricultural 24 algebraic 240 ancient 26-27, 35, 39-40, 42, 45, 47, 53, 64, 78, 97-98, 116, 122, 176, 225-227, 229, 232, 250-251, 254

Arabic 9, 39, 102, 227, 254, 259 arithmetical 163, 240 astrological 18, 31, 93, 109, 137 astronomical 24, 26, 58, 77, 93, 137, 144, 246 calendrical 24 compendium 52 encyclopaedic 203 doxographical 9 Galenic 160, 251 geometrical 77, 233 Greek 27, 35, 38-40, 43, 46, 53-54, 64, 78, 116, 122, 256 historical 18 kalam 30, 175, 235 Latin 248 logical 18 mathematical 26-27, 30, 35, 38, 42, 45, 55, 70, 77-78, 80, 83, 100, 147, 153, 164, 168- 170, 174, 184, 227, 229-232, 235, 238, 240 Mamluk 76, 241 medical 9, 24, 35, 38, 42, 73, 91, 93, 96-97, 102, 122, 153, 159, 248-252, 254- 255 medieval 26, 97-98, 176, 229 Mughal 249 New Persian 35 Persian 9, 228, 240, 248 philosophical 9, 35, 38, 42, 47, 54, 93, 98, 102, 153, 163 problem 53 research 51 Sanskrit 64, 248 school 6, 12, 38, 91, 148, 182, 184, 237, 240-241, 258-259 scientific 13, 35, 37, 46-47, 49, 54, 64, 102, 155, 253 for students 51 synopsis 52 Syriac 35, 256 talismanic 31 teaching 12-15, 27, 44, 47, 55, 78, 80-81, 85-86, 88, 111, 121,

INDEX 333 142-143, 164, 184, 192, 196, 205, 225, 233, 235, 237-238, 241, 248, 257-258 translated 21, 35, 192 Turkic 9 textbook/s 10, 12, 14, 26, 30, 33, 38, 49, 51-52, 62, 66, 78, 83-84, 86, 101, 104, 112, 146, 207, 221, 223, 226-227, 241, 252, 258, 260 textual 12, 47, 53, 99, 171, 180, 182, 184, 207, 227, 231, 237, 241, 252 Thabit b. Qurra 40, 42, 49-55, 58, 78, 80, 236, 243, 251, 256, 284 Book of Abu l-Hasan Thabit b. Qurra al-Harrani to the Students on the Compound Ratios = On Compound Ratios 51-52, 78, 232-233 The Book on the Steelyard 53 edition of Autolycus’ Risings and Settings 232 On Geometrical Problems 53 On the Given [Things] 232 Liber karastonis 53 Thabit b. Sinan 50, 284 Theodosius of Bithynia 38-40, 77-78, 167, 231-233, 265 On Days and Nights 40, 78, 231 The Habitations = The Inhabited World 39, 78, 231 The Spherics 39, 77-78, 167, 231, 233-234 Theodosius II 38 Theon of Alexandria 38, 265 theurgy 200 Tikrit 103, 267 Timur 27 Timurid 30, 72, 81, 84-86, 100, 108-109, 111, 139, 141, 172, 175, 225, 227, 235- 236, 240-241, 245, 250, 263, 266, 268, 272, 274-275, 279, 281283, 285 Tlemcen 9, 11, 136-137, 152, 165, 173, 260, 280, 282 Tokat 128

training 11-12, 21, 34-35, 43, 58,65, 73, 83, 97, 107, 117, 122, 132-134, 136, 138, 149, 154, 166, 198, 235, 237-238, 251 astronomical 58 autodidactic 262 disputational 177 family 132-134 madrasa 145 mathematical 58, 232 medical 114, 131, 133, 161 philosophical 127, 177 practical 12 professional 116 transformation 30, 61, 72, 107, 159, 175, 209, 258 cultural 18 transform 23, 54, 61-62 translation/s 9, 17-19, 27, 33-35, 40, 42-43, 45, 50, 52, 54, 64, 78, 99, 102, 116, 137, 144, 156, 179, 210, 219, 229, 231, 236, 240, 251, 253, 256-257, 269, 281 Arabic 9, 17, 19, 33, 39-40, 208, 250 Hebrew 44 Latin 54 literal 208, 243 Persian 228, 237, 250 Syriac 9, 243 translate 10, 18, 21, 26, 30, 34-35, 37, 39, 42, 45, 50, 52, 54, 58, 131, 144, 146, 160, 190, 192, 197, 208, 225, 242, 253 translator/s 19, 53-54, 198, 208, 273 travel 6, 11, 24, 49, 56, 67, 76, 100, 104-105, 107, 111, 113-114, 116, 133, 135-136, 138-145, 147, 152, 172-173, 179, 212, 218, 250, 253, 257, 259, 262 Trebizond 144 Tunis 9, 11, 83-84, 133, 136-138, 165, 260, 271-272, 280 Tunisia 84, 101, 138, 143 Turkic 23, 26, 115, 128, 138, 140, 253, 259

334 INDEX Tus 171, 268, 283 al-Tusi, Nasir al-Din 26-27, 40, 80, 86, 90, 101, 104-105, 108, 134-135, 143144, 164, 167, 174, 176, 182-183, 193, 229-232, 234-235, 255, 257-261, 284 commentary on Ibn Sina’s Pointers and Reminders 176, 255 edition of Aristarchus’s On the Two Luminous Bodies 232 Archimedes’s Lemmas 232 On the Measurement of the Circle 231 On Sphere and Cylinder 231-232 Euclid’s Data 231 Elements 86, 228, 230-231, 235-237 Optics 231 Phenomena 231 Menelaus’s On Spherical Figures 232 Middle Books 86, 231 Ptolemy’s Almagest 224 Thabit b. Qurra’s On the Given [Things] 232 On Compound Ratios 232 Theodosius’s On Days and Nights 231 On Habitations 231 Spherics 167, 174, 231, 234 Memoir on Astronomy 84, 89-90, 171, 245, 247 The Purification of the Belief  219 On the Sector Figure 40 Twenty Chapters on the Astrolabe 247 Thirty Chapters on the Calendar 247 al-Tusi, Sharaf al-Din 232, 284 al-Tustari, ‘Abd al-Sammad 119, 121 Tyr 265

Ulugh Beg 81, 139, 141, 170-172, 225, 237, 247, 285 Umayyad/s 18, 38, 263, 273, 285 al-‘Urdi, Mu’ayyad al-Din 80, 89, 224, 245, 283 Commentary on the Almagest 245 al-‘Urdi, Muhammad b. Mu’ayyad al-Din, Shams al-Din 224, 285 Urdu 247 al-Urmavi, Siraj al-Din 140, 143, 152, 257-259, 285 The Rising Times of the Light 259 Uzun Hasan 141, 287 vizier 23, 33-34, 36, 39, 50, 53, 67, 80, 93, 121, 126, 128, 130, 172, 203, 206-207, 241, 261, 272 waqf  68, 92, 116, 124-126, 129, 131 Yahya b. ‘Adi 99, 285 Yazd 139, 208, 210, 235, 235, 242, 273, 277-278, 286-287 Yemen 72, 84, 143, 227, 263 Yuhanna b. Masawayh 117, 160, 285 Yusuf b. Jurjis 254, 285 Yusuf Mirza 141 Zabid 267 zahiri 180 al-Zahra 285 al-Zahrawi, Abu l-Qasim 253, 285 za‘irja 109 Zanjan 277 Zaragossa 270 Zayn al-Din Tahir 70 zij 110