Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures

Advisory Board

HO PENG YOKE, Needham Research Institute, Cambridge University, U.K.

DAVID TURNBULL, Deakin University, Geelong, Australia

JAN P. HOGEND UK, Mathematics Institute, University of Utrecht, The Netherlands

GLORIA T. EMEAGWALI, Central Connecticut State University, New Britain, CT, U.SA.

SEYYED HOSSEIN NASR, George Washington University, Washington, D.C., U.S.A.

SUSANTHA GOONATILAKE, United Nations, New York, NY, U.S.A. Encyclopaedia of the History of Science, Technology, and Medicine • Ill Non-Western Cultures

Editor

HELAINE SELIN Science Librarian, Hampshire College, Amherst, Massachusetts, U.S.A.

Springer-Science+Business Media, B. V. A C.I.P. Catalogue record for this book is available from the Library of Congress

ISBN 978-94-017-1418-1 ISBN 978-94-017-1416-7 (eBook) DOI 10.1007/978-94-017-1416-7

Printed on acid-free paper

02-0698-500 ts

AII rights reserved © 1997 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1997 Softcover reprint ofthe hardcover 1st edition 1997 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. A remarkable world-map centred on Mecca with a highly sophisticated mathematical grid for finding the direction and distance to Mecca from any location in the Islamic Commonwealth. The map is engraved on brass and was made in Iran ca. 1700. However, the geographical data on the map was compiled some 250 years previously, and the mathematics underlying the carto• graphical grid were known to Muslim scientists such as Habash in the 9th century and al-Biruni in the 11th century. (See: "Maps and Mapmaking: Islamic World Maps Centered on Mecca". Pri• vate collection, courtesy of the owner and D.A. King, contributor. Photo by Christies of London.) In Memoriam Madilyn J. Engvall 1936-1994 The process Is old light truth passing through new glass

-Tim Davis TABLE OF CONTENTS

Preface ...... x1

Personal Note from the Editor ...... xm

Acknowledgements ...... x1v

Introduction ...... xv

List of Entries A-Z with page numbers ...... xxi

Text of the Entries A-Z ...... 1

List of Authors ...... 1063

Index ...... 1079

IX PREFACE

The Encyclopaedia fills a gap in both the history of science and in cultural stud• ies. Reference works on other cultures tend either to omit science completely or pay little attention to it, and those on the history of science almost always start with the Greeks, with perhaps a mention of the Islamic world as a trans• lator of Greek scientific works. The purpose of the Encyclopaedia is to bring together knowledge of many disparate fields in one place and to legitimize the study of other cultures' science. Our aim is not to claim the superiority of other cultures, but to engage in a mutual exchange of ideas. The Western aca• demic divisions of science, technology, and medicine have been united in the Encyclopaedia because in ancient cultures these disciplines were connected. This work contributes to redressing the balance in the number of reference works devoted to the study of Western science, and encourages awareness of cultural diversity. The Encyclopaedia is the first compilation of this sort, and it is testimony both to the earlier Eurocentric view of academia as well as to the widened vision of today. There is nothing that crosses disciplinary and geographic boundaries, dealing with both scientific and philosophical issues, to the extent that this work does.

xi PERSONAL NOTE FROM THE EDITOR

Many years ago I taught African history at a secondary school in Central Africa. A few years before, some of the teachers in the country had de• signed a syllabus that included pre-European history, since the curriculum, left over from colonial days, did not include any mention of Africa before the Portuguese. After a year of teaching from this revised version, I asked my students what they thought was the most significant moment in African history, and virtually all of them said it was the arrival of David Livingstone. It may well be that that was the most important moment for Africa, but it shocked me at the time that no one considered any African achievements worth mentioning. Over the years I have come to see, with the help of scholars like Michael Adas, that the dominance of the West means not only that Westerners disparage the rest of the world but also that the rest of the world sees itself as inferior to the West. This book is meant to take one step towards rectifying that, by describing the scientific achievements of those who have been overlooked or undervalued by scholars in both the West and the East. The book is more than just a compilation of 600 disparate articles; it is a glimpse into how people describe and perceive and order the world. I hope the reader will do some exploring. In addition to reading about Maya astronomy, one can read about Mesoamerican mathematics and medicine, as well as a general article on Magic and Science, because all the fields are interrelated and entwined. It might be useful to read about astronomy in Africa and in Australia, to see how similar and different these cultures are. One can travel across disciplines, following the achievements of one culture, and across cultures, comparing the same discipline. And then it would be useful to read an essay on Transmission of Knowledge, or Rationality and Method, to put the articles and their contents in a broader philosophical and social context. My hope, and that of the advisors and contributors to the project, is that the Encyclopaedia will expand the horizons of scholars, teachers, and students by illustrating how extensive the accomplishments of non-Western scientists are. May our future students never believe that science is limited to a fraction of the world.

A note about the authors' names, especially Asian ones: I made many embarrassing errors confusing peoples' surnames and given names, but I was reluctant to change authors' names to conform to the Western style, as it went against the spirit of the Encyclopaedia. Therefore, I have left the names as the authors wrote them.

XIll ACKNOWLEDGEMENTS

My greatest thanks go to the scholars who participated in the project. They very generously gave me their work, their advice, their suggestions, and their time. Some members ofthe advisory board were more than just advisors; they helped to shape the work and give it clarity. Among the contributors and advisors, I must especially thank: Ho Peng Yoke, David Turnbull, Jan Hogendijk, H T. Huang, David King, Gloria Emeagwali, Ruben Mendoza, Cai Jingfeng, K.V. Sarma, Paul Kunitzsch, Boris Rosenfeld, Tzvi Langermann, Ruth Hendricks Willard, and Gregg de Young. I must of course thank my editor, Annie Kuipers, and her wonderful assistant Evelien Bakker, for taking on such a big project with enthusiasm and affection. I have never encountered two people who work so carefully and so hard. Annie believed in the project, and in me, from the very beginning of our association, and it is certainly true that credit for the quality of the work goes largely to her. I would also like to thank Kennie Lyman, my first editor, who offered support, ideas and advice, and the feeling that we were doing something very important together. At Hampshire College, I wish to thank my friends and colleagues Bonnie Vigeland, Serena Smith and Ann McNeil. They listened to my endless stories and complaints, and laughed and commiserated with me through all the ups and downs of this very complex undertaking. Tom Hart ably assisted with computer graphics, and Ken Hoffman helped with some of the mathematics. Amanda Seigel, a first year undergraduate student, was terrific both with the routine tasks and with fact and spelling checks. She became quite adept with Arabic and Sanskrit and did all the printing and reprinting with endless good cheer. Joseph Needham, editor of Science and Civilisation in China, died in Cam• bridge in March 1995, just as I was finishing compiling the encyclopedia. All of us in the field of non-Western science owe him an enormous debt for bringing the intellectual worlds of the East and West together. In a sense all of our work follows from his. Finally, I wish to thank my family for putting up with me. A project of this magnitude takes over your consciousness and your time. I'm sure I've been a horrible bore for six years but my lovely family has been very kind about it. I have kept Tim's poem ("I swallowed two pills that claim to heal unspecificity") on the wall in front of the computer, and Lisa's delicate flower drawings on the desk for inspiration. My deepest gratitude goes to my husband, Bob Rakoff; I would never have had the confidence to undertake this or the fortitude to complete it without him.

H. SELIN

XIV INTRODUCTION

In order to study the history of the science of non-Western cultures we must define both non-Western and science. The term non-Western is not a geo• graphical designation; it is a cultural one. We use it to describe people outside of the Euro-American sphere, including the native cultures of the Americas. The fact that the majority of the world's population is defined by not being something (in this case non-Western) is testimony to the power of European and American colonialism and to the cultural domination of the Western world today. In fact, for most of our recorded history the flow of knowledge, art, and power went the other way. Edwin Van Kley talks about this in his essay on East and West.

By 500 Be the globe supported four major centers of civilization: the Chinese, the Indian, the Near Eastern, and the West, considering Greek culture as antecedent to what eventually became the West. Of the four the West was probably the least impressive in terms of territory, military power, wealth, and perhaps even traditional culture. Certainly this was the case after the fall of the Roman Empire in the fifth century AD. From that time until about AD 1500 the West probably should be regarded as a frontier region compared to the other centers of civilization. No visitor from Mars would likely have predicted that the West would eventually dominate the globe. The gap between the rich and poor nations has widened over the years, as has the notion of Western science as the only science. In this view, Western science is science; everything else is anthropology. Although Eurocentrism has been challenged in many fields, especially in the arts and humanities, the challenge has not extended into science. If we wish to study science in non-Western cultures, we need to take several intellectual steps. First, we must accept that every culture has a science, a way of defining, controlling, and predicting events in the natural world. Then we must accept that every science is legitimate in terms of the culture from which it grew. We must extend this view to our own science, recognizing that it too is a reflection of its culture, and that culture plays a role in every step of doing science: in what we choose to study, how we collect the data, and how we interpret them. We say that Western science is superior because we consider it rational, objective, and value-free, and we look disparagingly at others' science and call it magic. The transformation of the word science as a distinct rationality valued above magic is uniquely European. It is not common to most non-Western societies, where magic and science and religion can easily coexist, even today. For example, the practice of feng shui, or geomancy, the art of finding the spiritually correct location for a building, is practiced in China and in Chinese communities all over the world. If we are to study this subject open-mindedly, we must see that even the concept of rationality is problematic, as it stems from Western ideas about what it is to be a knowing, moral, sane individual. David

XV XVI INTRODUCTION

Turnbull discusses this in his essay on Rationality, Objectivity, and Method. Certainly we accept that concepts of morality and sanity vary enormously in different cultures; we have to extend the same acceptance to the concept of knowing. Even naming this book the Encyclopaedia of the Hist01y of Science, Technology, and Medicine in Non-Western Cultures makes a value judgment about how knowledge is organized. There is no reason to assume that most cultures recognize the distinctions in those fields the way contemporary academics do. We must even be careful about the words we use to describe cultures other than our own. Historians of science looked disparagingly upon Chinese sci• ence because in traditional China knowledge did not come under the same groupings as in the West. The Chinese had a more holistic world view, so that material on natural history might be included in a pharmacopoeia, or the works of a great poet might contain information on astronomy and alchemy. Works on military science might mention meteorology, firearms, magic, and divination at the same time. In fact, divination and mathematics, as well as astronomy and music, were the same word. The same is true with astrology and astronomy. In both Arabic and Chinese, there is one word for both sciences. What is notewor• thy is that astronomy (naming the stars), the mere observing and recording of celestial phenomena, was considered inferior to astrology (studying the stars), the art of interpreting the data. Another example of this occurs among the Aztecs. The involved system of calendrics was largely based on astronomical observations, but the calendars themselves were applied both to ritual and practical ends. Medicine combined pragmatic remedies with shamanism and divination. Writing, architecture, and stone-, feather-, and metalworking all relied on sophisticated technologies; the resulting works served secular goals and/or displayed a complex religious symbolism. The empirical, scientific realm of understanding and inquiry was not readily separable from a more abstract, religious realm. Karen Jolly talks more about this in her essay on Magic and Science. Even when we use the same conceptualizations, the meanings may not be identical, and our understanding may be limited by our ethnocentric con• ception. Jens H0yrup, in an essay on Near Eastern Geometry, discusses the mathematical concept 7r (pi). If we assume that the Babylonians or the Egyp• tians looked for the ratio between the circumference and the diameter of a circle, then we misunderstand a basic element of their own mathematics. "To the Babylonians, the fundamental ratio was the ratio between the area of the circle and the area of the square on the circumference, and the terminology they used demonstrates that they really thought of this as a constructed ge• ometrical square. The Egyptians, for their part, were interested in the ratio between the sides of the squared circle and the circumscribed square. Both conceptualizations are fully legitimate, but they are certainly different from ours." INTRODUCTION xvii

We know that in academia a process of questioning the literary and historical canon has begun. We must extend this to the study of science, especially in the cases where the science practiced was not a precursor to our own. This is a particularly important contribution that the Encyclopaedia makes; it brings together the mathematics of the Aztecs and the Australian aboriginal people in the same space as that of the Indians and Muslims. We have always paid tribute to Hindu-Arabic mathematics, as some of it formed the basis for Western mathematics. But we certainly have not recognized the equally important numeric systems of cultures with very different structures from ours. This is the result of seeing the world as a continuous progression to higher levels. Most other cultures created science and technology in response to their needs, so had no use for constant improvements. It is only in our time that this has worked the other way: that we create needs to meet the advancing technology. We have used this to disparage the lack of "achievement" of many of the world's peoples. It is interesting that in some areas people have become more receptive to other ways of knowing. In medicine, patients, especially those in pain, have begun to question the exclusive superiority of Western medicines, and to incorporate other medical traditions into their treatment. Medical schools have recently added courses in complementary medicine to their curricula. We know that laboratory medicine has not been completely successful in curing many contemporary diseases, and we are aware of the contributions that other cultures' medicine might make. In agriculture, we are beginning to admit that techniques presumed to be inferior may have superior results, if not for yield, then at least for the land, and maybe, incidentally, for the health of the people who work the land. We are less impressed with big science, and no longer see it as a force only for good and progress. This provides an opening for the study of the science of other cultures. In this project we are not trying to claim the superiority of other cultures; we wish to engage in a mutual exchange of ideas. In editing the Encyclopaedia, I tried to avoid ethnic cheerleading, and to edit out as many phrases as possible that fell into the "we were the first", "we were the best", "we were the only" categories. In the end, what does it matter who discovered gunpowder first? In fact, for many years, Western academics used the fact that the Chinese discovered gunpowder and did not "do" anything with it as proof of the Chinese people's essential lack of scientific acumen. For years scholars debated the question of why there was no scientific revolution in China. If we see that the Chinese used gunpowder, or paper or clocks or astronomical observatories, for the needs that they had at the time, we can marvel at their ability to respond to their needs without questioning why they didn't make new ones. The Encyclopaedia of the History of Science, Technology, and Medicine in Non- Western Cultures includes a range of essays from short biographical and descriptive ones to long philosophical ones. These more general articles xviii INTRODUCTION

cover topics such as Colonialism and Science, Magic and Science, East and West, Technology and Culture, Science as a Western Phenomenon, Values and Science, and Rationality, Objectivity, and Method. Since the study of non-Western science is not just a study of facts, but a study of culture and philosophy, we included these articles in order to make the entries on Indian trigonometry or Pacific Island medicine more meaningful. This project arose originally from a course on Comparative Scientific Tra• ditions taught at Hampshire College in Amherst, Massachusetts, USA. The Ford Foundation financed the course, and provided some extra money for library acquisitions to support it. As I am the Science Librarian, I bought the books for the library, and then produced an annotated bibliography of about 800 books called Science Across Cultures, published by Garland Publishing of New York in 1992. The encyclopaedia project grew from that. We had several goals for the encyclopaedia. The first was the simplest: to bring together knowledge of many disparate fields in one place. We united the Western academic divisions of science, technology, and medicine, because in ancient cultures these were connected; the study of the stars was interrelated to the study of the soil, navigation, mathematics, and healing. We also wanted to redress the balance in the number of reference works devoted to the study of Western science, and to encourage awareness of cultural diversity. We wanted to recognize the true value of the intellectual property of indigenous people. It is very important that the study of the science of non-Western people be added to the curriculum as a legitimate study in its own right and not just as a curiosity. Twenty years ago you could not study jazz in a major American conservatory, not to mention studying African or Brazilian music. Eventually, courses on ethnomusicology were introduced, as rather quaint but not quite serious additions. And today we know that there are complex patterns of drumming that Beethoven could not have conceived of, and you probably can not study music in an American conservatory without studying jazz. The same process happened with literature, from having a professor read a haiku poem in a class, to courses on Literature of the Other, to Nobel prizes for Chilean poets. We hope the same process will occur with science. Some people now incorporate bits and pieces of information about other cultures' science into their courses; we hope that in ten years minds and curricula will have expanded to include much more of this material. The field of the history of non-Western science is not one without contro• versy. History is not fact objectively related; it is open to interpretation, and the interpretations change. When I began working on the book, I was quite innocent of these controversies, but I now know that many scholars disagree quite strongly with others in the field. In Islamic science, for instance, there seemed to be enough dissension in the scholarly community to include an article on the current debate in Islamic science. We believe this is the first compilation of this sort, and it is testimony INTRODUCTION XIX

both to the Eurocentricity of academia before, and to the growing widening of its vision that we can produce it now. The history of the science of non• Western cultures is a relatively new field to Western academics, and it is a rich and fascinating one. The Encyclopaedia can be used to provide both factual infonnation about the practices and practitioners of the sciences as well as insights into the world views and philosophies of the cultures that produced them. There are also many articles that in a sense provide the background to studying these sciences. Given the disparity in the number of articles on some cultures, such as the Chinese and Islamic, it might appear that they had more to contribute to world knowledge. The cultures that had writing and were less exploited by warfare and colonialism have left more behind for us to study. Surely there were mathematicians in the Pacific Island countries and in the Americas with skill equal to Zhu Shijie or Ibn al-Haytham. But no records survive. We hope that this apparent lack of balance will not be seen as a failing of the Encyclopaedia, but as an impetus for further research. We hope that readers will achieve a deeper understanding of the relationship between science and culture and a new respect for the accomplishments of these ancient civilizations. If we continue to think of science as a purely Western phenomenon, we eliminate a world of possibilities and preserve a narrow view of life. As the Bantu proverb says, "He who never goes visiting thinks mother is the only cook".

HELAINE SELIN Amherst, Massachusetts Spring, 1997 LIST OF ENTRIES

Abacus ...... Armillary Spheres in China ...... 70 Abortion ...... 2 Armillary Spheres in India ...... 71 Abu Ja'far al-Khazin ...... 3 Aryabhata ...... 72 Abu Kamil...... 4 Asada Goryu ...... 73 Abii Ma'shar' ...... 5 Astrolabe ...... 74 Abu'l-Barakat ...... 6 Astrology in China ...... 76 Abu'l-Fida' ...... 7 Astrology in India ...... 78 Abu'l-$alt ...... 8 Astrology in Islam...... 81 Abu'l-Wara' ...... 8 Astronomical Instruments in India ...... 83 Acoustics in Chinese Culture ...... I 0 Astronomical Instruments in the Islamic World . . . . . 86 Acupuncture ...... 12 Astronomy ...... 88

Acyuta Pi~ara!i ...... 13 Astronomy in Africa ...... 96 Agriculture in Africa ...... 14 Astronomy in Native North America ...... I 00 Agriculture in China ...... 17 Astronomy of the Australian Aboriginal People . . . . I 05 Agriculture in India ...... 19 Astronomy in China ...... I 08 Agriculture in the Islamic World ...... 20 Astronomy in Egypt ...... I I I Agriculture in Japan ...... 23 Astronomy of the Hebrew People ...... I 12 Agriculture of the Maya ...... 24 Astronomy in India ...... 114 Agriculture in the Pacific ...... 27 Astronomy in the Indo-Malay Archipelago ...... I 17 Agriculture in South and Central America ...... 30 Astronomy in the Islamic World ...... 125 Agroforestry ...... 33 Astronomy in Mesoamerica ...... 134 Agroforestry in Africa...... 34 Astronomy in Tibet ...... 136 Agroforestry in the Pacific ...... 35 Atomism in Islamic Thought ...... 139 Aida Yasuaki ...... 37 Atreya ...... 142 Ajima Naonobu ...... 38 Aztec Science ...... 142 Alchemy in China ...... 39 Bakhshali Manuscript ...... 14 7 Alchemy in India ...... 41 The Balkhl School of Arab Geographers ...... 149 Alfonso X ...... 43 Bamboo ...... 150 Algebra in China ...... 43 Banu Musa ...... 150 Algebra in India: Bijaganita ...... 47 Bar l:fiyya- Abraham (Savasorda) ...... 15 1 Algebra in Islamic Mathematics ...... 48 al-Battanl ...... 152 Algebra, Surveyors' ...... 52 Baudhayana ...... 153 Almagest: Its Reception and Transmission in the Islamic Ben Cao Gang Mu ...... !54 World...... 55 Bhaskara II ...... , ...... 155 Alphabet ...... 56 Sian Que ...... 157 Americas: Native American Science ...... 60 al-Birunl(Part I) ...... !57 Animal Domestication ...... 64 al-Birunl (Part 2: Geographical Contributions) . . . . . 158 Approximation Formulae in Chinese Mathematics . . 65 al-Bi!rujl ...... 160 Arithmetic in India: Patfga1Jita ...... 67 Bitumen in Premodern China ...... 160 Arithmetic in Islamic Mathematics ...... 68 Brahmagupta ...... 162

xxi xxii LIST OF ENTRIES

Calculus ...... •• ••• • • • 0 •• • •• • •••• • • 164 East and West: Africa in the Transmission of Calendars in East Asia ...... 164 Knowledge from East to West ...... 259 Calendars in Egypt ...... 16 7 East and West: China in the Transmission of Calendars in India ...... 168 Knowledge from East to West ...... 261 Calendars in Islam ...... 171 East and West: India in the Transmission of Knowledge from East to West ...... 266 Calendars in Mesoamerica ...... 173 East and West: Islam in the Transmission of Calendars in South America ...... 180 Knowledge from East to West ...... 270 Candrasekhara Samanta ...... 182 Eclipses ...... 275 Caraka ...... 183 Elements - Reception of Euclid's Elements in the Arabic Celestial Vault and Sphere ...... 184 World ...... 277 Chao Yuanfang ...... 185 Engineering ...... 280 Chemistry in China ...... 185 Environment and Nature: Africa ...... 283 Chen Yan ...... 187 Environment and Nature: the Australian Aboriginal Childbirth ...... 187 People ...... 287

China • •• •••••• • • • •• • • 0 •• • ••• • •• • • • •••• • •• • • 191 Environment and Nature: Buddhism ...... 290 Chinese Minorities ...... 197 Environment and Nature: China ...... 291 City Planning: Aztec City Planning ...... 200 Environment and Nature: the Hebrew people...... 293 City Planning: Inca City Planning ...... 202 Environment and Nature: India ...... 295 City Planning in India ...... 204 Environment and Nature: Islam ...... 296 City Planning: Maya City Planning ...... 205 Environment and Nature: Japan ...... 298 Clocks and Watches ...... 208 Environment and Nature: Native North America . . . . 302 Clocks: Astronomical Clocks in China ...... 211 Environment and Nature: South America - The Colonialism and Medicine in Malaysia ...... 211 Amazon ...... 305 Colonialism and Science ...... 215 Environment and Nature: South America - The Colonialism and Science in Africa ...... 220 Andes ...... 307 Colonialism and Science in the Americas ...... 221 Epilepsy in Chinese Medicine ...... 309 Colonialism and Science in India ...... 223 Epilepsy in Indian Medicine ...... 310 Colonialism and Science in the Malay World ...... 226 Ethnobotany ...... 3 I 1 Combinatorics in Indian Mathematics ...... 229 Ethnobotany in China 312 Combinatorics in Islamic Mathematics ...... 230 Ethnobotany in India ...... 315 Compass ...... 232 Ethnobotany in Mesoamerica ...... 317 Computation: Chinese Counting Rods ...... 233 Ethnobotany in Native North America ...... 321 Conics ...... 235 Ethnobotany in the Pacific ...... 323 Construction Techniques in Africa ...... 236 Ethnomathematics ...... 326 Crescas - l:fasdai ...... 240 331 Crops in Pre-Columbian Agriculture ...... 241 ai-Farghanl ...... Cuneiform ...... 243 al-Fazarl ...... 331 Al-Damlrl ...... 247 Five Phases (Wuxing) ...... 332 Decimal Notation ...... 247 Food Technology in Africa ...... 333 Ddantara 248 Food Technology in China ...... 336 Devacarya 248 Food Technology in Latin America ...... 338 Divination in China ...... 249 Forestry in India 340 342 Dyes ...... • • • • • 0 ••••• ••• • 0 •• 251 Gaitian East and West 253 Gan De 342 LIST OF ENTRIES XXIII

Gas: Exploitation and Use of Natural Gas in Ibn al-Majusi ...... 409 Premodern China ...... 342 Ibn ai-Nafis ...... 409 Ge Hong ...... 344 Ibn al-Quff(al-Karaki) ...... 411 Gender and Technology ...... 346 Ibn al-Raqqam ...... 412 Geodesy ...... 346 Ibn al-Sha!ir ...... 412 Geographical Knowledge ...... 347 Ibn a!-Yasamin ...... 414 Geography in China ...... 351 Ibn ai-Zarqallu ...... 415 Geography in India ...... 352 Ibn Bagura ...... 416 Geography in the Islamic World ...... 354 Ibn Burian ...... 417 Geography in Mesoamerica ...... 357 Ibn Ezra - Abraham ...... 418 Geography of Native North Americans ...... 358 Ibn f:lawqal ...... 419 Geomancy in China ...... 360 Ibn Hubal ...... 419 Geomancy in the Islamic World ...... 361 Ibn Is~aq a!-Tunis! ...... 420 Geometry ...... 363 Ibn Juljul ...... 421 Geometry in Africa: Sona Geometry ...... 367 Ibn Jumay' ...... 421 Geometry in China ...... 368 Ibn Khaldun ...... 422 Geometry in India ...... 372 Ibn Khurdadhbih ...... 423 Geometry in the Islamic World ...... 375 Ibn Majid ...... 424 Geometry in Japan ...... 378 Ibn Masawayh, Yu~anna ...... 424 Geometry in the Near and Middle East...... 380 Ibn Mu'adh ...... 426 Globes ...... 383 Ibn Mun' im ...... 427 Gnomon in India ...... 384 Ibn Qunfudh ...... 428 Gou-Gu Theorem, The ...... 387 Ibn Qutayba ...... 4 29 Gunpowder ...... 389 Ibn Ri<,lwan ...... 429 Guo Shoujing ...... 390 Ibn Rushd (Averroes) ...... 43 1 f:labash al-f:lasib ...... 392 Ibn Sahl ...... 432 al-f:lajjaj ...... 392 Ibn Sarabi (Serapion) ...... 4 33 ai-Hamdani ...... 393 Ibn Sina (Avicenna) ...... 434 Haridatta ...... 394 Ibn Tawus ...... 436 al-Hashimi ...... 394 Ibn Tibbon ...... 43 7 Hay'a ...... 395 Ibn Tufayl ...... 437 Huangdi Jiuding Shendan Jing ...... 397 Ibn Wafid ...... 438 Huangdi Neijing ...... 397 Ibn Yunus ...... 438 Huangfu Mi ...... 398 Ibn ~uhr ...... 440 f:lunaynibn I s ~ a q ...... 399 Ibrahim ibn Sinan ...... 44 1 Huntian ...... 400 ai-Idrisi ...... 442 Ibn 'Abbad ...... 401 Ikhwan al-$ara' ...... 443 Ibn ai-A' lam ...... · .. . 401 India: Medieval Science and Technology ...... 444 Ibn al-'Arabi ...... 402 Ino Tadataka ...... 447 Ibn ai-Banna' ...... 404 Irrigation in India and Sri Lanka ...... 44 7 Ibn al-Bayrar ...... 404 Irrigation in the I slamic World ...... 450 Ibn al-Ha' im ...... 405 Irrigation in South America ...... 452 Ibn ai-Haytham (Alhazen) ...... 405 !sa Tarjaman ...... 454 Ibn al-Kammad ...... 408 Is~aq ibn f:lunayn ...... 454 XXI\. LIST OF ENTRIES

Islamic Science: The Contemporary Debate ...... 455 Lunar Mansions in Islamic Astronomy ...... 520 Jabir ibn Aftai:J ...... 459 Luoxia Hong ...... 520 Jabir ibn J:Iayyan ...... 459 Madhava of Sm'lgamagrama ...... 522 Jagannatha Samra! ...... 460 Magic and Science ...... 523 Jai Singh ...... , . .. .. 461 Magic Squares in Chinese Mathematics ...... 528 Jamu ...... 463 Magic Squares in Indian Mathematics ...... 529 Japanese Science ...... 464 Magic Squares in Islamic Mathematics ...... 536 AI-Jawharl ...... 470 Magic Squares in Japanese Mathematics ...... 538 Jayadeva ...... 4 72 Magnetism in China ...... 540 al-Jazarl ...... 4 72 Magnetism in Mesoamerica ...... 543 Jia Xian ...... 473 Mahadeva ...... 544 al-Jurjanl ...... 474 al-MahanT ...... , ...... 544 Kamalakara ...... 4 75 Mahavlra ...... 545 AI-Karajl ...... 475 Mahendra Suri ...... 546 Al-Kashl ...... 4 76 al-Majrm ...... 547 AI-Khalm ...... 477 Makaranda ...... 54 7 AI-Kharaql ...... 478 al-Ma'mun ...... 548 al-Khayyam- 'Umar ...... 479 Maps and Mapmaking ...... 549 Al-Khazinl...... 480 Maps and Mapmaking in Africa ...... 554 AI-Khujandl ...... 481 Maps and Mapmaking in Asia (Prehistoric) ...... 558 AI-Khwarizml ...... 482 Maps and Mapmaking of the Australian Aboriginal Al-Kindl ...... 483 People ...... 560 Knowledge Systems: Local Knowledge ...... 485 Maps and Mapmaking: Celestial East Asian Maps . . 562 Knowledge Systems of the Australian Aboriginal Maps and Mapmaking: Celestial Islamic Maps . . . . . 565 People ...... 490 Maps and Mapmaking in China ...... 567 Knowledge Systems in China ...... 494 Maps and Mapmaking: Chinese Geomantic Maps . . . 570 Knowledge Systems of the Incas ...... 495 Maps and Mapmaking in India ...... 571 Knowledge Systems in India ...... 500 Maps and Mapmaking: Islamic Terrestrial Maps 573 Korean Science ...... 502 Maps and Mapmaking: Islamic World Maps Kushyaribn Labban ...... 506 Centered on Mecca ...... 577 Lalla ...... 508 Maps and Mapmaking in Japan ...... 578 Leo the African ...... 508 Maps and Mapmaking in Korea ...... 580 Levi Ben Gerson ...... 509 Maps and Mapmaking: Marshall Island Stick Charts . 587 Li Bing ...... 509 Maps and Mapmaking in Mesoamerica ...... 590 Li Chunfeng ...... 510 Maps and Mapmaking in Native North America . . . . 592 Li Gao ...... 511 Maps and Mapmaking in Southeast Asia ...... 594 Li Shanlan ...... 511 Maps and Mapmaking in Tibet ...... 596 LiShizhen ...... 512 Maps and Mapmaking in Vietnam ...... 597 Li Zhi ...... 513 Maragha ...... 599 Liu Hong ...... 514 al-Marid!n!, Jamal ai-Din and Badr ai-Din ...... 60 I Liu Hui and the Jiu:::hang Suanshu ...... 514 Masha'allah ...... 602 Long Count ...... 515 ai-Mas'udf ...... 604 Lunar Mansions in Chinese Astronomy ...... 516 Mathematics ...... 604 Lunar Mansions in Indian Astronomy ...... 519 Mathematics in Africa South of The Sahara ...... 611 LIST OF ENTRIES XXV

Mathematics of Africa: the Maghreb ...... 613 Military Technology ...... 741 Mathematics in West Africa: Traditional Mathematical Moses Maimonides ...... 744 Games ...... 616 Mound Cultures ...... 746 Mathematics of the Australian Aboriginal People . . . 619 Moxibustion ...... 748 Mathematics of the Aztec People ...... 622 Mummies in Egypt ...... 749 Mathematics in China ...... 626 Mummies in South America ...... 750 Mathematics in Egypt ...... 629 Munlsvara ...... 752 Mathematics of the Hebrew People ...... 632 al-Muqaddasl...... 753 Mathematics in India ...... 634 al-Mu'taman ibn Hud ...... 753 Mathematics in Islam 637 Namoratunga ...... 755 Mathematics in Japan ...... 640 Nanjing ...... 756 Mathematics in Korea ...... 643 Narayal)a Pal)<;iita ...... 756 Mathematics of the Maya ...... 646 Na~lr al-Dln ai-Tilsl ...... 757 Mathematics in Native North America ...... 651 Nasir-i Khusraw ...... 759 Mathematics in the Pacific ...... 657 Navigation in Africa ...... 759 Mathematics, Practical and Recreational ...... 660 Navigation in China ...... 762 Medical Ethics ...... 663 Navigation in the Indian Ocean and Red Sea ...... 765 Medical Ethics in China ...... 667 Navigation in the Pacific ...... 769 Medical Ethics in India ...... 669 Navigation in Polynesia ...... 773 Medical Ethics in Islam ...... 672 al-Nayrlzl ...... 776 Medical Texts in China ...... 673 Nazca Lines ...... 777 Medicinal Food Plants ...... 676 Nllakal)~ha Somayaji ...... 780 Medicine in Africa ...... 679 Number Theory in Africa ...... 781 Medicine in China ...... 683 Number Theory in India ...... 784 Medicine in China: Forensic Medicine ...... 688 Number Theory in Islamic Mathematics ...... 786 Medicine in Egypt ...... 689 Observatories in India ...... 788 Medicine in India: Ayurveda ...... 693 Observatories in the Islamic World ...... 792 Medicine in Islam ...... 695 Optics in Chinese Science ...... 793 Medicine in Japan ...... 698 Optics in the Islamic World ...... 795 Medicine in Meso and South America ...... 702 Ottoman Science ...... 799 Medicine in Native North and South America ...... 706 Pak~a ...... 806 Medicine in the Pacific Islands ...... 709 Paper and Papermaking...... 806 Medicine: Talmudic Medicine ...... 7 14 Paramesvara ...... 807 Medicine in Thailand: Traditional Medicine ...... 7 17 Paulisa ...... 808 Medicine Wheels ...... 719 Physics ...... 809 Metallurgy in Africa 720 Physics in China ...... 8 14 Metallurgy in China 725 Physics in India ...... 817 Metallurgy in Egypt 726 Physics in the Islamic World ...... 8 19 Metallurgy in India ...... 728 Pi in Chinese Mathematics ...... 822 Metallurgy in Meso and North America ...... 730 Pi in Indian Mathematics ...... 823 Metallurgy in South America ...... 733 Pirl Reis ...... 824 Meteorology in China ...... 735 Potato ...... 825 Meteorology in India...... 737 Precession of the Equinoxes ...... 827 Meteorology in the Islamic World ...... 739 Putumana Somayaji ...... 827 XXVI LIST OF ENTRIES

Pyramids ...... 828 Shushu Jiuzhang ...... 897 Qadi Zadeh al-Ruml ...... 830 al-Sijzl ...... 898 al-Qala~adl ...... 830 Silk and the Loom ...... 900 Qanat ...... 832 Sinan ibn Thabit ...... 902 Qi...... 832 Siyuan Yujian ...... 903 Qianjin Yao(ang ...... 833 Song Chi ...... 904 Qibla and Islamic Prayer Times ...... 834 Song Yingxing and the Tiangong Kaiwu ...... 904 906 Qin Jiushao ...... 836 Sphujidhvaja ...... 906 Quadrant ...... 83 7 Srldhara ...... 908 al-Qiihl (or al-Kuhl) ...... 83 7 Srlpati ...... 908 Quipu ...... 839 Stars in Chinese Science ...... 910 Qus!a ibn Liiqa ...... 841 Stars in Arabic-Islamic Science ...... 912 Rainwater Harvesting ...... 843 Stonemasonry - Inca ...... 914 Ramanujan ...... 843 Suanxue Qimeng ...... 915 Rationale in Indian Mathematics ...... 845 al-Siifi ...... 915 Rationality, Objectivity, and Method ...... 845 Sugar in Latin America 917 al-Razl ...... 850 Sulbasutras ...... 918 Religion and Science in China ...... 852 Sun Simo ...... 919 Religion and Science in Islam 1: Technical and Sun Zi Practical Aspects ...... 857 Sundials in China ...... 920 Religion and Science in Islam II : What Scientists Said Sundials in Islam ...... 921 About Religion and What Islam Said About Science 861 Surveying ...... 922 Religion and Science in the Native Americas ...... 865 Su1yasiddltiinta ...... 926 Road Networks in Ancient Native America ...... 868 Susruta ...... 927 Rockets and Rocketry ...... 872 al-Suyutl ...... 928 Sadr ai-Sharl

Time in Africa ...... 972 Weights and Measures in Japan ...... I 0 19 Time in China ...... 974 Weights and Measures in Mexico ...... I 023 Time in India ...... 977 Weights and Measures in Peru ...... I 026 Time in the Islamic World ...... 979 Western Dominance: Western Science and Time in Maya Culture ...... 981 Technology in the Construction of Ideologies of Colonial Dominance ...... I 028 Time and Native Americans: Time in the Pueblo World ...... , ...... 983 Windpower ...... I 032 Tangren Zhenjiu Shuxue Tujing ...... 984 Writing of the Mayas ...... I 034 Trephination ...... 985 Xiahou Yang ...... I 041 Tribology ...... 987 Xu Yue ...... 1041 Trigonometry in India ...... 987 Ya~ya ibn Abi Man~ur ...... I 043 Trigonometry in Islamic Mathematics ...... 990 Yang Hui ...... I 043 Ulugh Beg ...... 993 Ya'qub ibn Tariq ...... I 044 ... I 044 al-Uqlldisi ...... 993 Yavanesvara ...... I 045 al-'Ur4i ...... 994 Yinyang ...... 1046 Vii!..yakarana ...... 995 Yoga ...... Values and Science ...... 995 Yuktibhii.~ii of Jye~!hadeva ...... I 048 Varahamihira ...... 999 Zacut, Abraham ...... I 050 Zero ...... 1050 Va~esvara ...... I 000 . . . I 052 Wang Chong ...... I 002 Zhang Heng ...... Wang Xiaotong ...... I 002 Zhang Qiujian Suanjing ...... I 053 I 053 Wang Xi chan ...... I 003 Zhang Zhongjing ...... I 054 Wei Boyang ...... I 004 Zhenjiu Dacheng ...... I 055 Weights and Measures in Africa: Akan Gold Weights 1005 Zhenjiu Jiayijing ...... I 056 Weights and Measures in Burma: The Royal Zhoubi Suanjing ...... Animal-shaped Weights of the Burmese Empires I 007 Zhu Shijie ...... I 056 Weights and Measures in China ...... I 010 Zfj ...... 1057 Weights and Measures in Egypt ...... I 012 Zodiac in India ...... I 058 Weights and Measures of the Hebrews ...... I 0 14 Zodiac in Islamic Astronomy ...... I 059 Weights and Measures in the Indus Valley ...... I 01 7 Zou Yan ...... I 060 Weights and Measures in Islam ...... 1019 Zu Chongzhi ...... I 060