The Mathematics of Egypt Mesopotamia, China, India, and Islam
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1 The Mathematics of Egypt Mesopotamia, China, India, and Islam J3 Sourcebook Victor Katz, Editor Annette Imhausen Eleanor Robson Joseph Dauben Kim Plofker J. Lennart Berggren PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD
2 Contents Preface ix Permissions xi Introduction 1 Chapter 1 Egyptian Mathematics Annette Imhausen Preliminary Remarks 7. I. Introduction 9 a. Invention of writing and number systems 13 b. Arithmetic 14 c. Metrology 17 II. Hieratic Mathematical Texts 17 a. Table texts 18 b. Problem texts 24 «III. Mathematics in Administrative Texts 40 a. Middle Kingdom texts: The Reisner papyri 40 b. New Kingdom texts: Ostraca from Deir el Medina 44 IV. Mathematics in the Graeco-Roman Period 46 a. Context 46 b. Table texts 47 c. Problem texts 48 V. Appendices 52 a. Glossary of Egyptian terms 52 b. Sources 52 c. References 54
3 vi I Contents Chapter 2 Mesopotamian Mathematics Eleanor Robson I. Introduction 58 a. Mesopotamian mathematics through Western eyes 58 b. Mathematics and scribal culture in ancient Iraq 62 c. From tablet to translation 65 d. Explananda 68 II. The Long Third Millennium, c BCE 73 a. Uruk in the late fourth millennium 73 b. Shuruppag in the mid-third millennium 74 c. Nippur and Girsu in the twenty-fourth century BCE 76 d. Umma and Girsu in the twenty-first century BCE 78 III. The Old Babylonian Period, c BCE 82 a. Arithmetical and metrological tables 82 b. Mathematical problems 92 c. Rough work and reference lists 142 IV. Later Mesopotamia, c BCE 154 V. Appendices 180 a. Sources 180 b. References 181 Chapter 3 Chinese Mathematics Joseph W. Dauben Preliminary Remarks 187 I. China: The Historical and Social Context 187 II. Methods and Procedures: Counting Reds, The "Out-ln" Principle 194 III. Recent Archaeological Discoveries: The Earliest Yet-Known Bamboo Text 201 IV. Mathematics and Astronomy: The Zhou bi suan jing and Right Triangles (The Gou-gu or "Pythagorean" Theorem) 213 V. The Chinese "Euclid", Liu Hui 226 a. The Nine Chapters 227 b. The Sea Island Mathematical Classic 288 VI. The "Ten Classics" of Ancient Chinese Mathematics 293 a. Numbers and arithmetic: The Mathematical Classic of Master Sun 295 b. The Mathematical Classic of Zhang Qiujian 302
4 Contents I vii VII. Outstanding Achievements of the Song and Yuan Dynasties ( CE) 308 a. Qin Jiushao 309 b.lizhi(liye) 323 c. Yang Hui 329 d. Zhu Shijie 343 VIII. Matteo Ricci and Xu Guangxi, "Prefaces" to the First Chinese Edition of Euclid's Elements (1607) 366 IX. Conclusion 375 X. Appendices 379 a. Sources 379 b. Bibliographic guides 379 c. References 380 Chapter 4 Mathematics in India Kim Plofker I. Introduction: Origins of Indian Mathematics 385 II. Mathematical Texts in Ancient India 386 a.thevedas 386 b. The Sulbasutras 387 c. Mathematics in other ancient texts 393 d. Number systems and numerals 395 III. Evolution of Mathematics in Medieval India 398 a. Mathematics chapters in Siddhanta texts 398 b. Transmission of mathematical ideas to the Islamic world 434 c. Textbooks on mathematics as a separate subject 435 d. The audience for mathematics education 477 e. Specialized mathematics: Astronomical and a* cosmological problems 478 IV. The Kerala School 480 a. Madhava, his work, and his school 480 b. Infinite series and the role of demonstrations 481 c. Other mathematical interests in the Kerala school 493 V. Continuity and Transition in the Second Millennium 498 a. The ongoing development of Sanskrit mathematics 498 b. Scientific exchanges at the courts of Delhi and Jaipur 504 c. Assimilation of ideas from Islam; mathematical table texts 506
5 viii I Contents VI. Encounters with Modern Western Mathematics 507 a. Early exchanges with European mathematics 507 b. European versus "native" mathematics education in British India 508 c. Assimilation into modern global mathematics 510 VII. Appendices 511 a. Sources 511 b. References 512 Chapter 5 Mathematics in Medieval Islam J. Lennart Berggren I. Introduction 515 II. Appropriation of the Ancient Heritage 520 III. Arithmetic 525 IV. Algebra 542 V. Number Theory 560 VI. Geometry 564 a. Theoretical geometry 564 b. Practical geometry 610 VII. Trigonometry 621 VIII. Combinatorics 658 IX. On mathematics 666 X. Appendices 671 a. Sources 671 b. References 674 Contributors 677 Index 681
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COPYRIGHT NOTICE: Edited by Victor J. Katz: The Mathematics of Egypt, Mesopotamia, China, India, and Islam is published by Princeton University Press and copyrighted, 2007, by Princeton University Press.
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