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The Mathematics of Egypt, Mesopotamia, China, India, and Islam:
A Sourcebook
Edited by Victor J. Katz
Section Authors: Annette Imhausen, Eleanor Robson, Joseph W. Dauben, Kim Plofker & J. Lennart Berggren

Book Description | Reviews
Introduction [HTML] or [PDF format]


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

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. 3200-2000 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. 2000-1600 BCE 82
a. Arithmetical and metrological tables 82
b. Mathematical problems 92
c. Rough work and reference lists 142
IV. Later Mesopotamia, c. 1400-150 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 Rods, The "Out-In" 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
VII. Outstanding Achievements of the Song and Yuan Dynasties
(960-1368 CE) 308
a. Qin Jiushao 309
b. Li Zhi (Li Ye) 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. The Vedas 386
b. The Sīulbasutras 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
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
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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File created: 4/27/2015

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