The mathematics of Egypt, Mesopotamia, China, India, and Islam [Texte imprimé] : a sourcebook / Victor Katz, editor ; Annette Imhausen, Eleanor Robson, Joseph Dauben ... [et al.]

Index

Notes bibliogr.

Preface -- Permissions -- Introduction -- ch. 1. Egyptian mathematics / Annette Imhausen -- Preliminary remarks -- 1. Introduction -- a. Invention of writing and number systems -- b. Arithmetic -- c. Metrology -- 2. Hieratic mathematical texts -- a. Table texts -- b. Problem texts -- 3. Mathematics in administrative texts -- a. Middle Kingdom texts : the Reisner papyri -- b. New Kingdom texts : Ostraca from Deir el Medina -- 4. Mathematics in the Graeco-Roman period -- a. Context -- b. Table texts -- c. Problem texts -- 5. Appendices -- a. Glossary of Egyptian terms -- b. Sources -- c. References --

ch. 2. Mesopotamian mathematics / Eleanor Robson -- 1. Introduction -- a. Mesopotamian mathematics through Western eyes -- b. Mathematics and scribal culture in ancient Iraq -- c. From tablet to translation -- d. Explananda -- 2. The long third millennium, c. 3200-2000 BCE -- a. Uruk in the late fourth millennium -- b. Shuruppag in the mid-third millennium -- c. Nippur and Girsu in the twenty-fourth century BCE -- d. Umma and Girsu in the twenty-first century BCE -- 3. The old Babylonian period, c. 2000-1600 BCE -- a. Arithmetical and metrological tables -- b. Mathematical problems -- c. Rough work and reference lists -- 4. Later Mesopotamia, c. 1400-150 BCE -- 5. Appendices -- a. Sources -- b. References --

ch. 3. Chinese mathematics / Joseph W. Dauben -- Preliminary remarks -- 1. China : the historical and social context -- 2. Methods and procedures : counting rods, the "out-in" principle -- 3. Recent archaeological discoveries : the earliest yet-known bamboo text -- 4. Mathematics and astronomy : the Zhou bi suan jing and right triangles (The Gou-gu or "Pythagorean" theorem) -- 5. The Chinese "Euclid", Liu Hui -- a. The Nine Chapters -- b. The Sea Island Mathematical Classic -- 6. The "Ten Classics" of ancient Chinese mathematics -- a. Numbers and arithmetic : the Mathematical Classic of Master Sun -- b. The Mathematical Classic of Zhang Qiujian -- 7. Outstanding achievements of the Song and Yuan dynasties (960-1368 CE) -- a. Qin Jiushao -- b. Li Zhi (Li Ye) -- c. Yang Hui -- d. Zhu Shijie -- 8. Matteo Ricci and Xu Guangxi, "prefaces" to the first Chinese edition of Euclid's Elements (1607) -- 9. Conclusion -- 10. Appendices -- a. Sources -- b. Bibliographical guides -- c. References --

ch. 4. Mathematics in India / Kim Plofker -- 1. Introduction : origins of Indian mathematics -- 2. Mathematical texts in ancient India -- a. The Vedas -- b. The Śulbasūtras -- c. Mathematics in other ancient texts -- d. Number systems and numerals -- 3. Evolution of mathematics in medieval India -- a. Mathematics chapters in Siddhānta texts -- b. Transmission of mathematical ideas to the Islamic world -- c. Textbooks on mathematics as a separate subject -- d. The audience for mathematics education -- e. Specialized mathematics : astronomical and cosmological problems -- 4. The Kerala school -- a. Mādhava, his work, and his school -- b. Infinite series and the role of demonstrations -- c. Other mathematical interests in the Kerala school -- 5. Continuity and transition in the second millennium -- a. The ongoing development of Sanskrit mathematics -- b. Scientific exchanges at the courts of Delhi and Jaipur -- c. Assimilation of ideas from Islam ; mathematical table texts -- 6. Encounters with modern Western mathematics -- a. Early exchanges with European mathematics -- b. European versus "native" mathematics education in British India -- c. Assimilation into modern global mathematics -- 7. Appendices -- a. Sources -- b. References --

ch. 5. Mathematics in medieval Islam / J. Lennart Berggren -- 1. Introduction -- 2. Appropriation of the ancient heritage -- 3. Arithmetic -- 4. Algebra -- 5. Number theory -- 6. Geometry -- a. Theoretical geometry -- b. Practical geometry -- 7. Trigonometry -- 8. Combinatorics -- 9. On mathematics -- 10. Appendices -- a. Sources -- b. References -- Contributors -- Index.