Mathematics of Egypt, Mesopotamia, China, India, and Islam. A Sourcebook 9780691114859, 0691114854, 2006030851

Table of contents :
Preface
Permissions
Introduction
Chapter 1. Egyptian Mathematics. Annette Imhausen
Preliminary Remarks
I. Introduction
a. Invention of writing and number systems
b. Arithmetic
c. Metrology
II. Hieratic Mathematical Texts
a. Table texts
b. Problem texts
III. Mathematics in Administrative Texts
a. Middle Kingdom texts: The Reisner papyri
b. New Kingdom texts: Ostraca from Deir el Medina
IV. Mathematics in the Graeco-Roman Period
a. Context
b. Table texts
c. Problem texts
V. Appendices
a. Glossary of Egyptian terms
b. Sources
c. References
Chapter 2. Mesopotamian Mathematics. Eleanor Robson
I. Introduction
a. Mesopotamian mathematics through Western eyes
b. Mathematics and scribal culture in ancient Iraq
c. From tablet to translation
d. Explananda
II. 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
III. The Old Babylonian Period, c. 2000-1600 bce
a. Arithmetical and metrological tables
b. Mathematical problems
c. Rough work and reference lists
IV. Later Mesopotamia, c. 1400-150 bce
V. Appendices
a. Sources
b. References
Chapter 3. Chinese Mathematics. Joseph W. Dauben
Preliminary Remarks
I. China: The Historical and Social Context
II. Methods and Procedures: Counting Rods, The "Out-In” Principle
III. Recent Archaeological Discoveries: The Earliest Yet-Known Bamboo Text
IV. Mathematics and Astronomy: The Zhou bi suan jing and Right Triangles (The Gou-gu or “Pythagorean" Theorem)
V. The Chinese "Euclid”, Liu Hui
a. The Nine Chapters
b. The Sea Island Mathematical Classic
VI. The "Ten Classicsf, of Ancient Chinese Mathematics
a. Numbers and arithmetic: The Mathematical Classic of Master Sun
b. The Mathematical Classic of Zhang Qiujian
VII. Outstanding Achievements of the Song and Yuan Dynasties (960-1368 CE)
a. Qin Jiushao
b. Li Zhi (Li Ye)
c. gng Hui
d. Zhu Shijie
VIII. Matteo Ricci and Xu Guangxi, "Prefaces" to the First Chinese Edition of Euclid's Elements (1607)
IX. Conclusion
X. Appendices
a. Sources
b. Bibliographic guides
c. References
Chapter 4. Mathematics in India. Kim Plofker
I. Introduction: Origins of Indian Mathematics
II. Mathematical Texts in Ancient India
a.TheVbdas
b. The Śulbasūtras
c. Mathematics in other ancient texts
d. Number systems and numerals
III. Evolution of Mathematics in Medieval India
a. Mathematics chapters in Siddhanta 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
IV. 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
V. 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
VI. 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
VII. Appendices
a. Sources
b. References
Chapter 5. Mathematics in Medieval Islam. J. Lennart Berggren
I. Introduction
II. Appropriation of the Ancient Heritage
III. Arithmetic
IV. Algebra
V. Number Theory
VI. Geometry
a. Theoretical geometry
b. Practical geometry
VII. Trigonometry
VIII. Combinatorics
IX. On mathematics
X. Appendices
a. Sources
b. References
Contributors
Index