The Mathematics of Egypt, Mesopotamia, China, India, and Islam A Sourcebook.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Katz, Victor J.
Otros Autores: Imhausen, Annette, Robson, Eleanor, Dauben, Joseph Warren, Plofker, Kim, Berggren, J. Lennart
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton : Princeton University Press, 2007.
Temas:
Mathematics, Ancient > Sources.
Mathematics > History > Sources.
Mathématiques anciennes > Sources.
Mathématiques > Histoire > Sources.
Mathematics.
Mathematics, Ancient.
History.
Sources.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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