The History of Mathematics

Preface xxi Changes From the Second Edition xxii Elementary Texts on the History of Mathematics xxiii Part 1. What is Mathematics? 1 Chapter 1. Mathematics and its History 3 Chapter 2. Proto-mathematics 15 Part 2. The Middle East, 2000-1500 BCE 27 Chapter 3. Overview of Mesopotamian Mathematics 29 Chapter 4. Computations in Ancient Mesopotamia 39 Chapter 5. Geometry in Mesopotamia 47 Chapter 6. Egyptian Numerals and Arithmetic 57 Chapter 7. Algebra and Geometry in Ancient Egypt 67 Part 3. Greek Mathematics From 500 BCE to 500 CE 79 Chapter 8. An Overview of Ancient Greek Mathematics 81 Chapter 9. Greek Number Theory 93 Chapter 10. Fifth-Century Greek Geometry 105 Chapter 11. Athenian Mathematics I: The Classical Problems 117 Chapter 12. Athenian Mathametics II: Plato and Aristotle 131 Chapter 13. Euclid of Alexandria 143 Chapter 14. Archimedes of Syracuse 151 Chapter 15. Apollonius of Perga 163 Chapter 16. Hellenistic and Roman Geometry 173 Chapter 17. Ptolemy's Geography and Astronomy 181 Chapter 18. Pappus and the Later Commentators 195 Part 4. India, China, and Japan 500 BCE-1700 CE 205 Chapter 19. Overview of Mathematics in India 207 Chapter 20. From the Vedas to Aryabhata I 217 Chapter 21. Brahmagupta, the Kuttaka, and Bhaskara II 231 Chapter 22. Early Classics of Chinese Mathematics 243 Chapter 23. Later Chinese Algebra and Geometry 259 Chapter 24. Traditional Japanese Mathematics 271 Part 5. Islamic Mathematics, 800-1500 285 Chapter 25. Overview of Islamic Mathematics 287 Chapter 26. Islamic Number Theory and Algebra 297 Chapter 27. Islamic Geometry 307 Part 6. European Mathematics, 500-1900 317 Chapter 28. Medieval and Early Modern Europe 319 Chapter 29. European Mathematics: 1200-1500 331 Chapter 30. Sixteenth-Century Algebra 345 Chapter 31. Renaissance Art and Geometry 355 Chapter 32. The Calculus Before Newton and Leibniz 365 Chapter 33. Newton and Leibniz 379 Chapter 34. Consolidation of the Calculus 393 Part 7. Special Topics 407 Chapter 35. Women Mathematicians 411 Chapter 36. Probability 423 Chapter 37. Algebra from 1600 to 1850 439 Chapter 38. Projective and Algebraic Geometry and Topology 453 Chapter 39. Differential Geometry 469 Chapter 40. Non-Euclidean Geometry 485 Chapter 41. Complex Analysis 499 Chapter 42. Real Numbers, Series, and Integrals 515 Chapter 43. Foundations of Real Analysis 525 Chapter 44. Set Theory 537 Chapter 45. Logic 547 Literature 563 Subject Index 581 Name Index 609