Kapitel in diesem Buch

1. Frontmatter i
2. Contents v
3. Introduction ix
4. Acknowledgments xiii
5. Chapter 1. The Study and Status of Mathematics
6. 1.1 Plato, Republic 1
7. 1.2 Plato, Gorgias 7
8. 1.3 Archytas, On Things Scientific 8
9. 1.4 Aristotle, Metaphysics 9
10. 1.5 Aristotle, Prior Analytics 10
11. 1.6 Aristotle, Posterior Analytics 12
12. 1.7 Aristotle, Physics 14
13. 1.8 Philo of Alexandria, On Mating with the Preliminary Studies 16
14. 1.9 Nicomachus, Introduction to Arithmetic 18
15. 1.10 Iamblichus, On the General Science of Mathematics 20
16. 1.11 Proclus, Commentary on the First Book of Euclid’s Elements 26
17. 1.12 Boethius, On Arithmetic 31
18. 1.13 Aristophanes, The Clouds, The Frogs, The Birds 34
19. Chapter 2. Arithmetic
20. INTRODUCTION 38
21. 2.1 Euclid, Elements, 7–9 39
22. 2.2 Nicomachus, Introduction to Arithmetic 50
23. 2.3 Boethius, On Arithmetic 66
24. 2.4 Philo of Alexandria, On the Creation and Who Is the Heir of Divine Things? 70
25. 2.5 Pseudo-Iamblichus, The Theology of Arithmetic 74
26. 2.6 Diophantus, Arithmetica 82
27. 2.7 Demotic Papyri from Egypt 111
28. 2.8 Papyrus Michigan 620 113
29. 2.9 Papyrus Mathematics 114
30. 2.10 Papyrus Achmîm 115
31. 2.11 Selection of Arithmetical Tables 117
32. 2.12 Theon of Alexandria, Commentary on Ptolemy’s Almagest 124
33. 2.13 Archimedes, Sand Reckoner 126
34. 2.14 Pappus, Collection, 2 133
35. 2.15 Greek Anthology 137
36. Chapter 3. Euclid and the Beginnings of Theoretical Geometry
37. Introduction 141
38. 3.1 Plato, Timaeus 142
39. 3.2 Plato, Theaetetus 144
40. 3.3 Plato, Meno 146
41. 3.4 Aristotle, Physics 152
42. 3.5 Hippocrates, Quadrature of Lunes 155
43. 3.6 Archytas, Two Mean Proportionals 159
44. 3.7 Proclus, Commentary on the First Book of Euclid’s Elements 161
45. 3.8 Euclid, Elements, 1, Including Commentary by Proclus 168
46. 3.9 Simplicius, Commentary on Euclid’s Elements 196
47. 3.10 Euclid, Elements, 2–6 200
48. 3.11 Euclid, Data 229
49. 3.12 Euclid, On Divisions 238
50. 3.13 Euclid, Elements, 10 242
51. 3.14 Pappus, Commentary on Euclid’s Elements, Book 10 248
52. 3.15 Euclid, Elements, 11–13 251
53. 3.16 Hypsicles, Elements, 14 265
54. 3.17 Pappus, Collection, 3, Problems and Theorems 269
55. 3.18 Pappus, Collection, 3, Inscribing Polyhedra in a Sphere 271
56. 3.19 Pappus, Collection, 4, Generalization of the Pythagorean Theorem 274
57. Chapter 4. Archimedes and Related Authors
58. Introduction 278
59. 4.1 Polybius, The Histories 279
60. 4.2 Archimedes, Measurement of a Circle 281
61. 4.3 Archimedes, Quadrature of the Parabola 285
62. 4.4 Archimedes, Sphere and Cylinder I 293
63. 4.5 Archimedes, Sphere and Cylinder II 307
64. 4.6 Archimedes, Planes in Equilibrium 317
65. 4.7 Archimedes, On Spirals 323
66. 4.8 Archimedes, The Method 339
67. 4.9 Archimedes, On Floating Bodies 350
68. 4.10 Carmen de Ponderibus et Mensuris 354
69. 4.11 Pappus, Collection, 4, Spiral Area 356
70. 4.12 Pappus, Collection, 4, Touching Circles 357
71. 4.13 Pappus, Collection, 5, Archimedean Solids 358
72. Chapter 5. Apollonius and Other Responses to Archimedes
73. 5.1 Apollonius, Conics, 1 363
74. 5.2 Apollonius, Conics, 2–4 390
75. 5.3 Apollonius, Conics, 5–7 423
76. 5.4 Apollonius, On Cutting Off a Ratio 450
77. 5.5 Nicomedes, On the Conchoid (from Eutocius) 453
78. 5.6 Pappus, Collection, 4, Quadratrix 457
79. 5.7 Diocles, On Burning Mirrors 459
80. 5.8 Pappus, Collection, 5, Hexagonal Form of Honeycombs 467
81. 5.9 Zenodorus, On Isoperimetric Figures 469
82. 5.10 Pappus, Collection, 4, Kinds of Geometrical Research 471
83. 5.11 Pappus, Collection, 4, Angle Trisection 472
84. 5.12 Pappus, Collection, 7, Analysis and Synthesis 476
85. 5.13 Pappus, Collection, 7, Three- and Four-Line Locus and Guldin’s Theorem 477
86. 5.14 Pappus, Collection, 7, Constructing Conics using Focus and Directrix 479
87. 5.15 Serenus, On the Section of a Cylinder 484
88. Chapter 6. Applied Geometry
89. 6.1 Philo of Byzantium, Belopoeika 491
90. 6.2 Heron, Belopoeika 493
91. 6.3 Heron, Metrica 496
92. 6.4 Babylonian Tablet BM 34568 514
93. 6.5 Papyrus Cairo 517
94. 6.6 Columella, Of Husbandry 520
95. 6.7 Ayer Papyrus 523
96. 6.8 Papyrus Rainer 527
97. 6.9 Papyrus Genevensis 529
98. 6.10 Papyrus Cornell 530
99. 6.11 Papyrus Mathematics 531
100. 6.12 Corpus Agrimensorum Romanorum 533
101. 6.13 Polybius, The Histories 537
102. 6.14 Vitruvius, On Architecture 540
103. Chapter 7. Astronomy
104. Introduction 548
105. 7.1 Eudoxus of Cnidus (from Aristotle and Simplicius) 549
106. 7.2 Aristarchus, On the Sizes and Distances of the Sun and Moon 552
107. 7.3 Hypsicles, Little Work on Rising Times 558
108. 7.4 Theodosius, Sphaerica 562
109. 7.5 Menelaus, Sphaerica 572
110. 7.6 Ptolemy, Almagest 580
111. 7.7 Ptolemy, Handy Tables 598
112. 7.8 Ptolemy, Planisphere 601
113. 7.9 Ptolemy, Geography 607
114. 7.10 Antikythera Mechanism 615
115. 7.11 Cleomedes, On the Circular Motion of Heavenly Bodies 623
116. 7.12 A Hellenistic Horoscope 626
117. 7.13 Oxyrhynchus Astronomical Papyri 629
118. 7.14 A Parapegma from Miletus 630
119. Chapter 8. Music
120. Introduction 635
121. 8.1 Plato and Aristotle on Music Theor 636
122. 8.2 Archytas, from Porphyry and Ptolemy 638
123. 8.3 Aristoxenus, Elementa Harmonica 640
124. 8.4 Euclid, Sectio Canonis 640
125. 8.5 Nicomachus, The Manual of Harmonics 647
126. 8.6 Theon of Smyrna, Mathematics Useful for Reading Plato 651
127. 8.7 Ptolemy, Harmonics 652
128. 8.8 Boethius, Fundamentals of Music 660
129. Chapter 9. Optics
130. 9.1 Euclid, Optics 671
131. 9.2 (Pseudo-[?])Euclid, Catoptrics 682
132. 9.3 Heron, Catoptrics 684
133. 9.4 Ptolemy, Optics 685
134. Bibliography 695
135. Index 701