Index 575
approximations, 40, 301, 452–8
Arabic science, 2, 5, 7, 21–3, 37, 43–4, 48,
274–5, 286–9
‘Arabs’, 5, 274, 287
handling of ‘Greek’ mathematics, 286–9,
339–40
imitators of the Greeks, 289–90
Archimedes, 1, 2, 5, 20, 24–6, 28, 42, 62, 66,
69, 135, 140, 163–204, 276, 299–300,
305–6, 308, 351, 362
Heiberg’s edition of Archimedes’ writings, 20,
24–6, 86
Heiberg forcing divisions between types
of propositions and components of
propositions onto texts, 26
mechanical way of discovery, 28, 42
Palimpsest, 86, 147–8, 164–5, 179–80, 187,
189, 192, 195
Archimedes, works by
Arenarius , 178, 180–1, 186, 188–9, 190, 195,
203
Cattle Problem , 178, 186, 188, 203
Centres of Weights of Solids , 171
Conoids and Spheroids , 171, 178, 186, 188–9,
192–3, 199–201, 203
Floating Bodies , 164, 171, 178, 186–9, 194,
203
Measurement of Circle , 164–5, 171, 178–9,
186–8, 203
Method , 28, 42, 171, 178–9, 186–9, 195–203,
299–300, 308
proposition 14, 148, 158, 196–8
Planes in Equilibria , 164, 171, 177–9, 186–9,
193–5, 203
Polyhedra , 171, 188
Quadrature of Parabola , 171, 178, 186, 188–9,
193–4, 203
Sphere and Cylinder , 140, 146, 164–76,
178–9, 181–4, 186–9, 193–5, 203
m a n u s c r i p t Vatican Ottob. 1850, see
manuscripts (Latin)
Spiral Lines , 164–5, 171, 176, 178, 186–9, 190,
195, 203
Stomachion , 171, 178, 186–9, 203
Archytas, 190, 295, 298–9, 304
Aristarchus, 305
On the Sizes and Distances of the Sun and
Moon , 305
scholia, 156
Aristophanes, 297
Aristotle, 1, 17, 26–7, 66, 295–8, 300, 302–8,
325, 362–3, 377, 381
Prior Analytics and Euclid’s Elements , 377
Posterior Analytics and Euclid’s Elements , 1,
26–7
theory of demonstration in the Posterior
Analytics, 1, 17, 26–7, 66, 303–4
arithmetic, 9, 33, 267, 294, 297–8, 300, 302, 440,
451, 459, 473, 482–3, 507
with fractions, 50, 426, 431–6, 441–3, 447,
451–80, 483
Arithmetica , see Arithmetics , Diophantus of
Alexandria
arithmetical reasoning, 8, 34, 263, 269, 311–26,
504, 507
Arithmetics , 35–9, 44, 46, 283–4
critical analysis of Tannery’s edition, 36
see also Diophantus of Alexandria
Arnauld, A., 18
Arneth, A., 278–9
Arnzen, R., 87, 131
a r t i fi cial languages, 45–6, 65
Ā r y a b h a t. a, 244, 282, 487–90, 494, 500–1, 504–8
Āryabhat. īya , 51–3, 66, 487, 489–92, 494,
498–501, 504–8
Āryabhat. īyabhās. ya , 487–508
Asiatic Society, 230, 232, 239, 242, 257, 273
Assayag, J., 228, 256, 259
astronomy, 265, 274–5, 294, 297–8, 300, 304,
494–8, 508
history of Indian astronomy, 237, 239, 241,
258, 261, 262, 264, 272–3, 276, 494–8
inequality of the moon, 275
practical, 274
spherical, 274
Athenian public accounts, 10
Atiyah, M., 16, 17, 64
August, E. F., 137
authenticity, 79, 95, 97–9, 100–5, 110
Autolycus, 139
autonomous practical knowledge, 381
auxiliary construction, 209, 220, 221, 224
Averroes, 207, 223
axiom, 14, 304–5, 308; see also starting points
axiomatization, 15, 62
axiomatic–deductive structure, 14, 15, 23,
57–8, 62
in the nineteenth century, early twentieth
century, 12, 20, 26
outside mathematics in ancient Greece, 15, 29
ba gu wen ‘eight-legged essays’, 513
Babylonian mathematics, 1, 5, 12, 14, 18, 20, 31,
37, 39–49, 50, 55, 59, 62, 65, 370, 377,
379–81
seen as empirical, 363