582 Index
generality (cont.)
in Nicomachus’ Introduction to Arithmetic ,
33–5
of diagrams, see diagram
of objects, 33, 427, 460–1, 474, 481
of problems, 57, 424, 463
of proofs, 429, 441, 468, 471, 474, 481
see also paradigm, rule
generalization, 264, 286, 313, 322, 324
Geng Shouchang , 518
Geography , see Ptolemy
geometrical demonstration, 3, 6, 8, 29, 41–2,
58, 65, 245–6, 249, 252, 271
geometrical problem, 41, 146–7, 151, 158
geometrical progression, 385, 391, 399, 405,
408–9, 416
geometry, 2–3, 41, 48–9, 232–4, 236, 239,
242–3, 245–6, 248–9, 256, 260, 267,
271–3, 278, 294–5, 297–301, 304,
491–503, 507, 512
cut-and-paste, 312
Greek, 1, 9, 12, 14, 20, 22, 24, 26, 28–30, 43,
52, 66, 135–60, 267, 275, 277, 425
Indian, 8–9, 260, 267, 271–3, 280–1, 289,
491–503, 507
practical, 286, 289
Gerard of Cremona, 86, 87, 89, 90, 91, 93, 95,
96, 98, 103–5, 106, 109, 117, 119, 126–7,
130, 133
German logicians, 288
Gillon, B. S., 533
Gnomon of the Zhou, see Zhou bi
Gnomon of the Zhou [dynasty] ( Th e ), see Zhou bi
gnomons, 492–5, 498
Goldin, O., 223
Gougu procedure (‘Pythagorean
procedure’), 553, 566, 569
Gougu Suanshu ( Mathematical
Procedures on Gougu) , 553
Gougu Suanshu Xicao
(abbreviated as GGSX ), Detailed
Outline of Mathematical Procedures for
the Right-Angled Triangle ), 552–4, 556,
558, 560, 564–5, 567, 569–70
Gougu yi , Th e Principle of Gougu , 566,
568–9
Gow, J., 324
Grabiner, J., 13, 65
grammar, 31, 51, 261, 281
empirical, 281
etymological, 281
logical, 281
syntactical, 281, 357–9Great Compendium of the Computational
Methods of Nine Categories [and their]
Generics , see Jiu zhang suan fa bi lei da
quan
greater common divisor (in Chinese, ‘equal
number’, dengshu ), 470
Greek philosophy and mathematical proof,
1, 362
Greek science, 2, 3, 5, 7–8, 12, 14, 20, 21–4, 26,
28–30, 32–4, 37–8, 52, 56, 60, 62, 66,
67
Greeks, 1, 2, 5, 8, 9, 264, 267, 274, 280–4,
286–91
‘apodictic rationality’, 280
‘Greek miracle’, 1
‘logical Greek’, 274–92
Gregory (Gregorius), D., 82, 138, 275–6, 279,
280, 284, 285, 290
Groningen, B. A. van., 340, 361
Grundlagen der Mathematik , 312
Grynée (Grynaeus), S., 82, 138
Gu Yingxiang ᆌࠥ , 553
gui [ chu ] ‘returning [division]’, 538–9,
542
Guidance for Understanding the Ready-made
Computational Methods, see Chỉ minh
lập thành toán pháp
Günther, S., 279
Guo Shuchun , 12, 42, 49, 52, 55,
423–85, 531, 560
Guo zi jian ‘Directorate of Education’,
514
Hacking, I., 3, 10, 11, 13, 15, 40, 65
Hai dao , 515–16, 518, 522; see also Hai
dao suan jing
Hai dao suan jing , 516, 532, 534,
536–7, 546; see also Hai dao
Hajjâj (al-) (al-Hajjâj ibn Yûsuf ibn Matar), 78,
86, 89, 91, 93, 105, 106, 109–10, 117–21,
130, 133
Han Yan , 516, 518, 520, 532
Hankel, H., 277–90
Hankinson, R. J., 306
Harari, O., 14, 26–7, 39, 65
harmonics, 294–5, 297–8, 304
Hart, R., 291
Hayashi, T., 12, 260, 488, 501, 503, 506
Haytham (‘Ibn al-), Abû ‘Alî al-Hasan ibn
al-Hasan Ibn al-Haytham, 85, 87,
132
Heath, T., 83, 163, 186, 311, 317–18, 323, 330,
345, 349