586 Index
mathematical education (cont.)
in scribal schools, 41, 43–4, 62, 387, 389–90,
403, 405, 408–10, 412–16; see also
scribal school
mathematical education and commentaries,
54–5
mathematical examinations
in China, 54–5, 514, 520, 523–4, 530–1,
534, 536–7
in East Asia, 54, 55
in Vietnam, 523, 524
textbooks used in educational system, 2–3,
54, 509–10, 513–14, 516, 518–19, 523,
531–2, 534–5
mathematical proofs, motley practices of, 6, 15,
16, 19, 28–30, 34, 50, 61–4
mathematics, 260–73, 487–8, 503, 508
‘Chinese’, 3, 275, 509, 511, 513, 537
division between pure and applied, 12
‘Egyptian’, 285–6
‘foreign infl uences’, 282, 284–8
‘Greek’, 6, 282–5
‘Hindu’, 264
‘Indian’, 7, 260–1, 267, 275–7, 280–2, 503
‘Islamic’, 286–9
‘Muslim’, 279, 289
‘Oriental’, 7, 277ff
orientalized form of, 283–5
pre-scientifi c, 291
scientifi c, 291
Maximus Planudes, 284
McKeon, R. M., 382, 383
McKirahan, R., 223
McNamee, K., 340
meaning, 32, 45–6, 57, 263, 265, 269, 488,
490–1, 500–1, 503
‘higher meaning’ of an algorithm, 52, 481
formal meaning, 466, 468
material meaning, 42, 466–7
meaning ( yi ), ‘meaning, intention’ of a
computation, of a procedure, 42, 48,
426, 431, 436–40, 446–8, 453, 455,
464–7, 480–1
meaning ( yi’ ), ‘meaning, signifi cation’ of a
procedure, 52, 55, 58, 481, 521–2,
534–5
meaning as opposed to value, 40, 46, 438–9,
446–7, 453, 455
meaning in Sanskrit commentaries, 51–2, 263,
265, 269, 488, 490–1, 500–1, 503
meaning of operations, 37–8, 42, 48, 59, 62–3,
444, 480–1
use of the context of a problem to formulatethe ‘meaning’ of procedures, 42, 44, 48,
444–6
use of the geometrical analysis of a body to
formulate the ‘meaning’ of procedures,
44, 48
see also da yi ‘general meaning’
mechanical considerations, 42, 277
mechanics, 298–9
medicine, 301–2, 304–5
Mei Juecheng , 57
Mei Rongzhao , 548
Mei Wending , 66, 566
Mendell, H., 222
Mending Procedures , see Zhui shu
Menge, H., 70, 130, 139
Meno , 8, 15
Mesopotamia, 1, 5, 12, 14, 18, 20, 31, 37, 39–49,
50, 55, 59, 62, 65, 282, 384, 387, 389,
400, 410
meteorology, 295, 297, 301
Method , see Archimedes, works by
method, 11, 30–2, 34, 36, 37, 42–3, 50, 57, 66,
260, 264, 266–7, 268, 270–1, 273, 497,
505–7
debates about proper methods in numerous
domains of inquiry in ancient Greece,
29, 36, 294–308
see also exhaustion (method of )
methodology of science, 4, 8, 11
Michaels, A., 293
Mikami Yoshio , 510
Mill, J. S., 11
Ming dynasty , 510, 513
ming fa (lit. ‘[He Who] Understood the
[Juridical] Norms’), 520–1
ming jing (lit. ‘[He Who] Understood the
Classics’), 520–2
ming suan (lit. ‘[He Who] Understood the
Computations’), 520–2
ming zi (lit. ‘[He Who] Understood the
[Chinese] Characters’), 520–1
Minkowski, C., 261, 273
mithartum , 366–7
modes of analysis, 243
M o e r b e k e , see William of Moerbeke
Mogenet, J., 73, 131, 139
Molland, G., 288
Montucla, E., 234, 237–8, 258
Morrison D., 217
Moses ibn Tibbon, 87, 131
motivations for writing down proofs, 15, 17,
19, 31–2, 39–41, 52–3, 481; see also
epistemological values attached to proof