590 Index
proof (cont.)
proof as establishing mathematical attributes
that belong to their subjects essentially,
27
proof as providing corrections, 17
proof as providing feedback, 17
proof as support of a vision for the structure
of a mathematical object, 17, 33–4
proof as yielding clues to new and unexpected
phenomena, 17, 31, 52
proof as yielding ideas, 17
proof as yielding mathematical concepts, 17,
31, 52
proof as yielding new insights, 17
proof as yielding techniques, 17, 30–2, 38,
41, 52, 61
proof as yielding understanding, see
epistemological values attached to
proof
proof as yielding unexpected new data, 17
proof by example, 316–18
proof by mathematical induction, 320–5
proof for statements related to numbers and
computations, 9
proof in the wording, 40, 48, 468; see also
transparency
proof of the correctness of algorithms, 9–10,
18, 31, 38, 39–51, 53, 55, 57, 59–60,
423–84, 498–507
proofs as a source of knowledge, 17, 52, 429,
448, 471
proofs as opposed to arguments, 15, 16, 28,
29
proofs as opposed to insights, 16
proofs highlight relationships between
algorithms, 52
relations between proofs, 23, 445
rewriting a proof for already well-established
statements, 17
rigorous proof with diorismos, 289
role of proof in the process of shaping
‘European civilization’ as superior to
the others, 2–3, 4–5, 10
substitution of proof, 23, 90, 99, 107–10, 111,
125, 127, 129
technical terms for proof, 41, 42, 48, 52, 55,
425, 431, 448–9, 451, 456–8, 464–8,
473, 481–3, 498
there is more to proof than mere deduction,
52
tool-box, 30,
uses of proof, 2, 4
see also meaning upapattiproportional, see lü
proposition, 3, 5, 8, 23, 26, 31, 274, 314–19
arithmetical and general propositions, 33–4
purely arithmetical propositions, 34, 319
Protagoras, 297
protocol of computations, see lu
Proust, C., 20, 44–7, 50, 389–90, 402, 405, 420
Ptolemy, 300, 306
Almagest , 140
Geography , 149
Optics , 139
Pyenson, L., 292
pyramid,
circumscribed to a truncated pyramid, 430,
432, 436, 438–9, 444, 447
‘truncated pyramid with square or
rectangular base’ fangting , 427,
429–32, 436, 438–9, 441, 443–6, 455
‘truncated pyramid with a circular base’
yuanting , 426–52, 468, 476
see also volume (cone)
Pythagoras, 295
‘procedure of the right-angled triangle
( gougushu )’, 56
Pythagorean theorem, 3, 8, 58, 252, 490–2,
494, 497–8, 501–2, 507
Pythagoreans, 311
Qi gu , 515, 517, 522; see also Qi gu suan
jing
Qi gu suan jing , 511, 517–18, 533,
535, 546
Qian Baocong , 517–18, 520, 561, 568
Qin Jiushao (also Ch’in Chiu-shao ), ,
549
qing , 538, 542
quadratures, 295–7, 304
quadrilateral, 277
Quaestio de certitudine mathematicarum , 206,
223
quantity, 431–7, 442, 453–7, 459–79, 482–4
as confi guration of numbers, 432, 435, 460,
472, 477–8, 483
Quinn, F., 15–17, 64, 66
quotation, 75, 76, 77, 85, 163, 179, 184, 366,
367, 430, 520
Qusta Ibn Lūqā, 361
race
‘race apt to numerical computations’, 284
Indo-Aryan races, 292
Semitic races, 292
Rackham, H., 362