Index 589
Polygonal numbers ( On ) , 33–4, 311–26
Bachet’s editio princeps of the Greek text,
325
Polygons (On), 313–16
polynomial algebra, 57–8
Poncelet, J. V., 5, 15
porism, 23, 91, 92, 93, 103–4, 105, 115–16, 124,
126, 128
porismata , 284
Poselger, F. T., 323
positions, 435, 459, 478, 483
array of, 434–5, 478
positivism, 292
Posterior Analytics , 206, 207, 208, 209–10, 211,
215, 216, 217, 223, 325
postulates, 26, 301, 305
of parallels, 288
practical orientation, 6, 8
practical as opposed to speculative
orientation, 5
‘practical orientation’ of the mathematics of
the Arabs, 5
‘practical orientation’of the mathematics in
the Sulbasutras , 8, 12, 260, 266, 268,
270, 272
practices of computation, 40, 45; see also tool
for calculation
practices of proof, 1, 2, 4, 11–12, 15, 17, 21–3,
28–30, 31–2, 35, 38, 41, 47–51, 54–9,
61–3, 425, 426, 448–9, 462, 471, 483
history of, 19, 23, 30, 38, 43, 53, 60, 480–4
shaping of, 15, 18, 20, 32, 35, 38, 59, 62–3
pratyayakaran.a, 498, 503, 505
predication, 210, 212, 222
essential, 208, 209–12, 218
prediction, 16, 300
principle ( arkhê ), 112, 312
principle , 567–9
Principle of Gougu , see Gougu yi
Prior Analytics , 377, 383
problem (mathematical), 17, 31, 35–44, 47–8,
55–9, 65, 260, 295, 300, 387, 413, 427–9,
449, 452, 462–4, 467, 480, 491, 493, 498,
505, 507, 509–10, 512, 516, 522–32,
534–5, 539–41, 543–4, 546, 570–2
as general statements, 38, 57, 424, 441
as paradigms, 31, 63, 522, 529, 534
category of problems, 38, 424, 463, 510, 525
da ‘answer’, 55, 520–1
Diophantus’ problems relating to integers,
35–8
explanation pratipadita (Sanskrit) of an
algorithm by means of problems, 53
introduced by the term ‘to look for’ ( qiu ),
444–6
parallel between geometrical fi gures and
problems, 41–2, 44, 48
particular problems, 41, 58, 423, 424, 441
problems with which the understanding of
the eff ect of operations can be grasped,
41–2, 44, 48–9, 481
use of problems in proofs, 41–2, 44, 48–9, 53,
63, 65, 425, 445–6, 462–4
wen ‘problem’ (Chinese), 55, 520–1, 538,
541
problem-solving, 35–5, 57, 285
procedure, 263, 269, 271–2, 313, 487, 489–90,
492–4, 498–501, 503, 505, 507
arithmetical, 33, 313, 507
fundamental, 52, 61, 425, 451, 476, 480–1
see also algorithm
Proclus of Lycia, 27, 76, 121, 131, 206, 207, 208,
219–22, 224, 298, 304–6, 362
professionalization of science, 4–5, 11
programme for a history of mathematical
proof, 18–19, 59–64
programme of study in Mathematical College,
519, 522
advanced, 518–20, 534–5
regular, 518, 520, 535
Prony, G., 382
proof, 89–94, 99, 260, 263, 269–71, 265, 312,
317–25, 444–9, 498–507, 512, 559–60,
563, 565–9
activity of proving as tied to other dimensions
of mathematical activity, 16, 19, 43, 51,
53, 55, 60
actors’ perception of proof, 4, 263, 270,
498–507
alternative proof, 89–90, 107–10, 112, 114
analogical proof, 91–2, 120
double proofs, 23, 83, 89–90, 93, 99, 107–10,
114, 124, 126, 129
elementary techniques of proof, 30, 33, 44,
59–60, 62
functions ascribed to proof in mathematical
work, 15–19, 41, 263, 270
general proofs, see generality
goals of proof, 13, 14–15, 18–19, 28–35, 38,
41, 51–2, 58, 61–2
key operations in proof, 425–52, 480–1
pattern of argument, 2, 25–6, 30, 35
potential proof, 91–2, 120
proof and algorithm, 39–51, 423–84
proof as bringing clarity, 17, 18, 61
proof as bringing reliability, 17