584 Index
instrumentation, 274
intellectual inferiority, 274, 292
interpretation, 6, 9, 11, 22–3, 28, 30, 38–9, 43–8,
51–5, 60, 260, 271, 423–84, 487–90,
492–4, 498, 500, 503, 506–7
of operations, 38, 41, 42, 44, 48, 431, 439,
443–4, 446, 450, 458, 464–6, 473, 476,
480, 483, 498; see also meaning
problems in the interpretation of the sources,
9, 26–7, 29–32, 38–40, 44–6, 49, 63, 468
proof based on an interpretation involving a
plate, beads and pebbles, 43
skills required for, 38–43
Introduction to Arithmetic , 33, 311–18
Introduction to the learning of computations , see
Suan xue qi meng
intuition
‘Indian’ style of mathematical practice, 280
modern mathematics, 282, 290
inversion fan , 440, 442, 451, 459, 472,
475–80, 482–3
inverse operations, 437, 450, 452–8, 460, 472,
474, 482
of an algorithm, 455
see also algorithm, reverse algorithm
Irigoin, J., 70, 72, 73, 83, 133
irrationals, see number
Ishâq ibn Hunayn (Abû Ya’qûb Ishâq ibn
Hunayn), 78, 86, 89, 91, 93, 96, 103, 104,
106, 107, 109–10, 116–19, 126–7
Isocrates, 298
iteration, 385, 393, 396–7, 402, 413, 416–17
J a ff e, A., 15–17, 64, 66
Jain, P. K., 12, 66, 487, 489
Jami, C., 3, 20, 65, 66, 68, 230, 257
Japan, 54, 424
Jardine, N., 223
Jayyânî (al-), Abû ‘Abdallâh Muhammad ibn
Mu’âd al-Jayyânî al-Qâsî, 87, 132
Jesuits, 2–3, 67, 238, 257, 258, 275, 511
astronomers, 230, 241
historiography, 238
Ji yi , 515, 517, 522; see also Shu shu ji yi
( Records of the procedures of numbering
left behind for posterity )
Jia Xian , 553, 573
Jiegenfang (to borrow a root), 573
Jihe yuanben , Elements of geometry ,
567–8
Jin dynasty, 517
Jin dynasty, 514
jin shi (degree), 521Jiu Tang shu , 518, 532–3, 535
Jiu zhang , 515–16, 518–19, 522; see also
Jiu zhang suan jing , Jiu zhang suan shu
Jiu zhang suan fa bi lei da quan
, 526, 546
Jiu zhang suan jing , 519, 533; see also
Jiu zhang suan shu
Jiu zhang suan shu , 47–50, 54–6,
58, 67, 376, 384, 387, 389–90, 399, 403,
406–9, 411, 420, 423–86, 511–12, 516,
519, 525–6, 529, 531–3, 541, 546, 553,
566, 568–9 ; see also Jiu zhang suan jing
Joannès, F., 387
Johannes de Tinemue, 86, 127, 130
Johnson, W., 192
Jones, A, 71, 139, 149–50, 304
Jones, W., 237–8, 257, 258
juan , 519–20, 526, 535
Junge, G., 86, 130, 131, 161
j u s t i fi cation, 260, 263–4, 269–70, 388, 417,
488–90, 498
implicit
in equation algebra, 367
in Old Babylonian mathematics, 366–7,
369–80
mathematical and didactical explanation,
370, 377
mathematical justifi cation, 260, 263–4,
269–70, 363, 377, 488–90
Kai-Yuan li ( Rites of the Kai-Yuan era ),
521–2
Kant, I., 377
Karaji (al-), 287
Kejariwal, 230, 257
Keller, A., 8, 12, 20, 51–3, 60, 66, 260–72 ,
487–508
Khayyâm (al-), ‘Umar, 87, 132
Khwarizmi (al-), 43, 65, 67, 286, 288, 350
Klamroth, M., 21–3, 77–9, 81, 85, 89, 99, 100,
113–14, 116–19, 133
Klein, J., 328
Kline, M., 1, 9, 40, 363–4, 370, 383
Knorr, W., 20, 21, 66, 70, 79, 81, 84–5, 87–8, 95,
99, 110, 111, 114–15, 116–19, 122, 134,
149–50, 185–6, 198, 295, 345, 351
Korea, 54, 424
Kramer, S. N., 386, 410–11
Krob, D., 43, 66
Kuhi (al-), 289
Lakatos, I., 15, 52, 66
Langins, J., 5, 66