Index 581
E n g r o ff , J. W., 87, 106, 107, 116–18, 130
enlightenment, 228, 232, 258, 272
post-enlightenment, 228
Ennis, T. E., 523
epistemological values attached to proof, 4,
13–14, 18, 28–35, 52, 62,
conviction, 15, 17–18, 29
fruitfulness, 17, 28, 32, 61
increased clarity, 17, 18, 61
understanding, 17, 18, 41–4, 49, 59
see also certainty, generality,
incontrovertibility, rigour, value
epitomization, 116, 117, 120–1
equalities, 37, 49, 62
transformed qua equalities, 38, 44, 49, 449–50
equalization tong , 436, 463–6, 468, 470–1
equation, 287, 328, 348, 360
general, 57–8
Pell, 290
simultaneous linear, 509
symbolism for equations in China, 56–9
third-degree, 289, 518
ethnic characteristic, 286
Euclid, 1, 43, 69, 70–1, 136, 267, 276, 282, 288,
304, 308, 317–19, 362–3, 376
geometric algebra of Book ii of Elements ,
319–20
Optics , 141, 150
Phenomena , 139, 141
see also Elements
Eudoxus, 295–6, 299, 304–6
Euler, L., 15, 290
Eurocentrism (history of ), 292
Europe, 261, 264
E u r o p e a n
imperialism, 10
missionaries, 2–3, 10
vernacular languages, 2, 37
Eutocius, 178–9, 299
commentary on Apollonius’ Conics , 145
commentary on Archimedes’ Sphere and
Cylinder , 158
evaluation division, see shang chu; see also
division
evangelism, 2–3
exactness of results, 40, 50, 268, 437, 440, 447,
453–8, 482
examination by quotation, see tie jing; see also
tie du
excision (practice of ), see philology
exhaustion (method of ), 30, 296, 299, 308
explanation, 273, 487–8, 490, 497–501, 507,
559–60, 563–5, 567
by a formula, 392, 395
fi gures introduced for types of ‘explanation’,
41–3, 499–501
in mathematics, 41–2, 51–3, 214, 224
in natural sciences, 214
pratipadita, pradarsa to refer to algorithms
solving a problem, 53, 497–501
through middle terms, 207–9, 214–24
fa ‘divisor, norm’, 431–4, 459–62, 467–72,
478, 527–8, 538–9, 541, 543–4
factorization, 401, 408, 410–16
algorithm, 405, 411, 416
Fârâbî (al-), Abû Nasr Muhammad ibn
Muhammad ibn Tarhân, 87, 131, 133
Fecht, R., 136
fen ‘parts, shares’, 528, 538–40, 543–4 ; see
also fractions , number (fractions)
Feng Lisheng , 518
fenlü ‘aggregated shares/parts’, ‘multiples
of shares/parts’, parts-coeffi cients’,
‘parts-multiples’, 528–30, 539, 543–4
Filliozat, J., 230, 257
Five Departments , see Wu cao
Folkerts, M., 86, 130, 133, 279, 550
Follieri, E., 73, 133
formal system, 552–3, 557, 565, 569
formulaic expression, 37, 357–8
Fowler, D. H., 73, 133, 318, 327
fractions, 332, 356, 390, 402, 431–80
arithmetical operations on fractions, 458–80,
483; see also complexifi cation, division,
multiplication, simplifi cation
as parts, 434, 436, 458, 460–1, 463, 464–70,
473, 475–6, 478
as a pair of numbers, 435, 459–61, 467, 471–2,
478, 483
see also number
Freudenthal, G., 87, 131, 133
Freudenthal, H., 143
Friberg, J., 385–6, 404–5, 410–11, 416
Gadd, C. J., 386, 410–11
Galen, 304–6
Ganesa, 241, 248–9, 276
Gardies, J.-L., 18, 65
Gauss, K. F., 279, 381
general meaning, see da yi
generality, 8, 24, 31–2, 33–8, 52, 57–8, 60–3,
425, 432, 434–6, 441, 450, 452, 456, 462,
467–70, 476–9, 498, 507
in Diophantus’ Arithmetics , 38, 347–9
in Diophantus’ On Polygonal numbers , 33–5