Index 579
iconically representing the numbers as
confi gurations of units, 33, 313–16,
320, 323
indiff erence to geometric shape, 143, 145–8,
154, 160
indiff erence to metrical accuracy, 143–4,
153–5, 160
indiff erence to visual accuracy, 143–8
interpreting a diagram in terms of weight,
28, 42
lettered, 135, 157–8
L i Y e ’s Yigu yanduan (1259), 58
manuscript, 24–5, 32, 135–60
mathematical reconstruction, 24, 135–6
overspecifi cation, 25, 140–5, 154–5, 157, 160
parallel between geometrical fi gures and
problems, 32, 41–2, 44, 48, 63
redrawing, 136–7, 140, 153–9
representation of geometric object, 143, 157
representations of numbers as lines, 34
Sanskrit, 24, 42, 270, 272, 500–3, 506–8
schematic representation, 148–5, 157–60
specifi c, 24, 25, 33
three-dimensional representation, 169–72,
531
traditional, from China, 58
Y a n g H u i ’s 1261 commentary on Th e
Nine Chapters , 58
dialect, 179–80, 188–91
didactical explanation, 373, 376–7, 380
creating conceptual connections, 376–7
in Old Babylonian mathematics, 370
Dijian Shuli ຕ ( Th e Mathematical
Th eory of Dijian ), 573
Dijksterhuis, E. J., 186
Dimashqî (Abû ‘Uthmân ad-), 85
Dinostratus, 296
Diocles, 76,
On Burning Mirrors , 158, 162
Diogenes of Apollonia, 306
Diophantus of Alexandria (also Diophantos,
Diophantus), 9, 26, 33–9, 43, 44, 57, 63,
242, 244–5, 283–5, 287, 311, 318–25,
327–62
Directorate of Education, see Guo zi jian
Directorate of National Youth, see Guo zi jian
disaggregation (of parts) san , 461, 465–6,
469–70
discussion, 262–3, 270, 488–9, 507
on the relative value of proofs, 4, 11, 13, 14,
15–17, 27, 28, 29–30
on the standards of proof as a social
phenomenon, 29–30
dispositif, 41–3, 59, 62, 69
distortion of sources, 1–2, 289
distribution, 527, 529, 540
aggregated [weighted], 525–6
fl at-rate, 525, 528, 530
weighted, 525–30
dividend, see shi
division, 426–84, 491, 493, 498–9, 540, 542
as multiplication by the reciprocal, 390
at a stroke lianchu , 448–9, 451, 471–5,
480, 482–3
division together bingchu ᨸ , 474, 482
evaluation, see shang chu
execution of, 432–51, 460, 471–2, 476–8
in return baochu , 453, 457–9, 478–9,
482–3
of fractions, 426, 427, 430–1, 463–71
of integers plus fractions (procedure for
‘directly sharing’ jing fenshu ), 436,
442, 461–75, 477, 483
returning [division], see gui [ chu ]
square root extractions as division, 47, 454–8
d i v i s o r , see fa
Djebbar, A., 78, 81, 84, 87, 89, 107, 117, 118,
119, 120, 132, 133, 134
Donahue, W. H., 145
D o n g Q u a n , 517
Dorandi, T., 70, 71, 133
Du Shiran , 427, 433
Du Zhigeng , 67
Duhem, P., 292
Dunhuang, 510
Durand-Richard, M.-J., 12
early-modern Europe, 2, 6, 7, 11, 18, 30, 53,
289, 290
Ecole Polytechnique, 5, 66
Egypt, 5, 7, 285
Egyptians, 285–6
eight-legged essays, see ba gu wen
Eisenlohr, A., 285
Eleatic philosophers, 295
Elements (Euclid), 2–3, 4–5, 7, 9, 11, 13, 14, 18,
20–4, 26–7, 28, 33, 36, 37, 39, 69–134,
135–6, 140, 152, 168, 184, 267, 295, 298,
304, 306, 308, 552, 567–8
Book xi, 149
Book xii, 149
Chinese version of Euclid’s Elements , 2–3,
13, 56, 65
Clavius’ edition of the Elements , 2–3, 56, 67
direct tradition, 21, 74–7, 78–9, 113–14,
124–5