578 Index
critical editions, 138, 261
historical analysis of critical editions, 20–6,
35–9, 136, 163–204, 336–9
history of proof and history of critical
editions, 21, 22, 23, 25–6, 36
tacitly conveying nineteenth-century
or early-twentieth-century
representations, 22, 24, 26, 36
critique, in Old Babylonian mathematics, 377,
380
Crombie, A., 291
cross-contamination, see diagram
Crossley, J. N., 423, 427, 433, 486
cube root, 410–11, 413–14
Cullen, C., 423, 485, 518, 525–6, 533
cultures of proof, 42, 229
Cuomo, S., 301
curriculum, 389, 410–11, 413–14, 512–15,
519, 536
Curtze, M., 279
Czinczenheim, C., 139–40, 156
Czwalina-Allenstein, A., 163
D’Alembert, J., 6, 12
D’Ooge, Martin Luther, 311, 313, 324
da yi ‘general meaning’, 520–2
Dain, A., 70, 133
Dalmia, 264, 272
Datta, B., 271, 272
Dauben, J. W., 5, 65, 423, 485, 525
Davis, M., 17
Davis, S., 233, 236–9, 242, 249, 256, 257
De Groot, J., 213
De Haas, F. A. J., 210
De Rijk, L. M., 217
De Young, G., 78, 87, 89, 91, 104, 105, 110, 117,
130, 133
Decorps-Foulquier, M., 145
deductive structure, 2, 14–15, 20, 22–3, 26,
29–30, 52, 57–8, 62, 103–4, 109–10,
111–13, 119, 320–5, 440
defi nition, 14, 26, 92, 93, 107, 115, 124, 126,
303–5, 308, 313–16, 318
and explanation, 209, 216
arithmetical defi nition, 318
formal and material defi nition, 211, 214–15,
217
of polygonal numbers, 313–16
physical and mathematical defi nition, 213–14
see also number, starting points
Delambre, J., 5, 245, 247, 256, 258
Delire, J. M., 262, 271–2
Democritus, 295demonstration, 1, 3, 11, 26–7, 64, 66, 229, 231,
242, 245–52, 254, 256, 260, 271–2, 274,
276, 280, 300–4, 306–8, 325
algebraic demonstration, 6, 280–1; see also
algebraic proof
and Euclid’s Elements I.32, 208–9, 219–21,
288; see also Euclid
and syllogistic form, 27, 206, 209, 222, 224,
225
demonstratio potissima , 223
demonstratio propter quid , 223
demonstratio quid est , 223
illustrative [ Anschauungsbeweis ], 6, 276, 280,
285, 289
inductive, 3, 11, 285
in early-modern Europe, 2, 3, 7, 53, 289–90
logical, 5, 22, 274
physical versus mathematical, 214, 217–18,
221
primitive, 285, 290, 291
rigorous, 275, 289, 290
status and use of, in Arabic treatises, 5, 288–9
visual, 6, 251–2, 272
see also analysis, geometry, p r o o f , synthesis
denominator mu , 423, 431–4, 436, 438, 446,
448, 459–61, 463–71, 475–80, 538, 542
Densmore, D., 145
Des Rotours, R., 513, 515, 518, 520–1, 535
Detailed Explanation of the Nine Chapters of
Mathematical Procedures , see Xiangjie
Jiuzhang suanfa
Detailed Outline of Mathematical Procedures
for the Right-Angled Triangle , see Gougu
Suanshu Xicao
deuteronomy, 329, 353, 359
Dharampal, 257, 258
diagram, 22, 24–5, 32–4, 41–2, 52–3, 58, 270,
272, 303, 320, 323, 500–3, 506–8, 524,
531, 533
Archimedes’, 24, 140, 164–76
Chinese commentaries, 24, 52, 58
critical edition of, 22, 24–5, 32, 136, 138–40,
156–7
cross-contamination of manuscript
diagrams, 153–6
Euclid, 24, 136–9, 140–5, 147, 149, 152
generality of, 143, 157; see also generality
generic, 24
having particular dimensions, 6, 24, 32,
41–2
Heiberg turns Archimedes’ diagrams into
mere ‘aids’, dispensable elements, 25
iconic, 172–5