Index
abacus, see tool for calculation
Abbenes, J. G. J., 191
abbreviation, 36–7, 328–40, 349, 355–6
absence of demonstrations, 1, 9, 56, 276, 277,
280, 289
abstraction, 38, 354, 360, 452, 469, 471, 484,
485; see also generality, paradigm
Abū al-Wafāʾ, 286, 289
Academy of Science (Paris), 275
ācārya, 262, 266, 488
accuracy (indiff erence to visual), see diagram
Acerbi, F., 205
Adelard of Bath, 86, 87, 89, 90, 91, 93, 95, 105,
106, 109, 115, 117, 126–7, 130
aggregated shares/parts, see fenlü
Akkadian, 384–6, 391, 398, 411, 414
Akkadian method, 373
Alexandria, 361
algebra, 6, 9, 11, 43–4, 57, 317–19, 450
in India, 6, 235
Old Babylonian “algebra”, 364–80
numerical interpretation, 369
symbolic, 57, 327–8, 330
syncopated, 327–8, 330
Algebra with Arithmetic and Mensuration , 242,
246, 247
algebraic analysis, see analysis
algebraic formula, 46, 391, 393, 395
algebraic proof, 6, 7, 46, 47–51, 57–60
Diophantus’ impact on the text of algebraic
proof, 39, 318–25
in an algorithmic context, 47–51, 59,
423–86
history of, 7, 9, 39, 50, 60, 426, 450, 480–4
validity of linked to the set of numbers with
which one operates, 50, 311–26
algorithm, 9–10, 18, 38, 45, 51–3, 56, 59–60,
260, 270, 271–2, 359, 423–86, 487–8,
497–8, 500, 503, 506–8
algorithms reverse of one another, 47, 50; see
also reverse algorithm
as list of operations, 38, 40, 44, 59, 425, 428–9,
432, 436, 438–54, 500
as statements proved to be correct, 9–10, 18,31, 38, 39–51, 53, 55, 57, 59–60, 428,
436
computing reciprocals (or ‘reciprocal
algorithm’), 44–7
cancelling the eff ect of one another, 45–7, 50,
447, 455
meaning of, 41–2, 44–6, 52–3, 62, 500, 503,
507
procedure for the fi eld with the greatest
generality, 431–6, 439–40, 442–4, 459,
475–6, 483
transparent, 38, 40, 42, 48–9, 63; see also
transparency
use of, in proofs, 49, 426–81, 487–8, 497–8,
503, 508
see also factorization, procedure, square root,
text of an algorithm
Allard, A., 359
Allman, G., 279
allograph, 36, 37, 330, 338, 340–1, 359
Almagest , see Ptolemy
altitude, 494–6, 498
An Pingqiu , 517
an-Nayrîzî (Abû l’ Abbâs al-Fadl ibn Hâtim
an-Nayrîzî, also Nayzīrī (al-))
Analects ( Th e ), see Lun yu
analysis, 6, 12, 44, 280
algebraic, 6, 9, 242, 245, 246
indeterminate, 287
in Diophantus’ Arithmetics , 36, 44, 350–3
see also demonstration
Andersen, K., 150
annotation, 86, 95, 103, 120
Anschauungsgeometrie , 276, 280, 285, 289
anti-Arab ideology, 275
Antiphon, 296–7
Apollonius of Perga, 1, 69, 70, 135, 140
Conics
Book I, 149
m a n u s c r i p t Va t i c a n 206 , see manuscripts
(Greek)
Proposition I 13, 149
Proposition I 16, 145–6
574 applications, 13, 274, 287