Index 577
Cicero, 362
circle (ratio between circumference and
diameter, between area and square of
diameter), 427–31, 438, 444–5, 447–8,
453, 468
circulation of practices of proof, 3, 19, 30, 43,
48, 52, 53–9
citizens, 294
claims of identity, 13, 64
classic
Chinese (jing ), 47–51, 423–86
commentaries justifying, 51–3
meaning of, 48–9, 51–3
proof in the commentaries on a classic
or treatise, 47–53, 56, 263, 423–86,
498–507
Sanskrit treatise or classic, 51–3, 56, 260–7,
487–8, 501
see also canon
Clavius, C., 2–3
codex, 71–3, 84, 88
co-latitude, 495–7
Colebrooke, H. T., 6–7, 9, 11, 42, 63, 228–9,
235–56, 257, 260, 275, 276, 279, 285
Collection , see Pappus
College of calligraphy, see Shu xue
Collegio Romano, 2
colonialism, 228, 229
commentaries, 8, 76, 85–6, 87, 260, 262–3,
267, 270, 272–3, 487–9, 490, 493,
498–508, 511, 519, 521–2, 529, 531,
533–7
justifying their interpretation of a classic,
487–9
proof in the commentaries on a classic, 8,
47–50, 56, 263, 423–86, 490, 498–507
see also Li Chunfeng, Liu Hui, zhu
‘commentary
communication (‘make’ ... ‘communicate ( tong
)’), 436–8, 440, 450, 463–8, 470–3,
476, 538, 542
complexifi cation (of fractions) fan , 461,
466–7
computation, 9–10, 17, 37–8, 40–1, 45–7, 50,
58, 271, 355–6, 358–9, 446, 448, 456,
465, 470, 474, 489, 491, 493–4, 497–501,
505
computational reasoning, 260
execution, 45, 46, 426, 432–7, 442–3, 459,
462–4, 470–1, 477
layout, 45, 46, 432–5, 437–8, 443, 472, 477–8,
483
see also calculation, cao, historiography
of mathematics (historiography of
computation)
Computational procedures [found] in the Five
Classical books , see Wu jing suan shu
Computational procedures of Nine categories , see
Jiu zhang suan shu
Computational treatise [beginning with a
problem] about a sea island , see Hai dao
suan jing
Computational treatise of Five Departments , see
Wu cao suan jing
Computational treatise of Master Sun , see Sun
zi suan jing
Computational treatise of Xiahou Yang , see
Xiahou Yang suan jing
Computational treatise on the continuation of
[traditions] of ancient [mathematicians] ,
see Qi gu suan jing
Computational treatise on the Gnomon of
Zhou [dynasty] , see Zhou bi suan
jing
Computations in the Five Classical Books , see
Wu jing suan
Comte, A., 5, 11, 292
Conica , see Apollonius of Perga ( Conics )
conjecture, 300–1
consensus theory of proof, 229
consequence (logically deduced), 274
constant norm, see chang fa
Continuation [of traditions] of ancient
[mathematicians] , see Qi gu
continuity, 24, 43–4, 54–9
historical continuity between modes of
argumentation in Babylonian scribal
milieus and proofs in Arabic algebraic
texts, 43–4, 48
historical continuity between thirteenth-
century algebraic texts in China and
Li Rui’s approach to the right-angled
triangle, 58–9
correctness of algorithms (or procedures), 9,
10, 18, 31, 33, 36, 38–60, 269, 271–2,
423–86
inscription designed to note down an
algorithm while pointing out the
reasons for its correctness, 38, 46, 63
simultaneously prescribing operations and
giving rationale of a procedure, 40, 42,
43, 48–9, 63; see also transparency
counting rods, see suan
creation of specifi c languages, 65
Diophantus’ Arithmetics , 37–8
formulaic expressions, 37, 63