Index 587
Mueller, I., 33–5, 37, 62, 100, 296, 306, 311–26
Mugler, C., 164, 186
multiple, see lü
multiples of shares/parts, see fenlü
multiplication, 426–84, 491, 493, 499, 506,
526, 540
execution of, 432–5, 443, 460
of fractions (procedure for multiplying
fractions ), 426, 427, 467, 472,
475–80
of integers plus fractions (procedure for
the fi eld with the greatest generality
), 433–6, 439–40, 442–4, 459,
475–6, 483
with sexagesimal place value notation,
388–91, 394–7, 400, 402–4, 415–17
see also tables
Murdoch, J., 83, 86, 89, 120, 134
Muroi, K., 411
Murr, S., 258
music theory, 297, 302
Nâsir ad-Dîn at-Tûsî, 78, 89, 105, 109–10, 117,
118
nation, 284
‘non-geometrical nation’, 282
‘oriental nations’, 5, 274
Nayrīzī (al-) (also an-Nayrîsî), 138–9
commentaries on the Elements, 76, 85, 87,
113, 117, 130, 131, 132, 133, 138–9
Needham, J., 57, 67, 510, 513
neopythagoreanism, 362
Neo-Sumerian, 390
Nesselmann, G. H., 278, 323–4, 327–8, 330, 336
Netz, R., 24–6, 30, 35–9, 46, 64, 135, 140, 145,
148, 158, 163–205, 306–7, 329, 341, 351
Neugebauer, O., 37, 71, 136, 139, 345, 363,
369–70, 376, 386, 389, 392, 410, 412
New History of the Tang [dynasty] ( Th e ), see Xin
Tang shu
Nguyễn Danh Sành, 523
Nguyễn Hữu Th ận , 526
Nicomachus of Gerasa, 33–4, 311–18
Nine categories , see Jiu zhang
Nine Chapters (Th e ) , abbreviation of Nine
Chapters on Mathematical Procedures
(Th e ), see Jiu zhang suan shu
Nine Chapters on Mathematical Procedures
(Th e ) , abbreviated as Th e Nine Chapters ,
see Jiu zhang suan shu
Nippur, 384, 387, 389, 390, 399, 403, 406–9,
411, 420, 421, 422
Noack, B., 156
Noel, W., 148
‘non-Western’, 10, 20, 50
astronomy, 228
mathematics, 229
norm, see fa
norm of concreteness, 379
Northern Zhou dynasty , 514, 534
numbers, 9, 10, 33–9, 44–7, 60, 268, 263, 283,
311–26, 441, 452–5, 460, 489, 504
abstract, 389, 402, 460, 462, 467, 469
actual fi rst number, 311–12
and algebraic proof, 50, 59, 423–86
as confi guration, 33
as multiplicities of units, 33, 311–12
c l a s s i fi cation of, 317
defi nition of polygonal, 33–5, 313–16
fractions, 50, 423, 426, 431–8, 441, 447,
454–7, 459–80, 482–4
geometric or confi gurational representation
of, 34, 313–16, 470
Greek way of writing, 37, 311–12
integers plus fractions, 431–8, 440, 447,
453–7, 460–77
integers, 35, 50, 431–8, 441, 452–3, 456–7,
460, 463–77
irrational, 283
quadratic irrationals, 50, 452–7, 472, 483–5
natural representation of, 311–12
negative, 244, 283, 388, 563
polygonal, 33–5, 62, 311–26
positive, 244, 283, 388, 563
potential fi rst number, 312
rational, 283
regular, 44–5, 390–1, 394–5, 397, 400, 402–3,
413, 416–17
representation of, 9, 34, 37
results of divisions, 50, 431–3, 437, 440–1,
447, 453–60, 472, 478–80, 482–3
results of root extraction, 50, 452–8, 482
sequence of, 33, 34, 312–19
table of, 34, 317
yielded by procedure of generation, 33
see also fractions, sexagesimal place value
notation
Numbers of three ranks , see San deng shu
numerator zi , 423, 431–4, 436, 459–61,
464–71, 475–80
numerical methods, 44, 290
Nuñez, P., 380, 383
objects
composite versus incomposite, 211–12,
214–15, 218