Mathematical Physics. An account of the history of mathematics and allied sciences in the last century would be misleading if there were no reference to the application of mathematics to numerous problems in heat, elasticity, light, electricity, and other physical subjects. The history of mathematical physics is, however, so extensive that I could not pretend to do it justice, even were its consideration properly included in a history of mathematics. At any rate I consider it outside the limits I have laid down for myself in this chapter. I abandon its discussion with regret because the Cambridge school has played a prominent part in its development, as witness (to mention only three or four of those concerned) the names of Sir George G. Stokes, professor from 1849 to 1903, Lord Kelvin, J. Clerk Maxwell (1831-1879), professor from 1871 to 1879, Lord Rayleigh, professor from 1879 to 1884, and J. J. Thomson, professor from 1884.
Abacus, description of, 123-5
ref. to, 3, 26, 57, 113, 127, 131,
138, 139, 183
Abd-al-gehl, 161-2
Abel, 461-62
ref. to, 392, 424, 425, 438, 447,
452, 461, 463, 465, 469, 473
Abel's theorem, 462, 481
Abelian functions, 396, 424, 452,
461, 462, 465, 465-7, 468, 478,
480
Aberration (astronomical), 380
Abu Djefar; see Alkarismi
Abul-Wafa; see Albuzjani
Academy, Plato's, 42
the French, 282, 315, 457-8
the Berlin, 315, 356
Accademia dei Lincei, 315
Achilles and tortoise, paradox, 31
Action, least, 398, 403, 408
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Albategni, 161
Albèri on Galileo, 247
Albuzjani, 161
Alcuin, 13-45
Alembert, d'; see D'Alembert
Alexander the Great, 46, 51
Alexandria, university of, 51, 92,
96, 113, 115
Alexandrian library, 51, 83, 115
Schools, chapters IV, V
symbols for numbers, 126-7
Alfarabius, ref. to, 166
Alfonso of Castile, 175
Alfonso's tables, 175
Alfred the Great, ref. to, 133
Algebra. Treated geometrically by
Euclid and his School, 57-60, 102.
Development of rhetorical and
syncopated algebra in the fourth
century after Christ, 102-10.
Discussed rhetorically by the
Hindoo and Arab mathemati-
cians, chapter IX; by the early
Italian writers, chapter x; and
Pacioli, 210. Introduction of
syncopated algebra by Bhaskara,
153, 154; Jordanus, 171-3;
Regiomontanus, 202-5; Record,
214; Stifel, 215-17; Cardan,
223-5; Bombelli, 228; and Ste-
vinus, 228. Introduction of sym-
bolic algebra by Vieta, 230-34;
Girard, 235; and Harriot, 238.
Developed by (amongst others)
Descartes, 275-6; Wallis, 292-3;
ref. to, 167, 183, 224
Alkarki, 159-60
Alkayami, 159
Al-Khwarizmi; see Alkarismi
Allman, G. J., ref. to, 13, 14, 19,
24, 28, 29, 35, 41
Almagest, the, 96-8
ref. to, 81, 86, 111, 146, 156,
158, 160, 162, 164, 165, 166, 171,
176, 177, 179, 180, 201, 227
Al Mamun, Caliph, ref. to, 145,
156
Almanacks, 178, 186-7
Al Mansur, Caliph, ref. to, 146
Alphonso of Castile, 168
Alphonso's tables, 169
Al Raschid, Caliph, ref. to, 145
Amasis of Egypt, ref. to, 16
America, discovery of, 200
Ampère, 436. ref. to, 451
Amthor, A., 72
Amyclas of Athens, 46
Analysis, Cambridge School, 438-43
higher, 482
in synthetic geometry, 43
Analytical geometry, origin of, 264,
272-5, 298; on development of,
see chapters XV-XIX
Anaxagoras of Clazomenae, 34
Anaximander, 18
Anaximenes, 18
Ångström, 495
Angular coefficient, 312
Anharmonic ratios; see Geometry
(modern synthetic)
Anthology, Palatine, 61, 102
Antioch, Greek School at, 145
Antipho, 38
Apian on Jordanus, 171
Apices, 125, 138
Apogee, sun's, 161
Apollonius, 77-83
ref. to, 52, 89, 112, 146, 158,
161, 164, 171, 227, 230, 234,
274, 293, 311, 316, 350, 380,
483
Appell, P. E., 467, 468, 482
Appell, C. E., 492
Apse, motion of lunar, 374, 389
Arabic numerals, 117, 128, 147,
152, 155, 158, 166, 168, 169,
184-7
-origin of, 184, 185
Arabs, Mathematics of, chapter IX
introduced into China, 9
introduced into Europe, chap. x
Aristotle, ref. to, 13, 14, 25, 52,
133, 145, 227
Aristoxenus, 21
Arithmetic. Primitive, chapter VII
Pre-Hellenic, 2-5. Pythagorean,
24-8. Practical Greek, 58, 101,
112, 127, 128. Theory of, treated
geometrically by most of theGreek
mathematicians to the end of the
first Alexandrian School, 58; and
thenceforward treated empirically
(Boethian arithmetic) by most of
the Greek and European mathe-
maticians to the end of the four-
teenth century after Christ, 95,
127-8, 182-3. Algoristic arith-
metic invented by the Hindoos,
152; adopted by the Arabs, 154,
158; and used since the four-
teenth century in Europe, 165,
168, 184-7; development of
European arithmetic, 1300-1637,
chapter XI
Arithmetic, higher; see Numbers,
theory of
Arithmetical machine, 282, 354, 441
problems, 61, 72, 73
progressions, 27, 69, 151
triangle, 219, 231, 284-5
'Api@unTiký, signification of, 57
Aronhold, S. H., 479
Arts, Bachelor of, 142
Master of, 142-3
Arya-Bhata, 147-8
ref. to, 150, 152, 154, 161
Aryan invasion of India, 146
Arzachel, 165
Assumption, rule of false, 151, 170,
208, 209
Assumptions, 489
Assurance, life, 389
Astrology, 152, 179-80, 255
Astronomical Society, London, 441,
Astronomy. Descriptive astronomy
outside range of work, vi. Early
Greek theories of, 17, 18, 34, 46,
61, 62, 76, 83. Scientific astro-
nomy founded by Hipparchus,
86-7; and developed by Ptolemy
in the Almagest, 96-8. Studied
by Hindoos and Arabs, 147, 148,
150, 151, 160-61, 165.
theory of, created by Copernicus,
213; Galileo, 249, 250; and
Kepler, 256-7. Physical astro-
nomy created by Newton, chap-
ter XVI. Developed by (amongst
others) Clairaut, 373-4; La-
grange, 405, 406-7; Laplace,
414-18; and in recent times by
Gauss and others, chapter XIX
Asymptotes, theory of, 340
Athens, School of, chapter III
second School of, 111-13
Athos, Mount, 118
Atomic theory in chemistry, 431
Atomistic School, 31
Attalus, 77
Attic symbols for numbers, 126-7
Attraction, theories of, 321-3, 330,
333-5, 373, 387, 406, 413, 422,
436, 439, 446, 453, 491, 492
Australia, map of, 254
Autolycus, 61
Auwers, A., 494
Avery's steam-engine, 91
Babbage, 441. ref. to, 439, 442
Babylonians, mathematics of, 5, 6
Bachelor of Arts, degree of, 142
Bachet, 305-6
ref. to, 221, 297, 298
Bachmann, P., 460
Bacon, Francis, 252. ref. to, 298
Bacon, Roger, 174-7
ref. to, 165, 167, 169
Baily, R. F., on Flamsteed, 338
Baize, R. L., 468
Baker, H. F., 468
Baldi on Arab mathematics, 155
Ball, W. W. R., ref. to, 37, 118,
141, 214, 236, 238, 253, 288, 295,
305, 306, 319, 336, 339, 440, 485
Barlaam, 117-18
Barnes, E. W., 462
Barometer, invention of, 282-3, 308
Barral on Arago, 437
Barrow, 309-12
ref. to, 52, 92, 237, 241, 275,
299, 321, 323, 324, 328, 341, 342,
347, 362, 394
Bastien on D'Alembert, 374
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