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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.

INDEX.

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
varying, 492
Adalbero of Rheims, 137
Adam, C., 268

Adams, J. C., 494-5. ref. to, 494
Addition, processes of, 188

symbols for, 5, 104, 105, 106,
153, 172, 173, 194, 206-8, 211,
214, 215, 216, 217, 228, 240
Adelhard of Bath, 165
- ref. to, 177
Adhémar, R. d', 445
Africanus, Julius, 114
Agrippa, Cornelius, ref. to, 119
Ahmes, 3-8. ref. to, 73, 103
Airy, G. B., 442

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 ;

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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

Anchor ring, 46, 86

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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
Arago, 437-8

ref. to, 91, 400, 433, 450, 494
Aratus, 46, 86

Arbogast, 401.

ref. to, 400

Archimedean mirrors, 65

screw, 65
Archimedes, 64-8

- ref. to, 52, 62, 79, 81, 82, 85,
86, 91, 101, 102, 112, 146, 158,
164, 171, 227, 244, 259, 288,
310, 311, 367, 387

Archippus, 28
Archytas, 28-30

ref. to, 26, 36, 42, 44
Area of triangle, 89-90
Areas, conservation of, 256
Arendt, G., on Dirichlet, 454
Argand, J. R., 471
Argyrus, 118
Aristaeus, 48

- ref. to, 46, 57, 77, 78, 316
Aristarchus, 62-4. ref. to, 86, 227
Aristotle, 48-9

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
'Api0unTik, 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,
474

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. Modern
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

ref. to, 467, 475

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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Berkeley on the calculus, 386
Berlet on Riese, 215

Berlin Academy, 315, 356
Bernelinus, 139

Bernhardy on Eratosthenes, 83
Bernoulli, Daniel, 377-8

Bernoulli, Daniel, ref. to, 368, 393
Bernoulli, James, 366-7

ref. to, 243, 316, 365
Bernoulli, James II., 369
Bernoulli, John, 367-8

ref. to, 224, 243, 350, 359, 363,
365, 368, 369, 379, 391, 393, 394,
396

Bernoulli, John II., 368
Bernoulli, John III., 369
Bernoulli, Nicholas, 368

ref. to, 341, 367, 393
Bernoulli's numbers, 367
Bernoullis, the younger, 368-9
Bertrand, 281, 374, 479, 482, 492,

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metic
Boethius, 132-3

ref. to, 95, 114, 135, 136, 138,
142, 175, 182

Boetius; see Boethius

Bologna, university of, 139, 140,
180

Bolyai, J., 485, 486

Bombelli, 228, 313

ref. to, 224, 226, 232, 242
Bonacci; see Leonardo of Pisa
Boncompagni, ref. to, 9, 155, 156,
166, 167, 206
Bonnet, P. O., 481

Book-keeping, 187, 209, 245
Boole, G., 474.

482

ref. to, 473, 474,

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