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 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 ;
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
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
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
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,
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.
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