by E. T. Bell
Dr. Bell died in December 1960, just before the publication of his latest book, The Last Problem.
We hope you enjoyed reading this Touchstone eBook.
* * *
Join our mailing list and get updates on new releases, deals, bonus content and other great books from Touchstone and Simon & Schuster.
CLICK HERE TO SIGN UP
or visit us online to sign up at
eBookNews.SimonandSchuster.com
Index
Abel, Niels Henrik, 3, 164, 167, 223, 229–30, 260, 270–2, 295, chap. 17, 328–9, 335–7, 362, 364, 366, 368, 377, 381, 407–8, 412, 415, 418, 437, 448, 452–3, 457, 460, 473, 476–8, 541
Abelian integral, 338, 419
Adams, John Couch, 350
Airy, G. B., 198, 345, 351, 353
Alexander, J. W., 268
Alexander the Great, 537
algebra, 13, 21, 40, 52–4, 61–2, 64–5, 97, 123, 140, 149, 163–6, 168, 199, 208, 211, 213, 222–3, 225, 227, 231–6, 238, 253–4, 260–1, 272, 282–4, 287, 309–14, 317, 321–2, 324, 328, 330, 334–5, 337–8, 347–9, 354–60, 364, 368, 372, 376, 386, 388–91, 394–5, 398–404, 408, 437–9, 442–5, 448, 450–1, 453, 456–7, 459–61, 463–4, 470, 472–9, 482, 489, 493, 511, 517–8, 527–29, 540–1, 564–5, 568–9
algebraic forms, 394, 458
algebraic integers, 470–2, 514, 518, 522, 524
algebraic numbers, 462, 464, 469–71, 474, 477–8, 482, 523–4, 562, 564–5, 567–9
algebraic number field, 470–4, 513, 522–4
algorithm, 140
Ampère, A. M., 318
analysis, 13, 16, 22–3, 54, 64, 70, 87, 117–8, 139–40, 144, 150–2, 154–5, 161–3, 166, 168–9, 171, 174, 176, 183, 187, 198, 201–2, 207, 213, 222–4, 236–7, 248–52, 268, 270–2, 275, 286, 311–2, 316, 319, 322, 327, 334–5, 338–9, 346, 364, 377, 400, 406–8, 413–4, 416–7, 419, 421–3, 429, 446, 451, 456–7, 460–1, 469, 474–5, 477–81, 488–90, 494, 510, 513, 519, 521–2, 526–7, 537–8, 541–2, 544, 547, 556–7, 561, 567, 571, 575, 579
analysis situs, 263, 267, 492, 545
Antoinette, Marie, 166, 170
Apollonius, 7, 27, 78, 317, 400
Appell, Paul, 454
Arago, F. J. D., 139, 150, 190, 193, 205
Archimedes, 7, 19–20, 28–34, 59, 102, 114, 120, 147, 153, 162, 218, 220, 230, 237, 240–1, 255–6, 400, 459, 533
Archytas, 25
Aristotle, 20, 25, 78, 240, 278, 569, 575, 577–8
arithmetic, 21, 64, 118, 152, 161–2, 168, 185, 208, 221, 223, 225–6, 227–9, 231–2, 234–8, 240–1, 248, 252–4, 256, 260–3, 267, 271–2, 276, 284, 356, 368, 408, 419, 438, 446, 451, 455–8, 470–4, 477–8, 481, 485, 488, 500, 510, 513, 517–8, 522–5, 527–9, 541, 551, 561, 574–5, 577
arithmetical theory of forms, 356
Arnauld, A., 83, 128–9
associative, associativity, 278–9, 280, 356
Ausonius, 39
Austen, Jane, 380
axioms, 20–1, 305–6, 333, 419, 503, 576
Ayscough, Rev. Wm., 91–2
Babbage, Charles, 438
Bachet de Méziriac, 71
Baillet, A., 39
Balzac, Honoré de, 548
Barrow, I., 96, 106–7, 118
Bartels, Johann Martin, 222–4
Bauer, Heinrich, 328
Beethoven, L. v., 405
Berkeley, Bishop, 90, 345
Bernoullis, 115, 126, 132, chap. 8, 143–5, 155–6
Berthollet, Count Claude-Louis, 183–4, 189–90, 193–4, 196, 273
Bertrand, J. L. F., 453
Bessel, Friedrich Wilhelm, 245, 248, 250–1, 331
Biot, J. B., 181
Birkhoff, George David, 553
Bismarck, O. E. L., Prince von, 467
Blake, William, 10
Bliss, G. A., 133–4
Boeckh, P. A., 328–9
Bohr, N., 19
Bolyai, Johann, 231
Bolyai, Wolfgang, 220, 231, 243, 474, 505
Boole, George, 118, 121, 124, 213, 354, 389, 390, 406, chap. 23, 448, 486
Boole, Mary, 446–7
Borchardt, C. W., 332, 421, 426, 464, 501
Borel, Émile, 454, 566
boundary values, 339
Boutroux, Émile, 532
Brahe, Tycho, 110
branches, branch points, 493–5
Brewster, Sir David, 112, 269, 500
Brianchon, C. J., 216
Briggs, Henry, 426
Brinkley, John, 343–5
Brochard, Jeanne, 36
Brooke, Rupert, 398
Brouwer, L. E. J., 19, 24, 278, 569, 576–9
Bruno, Giordano, 46
Bunsen, R. W., 424–5
Burali-Forti, C., 575, 577
Burnet, John, 25
Butler, Samuel, 340
Byron, George Gordon, Lord, 257, 380
calculus, 5–7, 13, 23, 32–3, 56–7, 59, 61, 64, 95, 97–107, 109, 113–4, 117–8, 121, 125–6, 132–7, 139–40, 147, 149, 151, 154–6, 162, 169, 186, 208, 251, 270, 284, 286, 322, 324, 328, 330, 334, 348, 361, 364, 407, 442, 448, 488–9, 507, 517
calculus of variations, 437
calculus, tensor, 213, 256, 448, 528
Campanella, Tammaso, 46
Cantor, Georg F. L. P., 354, 406–8, 446, 482, 519–20, 522, chap. 29
Cantor, Marie Bohm, 558
Cantor, Moritz, 17, 19, 25
Cantor, Vally Guttman, 563
Cantor, Waldemar Georg, 558
Cardan, H., 323
Carnot, Lazare-Nicolas-Marguerite, 207, 285
Catherine the Great, 141, 145–7, 149–50
Cauchy, Augustin-Louis, 152, 164–5, 167, 169, 223, 250–1, 260, chap. 15, 317–8, 320, 335, 351, 368–9, 376–8, 407, 416, 457, 473, 482, 488–90, 518, 527, 541
causality, 306
Cavalieri, B., 118
Cayley, Arthur, 3–4, 213–4, 271, 282, 359, 368, chap. 21, 437, 448, 459, 474, 515, 534, 546
Chanute (French ambassador), 50–1
characteristic, 349
Charles I, 92
Charlet, Father, 36–7, 50
Chasles, Michel, 139
Chevalier, Auguste, 374, 377
Christ, Jesus, 573
Christine, Queen of Sweden, 49, 51, 82
Christoffel, E. B., 256, 391, 480
Cicero, 55, 363
class, 567–9, 570, 572–5, 577–8
Clifford, Wm. K., 294, 490, 503–4
Colburn, Zerah, 66, 342–3
Coleridge, Samuel Taylor, 344–5, 484
Columbus, Christopher, 338
combination, 280
commutative, 356, 360, 402
complex number, variable, 233–4, 248–50, 253, 260, 263, 267, 284, 293, 333–5, 356–60, 407, 457–9 487–93, 495, 510, 514, 529, 541
complex units, 474
Condorcet, N. C. de, 152, 180, 187–8
congruence, 225–7, 235–6, 252–3, 293
conjugates, 459
Conon, 30
continuity, continuous, 13, 22–3, 27, 59, 117, 140, 162, 200, 208–9, 211, 216, 234, 237, 268, 283, 286, 407, 430, 456, 488, 491, 504–5, 510, 520–1, 555, 557, 562, 569, 574–6, 579
convergence, 151, 222–3, 274, 286 7, 430–2, 487, 535, 541, 543, 561, 562
Copernicus, Nicolas, 46, 294, 306
Corneille, Pierre, 76
corpus, 355
correlation, 289
Cotes, R., 503
Couturat, L., 121, 565–7
covariant, 395
Crelle, August Leopold, 314, 316–7, 319–20, 326, 413, 416, 418–9, 421, 432, 562
Cromwell, Oliver, 93
curvature, 264–5, 500, 504–5, 507–9
cuts, 494–5, 519–21, 557
cyclotomy, 513
D’Alembert, Jean le Rond, 148–9, 155–62, 173, 187, 489, 544
Darboux, Gaston, 454, 531, 533, 536, 544
Darwin, Charles, 16, 137
Darwin, G. H., 529
/> Dedekind, Julie, 518
Dedekind, Richard, 19, 25, 223, 238, 253, 406–8, 468, 470, 472, 474, 489, 500, 502, chap. 27, 557, 563, 575–7, 579
Delambre, J. B. J., 154
De Long, Claire, 57
De Long, Louise, 58
De Morgan, A., 147, 354, 384, 387, 434, 438, 440–1
denumerable infinity, 539–40, 569, 572
Desargues, G., 74, 77, 79, 183, 208, 213, 285, 398
Descartes, René, 7, 14–5, 20, 32, chap. 3, 56–9, 62–4, 73–4, 80, 82, 93, 111, 121–2, 129, 140, 147, 211–2, 233, 245, 265–6, 347, 349, 376, 443, 457–8, 481, 505, 512
determinants, 338, 388
Dickens, Charles, 380, 436
Dickson, L. E., 261, 355
Diderot, Denis, 146–7
Diophantus, 70–1, 152
Dirac, P. A. M., 19, 515
Dirichlet, P. G. Lejeune, 236–7, 318, 332, 405, 458, 468–9, 473, 489, 496, 499, 500, 512, 517, 518
discrete, 13–4, 21, 24, 117, 140, 162, 283, 505
discriminant, 389–90, 401
distance, 505–9
distributive law, 356
divergent, 287
Dositheus, 30
duality, 214, 216–7
Dumas, Alexandre, 373
Dürer, Albert, 17
Eddington, Sir Arthur S., 484, 515
Edgeworth, Maria, 344
Edison, Thomas A., 548
Einstein, Albert, 5, 7, 15, 19, 138, 154, 213, 255–6, 305, 320, 350, 391, 448, 490–1, 546–7, 556
Eisenstein, F. M. G., 68, 237, 253, 390, 455–6, 468, 489
Elijah, 69
Elisabeth, Princess, 41, 49, 51, 129
elliptic functions, see functions, elliptic
elliptic integrals, 317, 322, 324, 336
equations, 52, 65, 68, 70, 136, 150, 155, 157, 162–5, 179, 186, 192, 198–9, 201, 211, 225, 232–5, 252, 265–6, 270–2, 282–3, 309–14, 317–8, 322, 328, 334–6, 338, 347, 354–6, 364, 368, 372, 376, 389–90, 404, 408, 416, 430, 438, 445, 450–3, 456–7, 459–64, 470, 472 4, 476–8, 482, 489–90, 492–3, 499, 514–5, 518, 528, 536, 538 40, 543–4, 561, 564–5, 568–9
Eratosthenes, 30–1
Essenbeck, Nees von, 240
Euclid, 7, 14, 19–20, 27, 75, 127, 153, 165, 176, 215–6, 223, 266, 299–303, 305–6, 314, 351, 358, 379, 399–400, 443, 454, 474, 514
Eudoxus, 19, 25–7, 407, 480, 483, 519, 522, 575
Euler, Albert, 149
Euler, Catharina Gsell, 145
Euler, Léonard, 69, 115, 132–3, 135–7, chap. 9, 155–6, 158–60, 175, 223–6, 242, 245, 263, 271, 277, 284, 308–9, 328–9, 354, 368, 378, 443, 450, 488–9, 492, 517, 532, 534, 541, 543
Euler, Marguerite Brucker, 143
Euler, Paul, 143
existence, 482
extrema, 304
factorials, 417, 462
factorization, 334, 569
factorization, unique, 514, 522
factors, prime, 522
Ferdinand II, 39
Ferdinand, Duke of Brunswick, 224, 231–2, 241, 243–6, 248
Fermat, Clément-Samuel, 58
Fermat, Dominique, 57
Fermat, Pierre, 7, 35, chap. 4, 73–4, 86, 102, 118–9, 133–4, 140, 152, 161–2, 228, 236–8, 253, 261, 284, 311, 337, 465, 472–3, 488, 510, 513–4
field, 355, 357, 469–70, 473, 514, 522
Fleming, Admiral, 50
Foncenex, D. le, 154
formalism, 287
Forsyth, A. R., 402
Fourier, Jean-Baptiste-Joseph, 105, 176, 178, chap. 12, 318, 338–9, 496, 538–9, 561
fractions, continued, 368
Franklin, Fabian, 397
Frederick the Great, 141, 148, 153, 159–60, 165, 244
Frege, Gottlob, 567, 575–7, 579
Fresnel, A. J., 351
Fricke, Robert, 516
Fuchs, Lazarus, 540
functions, 98–9, 101–4, 140, 169, 179, 201, 223, 232, 248–50, 252, 260, 263, 265, 275–7, 284, 318–20, 322–4, 329, 333–5, 338, 348–9, 364, 377, 407, 413, 430, 455, 457, 460–2, 480, 487–95, 508, 515, 529, 540–1, 550–1, 578
functions, Abelian, 338, 398, 408, 416, 419–20, 451, 455, 492, 495, 499–500
functions, automorphic, 530, 540–1
functions, elliptic, 127, 202, 228–9, 247, 253, 259–60, 282, 320, 322, 324, 329, 331, 333, 335–8, 372, 382, 386, 408, 413–4, 430, 453, 455, 461, 469, 477–9, 517, 539–41, 550
functions, multiple periodic, 408, 452–3, 455, 515, 539
Galileo, 16, 20, 26, 36, 41, 45–6, 80, 84, 93, 121, 129, 291, 566
Galois, Adélaïde-Marie Demante, 362
Galois, Evariste, 3, 164–5, 167, 270, 312, 362, chap. 20, 381, 408, 437, 449, 450, 476–7, 518, 536
Galois, Nicolas-Gabriel, 362, 369–70
Galton, Francis, 137, 202, 323
Gauss, Carl Friedrich, 3–4, 20, 28, 64, 67, 69, 72, 105, 108, 120, 146, 151, 161–2, 167, 186, chap. 14, 271, 284, 286, 297, 308, 313–4, 328, 331, 333, 335, 337, 354, 356, 359, 377, 380, 389, 405–7, 443, 448, 450, 455–8, 472–4, 478, 486, 488–89, 491–3, 495–8, 501, 507–8, 510, 512–8, 525, 527, 533, 535, 537, 539, 541, 547, 556–7, 561, 569
Gauss, Dorothea Benz, 219–20, 224
Gauss, Friederich, 219
Gauss, Johanne Osthof, 243
Gauss, Minna Waldeck, 243
Gelfond, Alexis, 463–4
Gelon, 29
geodesic, 302, 305–6, 507
geometry, 13–4, 20–2, 27, 31, 33, 40, 52–5, 59–62, 66–7, 74–8, 84–5, 96, 109, 123, 127, 140, 147, 154, 183–4, 186–7, 207–17, 223, 227–8, 233, 236, 242, 254, 256, 260, 263–8, 272, 277, 282, 284, 286, 294, 299–306, 317, 322, 324, 346–9, 355, 358, 364, 367–9, 381–2, 398–400, 403, 443, 448, 451, 458, 464, 469, 474, 478–81, 485, 489–91, 493, 498, 500, 503–4, 506, 508, 510, 513–7, 522, 527, 531, 535, 537, 541, 569, 577
geometry, analytic, 5–7, 32, 40–1, 52–7, 59–64, 93, 123, 133, 139, 147, 154, 199–200, 211–2, 233, 248, 399, 517
geometry, descriptive, 183, 185 −6, 207, 240, 452
geometry, foundations, 497–8, 502–3
geometry, n-dimensional, 399–400
geometry, non-Euclidean, 6, 108, 127, 186, 214, 223, 230–1, 240, 256, 260, 264, 266, 294, 297, 300–6, 358–60, 379, 398–9, 439, 473–4, 493–5, 503–5, 507–9, 513, 550–1
geometry, projective, 78, 206–10, 212–7, 398–9
Germain, Sophie, 253, 261–3
Gibbon, Edward, 257
Gilbert, Wm., 36
Gilman, Arthur, 394
Goethe, J. W. von, 257
Goldbach, C., 405
Gounod, Charles François, 386
Grassmann, Hermann, 123
Gregory, D. F., 438
Gregory, James, 125
Grote, Geo., 381
groups, 6, 68, 165, 268, 271–2, 278–81, 283, 451, 495, 515, 518, 540, 551
groups, abstract, 282, 375–6
groups, continuous, 268, 529
Gudermann, Christof, 412–3, 424
Hachette, J. N. P., 318, 320
Hadamard, Jacques, 54, 212
Halley, Edmund, 105, 108–10, 153
Halphen, Georges, 403
Hamilton, Eliza, 345
Hamilton, James, 340–1
Hamilton, Sarah Hutton, 340
Hamilton, Sir Wm., 438–9, 440–1
Hamilton, William Rowan, 16, 29, 66, 123, 133–4, 155, 260–1, 270, 331, 334, 338, chap. 19, 514
Hansteen, Christoph, 319
Hardy, G. H., 488
Hegel, G. W. F., 239–41, 439, 469
Heiberg, J. L., 31
Heisenberg, W., 19, 402
Helmholtz, H. von, 424
Henry, C., 86
Herbart, J. F., 491
Hermite, Charles, 4, 164, 183, 273, 307, 320, 368, 422, chap. 24, 476–7, 501, 515, 535–6, 543, 568, 571
Hermitian forms, 458–9
Herschel, Sir William, 239, 438
Hertz, H
einrich, 16
Hieron II, 29, 33
Hilbert, David, 63, 239, 443, 463, 566, 576–8
Hipparchus, 109, 361
Hitler, Adolf, 516
Holmboë, Bernt Michael, 308–9, 312, 315, 318, 325, 329
Hooke, Robert, 107–8
Horace, 307, 320, 397
Humbert, Georges, 540
Humboldt, Alexander von, 204, 242, 245, 259, 333
Hume, David, 146
Huntington, E. V., 444
Huygens, Christian, 84, 107, 123–5, 129, 134, 350–1
ideals, 408, 510, 513, 522–4
ideal, prime, 524
identical operation, identity, 279–80
imaginaries, 356, 372, 399, 493
infinite, 6, 22–5, 27, 69–71, 75, 89, 123, 151, 168–9, 199, 201, 211–2, 216, 222–4, 236–7, 250, 274, 283, 286–7, 309, 351, 355, 394, 400, 407–8, 446, 448, 462–3, 480, 487–8, 492, 514, 520–3, 539–41, 543, 549, 553, 555–8, 561–2, 564–71, 573–9
invariance, invariants, 6, 78, 165, 230, 283, 378–9, 382–3, 386, 388, 390–2, 395, 398, 401, 403, 437, 448, 459, 509, 540, 545
irreducibles, 472, 515, 569
Jacobi, Carl Gustav Jacob, 16, 21, 52, 140, 229–30, 259–60, 270, 320–4, chap. 18, 346–77, 408, 418, 420, 448, 452–6, 463, 468–9, 489, 512, 515, 517, 528, 541, 544
Jacobi, M. H., 327
James II, 111
Jansen, Cornelius, 79
Jeans, Sir James H., 17, 21, 177, 529
Jeffreys, George, 111
Jerrard, G. B., 460
Joachim, Joseph, 559
Jourdain, P. E. B., 185
Kant, I., 177, 240, 345, 358–9
Kelvin, Lord (William Thomson), 16, 183, 293, 452
Kepler, J., 28, 93, 105, 109, 121
Kingsley, Chas., 385
Kipling, Rudyard, 324
Kirchoff, G. R., 424
Klein, Felix, 206, 214, 282, 379, 398, 419, 540, 548
Kneser, Adolf, 467
Königsberger, L., 424–5
Kowalewski, Sonja, 261, chap. 22
Kronecker, Leopold, 19, 164, 218, 234, 238, 293, 406–8, 419, 422, 431, chap. 25, 501, 512–3, 521, 529, 556, 559–63, 568–71, 573, 577–9
Kummer, Ernst Eduard, 238, 253, 467–70, 473–4, 476, 478–9, 486, 501, chap. 27, 510, 535, 561
Lacroix, S. F., 318
Lagrange, Joseph-Louis, 5, 9, 62, 115, 133, 142, 148–9, chap. 10, 174, 177–8, 180–1, 185–6, 197, 223–6, 237, 247, 262–3, 270–1, 274–7, 284, 308, 311, 328–9, 338, 346, 364, 381, 389, 400, 437, 450, 541, 543–4
