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Newman J.R. — The World of Mathematics, Volume 1
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Название: The World of Mathematics, Volume 1Автор: Newman J.R. Аннотация: Volume 1 of a monumental 4-vol. set includes a general survey of mathematics; historical and biographical information on prominent mathematicians throughout history; material on arithmetic, numbers and the art of counting, and the mathematics of space and motion. Non-technical articles by and about scores of eminent mathematicians as well as literary figures, economists, biologists. and many other thinkers. Informative commentary by noted mathematics scholar James R. Newman precedes essays by Eric Temple Bell, W. W. Rouse Ball, Leonhard Euler, Bertrand Russell, Alfred North Whitehead, many others. Numerous figures.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2000Количество страниц: 724Добавлена в каталог: 02.04.2008Операции: Положить на полку |
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Gnomon, L-shaped border 84—85 Goldbach, Christian 365 367 499 507 Golden section, Great Pyramid 80 Golden section, ladder of numbers 98 Golden section, star pentagram 88 Golenischev papyrus 169 Goths, alphabetic numerals 451 Gottschalk, E. 510 Grammar, arithmetic needful for 214 Grapes, fermenting (optically dextroactive) 689 Graph, configuration 572 Graphic representation 605 Grassmann, Hermann, Ausdehnungslehre 396 Grassmann, Robert 293 fn. Gravitation, Einstein's theory 146 328 409 Gravity, law of 62 111 142 144 145 146 256 257—258 266 268 315 548 Greater Logic (Hegel) 387 Greatest common measure 16—17 101 Greek Mathematics, A Manual of (Heath) 76 191 Greeks, algebra 13 16 Greeks, analytical geometry 236 Greeks, astronomy 14 Greeks, curvilinear figures 34 40 41 42 53 Greeks, ellipse 229 Greeks, Euclidean construction 502 Greeks, fractions, reducing 12 Greeks, geometry 10 11 13 61 68—69 Greeks, incommensurable lines 26 528 Greeks, irrational numbers 89 Greeks, logistica 498 Greeks, mathematics 18 89 116 188 Greeks, motion, conception of 19 Greeks, notation 92 99 114—115 Greeks, number symbols 418 443 446 Greeks, numbers and magnitudes, distinction 17 61—63 Greeks, polyhedra, tabulation 723 Greeks, problems, classification 91 Greeks, projective geometry 632 Greeks, prolixity 38 Greeks, tangent to a curve 36 Greeks, triquetrum 714 Greeks, “symmetric”, use of word 720 Greene, Robert, quoted 489 Gregory, James 78 137 138 139 140 143 Grimaldi, Francesco Maria, on nature of light 260 262 Gross, Mason 399 fn. Grosseteste, Robert 605 Ground of Artes, The (Recorde) 210—211 Groups, automorphisms 696 Groups, relationships, numbers 402 Groups, theory 167 Groups, units, comparing 492 Growth and Form (Thompson) 708 Gruppen von endlicher Ordnung, Theorie der (Speiser) 702 Guldin, Paul 111 Gulliver's Travels (Swift) 26 Hadamard, Jacques S., prime number theory 158 507 Haddon, A.C. 440 fn. Haeckel, Ernst, Challenger Monograph 708 720 Haeckel, Ernst, Kunstformen der Natur 707 Haldane, Elizabeth S. 235 fn. Halley, Edmund, Newton's Principia 286 Halley, Edmund, planetary motion 144 264 278 Halley’s comet 144 Halphen, Georges 363 Hambidge, J., Dynamic Symmetry 718 fn. Hamilton, William Rowan, algebraic discoveries 76 Hamilton, William Rowan, biography 161 Hamilton, William Rowan, Characteristic Function 161 162 164 Hamilton, William Rowan, dynamics, laws of 659 Hamilton, William Rowan, least action, principle 110 132 Hamilton, William Rowan, quaternions 76 162 163 164 332 Hamilton, William Rowan, Rays, Account of a Theory of, quoted 161 Hardy, Godfrey Harold, analytic theory of numbers 158 Hardy, Godfrey Harold, definite integrals 371 Hardy, Godfrey Harold, partitions of n 167 Hardy, Godfrey Harold, prime number theorem 508 Hardy, Godfrey Harold, Ramanujan 366 fn. 367 370—373 375 Hardy, Godfrey Harold, Waring problem 515 Harmonic progressions, civil life 127 Harmonices Mundi (Kepler) 126 127 Harmonics (Ptolemy) 232 harmony, applications 671 Harmony, Elements of (Aristoxenus) 192 Harriot, Thomas 23 29 Harrison, R.G. 692 Hartshorae, Charles 395 fn. Heap, symbol 12 Heart, mammals, an asymmetric screw 687 Heart-beats, atom 164 Heath, Thomas, Archimedes, The Works of 181 fn. 197 198 Heath, Thomas, Euclid's Elements, The Thirteen Books of 191 fn. Heath, Thomas, Greek Mathematics, Manual of 76 191 Heavenly Bodies, The Circular Motion of the (Cleomedes) 205 Heawood, four-color problem 591 Hebrews, numerals 451 Hegel, Georg Wilhelm Friedrich 314 316 387 Heiberg, Johan Ludvig 94 Heisenberg, Werner, quantum mechanics 362 396 Heisenberg, Werner, wave mechanics 164 Heliocentric theory, Copernicus 110 120 218 226 227 Heliodorus of Larissa, perspective 605 Heliotrope, invention 327 Hemisphere, area of 175 Heptagon, angle, determining 80 Heracleides 179 Heraldic symmetry 674 675 Hermite, Charles 514 Hero (Heron) of Alexandria, fractions 172 Hero (Heron) of Alexandria, inventions 110 Hero (Heron) of Alexandria, plane mirrors 110 132 154 Hero (Heron) of Alexandria, relativity 110 Herodotus 10 80 Herodotus, quoted 79 Hertz, Heinrich, quoted 521 Hertz, Heinrich, wireless telegraphy 9 644 Herzfeld, Ernst 675 Hexagon, Egyptian knowledge of 80 Hexagon, inscribed in a conic 134 Hexagonal cells, bees’ 80 111 208 Hexagonal symmetry 712 Hexagram, mystic 134 151 Hiero II (king of Sicily) 103 181 185 188 200 Higher algebra 136 Higher geometry 151 Higher plane curves, theory of 113 Higher space, geometry of 342 Hilbert, David, diophantine equations 509 Hilbert, David, quoted 510 Hilbert, David, transcendental numbers 514 Hilbert, David, Waring's conjecture 514 Hill, G.F., Arabic Numerals in Europe 454 fn. Hindu-Arabic numerals 453 Hindu-Arabic Numerals, The (Smith and Karpinski) 454 fn. Hindus see also “India” Hindus, diophantine equations 509 Hindus, rotation system 13 Hindus, trigonometry 18 Hipparchus, planetary motion 110 226 Hipparchus, trigonometry 18 109 Hippasus 83 Hippocrates of Chios, area of a circle 97 Hippocrates of Chios, method of exhaustion 92 101 193 Hippocrates of Chios, squaring the circle 90 Historic asymmetry 679 Historic continuity, heraldic symmetry 676 Histories, Book of (Tzetzes), quoted 187 Hobbes, Thomas, quoted 622 Holland, freedom of thought 235 Holmes, Oliver Wendell, quoted 467 Holy teractys 84 Homaloid space 656—657 homer 99 Honey cell, hexagon 80 110 208 Hooke, Robert, inverse square law 264 265 Hooke, Robert, Micrographia 261 Hooke, Robert, planetary motion 144 264 Houdin, Jean Eugene Robert 477 Huaman Poma de Ayala, Don Felipe 463 Hughes, Richard, quoted 537 Human bodies, in curved space 663—664 Human body, bilateral symmetry 671 674 686—687 Hundred, Roman numeral 448 Huxley, Aldous, quoted 277 Huxley, Julian S., Embryology, Elements of 691 fn. Huxley, Thomas Henry 166 239 Huygens, Christian, light, theory of 146 261 262 412 Hydrodynamics, confonnal mapping 337 Hydrodynamics, text-book 267 Hydrostatics, Archimedes’ work on 107 Hydrostatics, Stevinus’ work on 120 Hyperbola 34 87 91 93 97 258 Hyperbolic geometry 158—159 Hyperbolic table, Dase's 477 Hypergeometric series 324 369 i (defined), complex unity 30 Iceland spar 263 icosahedron 86 96 719—720 Ideal numbers 499 513 Ideas, Adventures in (Whitehead) 399 Idiot savants 465—466 imaginary numbers 29—30 34 119 148 309 Immediate occasion 407 Implication, mathematics 70 Inanimate objects, motions and rests 44 Inaudi, Jacques, mental calculations 475 478—480 481 482 Incommensurables 16 26 62 99 191 525 Increasing arithmetically, logarithms 124 Increment of, symbol 47—48 Indeterminate analysis 197 207 Indeterminate equations 105 116 India see also “Hindus” India, decimal notation 23 114 117 India, four, forms for 453 India, mathematicians 166 India, numerals 443 Indices, fractional 131 140 Indices, negative 131 Indices, notation 122 Indices, theory 89 106 125 Indivisibles, method of 31—43 53 135 137 Induction, process 68 Induction, theory of 405 Inertia, law of 52 665 Infinite descent, method 311 505 Infinite geometrical progression 94 Infinite plane dwellers, geometry 651 Infinite rapport 699 Infinite series 521—524 Infinitesimal calculus 43 48 52 53—62 95 127 142 146 286—293 411 Infinitesimal, meaning 152 Infinitesimals 40 41 57 Inflected language 406 Inkeri, K. 513 Integers 13 28 60 65 66 Integral calculus 42 47 90 103 104 135 139 142 143 258 Integration, differential 55—56 61 Integration, Leibniz's problem 58 Intellectual needs, satisfaction of 8—9 10 Interpolation, mathematics of 140 145 Invariance, illustrations 352—353 Invariance, projective geometry 640 Invariants, differential 363 Invariants, finite 164 Invariants, theory of 163 341—342 344 348 350 361 Invention, primitive 8 Inverse fluxions 258 Inverse square law 145 258 264 265 266 Inversion, art 684—685 Involution of six points 112—113 Iran (Persia), numerals 454 Irrational numbers 26 27 34 62—63 64 87—88 89 92 95—96 97 101 162 168 525—536 Irrationals, unordered 108 Irreducible equation of degree n 512 Isoperimetric figures 188 207—209 Isoperimetrical problem 153 Isosceles triangle 15 81 101 175 Italy, algebra introduced 23 Italy, mathematical treatises 210 Italy, mathematics 18 118 119 Ivory, James 151 Jacobi, Karl Gustav 306 331 370 Jaeger, F.M., “Symmetry and Its Applications in Natural Science” 689 Japan, abacus 457 Japan, numerals 445 Japan, symbol for “three” 444 Japan, symbol for “two” 443 Japp, F.R., “Stereochemistry and Vitalism” 690 Johns Hopkins University, founding 354—355 Johnson, A.H. 395 fn. 398 Johnson, Samuel 287 Johnson, Samuel, quoted 528 Jordan, Camille 589 Jordan, Camille, curve theorem 588—590 Jordan, Camille, quantum mechanics 396 Jordan, Pascual, life, beginnings 690 Joseph, Abraham 346 Joule, James Prescott, conservation of energy 643 fn. Jourdain, Philip E.B., commentary on 2—3 Jourdain, Philip E.B., “Mathematics, The Nature of” 4—72 Jurin, James 291 fn. Juvenal, quoted 189 489 Kaestner, Abraham Gotthelf 156 158 Kant, Immanuel, axioms of geometry 647 660 665 666 Kant, Immanuel, properties of space 645 Kant, Immanuel, quoted 274 Kant, Immanuel, space and time 684 Kapferer, H. 510 Kasner, Edward, quoted 420 Kelvin, Lord (W. Thomson), energy, conservation 643 fn. Kempe, A.B., four-color problem 591 Kepler, Johann (Johannes), astronomical speculations 120 Kepler, Johann (Johannes), Brahe, association with 125—126 223—225 Kepler, Johann (Johannes), commentary on 218—219 Kepler, Johann (Johannes), Durer's analytical geometry 613 Kepler, Johann (Johannes), Ephemerides 124 Kepler, Johann (Johannes), Harmonices Mundi 126 127 Kepler, Johann (Johannes), indivisibles 42 Kepler, Johann (Johannes), infinitesimal calculus 127 152 Kepler, Johann (Johannes), Mars, motion of 226—228 230 Kepler, Johann (Johannes), methods 233—234 Kepler, Johann (Johannes), pentagon 615 Kepler, Johann (Johannes), planetary laws 126—127 132 218 220—234 257 266 412 Kepler, Johann (Johannes), planetary system, reducing distances 720 Kepler, Johann (Johannes), planetary tunes 127—128 Kepler, Johann (Johannes), projective geometry 133 Kepler, Johann (Johannes), prophesying almanack 231 Kepler, Johann (Johannes), quoted 220 Kepler, Johann (Johannes), wine-cask geometry 127 137 Keser, Jacob 609 Keynes, Geoffrey 254 Keynes, John Maynard, quoted 254 Keynes, John Maynard, “Newton, the Man” 277—285 Keyser, Cassius J., Mathematical Philosophy 570 fn. Kinematical thought 142 King Lear (Shakespeare) 306 fn. Klein bottle 597 Klein, Felix, analysis 151 Klein, Felix, geometry discoveries 342 359 639 Klein, Felix, groups, theory of 167
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