Mathematics in western culture:
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| Format: | Book |
| Language: | English |
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London ; Oxford ; New York
Oxford University Press
1964
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| Edition: | First issued as an Oxford University Press paperback |
| Series: | Oxford paperbacks
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis Seite 473-476 |
| Physical Description: | x, 484 Seiten, 16 ungezählte Seiten Bildtafeln Illustrationen, Diagramme |
| ISBN: | 019500714X |
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MARC
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| 245 | 1 | 0 | |a Mathematics in western culture |c by Morris Kline |
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| 500 | |a Literaturverzeichnis Seite 473-476 | ||
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| adam_text | Index Abscissa, 168 Abstraction, 31, 51-3, 206, 461-2, 464-6 Academy of Plato, 41, 54, 79, no Acceleration, 187, 191, 202-3; instanta neous, 220, 222 Adams, John, 330, 333 Adams, John C., 210, 304 Addison, Joseph, 260-61, 279 Aesthetics, philosophy of, 285-6 Age of Reason, 121, 255, 276, 286, 360 Ahmes papyrus, 21 Alberti, Leone B., 132-3, ։35 35° Alexandria, 41, 60-67, 84-6, 89, 291 Algebra, 10, 34-5, 37-8, 165-6, 176, 351, 454, 457; of transfinite numbers, 4056 Almagest, 84 Ampère, André-Marie, 306, 309 Amplitude-modulation, 312-13 Amplitude of a trigonometric func tion, 29г, 298 Analysis, 233, 457 Angle, concept of, 14; trigonometric ratios of, 68 Apollonius, 40, 49 Arabs, 38, 93, too, 105, 111, 240, 287 Archimedes, 11, 12, 29, 62-6, 89, 112, 143, 182, 184, 413 Architecture, Babylonian, 20; Egyp tian, 20, 22; Greek, 11, 34, 39, 56-8; in Age of Reason, 285 Area, obtained by calculus, 223-4 Aristarchus, 84 Aristotle, 35, 41, 43, 54-5, 61, 84, 91, 94, 96, 118, 129, 142, 184-5, 187-90, 258, 409, 430, 449 Arithmetica, 31, 41 Arnold, Matthew, 271, 284 Ars Magna, 99-100 Art, mathematics as, 5, 28, 55, 431, 166-70; Byzantine, 128-30; Greek, 33- 4, 39, 55-8; in Age of Reason, 2846; modern, 467; Renaissance, 12643, 349-50; Roman, 86; see also Painting, Perspective Astrology, 19-20, 94-5 Astronomy, Babylonian, 22; Egyptian, 18, 22; Greek, 33, 35, 76-7, 79-85, 111-12; medieval, 94; Newtonian, 198-201, 206-12, 237, 286; Renais sance, 110-25, 183 Atheism, 262, 266-7 Athens, 31, 60, 62 Atomic theory, 381-2 Average, 344; arithmetic mean, 344, 346, 348-9, 369-71; mean of a sam ple,
372-3; median, 344; mode, 344, 851 Axioms, 43; of economics, 332-3; of ethics, 326; of human nature, 323-6; of politics, 328-9; properties of, 4556; see also Parallel axiom В Babylonian mathematics, 14-17, 35-7 Bach, Johann S., 301-2 Bach, Karl P. E., 301 Bacon, Francis, 104, 116-17, I82 84, 213 Bacon, Roger, 95, 104-5, ։84 Barrow, Isaac, 196-7, 259, 277 Base of a number system, 15 Beauty, in mathematics, 5, 469-70; laws of, 285-6; see also Art Beethoven, Ludwig v., 298, 303, 462 Bentham, Jeremy, 273-4, 277, 324-8, 330-3* Berkeley, Bishop G., 245-8, 324 Bernoulli, Johann, 241, 253 Bible, 89-90, 103, 123, 260, 267, 271, 330, 360, 430 477
478 INDEX Biology, 207, 237-8, 349-50, 356 Blake, William, 280, 282 Bolyai, John, 410, 413-18, 421-7, 429, 431, 444, 452 Bolzano, Bernard, 400 Botticelli, 142 Bougainville, Louis A. de, 270 Boyle, Robert, 207, 259, 261-2 Brahe, Tycho, 97, 113, 117, 383 Bramante, 134 Brianchon, Charles J., 150 Brunelleschi, 132, 140 Bruno, Giordano, 124, 257 Buffon, Comte de, 238 Burns, Robert, 282 Butler, Samuel, 280 Byron, Lord, 214, 282 Byzantine Empire, 100-101 C Calculus, 164, 197, 214-25, 229’33 247՜ 8, 351, 408, 457 Calendar, Egyptian, 18-19; Greek, 64; medieval, 95 Calvin, John, 123-4, 234 Campanella, Tommaso, 126 Cantor, Georg, 396-400, 402, 406-8, 431, 455 Cardan, Jerome, 95, 99-100, 123, 359, 361, 369 Catholicism, 262, 360; see also Chris tianity Cauchy, Augustin-Louis, 233 Causality, 107, 186, 248, 258, 450 Cavalieri, Bonaventura, 230-31 Cézanne, Paul, 467 Chemistry, 207-8, 237, 348 Chesterfield, Earl of, 246-7 Chords, 301-2 Christianity, 91-3, 430; in relation to Alexandria, 87, 91-2; philosophy of nature, 107-8; theology of, 85, 95-7, 117, 121-5, շ43 257-71; see a^so Reli gion Circle, 46-7, 49-50, 147-50; equation of, 168-9, 180 Clough, Arthur H., 257 Coleridge, Samuel T., 282 Condensation, 288-90 Condorcet, Marquis de, 238 Congruence, 45-6 Conic sections, 6, 47, 49-50, 51, 149-50, 164, 172; see also Ellipse, Hyperbola, Parabola Conical surface, 47 Co-ordinate geometry, four-dimen sional, 176-80; higher-dimensional, 180; three-dimensional, 172-6; twodimensional, 163-72 Co-ordinates of a point, 168, 173-4, 177 Copernicus, Nicolaus, 78, 85, 95, 97, 100-101, 110-24, г89, 196,
211-13, 23θ· 258· 3°4 32О 34շ. 383 4 39і» 4շ8, 431, 448, 452, 469; see also Helio centric theory Correlation, 356-7 Cosine, 68, 71 Cosmas, 89 Cosmology, medieval, 89-90; of Thales, 75 Cournot, Antoine A., 335 Cubists, 467 Curve, equation of, 167-8, 17073 D D’Alembert, Jean le R., 232, 241, 265 Dante, 122, 183 Darwin, Charles R., 428 De Morgan, Augustus, 144 De Prospettiva Pingendi, 132 Declaration of Independence, 125, 3293° Deduction, 26-30, 44-5; in science, 242 Deferent, 83 Definitions, 42; see also Undefined concepts Deism, 262, 264-5 Della Pittura, 132 Democracy, 236, 328-32 Derivative, 221 Desargues, Girard, 146-8, 150-51, 158 Descartes, René, 104-7, 109 I24՛ 14®· 159-72, ։77 *8», 184 j87 2I3’ 2։4· 226, 236, 239-41, 244-5, 252-3, 258, 262, 275, 282, 382, 452; see also Co ordinate geometry Determinism, 254-5, 259, 32021, 37693
INDEX Dialogue on the Two Chief Systems of the World, 124 Dictionary, Johnson’s, 273 Diderot, Denis, 265 Differential equation, 223, 30g, 320, 336, 465 Digit, 13 Dimension, 180 Diophantus, 63 Discourse on Method, 163, 17։ Discourses and Mathematical Demon strations Concerning Two New Sci ences, 195 Displacement current, 309-10; see also Electromagnetic waves Donatello, 132 Donne, John, 122 Doubling the cube, 50-51, 458 Dryden, John, 274, 277-9, 281 Duccio, 129-32 Dürer, Albrecht, 133-6, 143, 350 E Eccentric, 83 Economics, 322-5, 332-9, 352-5, 365 Eddington, Sir Arthur S., 229, 466 Egyptian mathematics, 14-17, 36 Einstein, Albert, 181, 198, 229, 382, 391, 432, 439-40, 442-9, 452, 469 Electricity, 208, 237, 252, 305-8, 31517, 320 Electromagnetic induction, 307-9, 318 Electromagnetic waves, 309-20, 465 Electromotive force, 306 Electrons, 306, 316-17 Elements of Euclid, 40, 42-9, 54-5, 81 Ellipse, 6, 47, 49-50, 149-50, 164 Ellipsoid, 178-9 Emerson, Ralph W., 278 Empirical mathematics, 22-7 Encyclopédie, 265 Enlightenment, 265 Epicycle, 83 Eratosthenes, 63-4 Ether, 242, 310, 317, 435-7, 45* Ethics, 269-71, 323-7, 339 Euclid, 10, 12, 16, 40-41, 43-4, 55, 66, 89 97 ‘39՛ ’43 44. 165- i83 ։87 204, 232, 271, 389-90, 410-14, 422-3, 428-9, 433, 444, 452, 456; see also 479 Elements of Euclid, Euclidean ge ometry, Greek, geometry Euclidean geometry, 10, 42-8, 53-8, 74, 81, 93, 107, 126, 140, 144-5, 47. 1645, 168, 172, 178, 251, 389-91, 410-11, 416, 427-30, 443-4, 451, 454, 468; and physical space, 417-22, 432-3; see also Elements of Euclid, Euclid, Greek geometry Eudoxus, 40, 80-81,
83, 212 Euler, Leonhard, 228, 232, 291 Event, 179-80, 441-3 F Faraday, Michael, 306-7, 309, 318 Felicific calculus, 326 Fermat, Pierre, 163-5, ։7°· 177, 181 214-15, 217, 226-8, 236, 360-61, 363, 369; see also Co-ordinate geometry Focus of a parabola, 171-2 Fontenelle, Le Bovier de, 275 Force, 187, 191; see also Gravitation Formula, 185-6, 206; fitted to data, 3515 Fourier, Joseph, 287-8, 296, 300-301, 303; theorem of, 296-8, 302-3 Fra Filippo, 132 France, Anatole, 358 Franklin, Benjamin, 265 Frederick the Great, 236 Free will, 255-6, 259, 269, 450 Freedom of press, 124-5, 23$, 2θ9· °։ speech, 123, 269 French Academy, 274, 288 Frequency-modulation, 313-14 Frequency of a trigonometric function, 293 «99 Function, 185; periodic, 291; trigono metric, 291-4, 301 G Galen, 94 Galileo, 78, 95, 97, 101, 105-9, 120, 4, 182-95, ։9® ։98 2Օ7՛ 211՜։3՛ 217, 236, 240-41, 252-3, 258, 262, 320, 342, 382, 384, 388, 395-6, 452 Galton, Sir Francis, 355-6, 385 Galvani, Luigi, 306 123շ։4 275, 399.
480 INDEX Gamma ray։. 315-16 Gate*. theory oí. »37. 3*0-* 1, 341, 373· 4· 380 Cium, Kari F„ 19g, 396, 413-15. 418-19 Geocentric theory. 81-5. 111-1* Geodetic 419-11, 444-5 Geographie, 71-3 Germanic tribe*. 91-3 Gibbon, Edward, *65-6 Gilbert, William. 305-6 Giotto, 1*9-3«, 40 Graph of ttatiitical data, 346-7 Graunt. John. 343-4 Gravitation. 6, 95. 197*06, *08, *n, •36. *5»-4· 3 «. 34· ЗЧ SM, 39«. 4*8, 434-5. 439· 445·«. 449 5» Greek geometry, 7, 33-8. 41-59. 19*, 3*3. 4*7; гее obo Euclid, Euclidean geometry H Halley, Edmond, 197 Hamilton, Alexander, 330 Hamilton, Sir William, **9 Hartley, David, 338 Harvey, William, *07, *38 Heat, theory of, *07-8, *37, *5*, 385 Heliocentric theory, ni-*5, 183, 188-9, »1*. *58, 4*8, 431 Helmholu, Hermann v„ 310 Henry, Jo*eph. 3067, 309 Heredity, 365-6 Heron, 6*-3, 184 Herta, Heinrich, 311, 31g Hilbert, David, 397 Hindu mathematic*, 15. 93, *40 Hipparchu*, 63. 67-7*, 81-4, 8g, 111, • i*, *91, 45* Hire, Philippe de la, 147, 151 Hőbbe*, Thoma*, »43-6, »5*, *55. »65· 6. 3*3. 3*8. 338 Hogarth, William. 143 Holbach. Baron Paul H. ď, »38, »53. »67 Hume, David, *4850, *58, *65-6, 3*4, 3*8 Huygen*. Chriatian. 97, 109, 184, *36, 44. »53- »58. »75 Hyperbola. 6. 47, 49-50, 149-50. 164 Hypercurve, 180 Hyperplane, equation of. 177-8 Hypenphere. equation of. 177 I Index of Prohibited Book*. 113, *36 Indirect meaturement, 67-73 Induction. *5-8 Induitrial Revolution, 33*, 34t Inertia. 187, 190 Infinite quantitic*. theory of. 5: гее abo Number, infinite Infra-red ray*, 315-16 Inquitition, 1*3-4, *35 Inttantaneou* rate of change, *16*4. 47 Imurance, 341, 358,
365-8 J Jame* I. *34 Jean*. Sir Jame*. * g. 466 Jeffenon, Thoma։, »65, 3*9-30 Johnion, Samuel, *46, *73, *77, *79 Jonton, Ben, i**, 183 К Kant, Immanuel *38, »49-51, 71, 3*3. 410, 413. 4*7-8 Keau, John, 81 Kelvin, Lord, 13. *56, 310 Kepler, Johanne», 4, 78, 85. 95. 97, 101, 105, 11**3. 196, *i*-i3, *36. »58. 304. S»°. 3»3· 34». 383-4. J86388, 390-91. 45*, 469 Kepler’։ law», 114-15. »04-6, »16, *3, »85. 383-4. 89° Kronecker, Leopold, 397 L Lagrange. Jourph L-, 159. *09, *13. »3». 4 . »55- »58 Lamb. Charle*, *8* Lambert, Johann H„ 134 Language, abitract, *73; mathematical, 8, 1767, »3940; of кіепсе, »41·» Lapbee, Pierre S, *10, *13. *41, 155. *58. »«7. З59. 369 Law, 463-4
INDEX Laws of motion, 190-95, 202-3, 228, »36, «5«· З1®· 3։9· 8*4» 89°· 45і Lecky, William E. H., 42? Legendre, Adrien Μ., 241 Leibniz, Gottfried W., 164, 184, 214· 15, 217, 231-2, 236, 239-41, 247, 253, 256, 258, 261-2, 269, 274, 287, 382, 396 Length, 437-8, 451; absolute, 439-40; local, 439-40, 448 Leonardo da Vinci, 4, 99, 105, 127, 153. ’35. Ч‘ч, 35° Leverrier, Urbain J. J., 210, 304, 446 Light, 197, 226-7, 237-8, 252, 310, 314435» 439· 447· 465: «« “be Op tics Limit, 230 Literature, Greek, 39, 56, 58; in New tonian age, 272-81, 284-5; Romantic reaction, 281-4 Lobatchevsky, Nicholas, 413-18, 421-7, 4*9· 43 . 444. 45« Locke, John, 244-6, 249, 263, 270-71, 275. »77» »82, 324» 328-3։ Logic, 54-5, 239-40; symbolic, 240 Logistica, 31 Lorenzetti, Ambrogio, 131-2 Loudness, 298 Lucretius, 405 Luther, Martin, 123-4, *84 Μ Maclaurin, Colin, 231 Madison, James, 330 Magellan, Ferdinand, 270 Magnetism, 305-6, 317, 320 Malthus, Thomas R., 333-4 Mantegna, 142 Map-making, 72, 151-7 Map projections, gnomonic, 152; Mer cator, 155-7; perspective cylindrical, 155; stereographic, 153-5 Martini, Simone, 129 Masaccio, 132, 140 Mass, 19091, soi-a, 434-5, 445-6; and ίηΜΈϊ· 447։ relativity of, 447 Materialism, 243-6, 252-4, 256, 259 Mathematical creation, 4-7, 43031,45660 48 i Mathematical Principles of Natural Philosophy, 197, 206-7, 23։» 236, 260, 264 Mathematics,- pure and applied, 462 Mathematics as method, 4, 161-2, 45461 Mather, Cotton, 234 Matter, geometrization of, 445, 452; structure of, 380-82, 385 Maupertuis, Pierre L. Μ. de, 228-9 Maximum-minimum principle, 226-9 Maxwell, James
C., 304-6, 308-11, 3142։. 374» 4θ5 Mécanique analytique, 209, 241 Mécanique céleste, 210, 241, 266 Mechanical philosophy of nature, 187, 237-8, 243-4, 26a, 319-20; see also Materialism Mechanics, Greek, 184, 188-go; New tonian, 189-95, 199-206, 241, 286, 445; relativistic, 446 Medicine, 94-5, 341-8, 357-8, 365, 368 Mendel, Gregor, 365-6 Menelaus, 63 Mercator, Gerard, 151, 155-7 Mercury, motion of, 446 Méré, Chevalier de, 359-60 Merz, Theodore, 340 Method in philosophy, 161-3 Mettrie, Julian O. de la, 238, 253, 267, 270 Michelangelo, 134, 142, 350 Michelson, Albert A., 436-7, 439, 451 Mill, James, 324, 331 Mill, John S., 332 Millay, Edna Յէ. V., 40 Milton, John, 89, 110, 122-3 Minkowski, Hermann, 441-2, 451 Miracles, 263-5 Montaigne, Michel de, 265 Montesquieu, Charles de S. de, 539 Moore, Eliakim H., 408 Morley, Edward W., 436-7, 439, 451 Motion, concept of, 404-5; see aba Laws of motion Museum of Alexandria, 61, 85, 87 Music, 33, 76, 94, 287-303, 457-8 Mysticism, in Babylonia and Egypt, 19-21; medieval, gi; Pythagorean, 40-41, 76-8
482 INDEX N Natural rights of man, 328-31 Negative numbers, 93 Neptune, discovery of, 210, 304 ■ Newman, Cardinal John H., 268 Newton, Sir Isaac, 4, 6, 11, 12, 78, 97, 101, 10g, 181, 184, 196-201, 204-6, 208-13, «4-15. ai7 223» аз1՜։, 23θ. 238, 240-41, 247, 253-4, 258-62, 264, շ66, 269, 275, 277, շ8ւ-շ, 304, з16, 8 9. 3«3. 3«6, 342. 382. 384. 388-9, 391, 413. 4«8, 433-5. 439՜4°. 449 5։. 4Ö9 Non-Euclidean geometry, 5. 7 25 і. 389, 4 3-3։. 444· 45і. 453֊5· 457. 466, 468; and physical space, 41819, 421-2, 424-6 Normal frequency curve, 347-51, 3697«. 378 Noyes, Alfred, 196 Number, abstract, 14; infinite, 397400; irrational, 36-7; prime, 458-9; rational, 35-6; transfinite, 398 Numbers, theory of, 5, 3։, 41, 164 О Oersted, Hans C., 306, 309 On the Revolutions of the Heavenly Spheres, 100, 110, 119 One-to-one correspondence, 396, 398 Optics, 81-2, 164-5, *7*! see a^° Light Ordinate, 168 Osler, Dr. William, 358 Oxford Movement, 268 P Painting, 4; Babylonian, 21; Byzan tine, 128-30; Greek and Roman, 128; in Age of Reason, 285; mod ern, 143; Renaissance, 126-44, 147, 150, 157-8, 467 Pappus, 63 Parabola, 6, 49-50, 149-50, 164, 171-2; equation of, 169-70 Paraboloid, equation of, 175-6 Paradox, Achilles and tortoise, 403; arrow, 403-4; logical, 406-8 Parallel axiom, Euclid, 411, 457; Lobatchevsky and Bolyai, 415; Rie mann, 423 Pareto, Vilfredo, 335, 353-4 Partials of a musical sound, 298-300 Pascal, Blaise, 147-50, 164, 207, 231, 267. 275. 359-6։. 363-4, 369, 374-5 Pascal triangle, 364-5, 368, 371 Pascal’s wager, 375 Pearl, Raymond, 335-8 Perspective, conceptual, 127-8; focused,
136-9, 143-5; mathematical, 127, 13243, 146-7, 151, 471; optical, 128-31, ։57 Petty, Sir William, 343-4 Philosophy, Cartesian, 161-3; Greek, 11, 28-9, 31-4, 39, 55-8, 110; me chanical, 237-8; of science, 183-8, 198, 206-7; of space and time, 44950; of Age of Reason, 243-56; Ren aissance, 103-9, ։82. J39-4°í see Determinism, Materialism, Statisti cal view of nature Phonodeik, 290, 303 Physiocrats, 332 Picasso, Pablo, 467 Piero della Francesca, 133, 140-41 Pitch, 298-9 Place value, 14-15, 93, 240 Plane, equation of, 175-6 Plato, 6, 24, 29, 31-3, 47, 50, 54, 61, 74, 78-80, 84, 91, 95, 114, 14г, 178, 184, 213 Platonic doctrine of ideas, 32-3 Poetry, 276-84 Poincaré, Henri, 397 Politics, 323-5, 328-32, 339 Pope, Alexander, 234, 272, 275, 27881, 322, 376, 432 Pope Gregory XV, 235 Pope Urban VIII, 124 Population growth,· 333-7, 357 Primitive civilizations, 13 Principle of Least Action, 228-9 Principle of Least Time, 226-7 Printing, 102 Probability, theory of, 5, 361-2, 374, 377-93 Projectile motion, 6, 194-5 Projection, 135-9, 45’57
483 INDEX Projective geometry, 5, 144-5։, »57-8, 468-9 Proof, mathematical, 27-8, 44-5, 54, 458-9 Prose, emphasis on, 876-7; style, »74 Prudhomme, Sully, 60 Pseudosphere, 4Я1 Psychology, 838, 383, 338-9, 365 Ptolemy, Claudius, 61, 63, 78-3, 84-5, 8g, in-18, 117-18, iso, 122, 143, sis, S58, 391, 428, 458, 469 Ptolemy the First, 61 Pythagoras, 6, 89, 40-41, 61, 114, 143, 887 Pythagorean theorem, 8-9, 35-6, 168 Pythagoreans, 32, 36, 40-41, 55, 75-8, 108, 183, s 13, 254, 301 Q Quadrivium, 94, 887 Quality of a musical sound, 298-300 Quantitative interpretation of nature, 78, 184-7, ։»»· 2 87 Quantum theory, 452 Quesnay, François, 238, 332 Quételet, Lambert A. J., 349-50, 356 R Radar, 313-14 Radio, 311-14, 316-17; see also Electro magnetic waves Raphael, 134, 142-3 Rarefaction, 288-90 Rational spirit, 10, 53-4, 103-4, 238-9, 286, 322-3, 330, 338 Rationalistic supernaturalism, 263 Rationalization of nature, 74-85, 1049, 126-7, 187, 207-8, 837-8, 316-17 Rayleigh, Lord, 470 Reasoning by analogy, 25-8 Rectangular co-ordinate system, fourdimensional, 177; three-dimensional, 173-6; two-dimensional, 167-9 Reed, Lowell J., 335-8 Reformation, 102-3, “9 Regular polygons, 47 Regular polyhedra, 47-8 Relativity, theory of, 173, 229, 438-52; General Theory of, 443; Special Theory of, 442 Religion, Babylonian, 23; Christian, 85; Egyptian, 19, 23; freedom of, 235-6, 269; Greek, 40; influence of rationalism on, 257-71; influence of statistical view of nature on, 388; relation to a maximum-minimum principle, 228-g; see also Christi anity Renaissance, 97, 100-109, 184, 237, 268 Revelation, 263,
265 Reynolds, Sir Joshua, 285 Ricardo, David, 334 Riemann, Bernhard, 422-7, 429, 431, 444- 45s Rigor, 229-33, 409 Rolle, Michel, 231 Rome, 11, 12, 66, 85-6, 93, 97, 287 Rousseau, Jean J., 249-50, 322-3 Royal Society, 274, 318 Russell, Bertrand, 5, 240, 403, 462, 470 S Saccheri, Girolamo, 412-14 Saint Augustine, 3, go Saint Thomas Aquinas, 96, 185, 258 Sampling, 371-3 Scales, equal-tempered, 301-2; musical, 287 Schoenberg, Arnold, 302 Scholastics, 96-7 Science, compared with mathematics, 10, 431; emancipation from theol ogy, 125; mathematization of, 24042, 316-17, 451-2; medieval concept of, 185; modern approach to, 18391, 198, 206-8; Renaissance concept of, 108-g, 112 Scientific laws, nature of, 377-94» 483՜ 4» 439 Sculpture, Greek, 11, 38 4» 89» 57» Roman, 34, 86 Section, 135-9, »45 57 Seurat, Georges, 467 Shaftesbury, Third Earl of, 270 Shelley, Percy B., 28a Signorelli, 134
482 INDEX N Natural rights o£ man, 328-31 Negative numbers, 93 Neptune, discovery of, 210, 304 • Newman, Cardinal John H., 268 Newton, Sir Isaac, 4, 6, ։։, 12, 78, 97, 101, 109, 181, 184, 196-201, 204-6, 208-13, 214-15, 217, 223, 231-2, 236, 238, 240-41, 247, 253-4, 258-62, 264, 266, 269, 275, 277, 281-2, 304, 316, 3։9 3*8· 3*6. 34«. 38«· 384. 388 9. 391, 413, 428, 433-5, 439-40, 449-51, 469 Non-Euclidean geometry, 5, 7, 251, 389. 413 3։ 444· 451. 453 5· 457· 466, 468; and physical space, 41819, 421-2, 424-6 Normal frequency curve, 347-51, 3697«· 378 Noyes, Alfred, 196 Number, abstract, 14; infinite, 397· 400; irrational, 36-7; prime, 458-9; rational, 35-6; transfinite, 398 Numbers, theory of, 5, 3։, 41, 164 О Oersted, Hans C., 306, 309 On the Revolutions of the Heavenly Spheres, 100, 110, 119 One-to-one correspondence, 396, 398 Optics, 81-2, 164-5, ։?я; see ako Light Ordinate, 168 Osler, Dr. William, 358 Oxford Movement, 268 P Painting, 4; Babylonian, 21; Byzan tine, 128-30; Greek and Roman, 128; in Age of Reason, 285; mod ern, 143; Renaissance, 126-44, 47 15°. i57 8 467 Pappus, 63 Parabola, 6, 49-50, 149-50, 164, 171-2; equation of, 169-70 Paraboloid, equation of, 175-6 Paradox, Achilles and tortoise, 403; arrow, 403-4; logical, 406-8 Parallel axiom, Euclid, 411, 457; Lobatchevsky and Bolyai, 415; Rie mann, 423 Pareto, Vilfredo, 335, 353-4 Partials of a musical sound, 298-300 Pascal, Blaise, 147-50, 164, 207, 231, «67. «75. 359 61. 8бЗ-4. 369. 374-5 Pascal triangle, 364-5, 368, 371 Pascal s wager, 375 Pearl, Raymond, 335-8 Perspective, conceptual, 127-8; focused,
136-9, 143-5; mathematical, 127, 13243, 146-7, 151, 471; optical, 128-31, 57 Petty, Sir William, 343-4 Philosophy, Cartesian, 161-3; Greek. 11, 28-9, 31-4, 39, 55-8, 110; me chanical, 237-8; of science, 183-8, 198, 206-7; °։ space and time, 44950; of Age of Reason, 243-56; Ren aissance, 103-9, 132, 139-40; see also Determinism, Materialism, Statisti cal view of nature Phonodeik, 290, 303 Physiocrats, 332 Picasso, Pablo, 467 Piero della Francesca, 133, 140-41 Pitch, 298-9 Place value, 14-15, 93, 240 Plane, equation of, 175-6 Plato, 6, 24, 29, 31-3, 47, 50, 54, 61, 74, 78-80, 84, 91, 95, 114, 142, 178, 184. «13 Platonic doctrine of ideas, 32-3 Poetry, 276-84 Poincaré, Henri, 397 Politics, 323-5, 328-32, 339 Pope, Alexander, 234, 272, 275, 27881, 3««. З?6· 43« Pope Gregory XV, 235 Pope Urban VIII, 124 Population growth,· 333-7, 357 Primitive civilizations, 13 Principle of Least Action, 228-9 Principle of Least Time, 226-7 Printing, 102 Probability, theory of, 5, 361-2, 374, 377 93 Projectile motion, 6, 194-5 Projection, 135-9, 145-57
INDEX Projective geometry, 5, 144-51, 157-8, 468-9 Proof, mathematical, 27-8, 44-5, 54, 458-9 Prose, emphasis on, 276-7; style, 274 Prudhomme, Sully, 60 Pseudosphere, 421 Psychology, 238, 323, 338-9, 365 Ptolemy, Claudius, 61, 63, 72-3, 84-5, 89, in-12, 117-18, 120, 122, 143, 212, 258, 391, 428, 452, 469 Ptolemy the First, 61 Pythagoras, 6, 29, 40-41, 61, 114, 143, 287 Pythagorean theorem, 8-9, 35-6, 168 Pythagoreans, 32, 36, 40-41, 55, 75-8, 108, 123, 213, 254, 301 Q Quadrivium, 94, 287 Quality oí a musical sound, 298-300 Quantitative interpretation of nature, 78, 184-7, *։i֊ *87 Quantum theory, 452 Quesnay, François, 238, 332 Quételet, Lambert A. J., 349-50, 356 R Radar, 313-14 Radio, 311-14, 816-17; see aho Electro magnetic waves Raphael, 134, 142-3 Rarefaction, 288-90 Rational spirit, 10, 53-4, 103-4, 238-9, 286, 322-3, 330, 338 Rationalistic supernaturalism, 263 Rationalization of nature, 74-85, 1049, 126-7, ։87, 207-8, 237-8, 316-17 Rayleigh, Lord, 470 Reasoning by analogy, 25-8 Rectangular co-ordinate system, four dimensional, 177; three-dimensional, 173-6; two-dimensional, 167-9 Reed, Lowell J., 335-8 Reformation, 102-3, 1*9 Regular polygons, 47 Regular polyhedra, 47-8 483 Relativity, theory of, 173, 229, 432-52; General Theory of, 443; Special Theory of, 442 Religion, Babylonian, 23; Christian, 85; Egyptian, 19, 23; freedom of, »35-6, 269; Greek, 40; influence of rationalism on, 257-71; influence of statistical view of nature on, 388; relation to a maximum-minimum principle, 228-9; see also Christi anity Renaissance, 97, 100-109, 184, 237, 268 Revelation, 263,
265 Reynolds, Sir Joshua, 285 Ricardo, David, 334 Riemann, Bernhard, 422-7, 429, 431, 444. 45« Rigor, 229-33, 409 Rolle, Michel, 231 Rome, 11, 12, 66, 85-6, 93, 97, 287 Rousseau, Jean J., 249-50, 322-3 Royal Society, 274, 318 Russell, Bertrand, 5, 240, 403, 462, 470 S Saccheri, Girolamo, 412-14 Saint Augustine, 3, 90 Saint Thomas Aquinas, 96, 185, 258 Sampling, 371-3 Scales, equal-tempered, 301-2; musical, 287 Schoenberg, Arnold, 302 Scholastics, 96-7 Science, compared with mathematics, 10, 431; emancipation from theol ogy, 125; mathematization of, 24042, 316-17, 451-2; medieval concept of, 185; modern approach to, 18391, 198, 206-8; Renaissance concept of, 108-9, t։« Scientific laws, nature of, 377-94, 433՜ 4. 439 Sculpture, Greek, 11, 33-4, 39, 57! Roman, 34, 86 Section, 135-9, 145-57 Seurat, Georges, 467 Shaftesbury, Third Earl of, 270 Shelley, Percy B., 282 Signorelli, 134
INDEX 4 «4 Similarity, 46, 67-8 •Simultaneity, 437-4° Sine, 68, 70, 291-4, 308 Skepticism, 262, 266 Smith, Adam, 332 Snell, Willebrord, 226 Society, influence of, 5-6, 29, 101-2, 214-15 Socrates, 31, 54, 74, 142 Sound, 207, 287-303, 311-13, 385; see also Music Space, 106-7, 439: absolute, 434; de piction of, 12g; four-dimensional, 177-80; mathematical compared with physical, 428-9; relation to time, 442; three-dimensional, 129, 175; see also Dimension Space time, 179-80, 22g, 442, 445, 44g, 45» Space-time interval, 441-3 Speed, instantaneous, 216, 218 Sphere, equation of, 174; geometry on, 425-7 Squaring the circle, 50-51, 458 Stability of solar system, 208-11, 258 Standard deviation, 345-6, 369-71 Statistical view of nature, 386 Stephen, Sir Leslie, 279 Straight line, equation of, 166-7; struc ture of, 400-402 Style, mathematical, 8 Summa Theologiae, 96 Superstition, 234-5; freedom from, 269 Surface, equation of, 175 Swift, Jonathan, 30, 38, 272, 276 Symbolism, 7-8, 221 T Tangent of an angle, 68-9 Taylor, Brook, 134 Television, 315 Tennyson, Alfred, 267 Thales, 24, 40-41, 75, 305 The Harmony of the World, 120 Thomson, James, 25g Time, 106-7, 437-8, 451-2; absolute, 434- 439-4°; local, 439-40, 448; rela tion to space, 442; structure of, 402 Tintoretto, 143 Tolerance, 268-9 Topographia Christiana, 89 Trattato della Pittura, 132 Trigonometry, 10, 67-73, 84 Trisecting the angle, 50-51, 458 Tristram Shandy, 395, 405-6 Truth, 9, 160-62, 243, 389-90, 410, 42931; problem of, 243-52 U Uccello, 140 Ultra-violet rays, 315-16 Undefined concepts, 42-3, 420, 454, 460-64 Universal
laws, 212-14, 224. 226-9 Universal mathematics, 165, 239-40 Utilitarianism, 330-31 V Vanishing point, 137-9 Variable, 185 Vasari, Giorgio, 140 Volta, Alessandro, 306 Voltaire, 232, 255-6, 264-5, 328. 395 W Wallis, John, 244 Weight, 201-2, 434-5, 445-6 Wesley, John, 234, 268 Whitehead, Alfred N.. 11, 240, 450. 453· ,4θ5 Witchcraft, 234-5 Wordsworth, William, 282-4 X X-rays, 315-17 Z Zeno, 403-4 Zero, 15-16, 93
|
| any_adam_object | 1 |
| author | Kline, Morris 1908-1992 |
| author_GND | (DE-588)131716271 |
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| building | Verbundindex |
| bvnumber | BV025987947 |
| classification_rvk | SN 100 |
| ctrlnum | (OCoLC)252386211 (DE-599)BVBBV025987947 |
| discipline | Mathematik |
| edition | First issued as an Oxford University Press paperback |
| format | Book |
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| id | DE-604.BV025987947 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:40:46Z |
| institution | BVB |
| isbn | 019500714X |
| language | English |
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| physical | x, 484 Seiten, 16 ungezählte Seiten Bildtafeln Illustrationen, Diagramme |
| publishDate | 1964 |
| publishDateSearch | 1964 |
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| publisher | Oxford University Press |
| record_format | marc |
| series2 | Oxford paperbacks |
| spelling | Kline, Morris 1908-1992 Verfasser (DE-588)131716271 aut Mathematics in western culture by Morris Kline First issued as an Oxford University Press paperback London ; Oxford ; New York Oxford University Press 1964 x, 484 Seiten, 16 ungezählte Seiten Bildtafeln Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Oxford paperbacks Literaturverzeichnis Seite 473-476 Geschichte (DE-588)4020517-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Kultur (DE-588)4125698-0 gnd rswk-swf Westliche Welt (DE-588)4079237-7 gnd rswk-swf Mathematik (DE-588)4037944-9 s Westliche Welt (DE-588)4079237-7 g Kultur (DE-588)4125698-0 s Geschichte (DE-588)4020517-4 s DE-604 Erscheint auch als Online-Ausgabe, PDF 978-0-19-534545-2 Erscheint auch als Online-Ausgabe, EPUB 978-0-19-028113-7 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020371240&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kline, Morris 1908-1992 Mathematics in western culture Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd Kultur (DE-588)4125698-0 gnd |
| subject_GND | (DE-588)4020517-4 (DE-588)4037944-9 (DE-588)4125698-0 (DE-588)4079237-7 |
| title | Mathematics in western culture |
| title_auth | Mathematics in western culture |
| title_exact_search | Mathematics in western culture |
| title_full | Mathematics in western culture by Morris Kline |
| title_fullStr | Mathematics in western culture by Morris Kline |
| title_full_unstemmed | Mathematics in western culture by Morris Kline |
| title_short | Mathematics in western culture |
| title_sort | mathematics in western culture |
| topic | Geschichte (DE-588)4020517-4 gnd Mathematik (DE-588)4037944-9 gnd Kultur (DE-588)4125698-0 gnd |
| topic_facet | Geschichte Mathematik Kultur Westliche Welt |
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