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Newman J.R. (ed.) — The World of Mathematics, Volume 4
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Íàçâàíèå: The World of Mathematics, Volume 4Àâòîð: Newman J.R. (ed.) Àííîòàöèÿ: Volume 4 of a monumental 4-volume set covers such topics as mathematical machines, mathematics in warfare, a mathematical theory of art, mathematics of the good, mathematics in literature, mathematics and music, and amusements, puzzles, and fancies. Individual contributions by A. M. Turing, Aldous Huxley, Sir James Jeans, Lewis Carroll, and other notables. Informative commentary by noted mathematics scholar James R. Newman precedes each essay. Numerous figures.
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Phaedrus (Plato), quoted 79 Phenotypical inversion 694 Phidias 103 418 421 Philip uI (king of Spain), offer for discoverer of longitude measurer 781—782 Phillips, H.F. 1018 fn. Phillpotts, Eden, quoted 2369 Philo of Megara 1916 fn. Philolaus, treatise on mathematics 83 Philosophic der Griechen (Zeller), quoted 1555 Philosophical atheists 2376—2378 Philosophy and the Physicists (Stebbing) 1049 fn. 2276 Philosophy, arithmetic needful to 215 Philosophy, idealistic movement 412 Philosophy, mathematical 1580 Philosophy, mathematicians 27 Philosophy, modern, beginning 129 Philosophy, Principles of (Veitch) 2350 fn. Philosophy, relation to social conditions 393 Philosophy, revision by Descartes 132 Phon, scale of loudness 2305 Phosphorus, discovery 923 Photographs, breaking soap bubbles 896 Photometric Researches (Peirce) 1768 Phrenology 1149 Phyllotaxis 718 719 Phyllotaxis, Relations to Mechanical Laws (Church) 719 Physical Geography (Somerville) 2349 fn. Physical geometry 2035 Physical science, Aristotelian Logic 409 Physical science, beginning 120 Physical science, invariance 353 Physical Science, The Growth of (Jeans) 2277 Physical Science, The Philosophy of (Eddington) 1069 fn. Physical Sciences, The (Bragg) 1048 fn. Physical Sciences, The Connection of the (Somerville) 2349 fn. Physical World, The Nature of the (Eddington) 1050 fn. 1091 Physics, analysis, applications 1330 Physics, arithmetic needful for 214 Physics, differential equations 325 Physics, economy of thought 1792 Physics, History of (Von Laue) 851 fn. Physics, indeterminacy, principle of 1469 Physics, mathematical 52 399 1402 Physics, On Understanding (Watson) 1049 fn. Physics, probability calculus 1403 Physics, quantitative and qualitative assertions 1071—1072 Physics, the Elements (Campbell) 1796 Physics, theoretical, mathematics 2061—2063 Physics, universal 1742—1744 Physics, work done by a body 1399 1400 Physiological Optics (Helmholtz) 643 644 Physique of Young Males, The (Martin) 1505 Piaggio, H.T.H. 1092 Piazzi, Giuseppe 313 Picard, Abbe Jean 787 788 792—793 803 Picot, George 786 fn. Pigafetta, Antonio, navigation 780 789 Pilgrim’s Progress (Bunyan) 952 Pillai, S.S., Waring problem 515 Pisa, leaning tower, rotary symmetry 705 Pitch, optical polishing 263 Planck, Max 874 1203 Planck, Max, quantum theory 841 974 976 1048 1089 2467 Plane Equilibriums, On (Archimedes) 195 Plane geometry, axiomatic system 568 1640—1641 1651 1672—1673 Plane geometry, rotational group of order n 719 Plane mirrors, reflecting 110 132 153—154 Plane, at infinity 1702—1706 Plane, complex numbers 31 Plane, curve 31—32 37 151 344 Plane, figure, rotation 659 Plane, figures, disentangling 133 Plane, geodesic surface 564 Plane, point, determining 61 Plane, problems 91 Plane, projective geometry 1551—1552 Plane, reflection in 682 Plane, rotations, finite groups 713 719 721 Plane, surfaces, motions on 729 740—742 746—747 Plane, symmetry 706 713 Planetarium, nainiature buu4 by Archimedes 179 Planetary motion, Aristarchus’s hypotheses 104 109 418—419 420 Planetary motion, cause 223 Planetary motion, circular 96 126 227 Planetary motion, ellipse 126 218 1102 Planetary motion, Eudoxus’ theory 96 Planetary motion, Greek astronomy 14 Planetary motion, inertia, law of 52 Planetary motion, Kepler’s laws 126 132 218 220—234 257 266 412 Planetary motion, Newton’s theories 140 144—145 267 Planetary motion, predictions 44 Planetary motion, Rudolphine tables 225 232—233 Planetary motion, vortices, theory of 132 Planets, Bode’s law 221—222 fn. Planets, concentric sphere theory 96 Planets, Coperaican system 120 221 Planets, distances from sun 221 fn. Planets, eighth, search for 314 Planets, elliptic orbit 823—824 Planets, equilibrium of spinning 152 Planets, minor, distribution 1382—1383 1387 Planets, orbits, computing 313 Planets, perturbations 1317—1318 Planets, Ptolemaic system 221 Planets, speeds 1098 Planets, times and distances connected 218 Planets, tunes 127—128 Planisphere, Paris Observatory 794 Plank, Stephen 806 Plant-hybridization, experiments in 937—938 Plants, experimental, selection of 938—939 Plants, hybrids 940—941 Plants, mental life 1151 Plasma, bipotentiality 694 Plateau, Felix, Insect strength 1014 Plateau, Joseph Antoine Ferdinand, soap bubbles, geometrical construction 898 Plateau, Joseph Antoine Ferdinand, Statique des Liquides 898 Plateau, Joseph Antoine Ferdinand, surface tension, soap bubbles 891 Plateau’s problem 884 885 887 901—909 Platinum, discovery 923 Plato, Academy in Athens 95 Plato, analysis, method of 245 fn. 1991 Plato, anamnesis 1601 Plato, cardinal integers 389 Plato, cubes, solid 872 Plato, Euclid’s geometry 1295 Plato, geometrical analysis 16 245 Plato, geometry, views on 96 Plato, lecture on the Good 192 Plato, logarithmic series 138 Plato, mathematics, abstraction 1774 Plato, mathematics, philosophy of 188 193 Plato, mechanical instruments, use of 15 181 Plato, metaphors 1308 Plato, quoted 79 212 Plato, Republic 188 193 Plato, science, practical application of 15 Plato, stratification 95 Plato, symmetry, origin 674 Plato, Symposium 688 Plato, Timaeus 96 2325 Plato, treatise by Philolaus 83 Plato, universal cycle, doctrine 1455 Plato, “saving the phenomena” 727 Platonic solids 719 720 Playing cards, shuffling 1385 1387—1388 1461 Pluecker, Julius 359 Plurality 537 Plutarch 103 179 189 190 Plutarch, quoted 15 82 180—185 Poe, Edgar Allen, quoted 568 Poetry, metrics in 703 Poincare, Henri, axioms of geometry 645 fn. 2355 Poincare, Henri, commentary on 1374—1379 Poincare, Henri, conventionalism concerning geometry 1644—1646 Poincare, Henri, culture change and growth, process of 2361 Poincare, Henri, elliptic functions 1375 Poincare, Henri, fluid, gravitating mass in rotation 1377 Poincare, Henri, Fuchsian functions 1377 2044—2045 2361 Poincare, Henri, group theory 1552 Poincare, Henri, mathematical invention 2360 Poincare, Henri, publications 1375 Poincare, Henri, quoted 402 1378 1558 1668 Poincare, Henri, Science et Methode 2321 fn. Poincare, Henri, space 1607 Poincare, Henri, “Chance” 1380—1394 Poincare, Henri, “Mathematical Creation” 1377 2041—2050 Point set, dimensionality 1971—1972 Point set, theory of 1941—1945 Point-event, line intersections 352 Points and lines, reciprocation 112 Points, aggregates 562 563 Points, at infinity 1701—1706 Points, axioms 1588 Points, between zero and one 1060—1061 Points, boundaries of part of a line 555—556 Points, circle, tangents to 636 637 Points, co-ordinates 658—659 Points, collinearity 638 Points, congruent pairs 658 Points, continuum 1840—1841 Points, curve 889—890 Points, direction from 560 Points, functions 887 Points, geometrical 37 Points, in space 1942 Points, intersection 36 93 Points, involution 112 Points, line composed of 42 Points, measurements of position 656 Points, measuring distance between 660 Points, moving 17 19 20 82 1203—1204 1959—1960 1964 1965—1966 Points, on a curve 1972—1973 Points, parallel lines 628 634 Points, positions in space 2334 Points, saddle 1272—1273 1275 Points, shortest line between 651 654 Points, straight line 25—26 28 33 36 63 64 528 Points, two-dimensional manifold 336 Points, value variations 1206 Points, vertices 572 Poisson distribution 1257—1258 1259 Poisson, Simeon Denis, biography 2419 Poisson, Simeon Denis, large numbers, law of 1448 1450 Poisson, Simeon Denis, Petersburg Paradox 1368 1370 Poker, strategic determination 1264 Polanyi, M. 979 Polar axis, egg 691 Polar triangle 121 Polarization phenomena 263 Pole star, latitude, reckoning 778 Pole, W. 486 Political arithmetic 1416 Political Arithmetic (Buffon) 1333 Political economy, distribution of commodity 1228—1229 Political economy, disutility and discommodity 1227—1228 Political economy, economics, relation to ethics 1221 Political economy, exact measurement 1219 Political economy, exchange, theory of 1231—1235 Political economy, feeling and motives, measurement 1219—1220 Political economy, indifference, law of 1229—1231 Political economy, labor, theory of 1235—1237 Political economy, mathematical and exact sciences, confusion between 1218—1219 Political economy, mathematical character 1217—1218 Political Economy, Principles of (Mill) 1234 fn. Political economy, symbolic statement of theory 1233—1235 Political Economy, The Theory of (Jevons) 1202 1217—1237 Political economy, utility, theory of 1222—1235 Political science, economics, logical method 1220—1221 Political verse, Byzantine 187 fn. Politics, content-analysis techniques 1312 Pollen-grains, magnitude 1038 1038 Polya, George, commentary on 1979 Polya, George, How to Solve It 1978—1992 Polya, George, symbolism 1853 Polybius 181 fn. 182 Polygon 40—41 56 107 208 303 502 719 2389 Polygonal Numbers (Diophantus) 114 Polyhedra tabulation 723 Polyhedron, Euler’s formula 571 581—585 Polykleitos, symmetry 671 671 713 Polynomial, graph 309 Poncelet, Jean Victor 91 359 631 632 Pope, Alexander, quoted 295 1074 1094 1576 2268 2412 Popoff, M. 1032 fn. Poppy seeds and large numbers, commentary on 418—419 Poppy seeds and the universe 420—425 Population and food, mathematics of 1193—1197 Population As It Affects the Future Improvement of Society, Principle of (Malthus) 1189—1190 Population, checks to 1197—1199 Population, equilibrium 967—968 Population, increase 1189 1190 1194 1196—1197 Porisms (Diophantus) 114 Porisms (Euclid) 102 Porson, Richard 1179 Port Royal Logic 1361 1372 Portsmouth Papers 274 284 Portugal, Bull of Demarcation 781 Poseidonius, earth, measurement 792 Position, change of 64 fn. Position, geometry of 573 Positive and negative electricity, equivalence 686 Positive numbers 27—28 34 65 96 Positivism 1733 1784 Positivism (von Mises) 1617 Possibility, mathematics of 1322 Postulates, reasoning pattern 407—408 Postulational system 1295—1296 Potential, dynamical concept 1835 Potter, George Reuben, “Swift and Natural Science” 2212 fn. Poultry, broodiness 969 Pound, Roscoe 2206 Powder grains suspended in water 1385 1388 Powers, symbol 23 Pragmatism 1307 1769 Prasad, Ganesh 1374 fn. Pre-linguistic thinking 495—496 Precision, limits 1048 Predicate, quantified 1862—1863 Predicting future events 43 44 Prepositional calculus 1910 Preston, Thomas, Light, The Theory of 882 fn. Prevost, Pierre 1005 fn. Prichard, J.C. 2359 Primary matter 918 Prime numbers 101 157 501 505—508 1678—1679 Prime numbers, infinity of 2030 2033 2437 Primes, rational 512 Primitive propositions 1895—1896 Principia (Newton) 62 144 145 257—259 264 268 269 272—275 279 280 282 284 286 1307 1648 1725 2055 Principia (Newton), quoted 265—266 267 Principia Mathematica (Russell-White-head) 378 388 389 390 392 397 1668 1678—1681 1855 1874 1875 1894—1900 1953 Principia Mathematica (Russell-White-head), Goedel’s Proof 1685—1695 Principia Mathematica (Russell-White-head), theorems 1894—1900 Principles, calculus of probabilities 1329—1333 Prisms, volumes 174 Probabilism, Jesuit doctrine 1360—1361 Probabilites, Calcul des (Bertrand) 1380 Probabilities, A Philosophical Essay on (Laplace), quoted 1047 Probabilities, Letters on (Quetelet) 1181 1183
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