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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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One-dimensional ornament 699 One-to-one correspondence 540 Ophthalmoscope, invention 643 Oppe, Paul, “Right and Left in Raphael's Cartoons” 685 Optical polishing 263 Optically active crystalline substances 680 689 Opticks (Newton) 259 260 261 263 264 269 272 Opticks (Newton), quoted 266 273 286 Optics (Kepler) 141 Optics, Newton's discoveries 258 Optics, principle of least action 110 161 Orbium Coelestium, De Revolutionibus (Copernicus) 218 232 Order functions, concept 508 Order, abstract concepts of 403 Order, theory of 508 Ordinal numbers 66 Ordinate 33 Oresme, Nicole 236 Organism, philosophy of 398 400 Organisms, ontogenesis 691—694 Organisms, phylogenesis 690—694 Oribasius 181 fn. Orientals, astronomy 14 Origin, crossing of axes 33 Origin, point of 25 Orthogonats 603—604 Oversight, dangers of 405 Palatine Anthology 207 Panofsky, Erwin, “Durer as a Mathematician” 601 603—619 Paper folding 601—602 Pappus, analysis 245 fn. Pappus, Collection 110 207 245 Pappus, curves, defining 34 Pappus, fundamental theories of geometry 16 Pappus, geometry, revival 207 Pappus, involution of six points 112—113 Pappus, isoperimetric figures 188 Pappus, porisms 102 Pappus, surface of revolution 111 Papyrus, Moscow 89 169 175 Papyrus, Rhind 11 79 89 169—178 Parabola, conic section 204 fn. Parabola, curve 34 91 Parabola, discovery 93 Parabola, focus to 108 126 Parabola, introduction of term 87 Parabola, point at infinity 127 Parabola, point in common 628 634 Parabola, pseudospherical space 662 Parabola, spiral 137 Parabolic area, circumscribing parallelogram 105 Parabolic geometry 159 Parabolic motion 49 Paradox, proving 167—168 Parallax, pseudospherical space 660 Parallel axiom 102 158 168 546 565 648 649 652—655 657 660 Parallel lines, painting 626 Parallel projection 606 613 Parametric representation 336—337 Pardies, Ignatius 260 Paris, France, Academy of Sciences 129 134 143 Particles, electrical nature 273 Partition, division 24 Partition, theory of 348 515 Pascal, Blaise, algebra 135 Pascal, Blaise, arithmetic triangle 135—136 140 Pascal, Blaise, biography 134 135 Pascal, Blaise, calculating machine 515—516 Pascal, Blaise, Christian Faith, Apologia of the 135 Pascal, Blaise, integral calculus 42 Pascal, Blaise, Leibniz, influence on 143 Pascal, Blaise, Letter Written to a Provincial, A 135 Pascal, Blaise, Nouvelles Experiences sur le vide 134 Pascal, Blaise, Pensees 135 Pascal, Blaise, projective geometry 133 359 629—630 631 640 641 Pascal, Blaise, projective geometry, dual statement of 637 Pascal, Blaise, quoted 136 Pascal, Blaise, “L’hexagramme mystique” 134 151 Past and future, equivalence 686 Pasteur, Louis, crystals, reproducing 688—689 690 Pattern of relationships, abstract conditions 407 Pattern, number 136 Peano, Giuseppe, symbolic logic 378 388 397 Peano, Giuseppe, vocabulary of arithmetic 390 Peckham, perspective 605 Peirce, Charles Sanders, abstract algebra 76 164 Pemberton, Henry 261 265 269 Pensies (Pascal) 135 Pensies (Pascal), quoted 136 Pentagon, angles 86 208 Pentagon, Durer's construction 615 Pentagon, Euclidean construction 502 Pentagon, Great Pyramid 80 Pentagon, ladder-arithmetic 98 Pentagonal symmetry 712 Pentagondodecahedron, discovery 719—720 Pentagram, Dr. Faust's 697 Perfect numbers 101 498 506 Perfect proportion 89 Pericles 91 Periodicity, theory of 411—412 416 Persians, numerals 443 Perspectiva, De artificiali (Pelerin) 604 Perspective picture, construction 610—611 Perspective, mechanical means 609—610 Perspective, projective geometry 107 Perspective, scientific theory 603 Pfaff, Johann Friedrich 156 307 316 Phaedrus (Plato), quoted 79 Phenotypical inversion 694 Phidias 103 418 421 Philolaus, treatise on mathematics 83 Philosophy, arithmetic needful to 215 Philosophy, idealistic movement 412 Philosophy, mathematicians 27 Philosophy, modern, beginning 129 Philosophy, relation to social conditions 393 Philosophy, revision by Descartes 132 Phyllotaxis 718 719 Phyllotaxis, Relations to Mechanical Laws (Church) 719 Physical science, Aristotelian Logic 409 Physical science, beginning 120 Physical science, invariance 353 Physics, arithmetic needful for 214 Physics, differential equations 325 Physics, mathematical 52 399 Physiological Optics (Helmholtz) 643 644 Piazzi, Giuseppe 313 Pillai, S.S., Waring problem 515 Pisa, leaning tower, rotary symmetry 705 Pitch, optical polishing 263 Plane Equilibriums, On (Archimedes) 195 Plane geometry, axiomatic system 568 Plane geometry, rotational group of order n 719 Plane mirrors, reflecting 110 132 153—154 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, reflection in 682 Plane, rotations, finite groups 713 719 721 Plane, symmetry 706 713 Planetarium, miniature built 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 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, Copernican system 120 221 Planets, distances from sun 221 fn. Planets, eighth, search for 314 Planets, equilibrium of spinning 152 Planets, orbits, computing 313 Planets, Ptolemaic system 221 Planets, times and distances connected 218 Planets, tunes 127—128 Plasma, bipotentiality 694 Plato, Academy in Athens 95 Plato, analysis, method of 245 fn. Plato, cardinal integers 389 Plato, geometrical analysis 16 245 Plato, geometry, views on 96 Plato, lecture on the Good 192 Plato, logarithmic series 138 Plato, mathematics, philosophy of 188 193 Plato, mechanical instruments, use of 15 181 Plato, quoted 79 720 Plato, Republic 188 193 Plato, science, practical application of 15 Plato, stratification 95 Plato, symmetry, origin 674 Plato, Symposium 688 Plato, Timaeus 96 Plato, treatise by Philolaus 83 Platonic solids 719 720 Plucker, Julius 359 Plurality 537 Plutarch 103 179 189 190 Plutarch, quoted 15 82 180—185 Poe, Edgar Allen, quoted 568 Poetry, metrics in 703 Poincarl, Henri, axioms of geometry 645 fn. Poincarl, Henri, quoted 402 Point-event, line intersections 352 Points and lines, reciprocation 112 Points, aggregates 562 563 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, direction from 560 Points, geometrical 37 Points, intersection 36 93 Points, involution 112 Points, lines composed of 42 Points, measurements of position 656 Points, measuring distance between 660 Points, moving 17 19 20 82 Points, parallel lines 628 634 Points, shortest line between 651 654 Points, straight line 25—26 28 33 36 63 64 528 Points, two-dimensional manifold 336 Points, vertices 572 Polar axis, egg 691 Polar triangle 121 Polarization phenomena 263 Pole, W. 486 Political verse, Byzantine 187 fn. Polybius 181 fn. 182 Polygon 40—41 56 107 208 303 502 719 Polygonal Numbers (Diophantus) 114 Polyhedra tabulation 723 Polyhedron, Eider's formula 571 581—585 Polykleitos, symmetry 671 671 713 Polynomial, graph 309 Poncelet, Jean Victor 91 359 631 632 Pope, Alexander, quoted 295 Poppy seeds and large numbers, commentary on 418—419 Poppy seeds and the universe 420—425 Porisms (Diophantus) 114 Porisms (Euclid) 102 Portsmouth Papers 274 284 Position, change of 64 fn. Position, geometry of 573 Positive and negative electricity, equivalence 686 Positive numbers 27—28 34 65 96 Postulates, reasoning pattern 407—408 Powers, symbol 23 Pre-linguistic thinking 495—496 Predicting future events 43 44 Prime numbers 101 157 501 505—508 Primes, rational 512 Principia (Newton) 62 144 145 257—259 264 268 269 272—275 279 280 282 284 286 Principia (Newton), quoted 265—266 267 Principia Mathematica (Russell — Whitehead) 378 388 389 390 392 397 Prisms, volumes 174 Probability, study of 236 Problems, cat and grain 175—178 Problems, cattle problem 105—106 116 188 197—198 207 418 Problems, loaves and men 172—174 Problems, Mother Goose rhyme 178 Problems, Rhind papyrus 79 171—178 Process and Reality (Whitehead) 398 Proclus, Euclid 189 190 Proclus, quoted 96 Progression, arithmetical and geometrical 123 Progression, harmonical logarithms 137 Projection and section 623—639 Projection, method of 134 Projection, parallel 606 Projective geometry, analytical 638 Projective geometry, creation 359 Projective geometry, Desargues' theorem 627—628 629 631 Projective geometry, dual statement of 635 Projective geometry, duality, principle of 634—638 Projective geometry, Euclidean geometry, relationship 638 640 Projective geometry, Kepler 133 Projective geometry, neglect 631 Projective geometry, new theorems, discovery 638 Projective geometry, parallel lines 628—629 634 Projective geometry, Pascal's theorem 629—630 631 Projective geometry, Pascal's theorem, dual statement of 637 Projective geometry, perspective 107 Projective geometry, porisms 102 Projective geometry, sections, common geometrical properties 626 Prolixity, mathematics 38 Proof, analytical method 16 Proof, binomial theorem 299 Proof, by congruence 650 Prophecies of Daniel and the Apocalypse of St. John, Observations upon (Newton) 274 Proportionality, triangle 18 Proportions, mechanics 50 Proportions, notion 82 Proportions, theory of 99 191 525 Proportions, two mean lines of 181 Propositional function 70 Propositions, true 11 Protons, electrons 415 Protons, positively charged 686 Pseudospherical space 657 660 662 663 Pseudospherical surface 652—654 Pterin, Jean, De artificiali Perspectiva 604 Ptolemy of Alexandria, Almagest 109 Ptolemy of Alexandria, circular motion 96 Ptolemy of Alexandria, founder of Alexandria library 100 Ptolemy of Alexandria, Harmonics 232 Ptolemy of Alexandria, planetary motion 109 110
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