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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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Space, continuity 558 Space, curvature 47—50 567 656 Space, divided into parts 555 Space, fiat 559 656—657 Space, intuition 661 665—666 Space, left and right distinction 679 Space, mathematical doctrine 648 Space, measurements 655—656 664 Space, motion, laws of 554 659 Space, perception 60 62 661 Space, point, finding position of 93 Space, point-aggregate 556—557 Space, pseudospherical 657 662 663 Space, rotation groups 721 Space, space-time 353 Space, spherical 657 663 664 666 Space, structure 681—682 695 696 Space, superposition 561 Space, symmetry 703 Space, three points in 551 Space, three-dimensional 360 557 Space, transformation 682 694 Space-filling figures 86 110 Space-filling substance, continuous motion 716 Space-relation, axioms of geometry 665 Space-relation, measurable 655 Spain, finger numerals 455—456 Spain, numerals 454 Spar, Iceland 263 Spatial existence, discontinuity 415 416 Spectrum 260 Speed and distance, law connecting 222 Speeds, simultaneous 142 Speiser, Andreas, five regular solids 720 Speiser, Andreas, Gruppen von endlicher Ordnung, Theorie der 702 Speiser, Andreas, music, mathematical treatment 703 Sphere, area 89 Sphere, concentric 96 Sphere, curvature 563 Sphere, describing 44 Sphere, elementary flatness 559 Sphere, equation 37 Sphere, Greek geometricians 11 Sphere, polyhedron formula, Euler's 585 Sphere, surface 592—593 595 651 Sphere-making (Archimedes) 179 Spherical aberration 263 Spherical space 657 663 664 666 Spherical symmetry 688 Spherical triangle 109 121 Spherical trigonometry 18 109 125 Spheroids, equilibrium of elliptical 149 Spiral, eqniangular 147 Spiral, logarithmic 716 717 Spiral, parabola 137 Spiral, tangent to 104 Square root, of two 525 Square, angles of 80 Square, describing 44 Square, half the co-efficient of x 115 Square, idea of 14 Square, incommensurable 16 Square, inverse 145 Square, numbers 84 85 Square, pattern of lines 82 Square, Pythagoras's theorem 84 Square, ratio of diagonal to side 88—89 97 Square, right-angled triangle 84 Stadia 424 Star pentagon, symbol 83 88 125 Statics 107 120 Statistical Mechanics (Fowler) 508 Staudt, Karl G.C. von, cross-ratio 639 Steam engine, invented by Hero 110 Stereometry 617 Stevin (Stevinus), Simon 120 Sticks, numeral arrangement 444 445 Stifel, Michael 120 STIRLING, JAMES 140 151 Stobaeus, Joannes, Extracts 193 212 Stout, G.F. 386 Stowe, Harriet Beecher, quoted 381 Straight line, abstract idea 14 Straight line, axioms 648 657 Straight line, continuity 528—529 Straight line, curve of the first order 113 Straight line, determining 660 Straight line, drawn across a triangle 109 Straight line, enclosing space 565 Straight line, equations 34 35 Straight line, geometry problems 239 241 243 Straight line, point in motion 665 Straight line, points on 25—26 28 33 36 63 64 528 Straight line, reflection 699 Straight line, regular equal steps 77 Straight line, velocity in 51 Straightest lines, pseudospherical surface 653—654 Straightest lines, surface 650 Strassburg Cuneiform texts 89 Stratification 95 Struik, Dirk 74 Struve, W., Mathematischen Papyrus 169 fn. Suardi, Bartolommeo (Bramantino) 606 609 Subtraction, concrete numbers 24 Subtraction, counting boards 460 Subtraction, logarithms 23 Subtraction, Roman numerals 451 Subtraction, symbol 27 28 Subtractive principle 449 Successive distances, law of 222 231—232 Sum of, symbol for 54 Sum to infinity of the series 63 Sumerians, bilateral symmetry 674 675 722 Sumerians, cuneiform numerals 443 Sumerians, numbers and numerals 430 442 Sun, diameter 421—425 Sun, planetary motion 104 110 120 144—145 Sunlight 263 Superposition, pstulate of 561—564 565 Surface, aggregate of directions 560 Surface, aggregate of points 556 Surface, applicability 337 Surface, boundary of a part of 555 Surface, curved 335—336 563 652 Surface, elementary flatness 560 561 Surface, Euler characteristic 594—595 597 Surface, genus 592—594 Surface, geodesic 564 565 Surface, geometry, Egyptian 14 Surface, one-sided 595—599 Surface, parametric representation 336 Surface, polished 566 Surface, pseudospherical 652—654 Surface, revolution, volume 111 Surface, straightest lines 650 Surface, superposition 562 Surface, theory of 160 Surface, two-dimension geometry 650 654 Surveying, early Egyptian 10 79 80 Surveying, geometry 11 Surveying, Roman 33 Svmmetry (Weyl) 671—724 Swastika 714 Swedenborg, Emanuel 274 Swift, Jonathan 26 284 539 Swift, Jonathan, quoted 489 Sylvester, James Joseph, canonical binary forms 358 Sylvester, James Joseph, commentary on 340 Sylvester, James Joseph, compound partitions 365 Sylvester, James Joseph, elliptic functions 348 Sylvester, James Joseph, invariants 163—164 341 342 348 350 Sylvester, James Joseph, Mathematical Papers 348 Sylvester, James Joseph, Mathematics, American Journal of 357 Sylvester, James Joseph, odd perfect number 506—507 Sylvester, James Joseph, quantics 355 Sylvester, James Joseph, reciprocants 363 Sylvester, James Joseph, roots of equations 145 273 364 Sylvester, James Joseph, Verse, The Laws of 354 357 Sylvester, James Joseph, Verse, The Laws of, quoted 355—356 357 363—364 Sylvester, James Joseph, “Invariant Twins” (Bell) 341—365 Sylvester, James Joseph, “On the Derivation of Co-existence” 346 Symbolic logic 378 388 397 Symbolism, analysis 67 Symbolism, calculation 28 Symbolism, economical value 16 Symbols, algebra 12 23 115 500 Symbols, brackets 27 Symbols, holy tetractys 84 Symbols, notation 114 Symbols, number 24 Symbols, Pythagorean 83 88 125 Symbols, thought-labor economy 61 Symbols, unknown quantity 116 Symmetry in Art, On the Problem of (Frey) 678 Symmetry, aesthetic value 674 Symmetry, algebra 116 Symmetry, crystals 688 712 Symmetry, cyclic 706 707 Symmetry, cylindrical 675 703 706 Symmetry, Dynamic (Hambidge) 718 fn. Symmetry, geometric 694 Symmetry, heraldic 674 675 Symmetry, hexagonal 712 Symmetry, octagonal 707 Symmetry, pentagonal 712 Symmetry, plane 706 713 Symmetry, reflexive 699 Symmetry, rotational 672 673 687—688 712 713 714 Symmetry, space 703 Symmetry, spherical 688 Symmetry, translator 699—700 702 Symmetry, translatory, rotational and related 694—724 Symmetry, two meanings 671 Tait, Peter Guthrie 719 Tangent, ellipse 107 Tangent, inverse of quadratures 55 Tangent, limit of secant 36 37 61 Tangent, to circle 37 53 Tangent, to curve 36—37 47 52 54 61 131 132 Tangent, to line circle 636—637 Tangent, to point circle 636 637 Tangent, to spiral 104 Tartatglia see “Niccolo Fontana” Taylor, Brook 78 139 151 Telegraphy, spark 219 Telegraphy, wireless, invention 9 Telekinesis 219 Telescope, Galileo's contribution 218 Telescope, reflecting 139 142 143 259 260 264 Temples, Egyptian, orientation 11 Tensor calculus 328 641 Tensors, theory of 641 Terrestrial measurements 17 Tetrachord, numerical ratios 99—100 Tetrahedron, characteristic shape of Are 96 Text-books, early 18 Thales of Miletus, biography 81 Thales of Miletus, discoveries 15 Thales of Miletus, geometry 13 14 82 90 Thales of Miletus, propositions ascribed to 81 Thales of Miletus, solar eclipse prediction 81 Thales of Miletus, triangle, measuring 17 Thales of Miletus, water philosophy 82 85 Theatetus, pentagon-dodecahedron 720 Theodorus of Cyrene, irrationals 97 Theon of Smyrna 97 207 Theoretical mechanics, text-book 267 Theorm motus (Gauss) 316 331 thermal conductivity 219 Thinking, Productive (Wertheimer) 467 fn. Thinking, unnamed 495—496 Thomas, Ivor, “Greek Mathematics” 188 189—209 Thompson, D’Arcy Wentworth, Growth and Form 708 Thompson, D’Arcy Wentworth, medusae, formation 712 Thought transference 219 Thought, function of pure mathematics 406 Thought, Laws of 68 Thought-labor, economy of 6 13 15 22 26 42—43 61 71 Thousand, Roman numeral 448 449 Three, early numeral 443 444 Three-dimensional bodies 617 Three-dimensional scenes, paintings 623 Three-dimensional space 360 Tides, theory of 268 Timaeus (Plato) 96 Time and space, infinitely divisible 41 Time, aggregate 655 Time, repetition, one-dimensional 702 Times, multiplication 24 Titchmarsh, E.C., Mathematics for the General Reader 3 Titius, J.D. 222 fn. Tone, Sensations of (Helmholtz) 643 Tones, aggregate 656 Tonstall (Tunstall) Cuthbert, Bishop 120 210 Topologie, Vorstudien zur (Listing) 571 Topology, connectivity 587—588 Topology, figures, properties of 585—592 Topology, geometry of distortion 570 Topology, Jordan curve theorem 588—590 Topology, knots 592 Topology, map, coloring 590—591 Topology, surfaces, classification 592—599 Topology, transformation 585—587 640 Transformation, concept 570 fn. Transformation, Congruent 696 Transformation, invariant 570 570 Transformation, projection and section 640 Transformation, space structure 682 694 Transformation, topological 585—587 640 Translation, congruence 697 699 Translatory symmetry 699—700 702 Transmutation of metals 272 Transposition, birds' ability to grasp 494 Trapezoids, area 174 Triangles, area, Rhind papyrus 174 175 Triangles, arithmetical 135—136 140 Triangles, differential 54 Triangles, equilateral 502 Triangles, fourth proposition, Euclid 69 Triangles, isosceles 15 81 101 175 Triangles, measuring 15 17—18 Triangles, pattern of lines 82 Triangles, polar 121 Triangles, problems, Rhind papyrus 175 Triangles, rectilinear 551 Triangles, self-dual 635 Triangles, sides 81 563 Triangles, spherical, angles 109 Triangles, straight line drawn across 109 Triangles, sum of angles 15 86 134 159 190 565 Triangular numbers 84 Trigonometry, abstract 412 Trigonometry, Indian progress 177 Trigonometry, invention 18 412 Trigonometry, logarithms 123 Trigonometry, mathematical functions 62 Trigonometry, separated from geometry 40 Trigonometry, spherical 18 109 125 Triplets, vectors 162 Tripod, rotational symmetry 714
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