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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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47 54 55 89 92 104 108 121 138 150—151 166 168 477 510 514 525 abacus 13 fn. 441 456—458 461 463 Abacus, The Ancient Peruvian (Wassen) 463 fn. Abbreviated construction, Italian painters 607 609 Abel, Niels Henrik 59 78 120 299 306 331 344 Abscissa 33 Absolute space 360 Abstract ideas, early societies 402 Abstract numbers 24 Abstraction, extensive 399 399 Achilles, race with tortoise 41 94 138 Activating optically inactive material 689 Addition, concrete numbers 24 Addition, direction of 460 Addition, generalization of number 30—31 Addition, logarithms 23 Addition, Roman numerals 451 Addition, series, numbers 63 Addition, symbols 27 28 Additive theory of numbers 515 Aerodynamics, conformal mapping 337 Aesthetic Measure (Birkhoff) 671 fn. 703 Aesthetic value of symmetry 674 Africa, mathematical learning 100 Age and Achievement (Lehman) 467 fn. Aggregate, continuous and discrete 557—559 Aggregate, directions 560 Aggregate, n dimensions 655 Ahmes (A‘h-mose) 78 Ahmes (A‘h-mose), arithmetical problems 12—13 Ahmes (A‘h-mose), geometrical analysis 16 Ahmes (A‘h-mose), letter signs 22 Ahmes (A‘h-mose), mathematical competence 171 Ahmes (A‘h-mose), Rhind papyrus 79 170 Air, characteristic shape 96 Airy, Sir George 268 Alberti, Leone Battista 603 606 607 609 616 Alexander of Macedonia 100 117 Alexander, History of (Anticleides) 189 Alexander, J.W. 339 Alexandria, Egypt 100 102 117 Alexandrian Museum 552 Alexandrian School, Second 109 Algebra, abstract 499 Algebra, classification 76 115 Algebra, Diophantus' invention 16 22 Algebra, division by zero 293 fn. Algebra, fundamental theorem 308 Algebra, geometry, application to 61 82 130 Algebra, higher 136 Algebra, logical 163 397 Algebra, matrices 361—362 Algebra, negative quantities 33 Algebra, notation 23—27 31 32 92 120 500 Algebra, quaternions 76 161 162 163 Algebra, reduction and cancellation, science of 117 Algebra, symbolic logic 396 Algebra, Universal (Whitehead) 396 399 Algebraic curves 131 Algebraic equations 509 Algebraic integers 511 Algebraic invariants 350 Algebraic letters, arguments 411 Algebraic numbers 313 326 499 511—514 Algebraic spectrum of the quantic 355 Algorithm, Euclidean 513 Alkarismi (Mohammed ben Musa) 23 Almagest (The Great Compilation), Ptolemy 109 Alphabetical numeration 22 99 Ampere, Andre Marie 465 470 Amthor, A. 197 fn. 198 Analogue computers 518 Analogue, two-dimensional 723 Analysis situs 334 338 339 570 Analysis, indeterminate 197 207 Analysis, mathematics 165 299 323—324 Analyst, The (Berkeley) 286—293 Analytic Engine, digital computer 517 Analytic functions, complex variable 323 Analytic theory of numbers 499 507 508 Analytical Calculation, Principles of (Woodhouse) 291 fn. Analytical geometry 17 31—43 56 112 116 129 133 155 235—237 359 411 631 Analytical Society, Cambridge University 517 Analytische Zahlentheorie (Bachmann) 508 Anatolius, Bishop of Laodicea 113 Anaxagoras 78 91 Anderson, Janet (Mrs. John Gregory) 139 Andrade, E.N. da Costa, “Isaac Newton” 255—276 Angle, abstract idea 14 Angle, magnitudes 561 563 Angle, measuring 660 Angle, solid 560 Angle, trisecting 90 113 121 139 Anhalt Dessau, Princess of, Euler's letters to 149 Animal Heat, Theory of (Helmholtz) 643 Animals, attainment of objectives 9 Animals, bilateral symmetry 686—688 707 Animals, counting ability 433 488 Animals, learning capacity 489—496 Anticleides 189 Apollodorus 189 Apollonius of Perga, biography 107 Apollonius of Perga, conic sections 103 107—108 112 126 200—205 Apollonius of Perga, curves 87 163 Apollonius of Perga, locus ad tres et quattuor lineas 108 112 130 Apollonius of Perga, shortest distance, point to ellipse 131 Apollonius of Perga, spherical trigonometry 109 Apollonius of Perga, Unordered Irrationals 108 Applied Mathematics, Elements of (Cobb) 72 Applied mathematics, Rhind papyrus 11—12 Approximative calculation 508 Arabic notation 13 117 410 Arabic Numerals in Europe, The Development of (Hill) 454 fn. Arabs, decimal numeration 23 122 Arabs, mathematical science 118 Arabs, mathematical text-books 18 Arabs, numerals 443 Arabs, perspective 605 Arabs, Ptolemy's astronomy 109 Arbitrary constants 35 Arbitrary functions, co-ordinates, use of 236 Arc, fluent of velocity 58 Archibald, R.C. 718 fn. Archimedes, axiom 77 99 106 126 152 Archimedes, cattle problem 105—106 116 188 197—198 207 418 Archimedes, commentary on 179 Archimedes, death 103—104 179 185 Archimedes, decimal notation 328 Archimedes, differentials 56 Archimedes, distances, expressing 25 Archimedes, earth, diameter 421—425 429 Archimedes, exhaustions, method of 92 Archimedes, floating bodies 199 Archimedes, fractions 172 Archimedes, Hiero's golden crown 185—186 188 Archimedes, infinitesimals 41 95 163 Archimedes, integral calculus 90 103 104 135 Archimedes, inventions 15 Archimedes, lever, principle 188 Archimedes, mathematics, autonomous science 315 327 Archimedes, Method 94 104 Archimedes, military machines 103 179 180 181—182 187 Archimedes, numbers, orders and periods 425—426 Archimedes, octads 418 426 Archimedes, Plane Equilibriums, On 195 Archimedes, planetarium 179 Archimedes, planetary motion 421 Archimedes, Plutarch, quoted on 180—185 Archimedes, pure mathematics 295 Archimedes, results, methods of achieving 105 Archimedes, Sand-Reckoner 106—107 418 420—429 Archimedes, solids, semi-regular 127 207 Archimedes, Sphere-making, On 179 Archimedes, spiral 104 137 Archimedes, sun, diameter 421—425 Archimedes, The Works of (Heath) 181 fn. 197 198 Archimedes, tomb 184 184 502 Archimedes, Tzetzes, quoted on 187 Archimedes, Vitruvius, quoted on 185—186 Architecture, On (Vitruvius), quoted 185—186 Architecture, symmetry 700 705 713 Archytas of Tarentum 14 78 90 96 Archytas of Tarentum, biography 93 Archytas of Tarentum, mechanics 15 94 180 Archytas of Tarentum, music intervals 99—100 Areas, method of application of 86—87 190 205 Aristarchus of Samos, planetary motion 104 109 418—419 420 Aristarchus of Samos, sun, diameter 421 Aristophanes, transition from spherical to bilateral symmetry 688 Aristotle, celestial bodies, spherical shape 672 Aristotle, continuity 557 558 Aristotle, irrational numbers 88 Aristotle, logic 409 Aristotle, man's ability to count 488 Aristotle, Nicomachean Ethics 671 Aristotle, origin of mathematics 79 Aristotle, planetary motion 226 228 Aristotle, Plato's lecture on the Good 192 Aristotle, quoted 85 93 170 Aristotle, science of reasoning 6 Aristotle, velocity 52 Aristoxenus, Elements of Harmony 192 Arithmetic, Arabic, introduction to Europe 18 Arithmetic, geometry, application 25 189 Arithmetic, histories 430 Arithmetic, ladder 97—98 104 138 Arithmetic, mental 465 467 Arithmetic, mysteries of 497 Arithmetic, progression 84 87—88 Arithmetic, Queen of Mathematics 294 498 Arithmetic, rational, fundamental theorem 512 Arithmetic, symbols 24 Arithmetic, triangle 135—136 140 Arithmetica (Diophantus) 114 509 Arithmetica Infinitorum (Wallis) 520 522 Arithmetica Universalis (Newton) 145 Arithmetica, Rara (Smith) 210fn. 211 Arithmeticae, Disquisitiones (Gauss) 305 306 307 309—312 315 321 325 327 333 498 Arithmetick, Grundgesetze der (Frege) 389 537 Arithmetick, Grundlagen der (Frege) 537 Armenia, abacus 458 Ars Magna (Lull) 119 Art and Nature, Mysteries of (Bates) 255 Art, bilateral symmetry 673 674 678—679 Artillery, Napier's invention 122 Arya-Bhata 78 117 Assemblages, theory of 167 Astronomical instruments, Brahe's invention 218 Astronomy, Archimedes' Sand-Reckoner 106—107 418 420—429 Astronomy, Copernicus's theory 120 Astronomy, Greek 14 89 Astronomy, Kepler's laws 126 Astronomy, logarithms 123 Astronomy, mathematical 315 Astronomy, Oriental 14 Astronomy, physical, Kepler founder of 218 Astronomy, practicable science of 6 Astronomy, Ptolemy's work 109 Astronomy, theoretical 52 58 Astronomy, universal gravitation 142 Asymmetry, absence of symmetry 676 678 Asymmetry, decisive factors 694 Asymmetry, historic 679 Athenaeus, helix 181 fn. Athene (goddess), attachment of seven 85 Athens, intellectual center 90 Athens, Plato's Academy 95 Atomic chemistry 154 Atomic theory, origin 94 Atoms, heart-beats 164 Atoms, periodicities 416 Attraction, law of 61 Aubry, M. 243 fn. Aurea sectio 719 Ausdehnungslehre (Grassmann) 396 Australia, native races’ number knowledge 432 Automorphism 682 695—696 697—698 Axioms, geometrical 647—668 Axis (co-ordinate) 32—33 64 Babbage, Charles, calculating machine 517 Babylon, counting 99 Babylon, numerals 443 444 Babylon, quadratic equations 89 Babylon, subtraction 449 Babylon, symmetry, seal stones 675 Bachmann, P., Analytische Zahlentheorie 508 Bacon, Roger, optical instruments 605 Bagehot, Walter, quoted 75 Bailey, Herbert W., Jr., “Topology” 572 fn. Ball, W.W. Rouse, Mathematical Recreations and Essays 243 fn. 466 Ball, W.W. Rouse, Mathematics, History of 71 74 305 Ball, W.W. Rouse, quoted 75 Ball, W.W. Rouse, “Calculating Prodigies” 467—487 Banach spaces 77 Band ornaments, motif 702 Band ornaments, symmetry 677 699 700 703 715 Barometer 134 Barrow, Isaac, differential triangle 54 55 Barrow, Isaac, Lectiones Geometricae 139 Barrow, Isaac, Lectiones Opticae 256 Barrow, Isaac, light, lectures on 258 Barrow, Isaac, Newton's genius 141 256 259 Barrow, Isaac, tangents to curves 53 Bartels, Johann Martin 298 300 Barycentric calculus 162 Basis Theorem 164 Basket, area 169 fn. Bates, John, Art and Nature, Mysteries of 255 Bees, communication 488 Bees, honeycomb construction 110 188 207 208—209 Bell, Eric Temple, biography 294 Bell, Eric Temple, number concept 526 Bell, Eric Temple, “Invariant Twins, Cayley and Sylvester” 341—365 Bell, Eric Temple, “Mathematics-Queen and Servant of Science” 497 Bell, Eric Temple, “Prince of Mathematicians, The” 295—339 Bell, Eric Temple, “Queen of Mathematics, The” 498—518 Bellamy, Elizabeth W. 436 fn. Beltrami, E., surface curvature 652 654 657 662 Benedetti, pentagon 615 Benz, Friederich 296 Berkeley, George, Bishop, commentary on 286—287 Berkeley, George, Bishop, Free-Thinking in Mathematics, A Defense of 287 Berkeley, George, Bishop, infinitesimals 57 152 286—293 Berkeley, George, Bishop, “Analyst, The” 286—293 Bernoulli, Daniel 148 149 Bernoulli, Jacob (James), tombstone 716—717 Bernoulli, John, analysis 147—148 Bessel, Friedrich Wilhelm 140 319 321 323 Bibliography, birds, ability to count 496 Bibliography, “Mathematics, The Nature of” 71—72 Bidder, George Parker, mental calculations 221 465 472—475 479 Bidder, George Parker, processes 480—486 Bifilar magnetometer 327 Bilateral symmetry, animal kingdom 686—688 707 Bilateral symmetry, human body 671 674 686—687 Bilateral symmetry, reflections or rotations 672 724 Billion, use of term 450 455 Binary scale 122 516—517
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