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Newman J.R. — The World of Mathematics, Volume 1
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Íàçâàíèå: The World of Mathematics, Volume 1Àâòîð: Newman J.R. Àííîòàöèÿ: 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.
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Triquetrum, magic symbol 714 Troll, W. 702 fn. Tube, volume 111 Tucker, Albert S., “Topology” 572 fn. Turkey, abacus 458 Turnbull, Herbert Westren, Great Mathematicians, The 75—168 Turnbull, Herbert Westren, Greek mathematics, survey 188 Turnbull, Herbert Westren, Mathematical Discoveries of Newton, The 520 fn. Turnbull, Herbert Westren, quoted 74 341 Turnbull, Herbert Westren, “Newton: The Algebraist and Geometer” 519 fn. Two, early numeral 443 Two-dimension geometry 650 654 Two-dimensional manifold 336 Two-dimensional surfaces 592 Twyman, Frank 263 Tyler, Edward Burnett, Primitive Culture 433 439 Tyndall, John 219 Tzetzes, John 179 181 Tzetzes, John, quoted 187 Uccello, Paolo 607 Uhler, H.S. 505 Ulfilas, Bishop 452 Umkiappungen 722 724 Uniform acceleration 48—49 Uniform convergence 108 Unit fractions 171 172 Unity, number 95 Universality and exactness, connection between 551 Universals, problem of 390 Universe, diameter 422—425 428 429 Universe, mathematical harmony 720 Universe, symbol of 101 Universe, system of 153 Unknown quantities, symbols for 28—29 116 Unnamed numbers 491 492 494 495 Unnamed thinking 495—496 Unordered Irrationals (Apollonius) 108 Uranus, discovery 313 Valuation, theory of 77 Van der Waerden, B.L. 169 fn. Vandiver, H.S. 510 Variable, behavior 132 Variable, dependent 39 Variable, differentials 55 Variable, equant 227 Variable, function 22 29 32 38 70 411 Variable, infinitesimal calculus 56 Variable, modern mathematics 19 Variable, notation 130—131 Variable, notion of 407 Variable, spheres 37 Variations, calculus of 111 153 267 274 Veblen, Oswald, analysis situs 339 Vectors 162 697 Velocities and times, multiplying 50 Velocity, curve 47—50 61 Velocity, dimensions and acceleration 51 Velocity, falling bodies 45—47 548 549 Velocity, fluxions 58 Velocity, straight line 51 Verification, process 405 Verse, The Laws of (Sylvester) 354 357 Viator, Johannes 604 Vibrations, theories of 412 415 Vieta (Viete), Francois, algebraic symbolism 115 Vieta (Viete), Francois, duality, principle of 121 Vieta (Viete), Francois, formula for 138 Vieta (Viete), Francois, modern mathematics 20 Vieta (Viete), Francois, symbolic algebra 115 120 236 249 Vinogradov, I.M., prime numbers 508 Vinogradov, I.M., Waring problem 515 Vision, Euclidean theory 605 Visual angle 605 Visual images, pseudospherical space 662—663 Visual sensation, one eye 624 Vitellio, Erasmus, perspective 605 Vitruvius 179 181 200 615 671 113 Vitruvius, quoted 185—186 Voltaire, quoted 145 180 268 284 von Frisch, Karl 488 von Goethe, Johann Wolfgang, Faust 271—272 von Goethe, Johann Wolfgang, Faust, spiral tendency in nature 718 von Goethe, Johann Wolfgang, Faust, tails of vertebrates 702 von Grafe, A. 643 fn. von Helmholtz, Hermann, Axioms of Geometry, The 550 fn. von Helmholtz, Hermann, commentary on 642—646 von Helmholtz, Hermann, energy, conservation 643 von Helmholtz, Hermann, geometry, assumptions 550 von Helmholtz, Hermann, metaphysics 645 fn. von Helmholtz, Hermann, ophthalmoscope, invention 643 von Helmholtz, Hermann, Physiological Optics 643 644 von Helmholtz, Hermann, sensations of tone 643 von Helmholtz, Hermann, space geometry 546 von Helmholtz, Hermann, space structure 645 647 681—682 696 von Helmholtz, Hermann, Theory of Animal Heat 643 von Helmholtz, Hermann, “On the Origin and Significance of Geometrical Axioms” 644 647—668 von Helmholtz, Hermann, “On the Origin and Significance of Geometrical Axioms”, metaphysics 645 fn. von Humboldt, Baron Alexander 316 318 330 von Leibniz, Gottfried Wilhelm, binary scale 516 517 von Leibniz, Gottfried Wilhelm, calculating machine 516 von Leibniz, Gottfried Wilhelm, differential calculus 152 275 286 von Leibniz, Gottfried Wilhelm, fluxions 143 von Leibniz, Gottfried Wilhelm, geometry of position 573 von Leibniz, Gottfried Wilhelm, infinitesimal calculus 48 57—59 61 292 von Leibniz, Gottfried Wilhelm, left and right indiscernible 680 von Leibniz, Gottfried Wilhelm, logarithm 137 138 von Leibniz, Gottfried Wilhelm, mathematical analysis 299 von Leibniz, Gottfried Wilhelm, motion 20 von Leibniz, Gottfried Wilhelm, notation 32 54 57—58 59 von Leibniz, Gottfried Wilhelm, past and future 686 von Leibniz, Gottfried Wilhelm, Philosophische Schriften 683 fn. von Leibniz, Gottfried Wilhelm, plane 564 von Leibniz, Gottfried Wilhelm, relative concepts 683—684 687 von Leibniz, Gottfried Wilhelm, space structure 682 695 von Leibniz, Gottfried Wilhelm, straight line 564 567 von Walterhausen, Sartorius 330 von Walterhausen, Sartorius, quoted 319 Vortices, theory of 132 257 259 Wakeford, E.K. 358 fn. Wallis, John, calculations 468 477 Wallis, John, fractional indices 131 140 Wallis, John, integral calculus 42 Wallis, John, limits 165 Wallis, John, logarithm 137 138 Wallis, John, parallel postulate of Euclid 158 Wallis, John, symbolic algebra 115 Ward, James 386 Ward, Seth 259 Waring's conjecture 514 Waring, E. 499 Wasps, counting ability 434 Wassen, Henry, The Ancient Peruvian Abacus 464 fn. Waste, prevention of 5 6 13 Water philosophy, Thales' 82 85 Water, characteristic shape 96 Wave mechanics 146 154 164 Weaver, Warren, “Mathematics of Communication” 518 Weber, Wilhelm, electromagnetic research 327 338 Weierstrass, Karl Theodor 291 fn. Weierstrass, Karl Theodor, analysis 65 76 165 287 291 299 323 Weierstrass, Karl Theodor, infinitesimal calculus 60 152 Weierstrass, Karl Theodor, irrational numbers 97 Weierstrass, Karl Theodor, limit, conception of 59 Weighing machine, geometrical 162 Weight, moving by force 179 181 Welby, Francis A. 642 fn. Werner, Johannes 612 613 618 Wertheimer, Max, Productive Thinking 467 fn. Western Philosophy, A History of (Russell) 235/n. Weyl, Hermann, symmetry 671—724 Whately, Richard, arithmetical powers 470 Wheel 8 135 Whetstone of Witte (Record) 23 210 Whewell, William 280 Whewell, William, quoted 265 443 Whirlpool theory, planetary motion 132 144 Whiston, William 280 281 Whiston, William, quoted 270 273 278 Whitehead, Alfred North, algebra of symbolic logic 396 Whitehead, Alfred North, Algebra, Universal 396 399 Whitehead, Alfred North, commentary of 395—401 Whitehead, Alfred North, extensive abstraction 399 Whitehead, Alfred North, mathematical physics 399 Whitehead, Alfred North, Mathematics, Introduction to 3 291 398 412 Whitehead, Alfred North, Mind and Nature, bifurcation 399 Whitehead, Alfred North, organism, philosophy of the 398 400 Whitehead, Alfred North, philosophical writings 398—399 Whitehead, Alfred North, Principia Mathematics 378 397 399 Whitehead, Alfred North, Russell, association with 377 396 397 Whitehead, Alfred North, Russell, association with, quoted 75 104 442 Whitehead, Alfred North, “Mathematics as an Element in the History of Thought” 402—416 Whittaker, Edmund T., space-time 399 399 Wickham, Anna, quoted 672 Widman, Johann 460 Wieferich, A. 510 Willsford, Thomas 211 fn. Wilson, B.M. 367 fn. Wilson, J., criterion for primafity 506 Wine casks, measuring 127 137 Wireless telegraphy 9 219 Wohler, Friedrich, urea, synthesized 690 Wohlgemut, Michael 600 Wolfflin, Heinrich 684 685 Woodhouse, Robert, Analytical Calculation, Principles of 291 fn. Words, analogies 25 Words, learning 491 Wordsworth, William, quoted 255 World function 162 World, The Mirror of the 210 fn. Wotton, Henry 128 Wren, Christopher 143 264 Wurm, J.F. 198 fn. x-axis 33 132 308 y-axis 33 34 Year, number of days in 82 Young, A. 77 Young, Thomas 655 Zamebone, Ugo 478 Zeitsehrift fur Math. u. Physik 197 fn.t 198 fn. Zeno, Achilles and the tortoise puzzle 94 Zeno, analysis 165 Zeno, equal ratios 99 Zeno, infinitesimals 41 Zeno, motion, conception of 19 Zermelo, Ernst 505 512 Zero, Arabic numeral 454 Zero, division by 293 fn. Zero, number 96 Zero, Zeta-unction 374 Zeta-function 374 Zeuxippus 420 Zoology, left-right problem 686—688 Zufti Indians, finger counting 438 440 “Aesthetics, Mathematical Theory of” (Birkhoff) 671 fn. 703 “Algebra the Second, reign of” 156 “Analytic Geometry, Invention of” (Boyer) 236 fn. “Arithmeticke, The Declaration of the Profit of” (Recorde) 212—217 “As I was going to St. Ives” 178 “Bernoulli's Numbers, Some Properties of”, (Ramanujan) 370 “Binomial Theorem for Fractional and Negative Exponents” (Newton) 521—524 “Binomial Theorem, The Story of the” (Coolidge) 519 fn. “Birds, The Ability to Count” (Koehler) 489—496 “Calculating Prodigies” (Ball) 467—487 “Costruzione legittima” 606—607 608 609 619 “Counting” (Conant) 432—441 “Directions for knowing all dark things” (Rhind papyrus) 12 79 “Exact Sciences, The Common Sense of the” (Clifford) 546 fn. “Geometrical Axioms, On the Origin and Significance of” (von Helmholtz) 647—668 “Great Compilation, The” (Ptolemy) 109 fn. “Invariant Twins, Cayley and Sylvester” (Bell) 341—365 “Irrational Numbers” (Dedekind) 528—536 “Konigsberg, The Seven Bridges of” (Euler) 571—580 “Mathematical Laws, The Exactness of” (Clifford) 548—551 “Mathematical Machines” (Davis) 518 “Mathematicians, The Great” (Turnbull) 75—168 “Mathematicians, The Prince of” (Bell) 295—339 “Mathematics as an Element in the History of Thought” (Whitehead) 402—416 “Mathematics of Communication, The” (Weaver) 518 “Mathematics, Queen of” (Bell) 498—518 “Newton's Principles and Modern Atomic Mechanics” (Bohr) 254 “Newton, Isaac” (Andrade) 255—276 “Newton, the Man” (Keynes) 277—285 “Newton: The Algebraist and Geometer” (Turnbull) 519 fn. “Number, Definition of” (Russell) 537—543 “Numbers to Numerals, From” (Smith and Ginsburg) 442—456 “Numerals to Computation, From” (Smith and Ginsburg) 456—464 “Optica”, classical 605 “Philosophy, Rules of Reasoning in” (Newton) 266 “Projective Geometry” (Kline) 622—641 “Prospective naturalis” 606 “Prospective”, medieval 605 “Pure Sciences, The Philosophy of the” (Clifford) 547 “Rhind Papyrus, The” (Newman) 170—178 “Right and left in paintings” 684—685 “Scientific Thought, On the Aims and Instruments of” (Clifford) 547 “Space Theory of Matter, On the” (Clifford) 568—569 “Space, Postulates of the Science of” (Clifford) 552—567 “Srinivasa Ramanujan” (Newman) 368—376 “Stereochemistry and Vitalism” (Japp) 690 “Theory of Numbers, Hunting Big Game in the” (Lehmer) 504 “Time, Measurement of” 784 fn. “Topology” (Courant and Robbins) 581—599
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