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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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Mesopotamia, Sumerians' numbers and numerals 430 442 Metals, transmutation 272 Metamerism 702 Meteorology 234 Method (Archimedes) 94 104 Method, Discourse on (Descartes) 129 Methods, infinitesimal 40 Metric geometry 570 Metric system adopted in France 155 Metrical geometry 103 359 Metrodoros 207 fn. Micaniquc Analytique (Lagrange) 153 154 155 Micanique Celeste (Laplace) 155 321 Michelangelo, Creation of Adam 684 Michelson — Morley experiment 640 Michelson, Albert A., quoted 262 Micrographia (Hooke) 261 Military machines, Archimedes’ 103 179 180 181—182 187 Military problems, application of mathematics 119 Mill, John Stuart 381 433 Million, use of word 455 Milne, Ј.A., Sir James Jeans 645 Mind and nature, bifurcation 399 Mind, The Analysis of (Russell) 389 Minimum vocabularies 390—391 Mirrors, Archimedes' concave 179 Mirrors, images 679 696 698 Mirrors, metal 260 263 Mirrors, reflecting 110 132 154 Mitchell, F.D. 467 fn. 471 478 483 Mnemonic equations 50—51 Model, working of the universe 43—44 Modern numerals 453 Modular equations 374 Moebius, August Ferdinand, four-color problem 591 Moebius, August Ferdinand, one-sided surface 595 Moebius, August Ferdinand, strip 595—597 Moeris, geometry discovery 189 Molecular theory 96 Moments 289 Mondeux, Henri 476 480 Monge, Gaspard 155 334 601 631 Monochord, musical intervals 189 Monochromatic light 263 Monogenic functions 322 Monreale mosaic, symmetry 677 699 Moon, celestial motions 145 266 268 Moon, diameter 421 Moon, gravitational pull 257 258 Moore, G.E. 377 386 387 More, Henry 261 268 281 Morice, A. 439 fn. Moscow papyrus 89 169 175 Mother Goose rhyme, problem 178 Motion, change of position 64 fn. Motion, circular 227 Motion, composition 52 Motion, conception 19 Motion, fluid 716 Motion, law of 44—48 Motion, matter 568 Motion, parabolic 49 Motion, resisting medium 267 Motion, rigid 717 Motion, transferred to space 659 Motion, transformation 570 Motion, variability 70 Motte, Andrew 266 fn. Muller, G.E. 467 fn. Multiplication, Ahmes' treatment 12 Multiplication, calculating prodigies 469 472 481—482 Multiplication, complex 371 Multiplication, Egyptians 172 Multiplication, fractions 17 25 Multiplication, generalization of number 30—31 Multiplication, grating method 461 Multiplication, Greek guiding process 117 Multiplication, logarithms 123 Multiplication, logical 25 Multiplication, matrices 361—362 Multiplication, negative number 29—30 Multiplication, repetitions 24 Multiplication, Roman methods 451 Multiplication, symbols 27 Multiplication, tables 460 Multiplication, velocities and times 50 Music, numerical ratios 99—100 Music, periodicities of notes 416 Music, rhythm 702—703 Musical intervals, planetary relations 127 Musical scale, harmonic progressions 85 189 Myriad 425 Mysterium (Kepler) 125 Mysticism and Logic (Russell) 379 n dimensions, geometry of 342 344 359 640 n partitions of a number (theorem) 167 n roots of algebraic equation 511 Named numbers 491 494 Napier's Bones 122 Napier, John, arithmetic triangle 135 Napier, John, biography 121 Napier, John, inventions 122 Napier, John, logarithms 23 123—125 137 140 142 148 Napier, John, quoted 123 Napier, John, spherical trigonometry 125 Napier, John, symbolic algebra 115 Natural bodies, mechanical properties 665 Natural Knowledge, An Enquiry concerning the Principles of (Whitehead) 398 Natural numbers 500 Natural science, ancient 15 Natural science, application of mathematics 43—52 69—70 Natural science, prevention of waste 5—6 Natural science, satisfaction of intellectual needs 10 Nature, economical tendencies 154 Nature, laws of, mathematically expressed 411 Nature, leftright symmetry 686 Nature, observation by scientists 411 Nature, The Concept of 398 Nature, uniformity 549 Nautical Almanac 5—6 43 44 233 Needham, Joseph, Order and Life 691 Nees von Essenbeck, Christian 314 Negative indices 131 negative numbers 6 27—28 30 33 34 65 96 115 119 147—148 162 Neugebauer, O. 89 169 449 Newman, James R., “Rhind Papyrus, The” 169—178 Newman, James R., “Srinivasa Ramanujan” 368—376 Newton, Humphrey 259 280 282 Newton, Humphrey, quoted 272 Newton, Isaac, achievement, period of 256—257 Newton, Isaac, analytical geometry 133 155 360 Newton, Isaac, apple story 145 257 328 Newton, Isaac, Arithmetica Universalis 145 Newton, Isaac, binomial theorem 139 140 256 258 519—524 Newton, Isaac, brachistrochrone problem 267 274 Newton, Isaac, calculus 256 258 267 279 Newton, Isaac, chemical operations 272—273 Newton, Isaac, chromatic aberration 260 Newton, Isaac, Chronology of the Ancient Kingdoms Amended 273 274 Newton, Isaac, commentary on 254 Newton, Isaac, curves, moving points 58 Newton, Isaac, earth measurements 267—268 Newton, Isaac, equations, imaginary roots 273 364 Newton, Isaac, experiments 268 279 Newton, Isaac, finite differences, calculus 267 Newton, Isaac, fits, theory of 262 Newton, Isaac, fluxions, method of 48 58 61 142—143 145 258 Newton, Isaac, gravitation, theory of 45 62 142 144 256—258 266—268 Newton, Isaac, honors 145—146 254 268 269—270 Newton, Isaac, Hooke misunderstandings 261 271 278 Newton, Isaac, hypotheses 260 266 Newton, Isaac, infinite series 521—524 Newton, Isaac, inverse square law 145 258 264 265 266 Newton, Isaac, least resistance, problem of 267 Newton, Isaac, Leibniz controversy 58—59 143 152 165 278 Newton, Isaac, letter to Royal Society 259 Newton, Isaac, light waves 262 263 267 Newton, Isaac, limits 165 291 Newton, Isaac, logarithm 137 Newton, Isaac, mathematical analysis 299 Newton, Isaac, mathematical astronomy 313 315 Newton, Isaac, mathematical discoveries 258 295 Newton, Isaac, metallic mirrors 260 263 Newton, Isaac, motion, theory of 45 Newton, Isaac, Motu Corporum, De 264—265 Newton, Isaac, Natura Acidorum, De 272 Newton, Isaac, Opticks 259 260 261 263 264 269 272 Newton, Isaac, Opticks, quoted 266 273 286 Newton, Isaac, optics, lectures 258—259 271 Newton, Isaac, planetary motions 52 132 140 144—145 257 264 267—268 Newton, Isaac, Portsmouth Papers 274 284 Newton, Isaac, Principia 62 144 145 257—259 264 268 269 272—275 279 280 282 284 286 Newton, Isaac, projective geometry 102 Newton, Isaac, Prophecies of Daniel and the Apocalypse of St. John, Observations upon 274 Newton, Isaac, quoted 265—266 267 Newton, Isaac, relative concepts 683 Newton, Isaac, sound, theory of 154 412 Newton, Isaac, space structure 696 Newton, Isaac, spectrum 260 Newton, Isaac, speculative theory, attitude to 262 Newton, Isaac, sphere, gravitational pull 268 279 Newton, Isaac, telescope, reflecting 142 259 260 264 Newton, Isaac, universe, system of the 153 Newton, Isaac, unpublished papers 280—282 284 Newton, Isaac, variations, calculus of 267 Newton, Isaac, waterclock 255—256 Newton, Isaac, white light discoveries 141—142 146 256 260—263 Newton, Isaac, wind force, ascertaining 140 Newton, Isaac, wind force, ascertaining, quoted 141 326 Newtonian viscosity 267 Nine, Roman numerals 449 Nineteen, Roman numerals 449 Niven, I.M., Waring problem 515 Noether, Emmy 333 Non-Euclidean geometry 102 158 165 306 332 342 396 546 Normal to a surface 335 Normals 108 Northrop, F.S.C. 399 fn. Notation, algebraic 12 22—24 26—27 32 92 120 130 Notation, Arabic 117 Notation, decimal 23 114 116 117 Notation, development 13 14 Notation, fluxions 58 Notation, integral calculus 54 Notation, Leibniz's 57—58 Notation, numerical 99 Notation, Viete's improvements 236 Notizen-journal (Gauss) 304 Nouvelles Experiences sur le vide (Pascal) 134 Number intelligence, birds 494 Number knowledge, poverty of 432 Number, concept 525—527 Number, definition 537—543 Number, digital 483 Number, group relationships 402 Number, origin 432 433 434 Number, properties 156 Numbers and limits, modern views 62—67 Numbers and Numerals (Smith and Ginsburg) 430 442—464 Numbers, abstract 24 511 Numbers, algebraic 26 313 326 499 511 Numbers, analytic theory of 158 374 499 508 Numbers, binary scale 516 Numbers, cardinal 389 Numbers, characteristic designs 84 Numbers, classes 65—66 Numbers, complex 31 60 71 119 162 308 309 321—322 529 Numbers, composite 101 Numbers, concrete 24 Numbers, diameter 207 fn. Numbers, discrete domain 507 Numbers, Fermat's theory 236 Numbers, fractionary 25 26 27 31 34 162 Numbers, generalization 25 26 30 Numbers, ideal 499 513 Numbers, identification 85 numbers, imaginary 29—30 34 119 148 309 Numbers, integer 13 28 60 65 66 Numbers, Introduction to the Theory of (Dickson) 500 Numbers, irrational 26 27 34 62—64 87—88 89 92 95 96 97 101 162 168 525—536 numbers, large 455 458 Numbers, logical definition 65—66 Numbers, magnitudes 17 Numbers, measures of lengths 17 35 Numbers, Mersenne 500—505 506 Numbers, named 491 494 Numbers, natural 500 numbers, negative 6 27—28 30 33 34 65 96 115 119 147—148 162 Numbers, octads 418 426 Numbers, orders and periods 425—426 Numbers, ordinal 66 Numbers, pattern 136 Numbers, perfect 89 101 498 506 Numbers, points and lines, correspondence 33 Numbers, positive 27—28 34 65 96 Numbers, prime 101 157 501 505—506 Numbers, proportion 50 Numbers, rational 326 511 513 525 538 Numbers, rational reality 85 Numbers, real 34 50 63 65 96 534—536 Numbers, redefinition 28 Numbers, relation 65—66 Numbers, sequences 62 63 Numbers, series 63 Numbers, side, finding 207 fn. Numbers, square 84 Numbers, status in realm of things 408 409 Numbers, symbols 24 Numbers, theory of 68 fn. 83 116 136 152 155 157 160 311 367 498—515 Numbers, transcendental 499 514 Numbers, triangular 84 Numbers, unnamed 491 492 494 495 Numbers, zero 96 Numerals to computation 456—464 Numerals, alphabetical 418 Numerals, Arabic 454 Numerals, beginnings 442 Numerals, changes in European (table) 454 Numerals, early Hindu 453—454 Numerals, finger 455—456 Numerals, large numbers 445 Numerals, modern 453 Numerals, modern, forbidden in commerce 451 Numerals, Roman, large numbers 458 Numerical algebra 26 Numero Terminorum Infinitas, De Analyst per Aequationes (Newton) 258 Nuremberg Council, Durer's paintings 600 fn. Observation, mathematical science 405 Occam's razor 389 Occasion, immediate 407 octads, Archimedes' system 418 426 Octagonal symmetry 707 Octahedron, characteristic shape of air 96 Ocular measure for distances 657 Odd perfect number 506 Ohm, Martin 293 fn. Olbers, Heinrich 312 319 331 334 One, Babylonian numeral 444 One, early numeral 443 448 One, number 65
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