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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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Erasmus, Desiderius 600 Eratosthenes, earth circumference 188 205—207 Errors, compensation of 56 292 Errors, normal distribution 303 Ether, concept 219 Eucharist, symmetry 675 677 Euclid (Proclus) 189 190 Euclid's Elements, The Thirteen Books of (Heath) 191 fn. Euclid, angles of triangle 159 188 190 Euclid, constructive intuition method 649 Euclid, continuity, postulate of 559 Euclid, elementary flatness 561 Euclid, Elements of Geometry 11 41 69 100 101—102 108 141 190 193 552—553 Euclid, exhaustion, method of 188 Euclid, Fallacies, Book of 102 Euclid, homaloid space 656 657 660 Euclid, infinite descent 505 Euclid, parallel postulate 102 158 168 546 565 Euclid, perfect numbers 506 Euclid, perspective, geometry of 605 625 627 Euclid, prime numbers 157 501 Euclid, profit from learning 101 193 212 Euclid, Pythagoras's theorem 188 190—192 Euclid, solids, five regular 222 Euclid, space structure 680 Euclid, space, geometric relations 546 Euclid, spherical trigonometry 109 Euclid, superposition 561 Euclidean algorithm 513 Euclidean construction 502 Eudemus 16 107 190 193 Eudemus, quoted 85 Eudoxus, biography 96 Eudoxus, divided line, geometry of 98 Eudoxus, equal ratios 99 117 527 Eudoxus, Euclid's Elements 101 Eudoxus, exhaustion, method of 92 Eudoxus, infinitesimals 41 152 Eudoxus, irrationals 96 165 Eudoxus, mechanics, art of 180—181 Eudoxus, planetary theory 96 Eudoxus, pure number 163 Eudoxus, ratios, definition 525 Eudoxus, sun, diameter 421 Euler, Leonhard, analytical geometry 133 Euler, Leonhard, biography 148—149 Euler, Leonhard, Cartesian and Newtonian systems, comparison 148 Euler, Leonhard, differential calculus 152 Euler, Leonhard, diophantine analysis 510 Euler, Leonhard, energy 571 Euler, Leonhard, infinitesimal calculus 59 Euler, Leonhard, isoperimetrical problem 153 Euler, Leonhard, mathematical analysis 299 Euler, Leonhard, partitions, theory of 515 Euler, Leonhard, perfect numbers 506 Euler, Leonhard, planetary motion 149 Euler, Leonhard, polyhedron, formula 571 581—585 587 591 Euler, Leonhard, prime numbers 501 Euler, Leonhard, quadratic reciprocity 301 302 Euler, Leonhard, surface, characteristic 594—595 597 Euler, Leonhard, topology 571 Euler, Leonhard, writings 157 Euler, Leonhard, “Seven Bridges of Konigsberg, The” 571—580 Europe, counters 459 Europe, decimal notation 114 117 Europe, mathematics, influence upon general thought 413 Europe, mathematics, introduction 13 18 Europe, modern numerals 452—453 Even perfect number 506 Evolute, curve 108 Evolution, Darwinian theory 413 Exact results, compensation of errors 56 Exact, practical and theoretical meaning 550 Exactness and universality, connection between 551 Excentric, planetary orbit 226 Excluded middle, law of 168 Exhaustion, method of 41 53 92 97 101 188 193—195 Experimental evidence, importance 120 Exponents, symbol 23 Extensive abstraction 399 Extracts (Stobaeus) 193 Eyck, Jan van 605 Factorization of large numbers 503 Faistauer, A., “Links und rechts im Bilde” 685 fn. Fallacies, Book of (Euclid) 102 Falling bodies, law of 548 549 Falling bodies, velocity 45—51 Fanti, Gismondo 617 Faust (Goethe), quoted 271—272 Feliciano, Felice 616 Ferrari, quartic equation 119 Ferro, Scipio 78 118 119 Fibonacci sequence 718—719 Fibonacci, Leonardo see “Leonardo of Pisa” Field, circular, measuring 14 Fifty, Roman numeral 448 Figures, Data and Division of (Euclid) 102 Figures, isoperimetric 188 207—209 Figures, measurement 12 Figures, relations between different parts 14 Figures, space-filling 86 Finger counting 435 436—441 455 Finger numerals 455—456 Finite and infinite classes 538 Finite differences, calculus of 267 Fink, Karl 71 Fire, characteristic shape 96 Five hundred, Roman numeral 450 Five, Arabic numeral 454 Five, Roman numeral 448 Five, symmetry of 720 Flat space 656—657 659—660 Floating Bodies (Archimedes) 199 Flowers, cyclic symmetry 707 Flowing quantities 289 Fluid, motion 267 323 716 Fluid, solid immersed m 185—186 188 199—200 Fluxions, A Treatise of (Maclaurin) 287 fn. Fluxions, method of 48 52 58 61 142 152 258 286 288—293 Fluxions, Sir Isaac Newton's Method of (Robins) 287 fn. Fontana, Niccolo (Tartaglia) 78 118—119 615 Fontenelle, Bernard de 256 Foppa, Vincenzo 606 Forsyth, Andrew Russell 267 Forsyth, quoted 362 Four, early numeral 445 453 Four, Roman numeral 448 Four-color problem, topology 590—591 Four-dimensional geometry 359—360 Fourier, Jean B.J. 59 155 Fowler, R.H., approximative calculation 508 Fractional indices 131 fractional numbers 25 26 27 31 34 162 Fractions, continued 104 105 374 Fractions, Egyptians’ 171 Fractions, Greek mathematicians 172 Fractions, multiplication 17 25 33 Fractions, reduction 12 79 Fractions, unit 171 172 France, geometrical work, decline 133 France, mathematical genius 128 France, mathematical treatises 210 France, mathematics, rise of 118 120 France, metric system adopted 155 France, scientific knowledge 59 France, scientists, treatment of 330 Francesca, Piero della, Prospectiva pingendi, De 606 608 Francesca, Piero della, three-dimensional bodies 618 Franklin, Fabian, quoted 357—358 Frederick II (king of Prussia) 149 154 317 Frederick the Great (Carlyle), quoted 128 Free-Thinking in Mathematics, A Defense of (Berkeley) 287 Frege, Gottlob 388 394 Frege, Gottlob, Arithmetic, Grundgesetze der 389 537 Frege, Gottlob, Arithmetik, Grundlagen der 537 Frege, Gottlob, vocabulary for mathematics 390 French Revolution 59 fn. 300 330 Frey, Dagobert, Symmetry in Art, On the Problem of 678 Fuller, Tom, idiot Savant 465 470 Function, analysis of 412 Function, conception 19 20 39 Function, dimensions 51 Function, generalization 411 Function, propositional 70 Function, signs for 32fn. Function, theory 125 160 Function, variability 22 29 32 38 70 411 Functional dependence 29 Galen, De temperamentis 671 Galileo (Galilei), astronomical discoveries 218 Galileo (Galilei), book of the Universe 153 Galileo (Galilei), cycloid 135 Galileo (Galilei), dynamics 120 Galileo (Galilei), falling bodies 44—49 51 52 57 58 61 549 Galileo (Galilei), motions, composition of 52 Galileo (Galilei), pendulum, behavior 412 Galileo (Galilei), pentagon 615 Galileo (Galilei), telescope 218 Galois, Evariste, group theory 509 Galton, Francis, Explorer in Tropical South Africa, Narrative of 433 Gases, kinetic theory 515 Gauricus, Pomponius 607 Gauss see also Bell “Prince Gauss, C.F., und die Seinen (Mack) 294 fn. Gauss, Carl Friedrich, algebra 308 313 Gauss, Carl Friedrich, analysis 165 299 334 338 339 Gauss, Carl Friedrich, Arithmeticae, Disquisitiones 305 306 307 309—312 321 325 327 333 498 Gauss, Carl Friedrich, astronomical calculations 314—316 320 324 334 498 Gauss, Carl Friedrich, binary theory 310 Gauss, Carl Friedrich, binomial theorem 298—299 310 311 325 Gauss, Carl Friedrich, biquadratic reciprocity 325 Gauss, Carl Friedrich, Ceres, discovery of 315—316 Gauss, Carl Friedrich, commentary on 294 Gauss, Carl Friedrich, complex numbers, analytical functions 322 332 Gauss, Carl Friedrich, congruences, theory of 310 498 Gauss, Carl Friedrich, differential geometry 334—335 Gauss, Carl Friedrich, discoveries 317 326 Gauss, Carl Friedrich, electromagnetic research 317 327 338 339 498 Gauss, Carl Friedrich, elliptic functions 304 305 332 Gauss, Carl Friedrich, errors, theory of 303 Gauss, Carl Friedrich, Fermat's Last Theorem 312 313 326 Gauss, Carl Friedrich, geodetic research 301 334 337 Gauss, Carl Friedrich, geometry, contributions to 498 Gauss, Carl Friedrich, heliotrope, invention 327 Gauss, Carl Friedrich, hyperbolic geometry 158—159 Gauss, Carl Friedrich, hypergeometric series 324 Gauss, Carl Friedrich, infinitesimal calculus 60 Gauss, Carl Friedrich, interpolation 140 Gauss, Carl Friedrich, invariants 350 Gauss, Carl Friedrich, least squares, method of 303 331 334 Gauss, Carl Friedrich, mathematical physics 334 Gauss, Carl Friedrich, non-Euclidean geometry 314 332 Gauss, Carl Friedrich, numbers, theory of 68 338 498 499 511 Gauss, Carl Friedrich, polygon, Euclidean construction 502 Gauss, Carl Friedrich, Prime Number Theorem 157—158 Gauss, Carl Friedrich, quadratic reciprocity, law of 301 302 310 325 Gauss, Carl Friedrich, quaternions 332 Gauss, Carl Friedrich, quoted 314 326 333 334 502 Gauss, Carl Friedrich, space geometry 546 Gauss, Carl Friedrich, surfaces, theory of 160 335—337 652—656 Gauss, Carl Friedrich, Theoria motus 316 331 Gauss, Carl Friedrich, writings 157 Gaussian complex integers 325 326 513 Gelfond, A. 514 Gelon (king of Syracuse), Archimedes’ Sand Reckoner 420 Geminus, perspective 605 Generalizations of number 25 26 30 Genotypical inversion 695 Geodesic line 563—564 Geodesic surface 564 565 Geodesy, heliotrope, invention 327 Geodetic surveying, least squares, method of 303 331 334 Geometric mean 92—93 Geometric symmetry 694 Geometrical conditions 404 Geometrical measurements 660—661 Geometrical Methods, A History of (Coolidge) 169 fn. 236 Geometrical Methods, A History of (Coolidge), quoted 237 fn. Geometrical progression 101 137—138 Geometrie, Elements de (Legendre) 158 Geometry, abstract mathematics 62 Geometry, algebra, application of 61 130 162 Geometry, analytical 17 31—43 56 112 116 129 133 155 236—237 359 411 631 Geometry, areas and solids 82 Geometry, arithmetic applied to 25 189 Geometry, assumptions analyzed 546 550 565 Geometry, bee 110 188 207 208—209 Geometry, characteristics 22 Geometry, circle 147 Geometry, conformal mapping 337 Geometry, cross-classification 77 Geometry, deductive 13—14 Geometry, descriptive 601 631 Geometry, differential 104 334 Geometry, Egyptian 13—14 68 Geometry, elliptic 159 Geometry, Essay on the Foundations of (Russell) 377 Geometry, Euclidean 570 Geometry, Euclidean and non-Euclidean unified 359 Geometry, four-dimensional 359—360 Geometry, Greek 10 61 68 Geometry, higher 151 Geometry, hyperbolic 158—159 Geometry, infinity, upon the plane at 554 Geometry, magnitudes 585 Geometry, many-dimensional 134 Geometry, metrical 103 359 570 Geometry, non-Euclidean 102 158 165 306 332 342 396 546 Geometry, number allocation 85 Geometry, of position 339 573 Geometry, On the Hypotheses That tie at the Bases of (Riemann) 546 645 Geometry, origin 10 11 79 Geometry, Parabolic 159 Geometry, plane 130 568 719 Geometry, Plato's views 96 Geometry, practical and theoretical 80 Geometry, problems 239 649 Geometry, pure and physical 152 Geometry, revival 207 Geometry, rhetorical 130 Geometry, Rhind papyrus 174 Geometry, scientific method 647 Geometry, solid 14 568 Geometry, space 67 86 110 342 Geometry, Thales’ 82 Geometry, The (Descartes) 26—27 31 32 237 520fn. Geometry, The (Descartes), quoted 234—253 Geometry, The Axioms of (Helmholtz) 550 fn. Geometry, topology 570 Geometry, trigonometry separated from 40 Germain, Sophie 325 332 333—334 Germany, mathematics, rise of 118 120 Germany, number designation by knots 463 Ghiberti, Lorenzo 616 Gibbon, Edward, quoted 381 Gilman, Daniel Coit 355 Ginsburg, Jekuthiel, Numbers and Numerals 430 Ginsburg, Jekuthiel, “From Numbers to Numerals” 442—464 Girard, Albert 23 Glanvill, Joseph, quoted 552
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