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Newman J.R. — The World of Mathematics, Volume 1
Newman J.R. — The World of Mathematics, Volume 1



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Название: The World of Mathematics, Volume 1

Автор: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 724

Добавлена в каталог: 02.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Delta$ (defined)      47
$\int$ symbol for “the sum of”      54 55
$\pi$      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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