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Àâòîðèçàöèÿ |
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Ïîèñê ïî óêàçàòåëÿì |
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Katz V.J. — A History of Mathematics: An Introduction |
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Ïðåäìåòíûé óêàçàòåëü |
79 89
295—296
(House of Wisdom) 239
of Euclid 58—95
of Euclid, Book I 63—67 71
of Euclid, Book II 67—73 124 249—250
of Euclid, Book III 73—76
of Euclid, Book IV 76—77
of Euclid, Book IX 86—88 458
of Euclid, Book V 77—82
of Euclid, Book VI 71—72 82—84 116
of Euclid, Book VII 84—86
of Euclid, Book VIII 86—87
of Euclid, Book X 88—90
of Euclid, Book XI 90—91 117
of Euclid, Book XII 91—94
of Euclid, Book XIII 94—95
of Euclid, Definitions and Postulates 60—62
of Euclid, structure of 59—60 (see also Euclid)
4
, geometry 20—23
, linear equations 14—18
, square root 29 (see also Chinese mathematics)
(abacists) 343—348
163—164 268
55—56
55—56
-dimensional geometry 792—797
see
-adic numbers 824—825 829
212
322 30—32
, in Archimedes 105 107
, in eighteenth century mathematics 585
, in Euclid 64—65
4 21 28—29
214
exam 679 816
4
cole Polytechnique 637—639 668 683 692 706—707
cole Polytechnique, and Cauchy 719 720
cole Polytechnique, and Germain 656
cole Polytechnique, and Monge 633 635
ryabhata 212—213 215—218 231
Ab Kmil ibn Aslam 250—251 293
Ab Nasr Mansr 277—281
Abacists 343—348
Abel, and Fourier series 720 723
Abel, and Jordan 670
Abel, and Kronecker 671—672
Abel, and Weber 675
Abel, biography 666
Abel, Niels Henrik 638 651 665—667 704 715
Abraham bar Hiyya 288 290—291 292—293
Abraham ibn Ezra 301—302
Absolute geometry 778
Abstract algebra, Boolean algebra 686—687 842—844
Abstract algebra, categories and functors 806 833
Abstract algebra, division algebra 682
Abstract algebra, equations 662—670
Abstract algebra, equivalence classes 671—672 732
Abstract algebra, fields 651 667 676—677 797 806 822—826
Abstract algebra, groups 339 617 620—621 651 662 667—676 791—792 797—799 832—833
Abstract algebra, ideals and ideal numbers 659—661 671—672
Abstract algebra, integral domain 831
Abstract algebra, matrices 687—695
Abstract algebra, number theory 652—661
Abstract algebra, rings 617 806 828—829
Abstract algebra, set theory 812
Abstract algebra, symbolic 677—687
Abstract algebra, vector spaces 763 794—795 833
Abu-l—Waf, Muhammad 277—281
Acarya Jayadeva 223
Acceleration 318—319 421—423
Acrostic 1 46 102 135 168 192 238 288 342 385 431 468 544 596 650 704 766 805
Addition see Arithmetic computations
Adelard of Bath 290—291
African mathematics 337—339 (see also Egyptian mathematics)
Agnesi, Maria Gaetana 565—567
al — Din, Sadr 271
al — Karaj, Ab Bakr 186 251—252 255 258
al — Khall ibn Ahmad 263—264
al — Khayym, ‘Umar 238 269—271 437 624
al — Khayym, ‘Umar, biography 260
al — Khayym, ‘Umar, cubic equations 259—262
al — Khwrizml, Muhammad 240—241 244—249
al — Khwrizml, Muhammad, biography 245
al — Samaw’al, ibn Yahy 252—255 258—259 376
al — Samaw’al, ibn Yahy, biography 253
al — Uqlds, Abu-l—Hasan 241—243
al-Brn, Abu-l-Rayhn 238 275—277 281 330
al-Battn, Abu ‘Abdallh 275
al-Fris, Kaml al-Dn 266
al-Ksh, Ghiyth al — Dn 243 281—282
al-Kh, Ab Sahl 273
al-Khwrizml, Muhammad, and European mathematics 293 350
al-Samaw’al, ibn Yahy, combinatorics 264
al-Samaw’al, ibn Yahy, number system 243
al-Tus, Nasr al — Dn 270—271 405
al-Tus, Sharaf al — Dn 262—263 363 437
Alberti, Leon Battista 389—390
Alcuin of Yor 289
Aleksandrov, Pavel Sergeiivich 832
Alexander, James W. 821—822
Alexandria Museum and Library 58—59 96 168 187 188
Algebra, and trigonometry 371—372
Algebra, Babylonian 16 35—39
Algebra, boolean 686—687
Algebra, Chinese 15—19 35 197—210
Algebra, Diophantine 173—183
Algebra, Egyptian 14—15
Algebra, etymology 244
Algebra, French 349—351
Algebra, geometric 67—73 95—96 122-125
Algebra, in Euler 614—619
Algebra, in Lagrange 619—621
Algebra, in Maclaurin 611—613
Algebra, in Newton 610—611
Algebra, in Vite 370—375 (see also Abstract algebra; Equations)
Algebra, Indian 225—228
Algebra, Islamic 243—263 343—346 348
Algebra, Italian 343—348 358—367
Algebra, linear 14—19 755
Algebra, medieval European 282—290 293 307—314 328—329
Algebra, polynomials 251—254 346—348
Algebra, quadratic equations 35—39
Algebra, symbolic 677—687
Algebra, twentieth century 822—833
Algebra, vectors 794—795
Algebraic symbolism 370—371 445—446
Algebraic symbolism, in Descartes 438
Algebraic symbolism, in Diophantus 174—175
Algebraic symbolism, in Fermat 432 435
Algebraic symbolism, in medieval Europe 312
Algebraic symbolism, in Renaissance mathematics 345—346 350—352 356 365
algorithm, defined 8
Algorithm, etymology 241
American Mathematical Society 805
American mathematics, computers 839—851
American mathematics, eighteenth century 640—642
American mathematics, twentieth century 823 828 830
Amicable numbers 266
Analysis, complex analysis 737—746
Analysis, eighteenth century 544—590
Analysis, nineteenth century 704—760
Analysis, probability and statistics 753—760
Analysis, summary 595 765
Analysis, vector analysis 746—752
Analytic geometry 431—434 633—635
Anasazi mathematics 336—337
| Angle of parallelism 775
Apogee 141
Apollonius 102—103 134 678
Apollonius, 117—129 184
Apollonius, and astronomy 140—141
Apollonius, and Renaissance mathematics 368
Apollonius, and seventeenth century mathematics 432—433 435 438 460
Apollonius, biography 118
Appel, Kenneth 805 851
Approximation methods 214—215
Arabia see Islamic mathematics
Arabic names 241
Arc length 293 469 496—498
Archimedes 55 102—117 134 368
Archimedes, 108
Archimedes, 114—115
Archimedes, 105—106
Archimedes, 108—111 187
Archimedes, 115
Archimedes, 113—114
Archimedes, 111—113
Archimedes, and Islamic mathematics 259 262—263 273
Archimedes, and Leibniz 531
Archimedes, and Renaissance mathematics 368
Archimedes, biography 102 107 111 116
Archimedes, engineering 107—108
Archimedes, geometry 111—116
Archimedes, Hilbert’s axioms 799
Archimedes, law of the lever 103—107
Archimedes, method of discovery 111—113
Archimedes, principle of insufficient reason 105
Archimedes, sums of series 113—115
Archimedes, velocity 160—161
Archytas 86—87
Area of circle 19—22 162 268 488
Area of polygon 161 296
Area of rectangle 622
Area of region bounded by curves 468—469 487—488 499-503 513—514 623 717—718
Area of segment of a circle 22 162 273 293 297
Area of segment of a parabola 113—115
Area of segment of a spiral 114—115
Area of surface 574—575
Area of surface of a sphere 115—116
Area of triangle 19—20 160—161 269
Argand, Jean — Robert 738
Aristaeus 117 134 184 186
Aristarchus 137 368
Aristotle 54—58 159
Aristotle, and astronomy 140
Aristotle, Hilbert’s axioms 800
Aristotle, in medieval Europe 314—316 319
Aristotle, logic 54—56
Arithmetic computations 349
Arithmetic computations, Babylonian 12—14
Arithmetic computations, Chinese 14
Arithmetic computations, Egyptian 8—12
Arithmetic computations, Greek 175
Arithmetic computations, in medieval Europe 307—308
Arithmetic computations, Indian 226
Arithmetic computations, Islamic 240 242
Arithmetic computations, Mayan 333
Arithmetic computations, with decimals 376—377
Arithmetization of analysis 683 729—737
Associative law 81 823
Astrolabe 294
Astrology 301—302
Astronomy, ancient 25—27
Astronomy, and logarithms 416—420
Astronomy, Babylonian 136 138 142
Astronomy, Chinese 195—197
Astronomy, early Greek 135—145
Astronomy, in Brahe 408
Astronomy, in Copernicus 404—408
Astronomy, in Kepler 409—416
Astronomy, in Newton 516—522
Astronomy, Indian 212 218 221
Astronomy, Islamic 274 277
Astronomy, Mayan 332
Astronomy, Ptolemaic 145—157
Astronomy, Renaissance 398—416
Astronomy, summary 167 (see also Trigonometry) )
Asymptote 122—123
Augustine 289
Autolycus 137 160 368
Axioms 55
Axioms, algebraic 822—823
Axioms, Boolean 686—687
Axioms, completeness 806
Axioms, for group theory 674—676
Axioms, for natural numbers 735—737
Axioms, for non — Euclidean geometry 781
Axioms, for set theory 810—814
Axioms, for topology 817—818
Axioms, for vector spaces 826—827 (see also Proof)
Axioms, Hilbert’s 767—768 797—800
Axioms, in Peacock 678—680
Axioms, of choice 809—810
Brgi, Jobst 416
Babbage, Charles 678 707 807
Babbage, difference and analytical engines 835—838 844
Babylonia 2
Babylonian mathematics 1—3
Babylonian mathematics, and Chinese mathematics 206
Babylonian mathematics, and Greek mathematics 67—68 70 72—73 96 176—177 181—182 188
Babylonian mathematics, and Islamic mathematics 239 240 243 244 263
Babylonian mathematics, arithmetic computations 12—14
Babylonian mathematics, astronomy 136 138 142 156
Babylonian mathematics, calendars 26—27
Babylonian mathematics, geometry 19—25
Babylonian mathematics, number symbols 6—8
Babylonian mathematics, place value system 230
Babylonian mathematics, quadratic equations 35—39
Babylonian mathematics, square roots 27—28
Babylonian mathematics, summary 45
Bakhshl manuscript 231
Banach space 827
Banach — Tarski paradox 812—813
Banach, Stefan 806
Banneker, Benjamin 641
Barrow, Isaac 498 500—503
Barrow, Isaac, biography 502
Bartels, Martin 654 775
Bayes, Thomas 605—608 755—756
Beltrami, Eugenio 783—784 789
Berkeley, George 582—583
Berkeley, George, response to 583—585
Bernoulli, Daniel 555 578 580—582 705 837
Bernoulli, Jakob (Jacques, James) 458 545 549 575
Bernoulli, Jakob (Jacques, James), 597—601
Bernoulli, Jakob (Jacques, James), biography 546
Bernoulli, Johann (Jean, John) 519 528 531—535 556—557 575
Bernoulli, Johann (Jean, John), biography 546
Bernoulli, Johann (Jean, John), differential equations 545—549
Bernoulli, Johann (Jean, John), orthogonal trajectories 551—552
Bernoulli, Nicolaus 552—553
Bessel, Friedrich Wilhelm 738 757
Betti number 820—821 833
Betti, Enrico 819—820
Bhskara I 214—215
Bhskara II 218—226
Bhskara II, and combinatorics 229—230
Bhskara II, biography 192 224
Billingsley, Henry 386
binary number 844
Binomial theorem 506—509
Boethius 173 289
Bolyai, Jnos 785
Bolyai, Jnos, biography 779
Bolyai, Jnos, non — Euclidean geometry 767 774 778—779
Bolzano — Weierstrass property 814—815
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