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| Kline M. — Mathematical thought from ancient to modern times |
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| Предметный указатель |
Abbati, Pietro 765
Abel's theorem 645 653 655 935 936
Abel, Niels Henrik 216 973 974 1024 1053 1097 1111 1137
Abel, Niels Henrik, Abelian integrals 653—655
Abel, Niels Henrik, biography 644 645
Abel, Niels Henrik, elliptic functions 645—650
Abel, Niels Henrik, rigorization of analysis 947 948 964 965 973 974
Abel, Niels Henrik, theory of equations 754 755
Abelian equation 755
Abelian function 665
Abelian integral 653 663 665 936 939 940
Absolute 907
Absolute differential calculus see "Tensor analysis"
Absolutely continuous function 1048
Abstract algebra 945 1136 1157
Abstract algebra, Lie algebra 1153—1156
Abstract algebra, non associative algebra 1153—1156 see "Abstract "Group" "Ideal" "Ring"
Abstraction 29 43—44 171
Academies 227 370 396 397 401 404 621 1023
Academy of Plato 27 42 43 45 130 190
Ackerman, Wilhelm 1208
Ad Locos Planos et Solidos Isagoge 302 317
Adams, John Couch 369
Adelard of Bath 205 207
Adjoint curve 935
Aesthetics 172 173
Affine geometry 918
Agrippa von Nettesheim 286
Ahmes 16 18 20
Airy's integral 1100 1102 1103
Akkadians 4
Al Battani 195
Al-Biruni 190 195 241
Alberti, Leone Battista 232 233 285
Alembert, Jean Le Rond d' 623 867 1029
Alembert, Jean Le Rond d', algebra 598
Alembert, Jean Le Rond d', calculus 425 465 954
Alembert, Jean Le Rond d', complex function theory 626—628
Alembert, Jean Le Rond d', complex numbers 595
Alembert, Jean Le Rond d', Fourier series 458 459
Alembert, Jean Le Rond d', mechanics 616
Alembert, Jean Le Rond d', ordinary differential equations 477 484 494 500
Alembert, Jean Le Rond d', partial differential equations 503—505 510 512 513 516 517 532 542
Alembert, Jean Le Rond d', rigor 619
Alexander the Great 4 101 102
Alexander, James W. 1176 1777 1179 1180
Alexandria 101—103
Alexandroff, Paul S. 1181
Algebra 364
Algebra and analysis 323 324 361
Algebra as analysis 279 280 323
Algebra vs geometry 49 136 197 198 279—282 318 323 365 391 392 834—836
Algebra, Arabic 191—195
Algebra, Greek (Alexandrian) 104 135—144
Algebra, Hindu 184 188
Algebra, of throws 13 25 31 32 33 34 850 851 see
Algebra, Renaissance 236 237
Algebraic geometry 920 924—946 1168 1169
Algebraic invariants 925—932
Algebraic invariants, absolute 926
Algebraic invariants, complete system 928 929
Algebraic invariants, covariant 926
Algebraic numbers 593 594 818—826 980 996 997
Alhazen 193 196
Almagest 54 122—125 133 159 191
Analytic continuation 642—644 1114
Analytic geometry see "Coordinate geometry"
Angle, pjojectivc definition of 907 911
Anharmonic ratio see "Cross ratio"
Apollonian problem 99
Apollonius 56 89 99 135 157 158 168 300
Application of areas 34 74 77
Arabs 181 190—199 205
Archimedes 37 105—116 134 163—166 168 286 395
Archimedes' principle 165 166
Archytas 27 28 42 46 48 49
areas 1042
Areas, calculation of 343 348—354 360
Areas, of surfaces 355 1020
Argand, Jean-Robert 630 631 776
Aristacus the Elder 48
Aristarchus 156 157 156 162 163 207 395 436 776 992 1028
Aristarchus, concept of mathematics 51 151 153
Arithmetic, Arabic 191 192
Arithmetic, Babylonian 5—8
Arithmetic, Egyptian 16 18
Arithmetic, Greek, (Alexandrian) 131—135
Arithmetic, Hindu 183—186
Arithmetic, primitive 3
Arithmetic, Renaissance 251—259
Arithmetica 139 143
Arithmetica Universalis 252 271 272 281 312 318 358 392 607
Arithmetization of analysis 947—972 1025 1026
Arnauld, Antoine 252
Aronhold, Siegfried Heinrich 928
Ars Conjectandi 273 442 451
Ars Magna 236 253 263—265 267 268
Aryabhata 184 187 189
Arzela, Cesare 1046 1077 1078
Ascoli, Giulio 1077
Astrology 13 168 169 179 196 202 203 222
Astronomy 250 470 471 490—497
Astronomy, Arabic 196
Astronomy, Babylonian 11 12
Astronomy, Egyptian 21 22
Astronomy, Greek 119 125 126 148 149 151 154 160
Astronomy, Hindu 189 see "Gravitational "Heliocentric "Three-body
Asymptotic series 1097—1109
Asymptotic series, semiconvergent 1097 1104 see
Athens 37 101
Atomism 150 329
Augustine, Saint 204
Autolycus of Pitane 54
Automorphic functions 726—730
Automorphic functions, elliptic modular 727
Automorphic functions, Fuchsian 729
Automorphic functions, Kleinian 730
Automorphism 1142
Axes of a conic 93—95
Axiom of Archimedes 81 991 1012 1013
Axiom of Choice 1002 1186 1209
Axiom of reducibility 1195 1196
Axiomatization 1026 1027
Axiomatization, of set theory 1185 1187
Axioms 50 52 59 60
Axioms, Hilbert for geometry 1010 1013
Axioms, of Euclid 59 60 1005—1007
Axioms, of non-Euclidean geometry 1015
Axioms, of number 988 991
Axioms, of projective geometry 1007 1010
Axioms, of set theory 1185 1186 see "Parallel
Babbage, Charles 259 622
Backlund, Albert Victor 703
Bacon, Francis 225 226
Bacon, Roger 145 207 208 213 226
Baire, Rene 1079 1186 1199
Baldi, Bemadino 223 229
Baltzer, Richard 879
Banach space 1088—1091 1159 1178
Banach, Stephen 1088 1092
Barrow, Isaac 252 281 339 346 347 356 357 380 383 384
Bartels, Johann M 862 878 879
Base 5 6
Bede, Venerable 202
Beeckman, Isaac 316 478
Beltrami, Eugenio 896 901 902 905 914 1030 1122 1130
Bendixson, Ivar 737
Benedetti, Giovanni Battista 223 229 234 478
Berkeley, George, Bishop 400 427 428
Bernays, Paul 1205
| Bernoulli numbers 449 451
Bernoulli, Daniel 401 446 479—481 492 507—510 512 521 524 578 677 1112
Bernoulli, James, calculus 380—383 407 412
Bernoulli, James, calculus of variations 575—577
Bernoulli, James, coordinate geometry 320
Bernoulli, James, differential geometry 562
Bernoulli, James, infinite series 439 442—446 451
Bernoulli, James, ordinary differential equations 471—475 478
Bernoulli, James, probability 273 274
Bernoulli, John 335 340 492 592
Bernoulli, John, calculus 380—383 387 388 406—411
Bernoulli, John, calculus of variations 574—577
Bernoulli, John, coordinate geometry 545
Bernoulli, John, differential geometry 556 562
Bernoulli, John, infinite series 441 442 444 446
Bernoulli, John, ordinary differential equations 472—476 478 479 497 503
Bernoulli, Nicholas (1687—1759) 412 447 461—463
Bernoulli, Nicholas (1695—1726) 401 475
Berry, G.G. 1183
Bessarion, Cardinal 238
Bessel functions 480—482 489 518 519 710 711
Bessel inequality 717 1083
Bessel, Friedrich Wilhelm 710 717 871 872 980
beta function 424
Betti numbers 1169 1173 1174 1176 1177 1179 1180
Betti, Enrico 1169
Beudon, Jules 703
Bezout, Etienne 553 606—608 796 798
Bhaskara 184—186 273
Bianchi, Luigi 554 1122
Binet, Jacques P.M. 796
Binoimal 560 561
Binomial equation 600 752 753 761—764
Binomial theorem 272 273 438 441 964 965
Biot, Jean-Baptiste 836
Biquadratic reciprocity 816—818
Biquaternions 792
Birational transformation 924 932
Birkhoff, George David 1106—1068 1178
Bocher, Maxime 599 607
Boethius, Anicius Manlius Severinus 201
Bolyai, John 873—874 877—881 914 921 1032 1033
Bolyai, Wolfgang Farkas 861 872 878 879
Bolzano, Bernhard 948 950—955 963 979 985 994 1025
Bombelli, Raphael 253—255 260
Bonnet, Ossian 865
Boole, George 927 1189—1191
Borchardt, Carl Wilhelm 624 667 981
Borel, Emile 953 954 1044 1078 1117—1119 1159 1186 1199
Bosse, Abraham 289
Bott, Raoul 1151
Bouquet, Jean—Claude 642 718 722
Bourbaki, Nicolas 1210
Boutroux, Pierre 1182
Bowditch, Nathaniel 496
Boyer, Carl B. 348
Boyle, Robert 227
Brachistochrone 574 575
Brahe, Tycho 203 219 242
Brahmagupta 183 184 192
Branch cut 642 656 657
Branch-point 641 657
Bravais, Auguste 768
Brianchon's theorem 841 848
Brianchon, Charles Julien 836 841
Briggs, Henry 275 276 440
Brill, Alexander von 938 940
Brillouin, Leon 1102
Briot, Charles A.A. 642 718 722
Brouncker, Lord William 255 278 468 469
Brouwer, Luitzen E.J. 1132 1162 1171 1177—1179 1199—1203 1208
Brunelleschi, Filippo 232
Bryson 42
Buchheim, Arthur 808
Burali Forti paradox 1003 1182
Burali-Forti, Cesare 1003
Burgi, Joost 258
Buridan, jean 211 212
Burnside's problem 1143
Burnside, William 1142—1145
Byzantine Empire 180 191 205 216
Caesar, Julius 178 180
Cajori, Florian 263 364
Calculus 342 390 400 435 615 798 see
Calculus of extension 782—785
Calculus of finite differences 440 441 452 453
Calculus of variations 573 591 685 739 751 1076 1078 1081
Calculus of variations, Jacobi condition 745
Calculus of variations, Legendre condition 589 590
Calculus of variations, Weieistrass conditions 748 see
calendar 12 13 21 22 119 178 179
Callett, jean-Charles (Francois) 463 464
Campanus, Johannes 217
Cantor, Georg 824 969 1021 1031 1040 1042 1044 1078 1159 1161 1184 1185
Cantor, Georg, irrational numbers 983—986
Cantor, Georg, sets and transfinite numbers 992—1003
Caratheodory, Constantin 838
Carcavi, Pierre de 275
Cardan, Jerome 221 222 234 236 251—253 260 263—271 1028
cardinal number 993
Carnot, Lazare N.M. 432 593 835 836 841
Carroll, Lewis see "Dodgson Charles
Cartan, Elie 1151 1155 1156
Cassini, Jacques 320 469
Cassini, Jean Dominque 320
Cassinian ovals 320
Cassiodorus, Aurelius 202
Castelnuovo, Guido 934
Catalan Eugene Charles 788
Cataldi, Pietro Antonio 278
Categoricalness 104 115
Catenary 382 472 579
Cauchy integial theorem 599 636 637 639 640 668 669
Cauchy integral formula 639
Cauchy Lipschitz thcoiem 718
Cauchy Riemann equations 627 628 635 658
Cauchy, Augustin-Louis 465 947 993 1024 1029 1076 1099 1100
Cauchy, Augustin-Louis, algebra 796 798 801 802 815 816
Cauchy, Augustin-Louis, biography 633 634
Cauchy, Augustin-Louis, complex function theory 634—642 667
Cauchy, Augustin-Louis, differential equations 535 680 681 698 701 702 717—721 739 743
Cauchy, Augustin-Louis, differential geometry 560 561
Cauchy, Augustin-Louis, foundations of analysis 948 950—958 961 963—965 973—974 979 1024 1096 1097
Cauchy, Augustin-Louis, geometry 843
Cauchy, Augustin-Louis, group theory 765 766 768 1137
Cauchy, Augustin-Louis, theory of numbers 819
Cavalieri, Bonvaventura 349 350 383 384
Cavalieri’s theorem 349
Cayley Hamilton theorem 807 809
Cayley numbers 792
Cayley, Arthur 478 768 769 792 796 804—807 812 944 1030 1033 1138 1139 1142 1143 1166
Cayley, Arthur, algebraic invariants 927—929 931
Cayley, Arthur, biography 805
Cayley, Arthur, non-Euclidcan geometery 907—909 921—923
Cech, Eduard 1181
Cellerier, Charles 955 956
Cesaro, Ernesto 1018 1112 1113
Chain 1171 1172
Chain rule 376
Chain, oscillations of 480 481
Chaldeans 4
Characteiistic triangle 346 375 387
Characteristic equation of a determinant 800 801
Characteristic equation of a differential equation 485
Characteristic equation of a matrix 807
Characteristic equation of quadratic forms 800 801
Characteristic function 706 707 715 716 1063 1068
Characteristic root of a determinant 800 801
Characteristic root of a matrix 807 808
Characteristic value 480 673 706 707 715 716 1063 1068
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