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Kline M. Ч Mathematical Thought from Ancient to Modern Times, Vol. 1
Kline M. Ч Mathematical Thought from Ancient to Modern Times, Vol. 1

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Ќазвание: Mathematical Thought from Ancient to Modern Times, Vol. 1

јвтор: Kline M.

јннотаци€:

Now available in a new three-volume paperback edition, Morris Kline's monumental work presents the major creations in mathematics from its beginnings in Babylonia and Egypt through the first few decades of the twentieth century. Organized around the central ideas of mathematical thought, as well as the men responsible for them, this comprehensive history provides a broad panorama of the development of mathematics, displaying the unity behind the disconnected branches of the discipline today. Beginning with the origins of mathematics in Babylonia and Egypt, Volume One includes chapters on classical Greek and Alexandrian mathematics, Hindu and Arabic contributions, algebra in the sixteenth and seventeenth centuries, coordinate geometry, and the creation of calculus.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1990

 оличество страниц: 432

ƒобавлена в каталог: 03.04.2008

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ѕредметный указатель
Abbati, Pietro      765
Abel's theorem      645 653Ч655 935Ч936
Abel, Niels Hemik      216 973Ч974 1024 1053 1097 1111 1137
Abel, Niels Hemik, Abelian integrals      653Ч655
Abel, Niels Hemik, biography      644Ч645
Abel, Niels Hemik, elliptic functions      645Ч650
Abel, Niels Hemik, rigorization of analysis      947Ч948 964Ч965 973Ч974
Abel, Niels Hemik, theory of equations      754Ч755
Abelian equation      755
Abelian function      665
Abelian integral      653 663Ч665 936 939Ч940
Absolute      907
Absolute differential calculus      See Tensor analysis
Absolutely continuous function      1048
Abstract algebra      945 1136Ч1157
Abstract algebra, Lie algebla      1153Ч1156
Abstract algebra, non associative algebra      1153Ч1156 see Group Ideal;
Abstraction      29 43Ч44 171
Academics      227 370 396Ч397 401 404 621 1023
Academy of Plato      27 42Ч43 45 190
Ackerman, Wilhelm      1208
Ad Locos Planas et Solidos Isagoge      302 317
Adams, John Couch      369
Adelard of Bath      205 207
Adjoint curve      935
Aestbetics      172Ч173
Affine geometry      918
Agrippa von Nettesheim      286
Ahmes      16 18 20
AI Battani      195
AI Biruni      190 195 241
AI-Karkhi      192
Aigeblaic invariants      925Ч932
Aigeblaic invariants, absolute      926
Aigeblaic invariants, complete system      928Ч929
Aigeblaic invariants, covariant      926
Airy's integral      1100 1102Ч1103
Akkadians      4
Al Kashi      254
Al Khowarizmi      192 93
Alberti, Leone Battista      232Ч233 285
Albuzjani      See Abu'l Wfa
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      626Ч628
Alembert, Jean Le Rond d', complex numbers      595
Alembert, Jean Le Rond d', Fourier series      458Ч459
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      503Ч505 510 512Ч513 516Ч517 532 542
Alembert, Jean Le Rond d', rigor      619
Alexander the Great      4 101Ч102
Alexander, James W      1176Ч1177 1179Ч1180
Alexandria      101Ч103
Alexandroff, Paul S.      1181
Algebra      364
Algebra: and analysis      323Ч324 361
Algebra: Arabic      191Ч195
Algebra: as analysis      279Ч280 323
Algebra: Greek (Alexandrian)      104 135Ч144
Algebra: Hindu      184Ч188
Algebra: of throws      850Ч851; see also Chaps 13 25 31 32 33 34
Algebra: Renaissance      236Ч237
Algebra: vs. geometry      49 136 197Ч198 279Ч282 318 323 365 391Ч392 834Ч836
Algebraic numbers      593Ч594 818Ч826 980 996Ч997
Algehraic geometry      920 924Ч946 1168
Alhazen      193 196
AlIIauld, Antoine      252
Almagest      54 122Ч125 133 159 191
Ampere, Andre Malic      703 750
Analytic continuation      642Ч644 1114
Analytic geometry      See Coordinate geometry
Anaxagoras      38 147
Anaximandel      27
Anaximenes      27
Angle, projective definition of      907 911
Anharmonic ratio      See Cross ratio
Antiphon      42
Apastamba      184
Apollonian problem      99
Apollonius      56 89Ч99 135 15758 168 300
Application of areas      34 74Ч77
Arabs      181 190Ч199 205
Archimedes      37 105 134 163Ч166 168 286 395
Archimedes' principle      165Ч166
Archytas      27 28 42 46 48Ч49
areas      1042
Areas of Surface      355 1020
Areas, calculation of      343 348Ч354 360
Argand, Jean-Robet t      630Ч631 776
Aristarchus      156Ч157
Aristat'us the Elder      48
Aristotle      26Ч27 35Ч37 51Ч54 151Ч153 155Ч156 162Ч163 207 395 436 776 992 1028
Aristotle, concept of mathematics      51 151Ч153
Arithmetic: Arabic      191Ч192
Arithmetic: Babylonian      5Ч8
Arithmetic: Egyptian      16Ч18
Arithmetic: Greek, (Alexandrian)      131Ч135
Arithmetic: Hindu      183Ч186
Arithmetic: primitive      3
Arithmetic: Renaissance      251Ч259
Arithmetica      139Ч143
Arithmetica Universalis      252 271Ч272 281 312 318 358 392 607
Arithmetization of analysis      947Ч972 1025Ч1026
Aronhold, Siegfried Heinrich      928
Ars Gonjectandi      273 442 451
Ars Magna      236 253 263Ч265 267Ч268
Aryabhata      184 187 189
Arzela, Cesale      1046 1077Ч1078
Ascoli, Giulio      1077
Astrology      13 168Ч169 179 196 202Ч203 222
Astronomy      250 470Ч471 490Ч497
Astronomy: Arabic      196
Astronomy: Babylonian      11Ч12
Astronomy: Egyptian      21Ч22
Astronomy: Greek      119 125Ч126 148Ч149 151 154Ч160
Astronomy: Hindu      189; see also Geocentric theory; Gravitational attraction; Heliocentric theory; Three-body problem
Asymptotic series      1097Ч1109
Asymptotic series, semiconvergent      1097 1104;
Athem      37 101
Atomism      150 329
Augustine, Saint      204
Autolycus of Pitane      54
Automorphic functions      726Ч730
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 1012Ч1013
Axiom of Choice      1002 1186 1209
Axiom of reducibility      1195Ч1196
Axiomatization      1026Ч1027
Axiomatization of set theory      1185Ч1187
Axioms      50 52 59
Axioms of Euclid      59Ч60 1005Ч1007
Axioms of Hilbert for geometry      1010Ч1013
Axioms of non Euclidean geometry      1015
Axioms of number      988Ч991
Axioms of projective geomety      1007Ч1010
Axioms of set theory      1185Ч1186 see
Babbage, Charles      259 622
Bacher, Maxime      599 607
Backlund, Albert Victor      703
Bacon, Franci      223Ч226
Bacon, Rogel      145 207Ч208 213 226
Baire, Rene      1079 1186 1199
Bal tels, Johann M.      862 878Ч879
Baldi, Belfiadino      223 229
Baltzel, Richald      879
Banach space      1088Ч1091 1159 1178
Bandch, Stephen      1088 92
Banow, Isaac      252 281 339 346Ч347 356Ч357 380 383Ч384
Base      5Ч6
Beeckman, Isaac      316 478
Beltlami, Eugenio      896 901Ч902 905 914 1030 1122 1130
Bendixson, Ivai      737
Benedetti, Giovallni Battista      223 229 234 478
Berkeley, George, Bishop      400 427
Bernays, Paul      1205
Bernoulli numhers      449 451
Bernoulli, Daniel      401 446 479Ч481 492 507Ч510 512 521 524 578 677 1112
Bernoulli, James: calculus      380Ч383 407 412
Bernoulli, James: calculus of variations      575Ч577
Bernoulli, James: coordinate geometry      320
Bernoulli, James: differential geometry      562
Bernoulli, James: infinite series      439 442Ч446 451
Bernoulli, James: ordinary differential equations      471Ч475 478
Bernoulli, James: probability      273Ч274
Bernoulli, John      335 340 492 592
Bernoulli, John, calculus      380Ч383 387Ч388 406Ч411
Bernoulli, John, calculus of variations      574Ч577
Bernoulli, John, coordinate geometry      545
Bernoulli, John, differential geometry      556 562
Bernoulli, John, infinite series      441 42 444 446
Bernoulli, John, ordinary differential equations      472Ч476 478Ч479 497 503
Bernoulli, Nicholas (1687-1759)      412 447 461Ч463
Bernoulli, Nicholas (1695-1726)      401 475
Berry, G.G.      1183
Bessarion, Cardinal      238
Bessel functions      480Ч482 489 518Ч519 710Ч711
Bessel inequality      717 1083
Bessel, Friedrich Wilhelm      710 717 871Ч872 980
beta function      424
Betic, Venuable      202
Betti numbers      1169 1173Ч1174 1176Ч1177 1179Ч1180
Betti, Enrico      1169
Beudon, Jules      703
Bezout, Etienne      553 606Ч608 796 798
Bhaskara      184Ч186 273
Bianchi, Luigi      554 1122
Binet, Jacques P.M.      796
Binomial equation      600 752Ч753 761Ч764
Binomial theorem      272Ч273 438 441 964Ч965
Binormal      560Ч561
Biot, Jean-Baptiste      836
Biquadratic reciprocity      816Ч818
Biquaternion      792
Birational tramformation      924 932
Birkhoff, George David      1106Ч1108 1178
Blanch cut      642 656Ч657
Bocthius, Anicius Manlius Severinus      201
Bolyai, John      873Ч874 877Ч881 914 921 1032Ч1033
Bolyai, Wolfgang Farkas      861 872 878Ч879
Bolzano, Bernhard      948 950Ч955 963 979 985 994 1025
Bombelli, Raphael      253Ч255 260
Bonnet, Ossian      865
Boole, George      927 1189Ч1191
Borchardt, Carl Wilhelm      624 667 981
Borel, Emile      953Ч954 1044 1078 1117Ч1119 1159 1186 1199
Bosse, Abraham      289
Bou, Raoul      1151
Bouquet, Jean-Claude      642 718 722
Bourbaki, Nicolas      1210
Boutroux, Pierre      1182
Bowditch, Nathaniel      496
Boyer, Carl B.      348
Boyle, Robert      227
Brachistochtone      574Ч575
Brahe, Tycho      203 219 242
Brahmagupta      183Ч184 192
Branch point      641 657
Bravais, Auguste      768
Brianchon's theorem      841 848
Brianchon, Charles Julien      836 841
Briggs, Henry      275Ч276 440
Brill, Alexander von      938 940
Brillouin, Leon      1102
Briot, Charles A.A.      642 718 722
Brouncker, Lord William      255 278 468Ч469
Brouwer, Luitzen E. J.      1132 1162 1171 1177Ч1179 1199Ч1203 1208
Brunelleschi, Filippo      232
Bryson      42
Buchheim, Arthur      808
Burali Forti paradox      1003 1182
Burali-Forti, Cesare      1003
Burgi, Joost      258
Buridan, jean      211Ч212
Burnside's problem      1143
Burnside, William      114245
Byzantine Empire      180 191 205 216
Caesar, Julius      178 180
Cajori, Florian      263 364
Calculus      342Ч390 400Ч435 615 798 see
Calculus of extension      782Ч785
Calculus of finite difference      440Ч441 452Ч453
Calculus of variations      573Ч591 685 739Ч751 1076 1078 1081
Calculus of variations, Jacobi condition      748
Calculus of variations, Legendre, condition      589Ч590
Calculus of variations, Weierstrass condition      745; see also Minimal surface
calendar      12Ч13 21Ч22 119 178Ч179
Callett, jean-Charles (Francois)      463Ч464
Campanus, Johannes      217
Cantor, Georg      824 969 1021 1031 1040 1042 1044 1078 1159 1161 1184Ч1185
Cantor, Georg, irrational numbers      983Ч986
Cantor, Georg, sets and transfinite numbers      992Ч1003
Caratheodory, Constantin      838
Carcavi, Pierre de      275
Cardan, Jerome      221Ч222 234 236 251Ч253 260 263Ч271 1028
cardinal number      995
Carnot, Lazare N.M.      432 593 835Ч836 841
Carroll, Lewis      See Dodgson Charles
Cartan, Elie      1151 1155Ч156
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      1014Ч1015
Catenary      382 472 579
Cauchy integral formula      639
Cauchy integral theorem      599 636Ч637 639Ч640 668Ч669
Cauchy Ч Lipschitz theorem      718
Cauchy Ч Riemann equations      627Ч628 635 658
Cauchy, Augustin-Louis      465 947 993 1024 1029 1076 1099Ч1100
Cauchy, Augustin-Louis, algebra      796 798 801Ч802 815Ч816
Cauchy, Augustin-Louis, biography      633Ч634
Cauchy, Augustin-Louis, complex function theory      634Ч642 667
Cauchy, Augustin-Louis, differential equations      535 680Ч681 698 701Ч702 739 743
Cauchy, Augustin-Louis, differential geometry      560Ч561
Cauchy, Augustin-Louis, foundations of analysis      948 950Ч958 961 963Ч965 973Ч974 979 1024 1096Ч1097
Cauchy, Augustin-Louis, geometry      843
Cauchy, Augustin-Louis, group theory      765Ч766 768 1137
Cauchy, Augustin-Louis, theory of numbers      819
Cavalieri's theorem      349
Cavalieri, Bonvaventura      349 383Ч384
Cayley number      792
Cayley Ч Hamilton theorem      807Ч809
Cayley, Arthur      478 768Ч769 792 796 804Ч807 812 944 1030 1033 1138Ч1139 1142Ч1143 1166
Cayley, Arthur, algebraic invariants      927Ч929 931
Cayley, Arthur, biography      805
Cayley, Arthur, non-Euclidean geometry      907Ч909 921Ч923
Cech, Eduard      1181
Cellerier, Charles      955 56
Ceso, Ernesto      1018 1112Ч1113
Chain      1171Ч1172
Chain rule      376
1 2 3 4 5 6
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