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



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

Àâòîð: Kline M.

Àííîòàöèÿ:

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.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1990

Êîëè÷åñòâî ñòðàíèö: 432

Äîáàâëåíà â êàòàëîã: 03.04.2008

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Abbati, Pietro      765
Abel's theorem      645 653—655 935—936
Abel, Niels Hemik      216 973—974 1024 1053 1097 1111 1137
Abel, Niels Hemik, Abelian integrals      653—655
Abel, Niels Hemik, biography      644—645
Abel, Niels Hemik, elliptic functions      645—650
Abel, Niels Hemik, rigorization of analysis      947—948 964—965 973—974
Abel, Niels Hemik, 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 algebla      1153—1156
Abstract algebra, non associative algebra      1153—1156 see Group Ideal;
Abstraction      29 43—44 171
Academics      227 370 396—397 401 404 621 1023
Academy of Plato      27 42—43 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      172—173
Affine geometry      918
Agrippa von Nettesheim      286
Ahmes      16 18 20
AI Battani      195
AI Biruni      190 195 241
AI-Karkhi      192
Aigeblaic invariants      925—932
Aigeblaic invariants, absolute      926
Aigeblaic invariants, complete system      928—929
Aigeblaic invariants, covariant      926
Airy's integral      1100 1102—1103
Akkadians      4
Al Kashi      254
Al Khowarizmi      192 93
Alberti, Leone Battista      232—233 285
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      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—1177 1179—1180
Alexandria      101—103
Alexandroff, Paul S.      1181
Algebra      364
Algebra: and analysis      323—324 361
Algebra: Arabic      191—195
Algebra: as analysis      279—280 323
Algebra: Greek (Alexandrian)      104 135—144
Algebra: Hindu      184—188
Algebra: of throws      850—851; see also Chaps 13 25 31 32 33 34
Algebra: Renaissance      236—237
Algebra: vs. geometry      49 136 197—198 279—282 318 323 365 391—392 834—836
Algebraic numbers      593—594 818—826 980 996—997
Algehraic geometry      920 924—946 1168
Alhazen      193 196
AlIIauld, Antoine      252
Almagest      54 122—125 133 159 191
Ampere, Andre Malic      703 750
Analytic continuation      642—644 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 89—99 135 15758 168 300
Application of areas      34 74—77
Arabs      181 190—199 205
Archimedes      37 105 134 163—166 168 286 395
Archimedes' principle      165—166
Archytas      27 28 42 46 48—49
areas      1042
Areas of Surface      355 1020
Areas, calculation of      343 348—354 360
Argand, Jean-Robet t      630—631 776
Aristarchus      156—157
Aristat'us the Elder      48
Aristotle      26—27 35—37 51—54 151—153 155—156 162—163 207 395 436 776 992 1028
Aristotle, 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
Aronhold, Siegfried Heinrich      928
Ars Gonjectandi      273 442 451
Ars Magna      236 253 263—265 267—268
Aryabhata      184 187 189
Arzela, Cesale      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 also Geocentric theory; Gravitational attraction; Heliocentric theory; Three-body problem
Asymptotic series      1097—1109
Asymptotic series, semiconvergent      1097 1104;
Athem      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
Axioms of Euclid      59—60 1005—1007
Axioms of Hilbert for geometry      1010—1013
Axioms of non Euclidean geometry      1015
Axioms of number      988—991
Axioms of projective geomety      1007—1010
Axioms of set theory      1185—1186 see
Babbage, Charles      259 622
Bacher, Maxime      599 607
Backlund, Albert Victor      703
Bacon, Franci      223—226
Bacon, Rogel      145 207—208 213 226
Baire, Rene      1079 1186 1199
Bal tels, Johann M.      862 878—879
Baldi, Belfiadino      223 229
Baltzel, Richald      879
Banach space      1088—1091 1159 1178
Bandch, Stephen      1088 92
Banow, Isaac      252 281 339 346—347 356—357 380 383—384
Base      5—6
Beeckman, Isaac      316 478
Beltlami, Eugenio      896 901—902 905 914 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      401 446 479—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 42 444 446
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
Betic, Venuable      202
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
Binomial equation      600 752—753 761—764
Binomial theorem      272—273 438 441 964—965
Binormal      560—561
Biot, Jean-Baptiste      836
Biquadratic reciprocity      816—818
Biquaternion      792
Birational tramformation      924 932
Birkhoff, George David      1106—1108 1178
Blanch cut      642 656—657
Bocthius, 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
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      574—575
Brahe, Tycho      203 219 242
Brahmagupta      183—184 192
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      114245
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 difference      440—441 452—453
Calculus of variations      573—591 685 739—751 1076 1078 1081
Calculus of variations, Jacobi condition      748
Calculus of variations, Legendre, condition      589—590
Calculus of variations, Weierstrass condition      745; see also Minimal surface
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      995
Carnot, Lazare N.M.      432 593 835—836 841
Carroll, Lewis      See Dodgson Charles
Cartan, Elie      1151 1155—156
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      1014—1015
Catenary      382 472 579
Cauchy integral formula      639
Cauchy integral theorem      599 636—637 639—640 668—669
Cauchy — Lipschitz theorem      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—702 739 743
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's theorem      349
Cavalieri, Bonvaventura      349 383—384
Cayley number      792
Cayley — Hamilton theorem      807—809
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-Euclidean geometry      907—909 921—923
Cech, Eduard      1181
Cellerier, Charles      955 56
Ceso, Ernesto      1018 1112—1113
Chain      1171—1172
Chain rule      376
1 2 3 4 5 6
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