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Kline M. — Mathematical Thought from Ancient to Modern Times, Vol. 2
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Íàçâàíèå: Mathematical Thought from Ancient to Modern Times, Vol. 2Àâòîð: 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: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1990Êîëè÷åñòâî ñòðàíèö: 480Äîáàâëåíà â êàòàëîã: 03.04.2008Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Abbati, Pietro 765 Abel's theorem 645 653—655 935—936 Abel, Abelian integrals 653—655 Abel, biography 644—645 Abel, elliptic functions 645—650 Abel, Niels Henrik 216 973—974 1024 1053 1097 1111 1137 Abel, rigorization of analysis 947—948 964—965 973—974 Abel, theory of equations 754—755 Abelian equation 755 Abelian function 663 Abelian integral 653 663—565 936 939—940 Absolute 907 Absolute differential calculus See Tensor analysis Absolutely continuous function 1048 abstract see also Field Group Ideal Ring Abstract algebra 945 1136—1157 Abstract Lie algebra 1153—1156 Abstract non associative algebra 1153—1156 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 Pianos 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-BirHni 190 195 241 al-Karkhi 192 Al-Kashi 254 Al-Khowarizmi 192—193 Alberti, Leone Battista 232—233 285 Albuzjani see Abu'l-Wefa Alexander the Great 4 101—102 Alexander, James W. 1176—1177 1179—1180 Alexandria 101—103 Alexandroff, Paul S. 1181 Algebra 13 25 31 32 33 34 364 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 Algebra Renaissance 236—237 Algebra vs geometry 49 136 197—198 279—282 318 323 365 391—392 834—836 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 54 122 133 159 191 Ampere, Andre-Marie 703 750 Analytic continuation 642—644 1114 Analytic geometry see Coordinate geometry Anaxagoras 38 147 Anaximander 27 Anaximenes 27 Angle, projective definition of 907 911 Anharmonic ratio see Cross ratio Antiphon 42 Apastamba 184 Apollonian problem 99 Apollonius 56 89 99 135 157—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 of surfaces 355 1020 Areas, calculation of 343 348—354 360 Argand, Jean-Robert 630—631 776 Aristaeus the Elder 48 Aristarchus 156—57 Aristotle 26—27 35—37 51—54 151—53 155—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 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 Gravitational Heliocentric Three-body Astronomy, Arabic 196 Astronomy, Babylonian 11—12 Astronomy, Egyptian 21—22 Astronomy, Greek 119 125—126 148—149 151 154—160 Astronomy, Hindu 189 Asymptotic series 1097—1109 (see also WKBJ method) Asymptotic series semiconvergent 1097 1104 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 Parallel 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 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, Bernadino 223 229 Baltzer, Richaid 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, Veneiable 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, Geoige, 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—77 1179—1180 Betti, Enrico 1169 Beudon, Jules 703 Bezout, Etienne 553 606—608 796 798 Bhaskara 184—186 273 Bianchi, Luigi 554 1122 Biirgi, Joost 258 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 Biquaternions 792 Birational transformation 924 932 Birkhoff, George David 1106—1108 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—76 440 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 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 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 Weierstrass conditions 748 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, irrational numbers 983—986 Cantor, sets and transfinite numbers 992—1003 Caratheodory, Constantin 838 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—1156 Cassini, Jacques 320 469 Cassini, Jean-Dominque 320 Cassinian ovals 320 Cassiodorus, Aurelius 202 Castelnuovo, Guido 934 Catalani, Eugene Charles 788 Cataldi, Pietro Antonio 278 Categoricalness 1014—1015 Catenaiy 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, algebra 796 798 801—802 815—816 Cauchy, Augustin-Louis 465 947 993 1024 1029 1076 1099—1100 Cauchy, biography 633—634 Cauchy, complex function theory 634—642 667 Cauchy, differential equations 535 680—681 698 701—702 717—721 739 743 Cauchy, differential geometry 560—561 Cauchy, foundations of analysis 948 950—958 961 963—965 973—974 979 1024 1096—1097 Cauchy, geometry 843 Cauchy, group theory 765—766 768 1137 Cauchy, theory of numbers 819 Cavalieri's theorem 349 Cavalieri, Bonvaventura 349—350 383—384 Cayley numbers 792 Cayley — Hamilton theorem 807—809 Cayley, algebraic invariants 927—929 931 Cayley, Arthur 478 768—769 792 796 804—807 812 944 1030 1033 1138—1139 1142—1143 1166 Cayley, biography 805 Cayley, non-Euclidean 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 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 800-1 Characteristic root of a matrix 807—808 Characteristic triangle 346 375 387
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