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Kline M. Mathematical Thought from Ancient to Modern Times, Vol. 3
Kline M.  Mathematical Thought from Ancient to Modern Times, Vol. 3







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: Mathematical Thought from Ancient to Modern Times, Vol. 3

: Kline M.

:

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.


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: 1990

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: 03.04.2008

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Abbati, Pietro      765
Abel, Niels Henrik      216 973974 1024 1053 1097 1111 1137
Abel, Niels Henrik, Abelian integrals      653655
Abel, Niels Henrik, biography      644645
Abel, Niels Henrik, elliptic functions      645650
Abel, Niels Henrik, rigorization of analysis      947948 964965 973974
Abel, Niels Henrik, theory of equations      754755
Abelian equation      755
Abelian function      665
Abelian integral      653 663665 936 939940
Abels theorem      645 653655 935936
Absolute      907
Absolute differential calculus      see Tensor analysis
Absolutely continuous function      1048
Abstract algebra      945 11361157 see Group Ideal Ring
Abstract algebra, Lie algebra      11531156
Abstract algebra, non associative algebra      11531156
Abstraction      29 4344 171
Academies      227 370 396397 401 404 621 1023
Academy of Plato      27 4243 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      172173
Affine geometry      918
Agrippa von Nettesheim      286
Ahmes      16 18 20
Airys integral      1100 11021103
Akkadians      4
Al Battani      195
Al Kashi      254
Al Khowarizmi      192193
Alberti, Leone Battista      232233 285
Albuzjani      see AbulWefa
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      626628
Alembert, Jean Le Rond d, complex numbers      595
Alembert, Jean Le Rond d, Fourier series      458459
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      503505 510 512513 516517 532 542
Alembert, Jean Le Rond d, rigor      619
Alexander the Great      4 1012
Alexander, James W.      11761177 11791180
Alexandria      101103
Alexandroff, Paul S.      1181
Algebra      364
Algebra and analysis      323324 361 see 25 31 32 33 34
Algebra and analysis of throws      850851
Algebra and analysis vs geometry      49 136 197198 279282 318 323 365 391392 834836
Algebra and analysis, Arabic      191195
Algebra and analysis, as analysis      279280 323
Algebra and analysis, Greek (Alexandrian)      104 135144
Algebra and analysis, Hindu      184188
Algebra and analysis, Renaissance      236237
Algebraic geometry      920 924946 11681169
Algebraic invariants      925932
Algebraic invariants, absolute      926
Algebraic invariants, complete system      928929
Algebraic invariants, covariant      926
Algebraic numbers      593594 818826 980 996997
Alhazen      193 196
Almagest      54 122125 133 159 191
AlBiruni      190 195 241
AlKarkhi      192
Ampere, Andre Maiie      703 750
Analytic continuation      642644 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 157158 168 300
Application of areas      34 7477
Arabs      181 190199 205
Archimedes      37 10516 134 163166 168 286 395
Archimedes Principle      165166
Archytas      2728 42 46 4849
areas      1042
Areas of surfaces      355 1020
Areas, calculation of      343 348354 360
Argand, JeanRobert      630631 776
Aristaeus the Elder      48
Aristarchus      156157
Aristotle      2627 3537 5154 151153 155156 162163 207 395 436 776 992 1028
Aristotle, concept of mathematics      51 151153
Arithmetic, Arabic      191192
Arithmetic, Babylonian      58
Arithmetic, Egyptian      16 18
Arithmetic, Greek (Alexandrian)      131135
Arithmetic, Hindu      183186
Arithmetic, primitive      3
Arithmetic, Renaissance      251259
Arithmetica      139143
Arithmetization of analysis      947972 10251026
Arnauld, Antoine      252
Aronhold, Siegfried Heinrich      928
Ars Conjectandi      273 442 451
Ars Magna      236 253 263265 267 268
Aryabhata      184 187 189
Arzcla, Cesare      1046 10771078
Ascoli, Giulio      1077
Astrology      13 168169 179 196 202203 222
Astronomy      250 470471 490497 see Gravitational Heliocentric Three
Astronomy Arabic      196
Astronomy Babylonian      1112
Astronomy Egyptian      2122
Astronomy Greek      119 125126 148 149 151 154160
Astronomy Hindu      189
Asymptotic series      10971109
Asymptotic series semiconvergent      1097 1104 see
Athens      37 101
Atithmetica Universalis      252 271272 281 312 318 358 392 607
Atomism      150 329
Augustine, Saint      204
Autolycus of Pitane      54
Automorphic functions      726730
Automorphic functions elliptic modular      727
Automorphic functions Fuchsian      729
Automorphic functions Kleinian      730
Automorphism      1142
Axes of a conic      9395
Axiom of Archimedes      81 991 10121013
Axiom of Choice      1002 1186 1209
Axiom of reducibility      11951196
Axiomatization      1026 1027
Axiomatization of set theory      1185 1187
Axioms      50 52 59 60
Axioms of Euclid      5960 10051007
Axioms of Hilbert for geometry      10101113
Axioms of non-Euclidean geometry      1015
Axioms of number      988991
Axioms of projective geometry      10071010
Axioms of set theory      1185 1186 see Parallel
Babbage, Charles      259 622
Backlund, Albert Victor      703
Bacon, Francis      225226
Bacon, Roger      145 207208 213 226
Baire, Rene      1079 1186 1199
Baldi, Beinadino      223 229
Baltzer, Richard      879
Banach space      10881091 1159 1178
Banach, Stephen      10881092
Barrow, Isaac      252 281 339 346347 356357 380 383384
Base      56
Battels, Johann M.      862 878879
Bede, Venciable      202
Beeckman, Isaac      316 478
Beikeley, George, Bishop      400 427428
Beltrami, Eugenio      896 901902 905 914 1030 1122 1130
Bendixson, Ivar      737
Benedetti, Giovanni Battista      223 229 234 478
Bernays, Paul      1205
Bernoulli numbers      449 451
Bernoulli, Daniel      401 446 479481 492 507510 512 521 524 578 677 1112
Bernoulli, James, calculus      380383 407 412
Bernoulli, James, calculus of variations      575577
Bernoulli, James, coordinate geometry      320
Bernoulli, James, differential geometry      562
Bernoulli, James, infinite series      439 442446 451
Bernoulli, James, ordinary differential equations      471475 478
Bernoulli, James, probability      273274
Bernoulli, John      335 340 492 592
Bernoulli, John, calculus      380383 387388 406411
Bernoulli, John, calculus of variations      574577
Bernoulli, John, coordinate geometry      545
Bernoulli, John, differential geometry      556 562
Bernoulli, John, infinite series      441442 444 446
Bernoulli, John, ordinary differential equations      472476 478479 497503
Bernoulli, Nicholas (16871759)      412 447 461463
Bernoulli, Nicholas (16951726)      401 475
Berry, G.G.      1183
Bessarion, Cardinal      238
Bessel functions      480482 489 518519 710711
Bessel inequality      717 1083
Bessel, Friedrich Wilhelm      710 717 871872 980
beta function      424
Betti numbers      1169 11731174 11761177 11791180
Betti, Enrico      1169
Beudon, Jules      703
Bezout, Etienne      553 606608 796 798
Bhaskara      184186 273
Bianchi, Luigi      554 1122
Biirgi, Joost      258
Binet, Jacques P.M.      796
Binomial equation      600 752 753 761764
Binomial theorem      272 273 438 441 964 965
Binormal      560561
Biot, JeanBaptiste      836
Biquadratic reciprocity      816818
Biquaternions      792
Birational transformation      924 932
Birkhoff, George David      11061108 1178
Bocher, Maxime      599 607
Boethius, Anicius Manlius Severinus      201
Bolyai, John      873874 877881 914 921 10321033
Bolyai, Wolfgang Farkas      861 872 878879
Bolzano, Bernhard      948 950955 963 979 985 994 1025
Bombelli, Raphael      253255 260
Bonnet, Ossian      865
Boole, George      927 11891191
Borchardt, Carl Wilhelm      624 667 981
Borel, Emile      953954 1044 1078 11171119 1159 1186 1199
Bosse, Abraham      289
Bott, Raoul      1151
Bouquet, JeanClaude      642 718 722
Bourbaki, Nicolas      1210
Boutroux, Pierre      1182
Bowditch, Nathaniel      496
Boyer, Carl .      348
Boyle, Robert      227
Brachistochione      574 575
Brahe, Tycho      203 219 242
Brahmagupta      183184 192
Branch cut      642 656657
Branchpoint      641 657
Bravais, Auguste      768
Brianchon, Charles Julien      836 841
Brianchons theorem      841 848
Briggs, Henry      275276 440
Brill, Alexander von      938 940
Brillouin, Leon      1102
Briot, Charles A.A.      642 718 722
Brouncker, Lord William      255 278 468469
Brouwer, Luitzen E.J.      1132 1162 1171 11771179 11991203 1208
Brunelleschi, Filippo      232
Bryson      42
Buchheim, Arthur      808
Burali Forti paradox      1003 1182
BuraliForti, Cesare      1003
Buridan, jean      211212
Burnside, William      11421145
Burnsides problem      1143
Byzantine Empire      180 191 205 216
Caesar, Julius      178 180
Cajori, Florian      263 364
Calculus      342390 400435 615 798 see
Calculus of extension      782785
Calculus of finite differences      440 441 452 453
Calculus of variations      57391 685 739751 1076 1078 1081
Calculus of variations Jacobi condition      745
Calculus of variations Weierstrass conditions      748 see
Calculus of variations, Legendre condition      589 590
calendar      12 13 21 22 119 178 179
Callett, JeanCharles (Francois)      463464
Campanus, Johannes      217
Cantor, Georg      824 969 1021 1031 1040 1042 1044 1078 1159 1161 11841185
Cantor, Georg, irrational numbers      983986
Cantor, Georg, sets and transfinite numbers      9921003
Caratheodory, Constantin      838
Carcavi, Pierre de      275
Cardan, Jerome      221222 234 236 251253 260 263271 1028
cardinal number      995
Carnot, Lazare N.M.      432 593 835836 841
Carroll, Lewis      see Dodgson Charles
Cartan, Elie      1151 11551156
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
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, AugustinLouis      465 947 993 1024 1029 1076 10991100
Cauchy, AugustinLouis, algebra      796 798 801802 815816;
Cauchy, AugustinLouis, biography      633634
Cauchy, AugustinLouis, complex function theory      634642 667
Cauchy, AugustinLouis, differential equations      535 680681 698 701702 717721 739 743
Cauchy, AugustinLouis, differential geometry      560561
Cauchy, AugustinLouis, foundations of analysis      948 950958 961 963965 973974 979 1024 10961097
Cauchy, AugustinLouis, geometry      843
Cauchy, AugustinLouis, group theory      765766 768 1137
Cauchy, AugustinLouis, theory of numbers      819
Cavalicri, Bonvaventura      349350 383384
Cavalieris theorem      349
Cayley Hamilton theorem      807809
Cayley numbers      792
Cayley, Arthur      478 768769 792 796 804807 812 944 1030 1033 11381139 11421143 1166
Cayley, Arthur, algebraic invariants      927929 931
Cayley, Arthur, biography      805
Cayley, Arthur, non-Euclidean geometery      907909 921923
Cech, Eduard      1181
Cellerier, Charles      955956
Cesaro, Ernesto      1018 11121113
Chain      11711172
Chain rule      376
1 2 3 4 5 6
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