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Kline M. — Mathematical Thought from Ancient to Modern Times, Vol. 3
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Íàçâàíèå: Mathematical Thought from Ancient to Modern Times, Vol. 3Àâòîð: 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.
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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 functions 706—707 715—716 1063 1068 Characteristic root of a determinants 800—801 Characteristic root of a matrix 807—808 Characteristic triangle 346 375 387 Characteristic value 480 673 706—707 715—716 1063 1068 Characteristics, theory of 535—538 700—703 Charpit, Paul 535 Chasles, Michel 523 834—836 844 846 849—850 Chevalier, August 756 Chladni, Ernst F.F. 697 Christianity 180—181 200—201 203—205 Christoffel symbols 894 1129 Christoffel, Elwin Biuno 666 896—899 1030 1122 1127—1128 Christoffel’s quadrilinear form 898 Christoffel’s quadrilinear form, 898—899 Chuquet, Nicolas 252 260 Cicero 179 Circular points 845 854 Cissoid 118—119 286 355 Clairaut, Alexis Claude, biography 557 Clairaut, Alexis Claude, calculus 425 Clairaut, Alexis Claude, coordinate geometry 545 548 551 Clairaut, Alexis Claude, differential equations 469—470 476—477 494 496—497 523 532 Clairaut, Alexis Claude, differential geometry 559 562—563 Clairaut, Alexis Claude, rigor 618—619 Clairaut, Alexis Claude, trigonometric scries 458 514 Clavius, Christophorus 1006 Clebsch — Gordan theorem 929 Clebsch, (Rudolf Friedrich) Alfred 808 929 934—940 943—944 Cleopatra 180 Clifford algebra 792 Clifford, William Kingdon 792 893 1167 Codazzi, Delfino 885 Cohen, Paul J. 1209 Collins, John 271 363 380 Colson, John 319 Commandino, Federigo 285 Commutator 1142 Complete continuity 1065 Complete quadrilateral 127 292—293 Completeness of axioms 1015 1207 Completeness of characteristic functions 717 COMPLEX 1171 Complex function theory 626—670 686—687 934—935 Complex integers 817—819 Complex number 143 253—254 407—408 594—595 635—636 687 775—776 815—816 Complex number, geometrical representation 594—595 628—632 Complex number, logarithms of 408—411 594 Composition indices 762 Composition series 762 767 Computing machines 258—259 Conchoid 117—118 286 Condorcet, Marie-Jcan-Antoine-Nicolas Caritat de 500 623—624 Conformal mapping 236 370 570—571 666—667 887 see Congruence of lines 567—569 Congruence of numbers 813—818 Conic sections 47—48 88—99 286 290 303—304 319 837—838 847—849 Connectivity 660—662 937 Consistency 880 913—917 1013—1014 1038 1182 1186 1206 1209 Constantine 180 Construction problems 38—42 47—48 118 195 234—235 309—310 312—314 753—754 763—764 840 Constructive proofs 1202—1203 Content 1041—1044 Continued fraction 187 254—256 459—460 1114—1116 Continuity 405 950—954 Continuity uniform 953 Continuous change 299 Continuous transformation 1160—1161 Continuous transformation group 1139—1140 1154—1155 Continuum Hypothesis 1002 1209 Convergence 460—466 see Convergence, Cauchy 961—966 Convergence, strong 1072—1073 Convergence, weak 1072—1073 Coordinate geometry 302—324 544—554 Coordinate geometry, higher plane curves 547—554 855—858 Coordinate geometry, importance of 321—324 Coordinate geometry, three—dimensional 320—321 545—547 see Quadric Copernicus, Nicholas 219 238 241—243 245—246 331 620 Cotes, Roger 408 439 460 600 Coulomb, Charles 507 Cours d’analyse algebrique 948 950 951—952 963—964 Cousin, Pierre 954 Covariant 926 Covariant differentiation 1127—1130 Cramer, Gabriel 440 552—554 606 796 Cramer’s paradox 553—554 856 Cramer’s Rule 606 Crelle, August Leopold 624 837 Cremona transformation 933—934 Cremona, Luigi 933 Cross ratio 121 22 127—128 219—220 848—849 831 907 Cross—cut 660 Ctesibius 116 Cubic equation 193—195 237 263—267 269 Cubic reciprocity 816 818 Cuneiform 5 Curl 781 785 789 Curvature 364 378 382—383 555—556 559—560 Curvature of a manifold 891—893 895—896 1126—1127 Curvature of surfaces 563—564 883—885 887 Curvature, mean 884 Curve and equation 303—304 310—317 see Algebraic Curve, concept of 174 312—314 1017—1022 1162 Curve, length of 343 348 354—355 414—416 938 1020 see Jordan Peano Curvilinear coordinates 687—689 713—714 Cusp. see Singular points of curves CYCLE 1172 Cycloid 338 350—353 355 367 469 472 556 575 Cyclotomic equation see Binomial equation Dandelin, Germinal 837 Danti, Ignazio 222—223 Darboux, Gaston 478 625 694 952 956—960 Dchn, Max 1008 1016 1143 De Analyst per Aequationes Numero Terminorum Infinitas 359 361 381 438 De Revolutionibus Orbium Coelestium 241 Dedekind, Richard 793 942—943 Dedekind, Richard, abstract algebra 1138 1142 1145—1146 1150 Dedekind, Richard, algebraic numbers 820—824 Dedekind, Richard, irrational numbers 983—988 Deferent 157 Deficiency 552 Definition, Aristotle’s concept of 51—52 Definition, in Euclid 58—59 68—71 73 78 81—82 1006 DEL 781 Delambre, Jean-Baptiste 623 Democritus 37 150 DeMorgan, Augustus 593 596 774—75 975—976 980 1096—1097 1182 1188—1189 DeMorgan’s laws 1189 Derivative 344—348 359—365 371—378 384—388 425—433 954—956 Desargues, Girard 128 285 288—295 300 840 Desargues’s involution theorem 292—293 Desargues’s theorem 291 845—846 Descartes, Rene 219—220 226—227 395 836 1028 1163 1187 Descartes, Rene, algebra 260 262 270—272 280—281 Descartes, Rene, biography 304—308 Descartes, Rene, calculus 345—346 Descartes, Rene, coordinate geometry 302 308—317 Descartes, Rene, functions 338 Descartes, Rene, music 478 Descartes, Rene, negative and complex numbers 252—254 Descartes, Rene, optics 314—315; Descartes, Rene, philosophy of science 325—331 333—334 Descartes’s rule of signs 270 Deschales, Claude-Francois Milliet 395 Descriptive geometry 235 Determinant 606—608 795—804 see Determinant, elementary divisors of 803 Determinant, infinite 732 Determinant, invariant factors 803 Determinant, similar 802 Developable surface 564—568 Developable surface, polar 566 Dialogue on the Great World Systems 327—328 Dialogues Concerning Two New Sciences 229 328 332—333 338 348 468 993 Diameter of a conic 93 98—99 294—295 Dickson, Leonard E. 792 794 1141 1146 1150—1151 Diderot, Denis 616 623 Differential 372—378 385 429—430 433 615 954 Differential geometry 554—571 881—902 430—435 Differential invariants 889—902 1122—1123 1127—1128 1130 DIMENSION 1021 1161—1162 1177 Dini, Ulisse 1040 Dinostratus 42 48 Diocletian 179 Diodes 118—119 168 286 Diogenes, Laertius 44 Dionis du Sejour, Achille-Pierre 554 Diophantus 135 138—144 192 Dirichlet principle 659—660 684—86 704—705 939 Dirichlet problem 685 703—705 Dirichlet series 830 Dirichlet, Peter Gustav Lejeune 819—820 829—830 948 950 966—967 1040 1145 Discourse on Method 226—227 304—305 Discrete vs. continuous 34—35 52—53 175—176 Disquisitiones Arithmeticae 752 813—815 826—828 870 Distance, projective definition of 908 910—911 Divergence 781 785 789 1129 Divergence theorem 790 Divergent series 466 973—977 1096—1120 see Infinite Division algebra 1151 Dodgson, Charles L. 803 Domain of rationality see Field Double points see Singular points of curves Du Bois—Reymond, Paul 694 700 705—706 970—971 973 992 998 1020 1040 1042 1052 Duality theorem 845—846 848—849 Duality, topological 1174 1179 Duns Scotus, John 208 Dupin indicatrix 569 Dupin, Charles 568—569 836 Durer, Albrecht 233—235 Dyck, Walther von 1141 1143 e 258 439 459—460 593 980—981 Eastern Roman Empire 180 191 205 216 Edge of regression 566—567 Eigenfunction see Characteristic function Eigenvalue see Characteristic value Einstein, Albert 1127 1130—1131 Eiscnstein, Fcrdinard Gotthold 818 927—929 Eisenhart, Luther P. 1134—1135 Elastica 413 558 Elasticity 468—469 485 697—698 739 Eleatic school 27 34—37 Elements of Euclid 25 27 33 37 52 56 88 172 220 393 597 866 1005—1007 Elimination see Resultant Ellipoidal harmonics 712—713 Elliptic functions 644—651 Elliptic functions, addition theorem of 648 Empedoclcs 150 Empiricism 227—230 330 Encyclopedie 432—433 465 510 595 597 616 Engel, Friedrich 878 Enriques, Federigo 1009 Entire functions 667—668 Envelope 378 556—557 Epicycle 157 Epicycloid 235 367 Eratosthenes 38 160—161 Erlanger Programm 917—920 1139 1159 Essential singularity 641 Euclid 56—89 145 579 Euclidean algorithm 78—79 187 Euclidean geometry 861—863 1005—1022 Euclidean geometry, Alexandrian Greek 104 107—119 126—129 Euclidean geometry, Arabic 195 Euclidean geometry, Babylonian 10—11 Euclidean geometry, Classical Greek 24—55 58—99 Euclidean geometry, Egyption 19—20 Euclidean geometry, Hindu 188—189 Euclidean geometry, nineteenth century 837—840 Euclidean geometry, solid 47 81—83 Euclidean geometry, spherical 89 119—121 Eudemus of Rhodes 26 29 53—54 Eudoxus 27 46 48—50 68 145 154 Euler — Maclaurin summation formula 452 Euler — Poincare formula 1171 Euler, Leonhard 614 623 739 918 948 1029 1163—1164 Euler, Leonhard, algebra 258 267 408—411 593—594 597—598 607 798 Euler, Leonhard, biography 401—403 616 Euler, Leonhard, calculus 417—421 429—430 618 Euler, Leonhard, calculus of variations 573 577—579 582 586—587 740 Euler, Leonhard, complex functions 627—628 Euler, Leonhard, coordinate geometry 545—547 550 553—54 Euler, Leonhard, differential equations 477—479 481—482 484—486 488—489 492—493 496—497 500 502 505—522 525 540—542 687 717—718 Euler, Leonhard, differential geometry 556 538—559 562—565 882 Euler, Leonhard, infinite series 439 446—454 460—465 1100 1103 1109—1110 1114 Euler, Leonhard, philosophy of science 620 Euler, Leonhard, special functions 422—424 Euler, Leonhard, theory of numbers 276 459—460 608—612 813 815 826 828—831 Euler, Leonhard, trigonometric series 454—459 Euler’s constant 450 892 Euler’s differential equation 578 584 589 Euler’s differential geometry theorem 563 Euler’s topology theorem 1163—1164 Eutocius 130 Evolute 98 555—556 Existence 599 see Partial Existence, in algebra 597—598 Existence, in Euclidean geometry 52 60 174 1010—1111 Existence, proof of 52 176—177 Exponents 260—261 Fagnano, Giulio Carlo deToschi de, Count 413—417 Fagnano, J. F. de’Toschi di 839 Fagnano’s theorem 415—416 Fatio de Duillier, Nicholas 382 557 Fatou, Pierre 1047 Feit, Walter 1142 Fejer, Leopold 1119 Fenn, Joseph 865 Fermat, Pierre de, biography 274 295 395 Fermat, Pierre de, calculus 344—348 350 352 356 383 Fermat, Pierre de, coordinate geometry 302—304 316—317 321 Fermat, Pierre de, optics 315 580—581 Fermat, Pierre de, probability 273 Fermat, Pierre de, theory of numbers 274—278 608—609 611 829 Fermat’s “theorem” 276—277 609 818—820 Ferrari, Lodovico 234 263 267—268 Ferro, Scipione dal 263 Feuerbach, Karl Wilhelm 837 fibonacci see Leonardo of Pisa Field 755 757 821—825 931 1146—1150 Field, adjunction 821 1148 Field, characteristic of 1148 Field, extension 821 1148 Field, finite 1149—1150 Field, Galois theory of 1149 Field, non—commutative 1151 Field, p-adic 1146—1147 Finsler, Paul 1135 Fior, Antonio Maria 263 Fischer, Charles Albert 1080 Fischer, Ernst 1071—1072 Fixed point theorem 1177—1179 Floquet, Gaston 713—714
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