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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
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 form      800—801
Characteristic function      706—707 715—716 1063 1068
Characteristic root of a determinant      800—801
Characteristic root of a matrix      807—808
Characteristic triangle      346 375
Characteristic value      480 673 706—707 715—716 1063 1068
Characteristic, 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's quadrilinear form      998
Christoffel's quadrilinear form $\mu$ ply form      898—899
Christoffel's quadrilinear form geometrical representaion      594—595 628—632
Christoffel's quadrilinear form, logarithm of      408—411 594
Christoffel, Elwin Bruno      666 896—899 1030 1122 1127—1128
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 equatiom      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 series      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 1167
Codazzi, Delfino      885
Cohen, Paul J.      1209
Collins, John      271 363 380
Colson, John      319
Commandino, Fedeligo      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 Integrals      817—819
Complex number      143 253—254 407—408 594—595 635—636 687 775—776 815—816
Composition indices      762
Composition series      762 767
Computing machines      258—259
Conchoid      117—118 286
Condorcet, Marie-Jean-Antoine-Nicolas Caritat de      500 623
Conformal mapping      236 370 570—571 666—667 887;
Congruence of lines      567—569
Congruence of numbers      813—818
Conic sections      47—48 88—99 286 299 303—304 319 837—838 847—849
Connectivity      660—662 937
Consistence      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
Continuity, uniform      953
Continuous change      299
Continuous transformation      1160 61
Continuous transformation group      1139—1140 1154—1155
Continuum Hypothesis      1002 1209
Convergence      460—466
Convergence, Cauchy      961—966
Convergence, strong      1072—073
Convergence, weak      1072—1073; see also Summability
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;
Copernicus, Nicholas      219 238 241—243 245—246 331
Cotes, Roger      408 439 460 600
Coulomb, Charles      507
Cours d'Analyse Algebrique      948 950 963—964
Cousin, Pierre      954
Covariant      926
Covariant diffcrentiation      1127—1130
Cramer's paradox      553—554 856
Cramer's rule      606
Cramer, Gabriel      440 552—554 606 796
Crelle, August Leopold      624 837
Cremona transformation      933—934
Cremona, Luigi      933
Cross cut      660
Cross ratio      121—122 127—128 219—220 848—849 851 907
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; Algebraic
Curve: concept of      174 312—314 1017—1122 1162
Curve: length of      343 348 354—355 414—416 958 1020;
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
De Analysi 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, algebers      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
Dehn, Max      1008 1016 1143
DEL      781
Delambre, Jean Baptiste      623
Democritus      37 150
DeMorgan's laws      1189
DeMorgan, Augustus      593 596 774—775 975—976 980 1096—1097 1182 1188—1189
Derivative      344—348 359—365 371—378 384—388 425—433 954—956
Desargues's involution theorem      292—293
Desargues's theorem      291 845—846
Desargues, Girard      128 285 288—295 300 840
Descartes's rule of signs      270
Descartes, Rene      219—220 395 836 1028 1163 1187
Descartes, Rene, algebra      260 262 270—272 345—346
Descartes, Rene, biography      304—308
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
Deschales. Claude-Francois Milliet      395
Descriptive geometry      235
Determinant      606—608 795—804
Determinant, elementary divisors of      803
Determinant, infinite      732
Determinant, invariant factors      803
Determinant, similar      802; see also Matrices
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 61—5 954
Differential geometry      554—571 881—902 11301135
Differential invariants      889—902 1122—1123 1127—1128 1130
DIMENSION      1021 1161—1162 1177
Dini, Ulisse      1040
Dinostratus      42 48
Diocles      118—119 168 286
Diocletian      179
Diogenes, Laertius      44
Dionis du Sejour, Achille-Pierre      554
Diophantus      135 138—144 192
Dirichlet principle      659—660 684—686 704—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 see
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      258 439 593 980—981
Eastern Roman Empire      180 191 205 216
Edge of regression      566—567
Eigenfunction      See Characteristic function
Eigenvalue      See Charactelistic value
Einstein, Albert      1127 1130—1131
Eisenhart, Luther P.      1134—135
Eisenstein, Ferdinard Gotthold      818 927—929
Elastica      413 558
Elasticity      468—469 483 697—698 739
Eleatic school      27 34—37
Elements of Euclid      23 27 33 37 52 56—88 172 220 393 597 866 1005—1007
Elimination      See Resultant
Ellipoidal harmonic      712—713
Elliptic functions      644—651
Elliptic functions, addition theorem of      648
Empedocles      150
Empiricism      227 30 330
Encyclopedie      432—433 465 510 595 597 616
Engel, Friedrich      878
Enriques, Federigo      1009
Entire functions      667—68
Envelope      378 556—557
Epicycle      157
Epicycloid      233 367
Eratosthenes      38 160—161
Erlanger Programm      917—920 1139 1159
Essential singularity      641
Euclid      56—89 145 579
Euclidean aIgorithm      78—79 187
Euclidean geometry      861—863 1005—1022
Euclidean geometry, Alexandrian Greek      104 107—119 126—129
Euclidean geometry, Arabic      193
Euclidean geometry, Babylonian      10—11
Euclidean geometry, Classical Gleek      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's constant      450 892
Euler's differential equation      578 584 589
Euler's differential geometry theorem      563
Euler's topology theorem      1163—1164
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      41721 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—554
Euler, Leonhard, differential equations      477—479 481—482 484—486 488—489 492—493 500 502 505—522 525 540—542 687 717—718
Euler, Leonhard, differential geometry      556 558—559 562—565 882
Euler, Leonhard, infinite series      439 460—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
Eutocius      130
Evolute      98 555—556
Existence      599
Existence in algebra      597—598
Existence in Euclidean geometry      52 60 174 1010—1011
Existence, proof of      52 176—177; Partial
Exponents      260—261
Fagnano's theorem      413—416
Fagnano, Giulio Carlo de'Toschi de, Count      413—417
Fagnano, J.F. de'Toschi di      839
Fatio de Duillier, Nicholas      382 537
Fatou, Pierre      1047
Feit, Walter      1142
Fejer, Leopold      1119
Fenn, Joseph      865
Fermat's "theorem"      276—277 818—820
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
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, ad junction      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
FLUENT      361
Fluxion      361
1 2 3 4 5 6
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