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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
Newton — Raph on method      381
Newton' laws of motion      366—367 490
Newton's parallelogram      439—440 552
Newton, Sir Isaac, algebra      252 254 271—272 281 600 607
Newton, Sir Isaac, astronomy      365—369 470
Newton, Sir Isaac, biography      365—369
Newton, Sir Isaac, calculus      354 359—365 384 387 556
Newton, Sir Isaac, calculus of variations      573—574
Newton, Sir Isaac, compared with Leibniz      378—380
Newton, Sir Isaac, coordinate geometry      548—549
Newton, Sir Isaac, differential equations      470 475 497
Newton, Sir Isaac, function concept      339—340
Newton, Sir Isaac, infinite series      437—442 461
Newton, Sir Isaac, methodology of science      331 334
Newton, Sir Isaac, philosophy of science      219 616 620
Nicholas of Cusa, Cardinal      241
Nichomachus      135—138 201
Nicole, Francois      548
Nicomedes      17—18 286
Nieuwentijdt, Bernard      385
Nine point cilcle      837
Noebeling, A. Georg      1162
Noether, Emmy      931—932 1153 1180
Noether, Max      933—934 940—941 944
Non Euclidean geomery      729 861—881 947 1014 1021
Non Euclidean geomery, applicability      872—873 877 921—922
Non Euclidean geomery, axiom for      1015
Non Euclidean geomery, consistency      880 913—917
Non Euclidean geomery, hyperbolic      905—906
Non Euclidean geomery, implications      879—880
Non Euclidean geomery, models      888 905—906 912—917
Non Euclidean geomery, priority of creation      877—879
Non Euclidean geomery, single and double elliptic      904 906 912—913;
Non Riemannian geometries      1133—1135
Non-Archimedian geometry      1016
normal      560—561
Novikov, P.S.      1143
NUMBER      29—30
Number, amicable      31 278 610
Number, hexagonal      31—32
Number, pentagonal      31
Number, perfect      31 78 137 278 610
Number, polygonal      137 277—278 829
Number, prime      see Prime number
Number, square      30
Number, triangular      29—30 828; Irrational Negative Theory
Ohm, Martin      976 987
Olbers, Heinrich W.M      818 872 980
Oldenburg. Henry      273
Olympiodorus      580
Operator      1076—1077 1082 1085—1089 1094
Operator, hermitian      1092—1093
Opticks      358
Optics      88 166—168 196 212—213 285—286 307 314—315 357 579—581
Ordinal number      1000—1001
Ordinary differential equation      468—500 578 709—738
Ordinary differential equation, adjoint      487
Ordinary differential equation, BernoulIi's      474
Ordinary differential equation, Bessel's      488—489 519
Ordinary differential equation, Clairaut's      476—477
Ordinary differential equation, exact      476
Ordinary differential equation, existence theorems      717—721 1178—1179
Ordinary differential equation, first order      451 471—478
Ordinary differential equation, Fuchsian      721—722 724—726
Ordinary differential equation, higher order      484—487
Ordinary differential equation, hypergeometric      489 712 723
Ordinary differential equation, Lame's      721—722
Ordinary differential equation, Legendre's      529 711
Ordinary differential equation, linear      485—487 730—732
Ordinary differential equation, Mathieu's      713—714
Ordinary differential equation, method of series      488—489 709—712
Ordinary differential equation, nonlinear      483—484 732—738
Ordinary differential equation, periodic solutions      713—714 730—732
Ordinary differential equation, Riccati      483—484
Ordinary differential equation, second order      478—484
Ordinary differential equation, singular solutions of      476—478
Ordinary differential equation, systems of      490—492 735 742
Ordinary differential equation, variation of parameters      497—499
Ordinary differential equation, Weber's      714; see also Asymptotic series Automorphic Sturm
Oresme, Nicole      210—211 241 437
Orthogonal system of functions      716 1066
Orthogonal trajectories      474—475
Osculating circle      556
Osculating plane      559 561
Ostrogladsky's theorem      See Divergence theorem
Ostrogradsky, Michel      683 789—790
Oughtred, William      258
Oval of Descaltes      315—316
Ozanam, Jacques      323 1028
P-adic fields      1146—1147
Pacioli, Luca      234—237 250—251 260
Painleve, Paul      737
Palseval, Marc-Antoine      716—717
Pappi      16 20 25 132
Pappu's Guldin theorem      129
Pappus      26 38 57 127—129 168 174 223 1005
Pappus's Theorem      128 297—298
Parabolic cylinder functions      714
Paradoxes of set theory      1182—1185
Parallel axiom      60 177 852 863—867 916 1012 1014
Parallel displacement      1130—1133
Parent, Antoine      545
Parmenides      27 150
Parseval inequality      1093
Parseval's theorem      716—717 971 1047
Partial derivative      425
Partial differential equation      362 502—543 567—568 671—707
Partial differential equation, classification      700—701
Partial differential equation, equation      524—529 659 682—687 703—705
Partial differential equation, existence theorems      685 699—707 1178—1179
Partial differential equation, first order      532—535
Partial differential equation, function      524 682—686
Partial differential equation, Hamilton Jacobi      744
Partial differential equation, heat equation      672—675 679 687—689
Partial differential equation, Helmholtz      693—696 1056
Partial differential equation, nonlinear      536—540
Partial differential equation, Poisson's      682 684—685
Partial differential equation, potential      524—529 659 681—687 703—705
Partial differential equation, reduced wave equation      693—694
Partial differential equation, separation of variables      516—517 673—674
Partial differential equation, systems of      540—542 690—699
Partial differential equation, total      532
Partial differential equation, wave equation      502—522 690—694
Pascal triangle      272—273
Pascal's theorem      297—298 848
Pascal, Blaise      219 252 258 272—273 395 1026 1028
Pascal, Blaise, bioglaphy      295—297
Pascal, Blaise, calculus      350 352—353 383—384
Pascal, Blaise, projective geometry      297—301 840
Pasch's axiom      1011—1012
Pasch, Moritz      1008—1009 1137
Peacock, George      622 773—775 974—975 980
Peano curve      1018 1161
Peano's axioms      988—989
Peano, Giuseppe      988—989 1009—1010 1014 1018 1020 1038 1042—1043 1137 1162
Peckham, John      213
Peirce, Beujamin      793 1023
Peirce, Charles S.      793 1144 1191
Peletier, Jacques      1005
Pell's equation      278 610—611
Pemberton, Henry      392
Pendulum motion      337 469 471—472 479 556
Pericles      37
Periodicity modules      641 662
Permanence of form      773—775
Permutation      See Substitution
Permutations and combinations      273
Persia      4 10
Perspective      231—234 286—287
Peurbach, George      238
Peyrard, Fraucois      57
Pfaff, Jobann Friedrich      489 870
Philolaus      28 147—148
Philoponus      211
PI      10—11 19 134—135 251 255 353 439 448 593 980—982
Piazzi, Giuseppe      870
Picard's theorems      668
Picard, (Charles) Emile      668 705—706 720 945 1025 1037 1170 1169
Pick, Georg      1131
Pieri, Mario      1009—010
Piero della Francesca      233 235
Pierpont, James      1096
Pitiscus, Bartholomaus      238
Pitot, Henri      545
Plateau, Joseph      750
Plato      26 38 42—47 47—48 150—151 154 395 1026
Plato, concept of mathematic      43—44 150—151 175
Platonic school      42—48
Playfair, John      865
Plucker formulas      857
Plucker, Julius      836 846 853—858 933
Plutarch      46 106
Poincare Bendixson theorem      737
Poincare conjecture      117576
Poincare's last theorem      1178
Poincare, Henri      706—707 709 1003 1025—1026 1056 1145
Poincare, Henri, algebra      732
Poincare, Henri, algebraic geometry      938—939
Poincare, Henri, asymptotic series      1097 1104—108
Poincare, Henri, automorphic functions      728—730 1139
Poincare, Henri, biography      706 1024 1170
Poincare, Henri, differential equations      704 706—707 732—737
Poincare, Henri, foundations      1086 1197—1199
Poincare, Henri, non-Euclidean geometry      916—917 921—922
Poincare, Henri, topology      1161—1162 1170—1176 1178—1179
Point at infinity      290
Poisson, Simeon-Denis      452 464 633 678—679 681—682 690—691 697 710 739—740 801 962 1024 1052 1100 1103 1110—1111
Polar coordinates      319
Pole and Polar      96—97 294 298—299 845
Polyhedra, regular      47 85—86
Poncelet, Jean Victor      834 836—837 840 841—846 900 933 1024
Pontrjagin, Lev S.      1180
Poree, Gilbert de la      206
Porphyry      57
positional notation      5—7 185
Potential theory      522—529 659 681—687 1055—1056
Poudra, N.G.      289
Power series      643—644; see also Taylor's theorem
Precession of the equinoxes      158 369
Primary and secondary qualities      326 329
Prime number      78 277 609 830—832;
Prime number theorem      830—832
Principia Mathematica      1193
Principle of continuity      385—387 841 843—845
Principle of duality      845—846 848—849 855
Principle of least action      581—582 587—589 620 739—745
Principle of least time      315 580—581
Principle of Stationary Phase      1099
Pringsheim, Alfred      1038
Printing      217
probability      273
Proclus      24 26 29 44 56 104 129 131 863—864 993 1005
Projectile motion      286 476 479
Projection      232 287
Projective geometry      233 285—301 834—859 1007—1010
Projective geometry and metric geometry      904—923
Projective geometry, algebraic      852—859
Projective geometry, relation to Euclidean geometry      850—852 909 1033
Projective geometry, relation to non-Euclidean geometry      909—912 1033;
Projective plane      290 1168
proof      14 20—22 34 44—46 50 144 171 198—199 282 383—389 393—394 426—434 617—619 1024—1026
Proof, indirect method of      33 44—45
Proportion      32 137—138 237
Proportion, Eudoxian theory of      68
Pseudosphere      893 905
Ptolemy dynasty      102—103
Ptolemy, Claudius      119 122—125 145 159—160 169 863 866
Puiseux's theorem      552—553
Puiseux, Victor      552 641—642
Pure and applied mathematics      1036—1038
Pythagoras      27—34 46
Pythagorean number philosophy      219
Pythagorean Theorem      10 20 33 63—64 184
Pythagorean triples      10 31—32 34
Pythagoreans      27—34 49 147—150
Quadratic equation      89 19 186—187 192—193
Quadratic equation, solved geometrically      76—77
Quadratic form      799—800
Quadratic form, reduction to standard form      799 801—802
Quadratic forminfinite      1063—1066; see also Law of inertia
Quadratic reciprocity      611—612 813—815 817
Quadratrix      39—40 48
Quadrature      42
Quadric surface      108—110 168 545—546 848
Quadrivium      146 149—150 201—202
Qualitative theory of ordinary differential equations      732—738 1170
Quantics      928
Quantitative versus qualitative knowledge      333—334
Quartic equations      267—270
Quaternion      779—782 791 1025
Quetelet, Lambert A.J.      569 845 933
Quintic equation      763
Raabe, Joseph L      1112
Radon, Johann      1050
Rameau, Jean-Philippe      515
Raphson, Joseph      381
Rate of change, instantaneous      344 360
Rayleigh, Lord (Strutt, John William)      684
Recorde, Robert      259—260
Reduction of singularities      941—942
Reformation      218
Regiomontanus      See Muller Johannes
Regius, Hudalrich      278
Relativity      894 1130—1131
Religious motivation      219—220 359
Residue      638 640
Resolvent equation      604 760
Resultant      606 8 797—798
Revival of Greek work      205—207 216—217
Rhaeticus, George Joachim      238—239
Riccati, Jacopo Francesco, Count      483—484 500
Ricci tensor      1127
Ricci's lemma      1129
Ricci-Curbastro, Gregorio      1122—1130
Richard, Jules      1183
Riemann four index symbol      894 1125
Riemann mapping theorem      666
Riemann surface      656—662 934—935 937
Riemann zeta function      831
Riemann — Lebesgue lemma      104647
Riemann — Roch theorem      665 940
Riemann, Georg Friedrich Bernhard      1021 1030 1033 1077 1122
Riemann, Georg Friedrich Bernhard, biography      655—656 889 924
Riemann, Georg Friedrich Bernhard, complex function theory      656—666 934 939
Riemann, Georg Friedrich Bernhard, differential equations      691—693 722—724 727
Riemann, Georg Friedrich Bernhard, differential geometry      889—899 904 1122
Riemann, Georg Friedrich Bernhard, foundations of analysis      955 967
Riemann, Georg Friedrich Bernhard, non Euclidean geometry      914
Riemann, Georg Friedrich Bernhard, theory of numbers      831
Riemann, Georg Friedrich Bernhard, topology      920
Riemann, Georg Friedrich Bernhard, trigonometric series      967—969 1040
Riemannian geometry      889—899 1126—1127 1131—1133
Riemannian geometry, applicability      893
Riemanu hypothesis      831
Riemanu problem      724 726 1069
Riesz representation theorem      108
Riesz — Fischer theorem      1072 1084
Riesz, Friedrich      1070—1073 1085—1087
Rigor      947—977 1025 1209;
Ring      821—822 931 1150—1153
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