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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.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1990Êîëè÷åñòâî ñòðàíèö: 448Äîáàâëåíà â êàòàëîã: 03.04.2008Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Netto, Eugen E. 1018 1139 Neugebauer, Otto 47 Neumann problem 685 Neumann, Carl Gottfried 666 685 704 711 1054 Neumann, John von 1092—1095 1186 1205 Newton — Raphson method 381 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 470 475 491—493 497 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 Newton’s laws of motion 366—367 490 Newton’s parallelogiam 439—440 552 Nicholas of Cusa, Cardinal 241 Nichomachus 135—138 201 Nicole, Francois 548 Nicomedes 117—118 286 Nieuwentijdt, Bernard 385 Nine-point circle 837 Nobeling, A. Georg 1162 Noether, Emmy 931—932 1153 1180 Noether, Max 933—934 940—941 944 Non Euclidean geometry 729 861—881 947 1014 1025 see Non Euclidean geometry, applicability 872—873 877 921—922 Non Euclidean geometry, axioms for 1015 Non Euclidean geometry, consistency 880 913—917 Non Euclidean geometry, hyperbolic 905—906 Non Euclidean geometry, implications 879—880 Non Euclidean geometry, models 888 905—906 912—917 Non Euclidean geometry, priority of creation 877—879 Non Euclidean geometry, single and double elliptic 904 906 912—913 Non-Archimedian geometry 1016 Non-Riemannian geometries 1133—1135 normal 560—561 Novikov, P.S. 1143 NUMBER 2930 see Irrational Negative Theory Number, amicable 31 278 610 Number, hexagonal 31—32 Number, pentagonal 31 Number, perfect 31 78 137 278 610 Number, poligonal 137 277—278 829 Number, prime see Prime number Number, square 30 Number, triangular 29—30 828 Ohm, Martin 976 987 Olbers, Heinrich W.M. 818 872 980 Oldenburg, Henry 273 370 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—581 740 Ordinal number 1000—1001 Ordinary differential equation 468—500 578 709—738 see Automorphic Qualitative Sturm Summability Ordinary differential equation, adjoint 487 Ordinary differential equation, Bernoulli’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, hypergeomctric 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 Oresme, Nicole 210—211 241 437 Orthogonal system of functions 716 1066 Orthogonal trajectories 474—475 Osculating circle 556 Osculating plane 559 561 Ostrogradsky, Michel 683 789—790 Ostrogradsky’s theorem see Divergence theorem Oughtred, William 258 Oval of Descartes 315—316 Ozanam, Jacques 323 1028 P-adic fields 1146—1147 Pacioli, Luca 234—237 250—251 260 Painleve, Paul 737 Pappus 26 38 57 127—129 168 174 223 1005 Pappus — Guldin theorem 129 Pappus’s theorem 128 297—298 Papyri 16 20 25 132 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, Marc-Antoine 716—717 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, existence theorems 685 699—707 1178—1179 Partial differential equation, first order 532—535 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—542 696—699 Partial differential equation, total 532 Partial differential equation, wave equation 502—522 690—694 Pascal triangle 272—273 Pascal, Blaise 219 252 258 272—273 395 1026 1028 Pascal, Blaise, biography 295—297 Pascal, Blaise, calculus 350 352—353 383—384 Pascal, Blaise, projective geometry 297—301 840 Pascal’s theorem 297—298 848 Pasch, Moritz 1008—1009 1137 Pasch’s axiom 1011—1112 Peacock, George 622 773—775 974—975 980 Peano curve 1018 1161 Peano, Giuseppe 988—989 1009—1010 1014 1018 1020 1038 1042—1043 1137 1162 Peano’s axioms 988—989 Peckham, John 213 Peirce, Benjamin 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, Francois 57 PfafF, Johann Fnedrich 489 870 Philolaus 28 147—48 Philoponus 211 Pi, 10—11 19 134—135 251 255 353 439 448 593 980—982 Piazzi, Giuseppe 870 Picard, (Charles) Emile 668 705—706 720 945 1025 1037 1040 1070 1169 Picard’s theorems 668 Pick, Georg 1131 Pieri, Mario 1009—1010 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 mathematics 43—44 50—51 175 Platonic school 42—48 Playfair, John 865 Plucker formulas 857 Plucker, Julius 836 846 853—858 933 Plutarch 46 106 Poincare conjecture 1175—1176 Poincare — Bendixson theorem 737 Poincare, Henri 706—707 709 973 1003 1025—1026 1056 1145 Poincare, Henri, algebra 732 Poincare, Henri, algebraic geometry 938—939 Poincare, Henri, asymptotic series 1097 1104—1108 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 Poincare’s last theorem 1178 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—846 906 933 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 Potential theory, equation 524—529 659 682—687 703—705 Potential theory, function 524 682—686 Poudra, N.G. 289 Power series 643—644 see Precession of the equinoxes 158 369 Primary and secondary qualities 326 329 Prime number 78 277 609 830—832 see Prime 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 see Projective geometry, algebraic 852—859 Projective geometry, and metric geometry 904—923 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, Victor 552 641—642 Puiseux’s theorem 552—553 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 8—9 19 186—187 192—193 Quadratic equation solved geometrically 76—77 Quadratic form 799—780 see Quadratic form, infinite 1063—1066 Quadratic form, reduction to standard form 799 801—802 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—608 797—798 Revival of Greek works 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 hypothesis 831 Riemann mapping theorem 666 Riemann problem 724 726 1069 Riemann surface 656—662 934—935 937 Riemann zeta function 831 Riemann — Lebcsgue lemma 1046—47 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—669 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
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