A Source Book in Mathematics, 1200-1800D. J. Struik Harvard University Press - 446 pages |
Table des matières
Euler Power residues | 33 |
Euler Quadratic residues and the reciprocity theorem | 47 |
ALGEBRA | 55 |
Descartes The new method | 83 |
Descartes Theory of equations | 91 |
Newton The roots of an equation | 97 |
Euler The fundamental theorem of algebra | 99 |
Lagrange On the general theory of equations | 102 |
Roberval The cycloid | 232 |
Pascal The integration of sines | 238 |
Pascal Partial integration | 241 |
Wallis Computation of by successive interpolations | 244 |
Barrow The fundamental theorem of the calculus | 253 |
Huygens Evolutes and involutes | 263 |
NEWTON LEIBNIZ AND THEIR SCHOOL Introduction | 270 |
Leibniz The first publication of his differential calculus | 271 |
Lagrange Continued fractions | 111 |
Gauss The fundamental theorem of algebra | 115 |
Leibniz Mathematical logic | 123 |
GEOMETRY Introduction | 133 |
Oresme The latitude of forms | 134 |
Regiomontanus Trigonometry | 138 |
Fermat Coordinate geometry | 143 |
Descartes The principle of nonhomogeneity | 150 |
Descartes The equation of a curve | 155 |
Desargues Involution and perspective triangles | 157 |
Pascal Theorem on conics | 163 |
Newton Cubic curves | 168 |
Agnesi The versiera | 178 |
Cramer and Euler Cramers paradox | 180 |
Euler The Bridges of Königsberg | 183 |
ANALYSIS BEFORE NEWTON AND LEIBNIZ Introduction | 188 |
Stevin Centers of gravity | 189 |
Kepler Integration methods | 192 |
Galilei On infinites and infinitesimals | 198 |
Galilei Accelerated motion | 208 |
Cavalieri Principle of Cavalieri | 209 |
Cavalieri Integration | 214 |
Fermat Integration | 219 |
Fermat Maxima and minima | 222 |
Torricelli Volume of an infinite solid | 227 |
Leibniz The first publication of his integral calculus | 281 |
Leibniz The fundamental theorem of the calculus | 282 |
Newton and Gregory Binomial series | 284 |
Newton Prime and ultimate ratios | 291 |
Newton Genita and moments | 300 |
Newton Quadrature of curves | 303 |
LHôpital The analysis of the infinitesimally small | 312 |
Jakob Bernoulli Sequences and series | 316 |
Johann Bernoulli Integration | 324 |
Taylor The Taylor series | 328 |
Berkeley The Analyst | 333 |
Maclaurin On series and extremes | 338 |
DAlembert On limits | 341 |
Euler Trigonometry | 345 |
DAlembert Euler Daniel Bernoulli The vibrating string and its partial differential equation | 351 |
Lambert Irrationality of π | 369 |
Fagnano and Euler Addition theorem of elliptic integrals | 374 |
Euler Landen Lagrange The metaphysics of the calculus | 383 |
Johann and Jakob Bernoulli The brachystochrone | 391 |
Euler The calculus of variations | 399 |
Lagrange The calculus of variations | 406 |
Monge The two curvatures of a curved surface | 413 |
| 421 | |
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Expressions et termes fréquents
abscissa Acta Eruditorum algebra angle arbitrary arithmetic asymptotes axis base Bernoulli calculus called circle conic sections Corollary cube curve cycloid Desargues Descartes diameter differential differential calculus Diophantus divided divisor equal equation Euclid's Elements Euler example expressed Fermat figure finite fluxions follows fractions function geometric given gives hence hyperbola infinite number infinitely small infinity integral intersection Jakob Bernoulli Johann Bernoulli Leibniz Lemma logarithms mathematicians mathematics method multiplied Newton nonresidues notation obtain Opera omnia ordinate parabola parallel parallelogram perpendicular plane prime number problem proof proportion Proposition quantities radius ratio rectangle residues roots Scholium segment Selection side Simon Stevin sine solid solution square straight line surface T. L. Heath tangent theorem translation triangle Viète