×

zbMATH — the first resource for mathematics

A source book in mathematics, 1200–1800. (English) Zbl 0205.29202
Source Books in the History of the Sciences. Cambridge, Mass.: Harvard University Press, xiv, 427 p. (1969).
See the review below.
Editorial addition:
Table of contents:
Chapter I: Arithmetic. Introduction. p. 1; Leonardo of Pisa, The rabbit problem. p. 2; Recorde, Elementary arithmetic. p. 4; Stevin, Decimal fractions. p. 7; Napier Logarithms. p. 11; Pascal, The Pascal triangle. p. 21; Fermat, Two Fermat theorems and Fermat numbers. p. 26; Fermat, The Pell equation. p. 29; Euler, Power residues. p. 31; Euler, Fermat’s theorem for \(n=3, 4\). p. 36; Euler, Quadratic residues and the reciprocity theorem. p. 40; Goldbach, The Goldbach theorem. p. 47; Legendre, The reciprocity theorem. p. 49.
Chapter II: Algebra. Introduction. p. 55; Al-Khwarizmi, Quadratic equations. p. 55; Chuquet, The triparty. p. 60; Cardan, On cubic equations. p. 62; Ferrari, The biquadratic equation. p. 69; Viète, The new algebra. p. 74; Girard, The fundamental theorem of algebra. p. 81; Descartes The new method. p. 87; Descartes, Theory of equations. p. 89; Newton, The roots of an equation. p. 93; Euler, The fundamental theorem of algebra. p. 99; Lagrange, On the general theory of equations. p. 102; Lagrange, Continued fractions. p. 111; Gauss, The fundamental theorem of algebra. p. 115; Leibniz, Mathematical logic. p. 123:
Chapter III: Geometry. Introduction. p. 133; Oresme, The latitude of forms. p. 134; Regiomontanus, Trigonometry. p. 138; Fermat, Coordinate geometry. p. 143; Descartes, The principle of nonhomogeneity. p. 150; Descartes, The equation of a curve. p. 155; Desargues, Involution and perspective triangles. p. 157; Pascal, Theorem on conics. p. 163; Newton, Cubic curves. p. 168; Agnesi, The versiera. p. 178; Cramer and Euler, Cramer’s paradox. p. 180; Euler, The Bridges of Konigsberg. p. 183.
Chapter IV: Analysis before Newton and Leibniz. Introduction. p. 188; Stevin Centers of gravity. p. 189; Kepler, Integration methods. p. 192; Galilei, On infinities and infinitesimals. p. 198; Galilei, Accelerated motion. p. 208; Cavalieri, Principle of Cavalieri. p. 209; Cavalieri, Integration. p. 214; Fermat, Integration. p. 219; Fermat, Maxima and minima. p. 222; Torricelli, Volume of an infinite solid. p. 227; Roberval, The cycloid. p. 232; Pascal, The integration of sines. p. 238; Pascal, Partial integration. p. 241; Wallis, Computation of \(\pi\) by successive interpolations. p. 244; Barrow, The fundamental theorem of the calculus. p. 253; Huygens, Evolutes and involutes. p. 263.
Chapter V: Newton, Leibniz and their school. Introduction. p. 270; Leibniz, The first publication of his differential calculus. p. 271; Leibniz, The first publication of his integral calculus. p. 281; Leibniz, The fundamental theorem of the calculus. p. 282; Newton and Gregory, Binomial series. p. 284; Newton, Prime and ultimate ratios. p. 291; Newton, Genita and moments. p. 300; Newton, Quadrature of curves. p. 303; L’Hôpital, The analysis of the infinitesimally small. p. 312; Jakob Bernoulli, Sequences and series. p. 316; Johann Bernoulli, Integration. p. 324; Taylor, The Taylor series. p. 328; Berkeley, The Analyst. p. 333; Maclaurin, On series and extremes. p. 338; D’Alembert, On limits. p. 341; Euler, Trigonometry. p. 345; D’Alembert, Euler, Daniel Bernoulli, The vibrating string and its partial differential equation. p. 351; Lambert, Irrationality of \(\pi\). p. 369; Fagnano and Euler, Addition theorem of elliptic integrals. p. 374; Euler, Landen, Lagrange, The metaphysics of the calculus. p. 383; Johann and Jakob Bernoulli, The brachystochrone. p. 391; Euler, The calculus of variations. p. 399; Lagrange, The calculus of variations. p. 406; Monge, The two curvatures of a curved surface. p. 413.
Index p. 421
Reviewer: Fl. T. Câmpan

MSC:
01A05 General histories, source books
01-06 Proceedings, conferences, collections, etc. pertaining to history and biography
00B60 Collections of reprinted articles
00B50 Collections of translated articles of general interest
01A35 History of mathematics in Late Antiquity and medieval Europe
01A40 History of mathematics in the 15th and 16th centuries, Renaissance
01A45 History of mathematics in the 17th century
01A50 History of mathematics in the 18th century
01A55 History of mathematics in the 19th century
Keywords:
Source book