A Source Book in Mathematics

This work presents, in English translation, the great discoveries in mathematics from the Renaissance to the end of the 19th century.

You are able to read the writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others, exactly as the world saw them for the first time. Succinct selections from 125 different treatises and articles, most of them unavailable elsewhere in English, offer a vivid, first-hand story of the growth of mathematics. The articles are grouped in five major sections:

I. THE FIELD OF NUMBER. 24 articles trace developments from the first steps in printed arithmetic, through selected number systems, to the early phases of modern number theory. Here is Dedekind on imaginary numbers, Euler on the use of e to represent 2.718 .., Gauss on number congruence, Delamain on the slide rule, Pascal on his caluclating machine, and more original articles.

I. THE FIELD OF ALGEBRA. 18 articles on algebra include writings by Fermat, John Wallis, Newton, Leibniz, Abel, Galois, etc. They write on equa-tions, symbolism, series, imaginary roots, early methods of solving the cubic and biquartic algebraic equations, and numerical equations of the higher degree.

III. THE FIELD OF GEOMETRY. 36 articles on geometry span 500 years. Here are the early writers such as Fermat, Desargues, Pascal, and Descartes; and some of the men who revived the study in the 19th century and developed non-Euclidian forms: Lobachevsky, Bolyai, Riemann, and others.

IV. THE FIELD OF PROBABILITY. Selections from Fermat, Pascal, De Moivre, Legendre, Chebyshev, and Laplace discuss crucial topics in the early history of this branch of modern mathematics.

V. THE FIELD OF CALCULUS, FUNCTIONS, QUATERNIONS. The development of the calculus, function theory, and quaternions is covered from early sources of the calculus to important advances relating to the commutative law in quaternions and Ausdehnunglehre. This section contains works of Bessel, Mobius, W.R. Hamilton, Leibniz, Berkeley, Cauchy, Fermat and six other pioneering mathematicians.

Each article is preceded by a biographical-historical introduction.