ARITHMETIQUE UNIVERSELLE DE NEWTON, Traduite du Latin en Francais; Avec Des Notes Explicatives, Par Noel Beaudeux.

Paris: Chez Bernard, 1802. 2 volumes bound as one. First French edition. Extensively illustrated with folding engraved diagrams of geometric problems. 4to, contemporary calf with gilt tooling on covers and spine. Red morocco lettering panel. Gilt stamp of the “Prix du College Royal D’Henry IV” on both covers. xxiv, 252; 258, errata,1 ad. A fine, especially bright copy with a small tear to upper spine. These algebraic lectures given by Newton at Cambridge were first published by William Whiston in 1707. Whiston “extracted from Newton a somewhat reluctant permission to print it. Among several new theorems on various points in algebra and the theory of equations, Newton here enunciates the following important results. He explains that the equation whose roots are a solution of a given problem will have as many roots as their are different probable cases..He extends Descartes rules of signs to give limits to the number of imaginary roots..The most interesting theorem contained in the work is his attempt to find a rule (analogous to that of Descartes for real roots) by which the number of imaginary roots of a equation can be determined.” Later, with the idea of stimulating annotations to the work, Gravedsande published SPECIMIN COMMENTARII IN ARITHMETICAM UNIVERSLAEM; and Maclaurins’s ALGEBRA seems to have been written in response to this.