A NEW FOUNDATION OF THE CALCULUS

LA GRANGE (LAGRANGE), JOSEPH LOUIS.

Two Papers. 1. Sur une Nouvelle Espece de Calcul rélatifs à différentiation & à l'intégration des quantités variables. - 2. Sur la Forme des Racines Imaginaires des Equations.

(Berlin, Ch. Fr. Voss, 1774). 4to. Large uncut copy, broadmargins, without wrappers as issued in "Nouvaux Memoires d l'Academie Royale des Sciences et Belles-Lettres. Année 1772." pp. 185-221 and pp. 222-258.

First edition of these two important papers. In the first paper "Sur une Nouvelle Espece de Calcul..." he made the most ambitious attempt to rebuild the foundation of the calculus. The paper is in fact an outline of his "Theorie des functions", issued later in 1797.
"This work greatly impressed Lacroix, Condorcet and Laplace. Based on the analogy between powers of biniminals and differentials, it is one of the sources of the symbolic calculuses of the nineteenth century. A typical example of Lagrange's thinking as an analyst in this sentence taken form the memoir: "Although the principle of the analogy (between powers and diffrentials) is nor self-evident, nevertheless, since the conclusions drawn from it are not thereby less exact, I shall make use of it to discover various theorems...""(Jean Itard in DSB).
The second paper "Sur la Forme..."When D'Alembert red the paper he gave the following respons:"Your demonstration on imaginary roots seem to me to leave nothing to be desired, and I am very much obliged to you for the justice you have rendered to mine, which, in fact, has the minor fault (pwerhaps more apparant than real) of not being direct, bu which is quite simple and easy. D'Alembert was alluding to his Cause de vents (1747)."(DSB).

Order-nr.: 38985