MONGE, (GASPARD). - THE NATURE OF THE ARBITRARY FUNCTION OF PARTIAL DIFFERENTIAL EQUATIONS.

Mémoire sur la Détermination des Fonctions Arbitraires qui entrent dans les intégrales des Équations aux differences partielles-

(Paris, Imprimerie Royale, 1776). 4to. Extracts from "Mémoires de Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans", Année 1773. Pp. 305-327. Clean and fine.

First printing of Monge's second paper on the theory of partial differential equations.

In this memoir Monge continued his investigations in "a field of study that was to hold his interest for many years: the theory of partial differential equations. In particular he, undertook the parallel examination of certain equations of this type and of the families of corresponding surfaces. The geometric construction of a particular, solution of the equations under consideration allowed, him to determine the general nature of the arbitrary, function involved in the solutions of a partial differential equation. Moreover, this finding enabled him to take a position on a question then being disputed by d Alembert Euler and Daniel Bernoulli."(DSB).

Order-nr.: 44968