MONGE, (GASPARD). - THE GENERAL REPRESENTATION OF DEVELOPABLE SURFACES.

Mémoire sur les Fonctions Arbitraires continues ou discontinues, qui entrent dans les Intégrales des Équations aux Différences finies. (1774) (+) Mémoire sur les Propriétés de plusieur Genres de Surfaces Courbes, particulièrement sur celles des Surfaces développables, avec une Application à Théorie des Ombres & des Pénombres. (1775). (2 Memoirs).

(Paris, Moutard, Panckoucke, 1780). 4to. Extract from "Mémoires fe Mathematique et de Physique, Présentés à l'Academie des Sciences par divers Savans", Tome IX. Pp. 345-381 a. 2 folded engraved plates. And pp. 382-440 a. 3 folded engraved plates. Clean and fine.

First printing of two importent papers by Monge in differential functions and infinitesimal geometry, - in the first he discussed the nature of the arbitrary functions involved in the integrals of, finite difference equations. He also considered the, equation of vibrating strings, a topic he later investigated more fully.
In the second memoir Monge returned to infinitesimal geometry. Working on the theory of developable surfaces outlined by Euler in 1772, he applied it to the problem, of shadows and penumbrae and treated several, problems concerning ruled surfaces. "It is in this paper that he gives a general representation of developable surfaces..."(Morris Kline "Mathematical Thoughts from Ancient to Modern Times", p. 567).

Order-nr.: 44972