Monge’s Descriptive Geometry in Three Examples

Abstract

Gaspard Monge (1746–1818) was at the center of developments in France in science, mathematics, and industry, and in education in those fields. He was the organizer of French industry in 1793 for producing the steel and guns essential for French military victory in 1794, and then among the founders of the École polytechnique. His descriptive geometry, first installed in the curriculum at the École royale du génie de Mézières, distills essential ideas from both military engineering and his pioneering work in the differential geometry of surfaces. Although much is written about the great influence of Monge on engineering education and on the next generation of French mathematicians, it is harder to find a detailed examination, at a basic level, of Monge’s descriptive geometry. Three example problems are here selected from materials prepared, around 1795, for use in the Écoles normales and the Polytechnique, indicating the concerns of Monge and the context of his work. Detailed solutions of those problems are provided.