Chapter 17 - Gaspard Monge, Géométrie descriptive, first edition (1795)

Abstract

On the one hand, descriptive geometry is the culmination of a long and slow evolution of different graphical methods used for representing space. On the other hand, it is the fruit of the fertile imagination of a talented geometrician, heir to the age of enlightenment, committed revolutionary and brilliant teacher. This ambiguous status between art and science confers to descriptive geometry. The concept of “New geometry” was born with the Monge lectures. In the prologue to his twelve lectures, which were to be the starting-point of the interest of French mathematicians in geometry and of the upheaval mathematics underwent in the 19th century, Monge defined descriptive geometry as an ‘art’. It is a ‘science’ replied in echo Michel Chasles in his Aperçu historique sur l’origine et le développement des méthodes en géométrie before pursuing word for word with the rest of Monge's definition. But at the same time, Chasles refused to admit that by itself, descriptive geometry had the power to demonstrate fundamental geometrical properties such as whether a curve is planar or not.