Considerations on the Relationship between Solid Problems and Their Relating Plane Geometry Theorems in Descriptive Geometry by Gaspard Monge

Abstract

　This paper introduces a work of Gaspard Monge on plane geometry relating to a solid problem in his textbook for Descriptive Geometry. Monge included some theorems on plane geometry in Chap.2 in the book, with relating to a solid problem in which tangential plane to a sphere is determined by use of cones in a sophisticated way, which gives an intuitive understanding to some of the theorems. These theorems are further developed to other ones to which corresponding solid problems are not treated in the chapter. It is conjectured that Monge was conscious of the relationship with geometry and also turned his eyes attention to development of geometry in Descriptive Geometry.