Introduction to Part II

Abstract

The present, second, part of my study is devoted to Descartes’ ideas on geometrical construction and exactness. In the General Introduction I sketched the structure of the story of construction (Section 1.3) as consisting of two periods and one central figure, Descartes. As in Part I, my primary subject is geometrical construction, and my main objective is to understand the processes involved in the interpretation of mathematical exactness. In the early modern period Descartes was the key figure with respect to these issues. His Geometry of 1637 was to be the dominating influence in mathematics for more than 50 years. It was, as I will show, largely motivated by the need, as perceived by its author, for a more precise and reasoned definition of exactness in geometry.