Abstract

The foci of this penetrating study are Euclid's geometry and Descartes' mathematics. It is a contribution to the history of mathematics, but it is much more, for the differing approaches to mathematics in the ancient and the modern worlds is shown to have deep consequences for both doing and knowing. The investigation is centered on the nature of geometrical construction in ancient and modern mathematics, and, by extension, the crucial importance of construction to the reality and self-understanding of modernity.