VCE: Preface

By extracting the 60 constructions from the body of 465 propositions of Euclid's Elements, we are able to reconstruct the essence of the geometry of the ancients.

In this website we are in the process posting the visual expansion (in VMI style) of all 48 of the two-dimensional (2D) constructions. So far, we have completed sketches for all 48 2D constructions. All of these, comprising the ancient plane geometry of the Pythagoreans, will be posted this year.

Eventually, these will be published as illustrated books, cdroms, and websites, as usual. We will include notes for students and teachers, extensive computer graphics, and animations with vocal commentary.

Revised 28 September 1997 by Ralph Abraham <>