Introduction

Euclid’s Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences. The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages.

Dr. Joyce created this version of Euclid’s Elements to rekindle an interest in the work, and to show how interactive diagrams could help bring the Elements alive on the web. The text of all 13 books is complete, and every figure — even those in the last three books on solid geometry that are three-dimensional — is illustrated by a live, draggable diagram.

This edition renders the diagrams with geomlib, a TypeScript port of the original 1996 Geometry Applet. The diagrams are interactive: drag a free point and the rest of the construction follows. For details on how to interact with the figures, see Using geomlib diagrams; for the full proposition list, head to the Table of Contents.

Also republished on this site are two related tutorials:

Compass Geometry — a seven-part introduction to Euclidean constructions using compass and straightedge.
Round triangles and related topics in spherical and inversive geometry.

Read the Elements →