Euclid's Elements
Clicking here will take you to David Joyce's translation of Euclid's Elements.
Over the past 2000+ years, the Elements has been translated from the original Greek into many languages. Two noteworthy translations into English include that by Thomas L. Heath in 1908 and that by Oliver Byrne in 1847. Heath's translation and his commentary on the text is available online at the Perseus Project. Byrne designed a wonderful version of the Elements with an imaginative use of color to illustrate geometry. Bill Casselman has made Book I available online at the University of British Columbia.
Euclid's Elements is divided into thirteen books. The first consists of definitions, common notions, postulates and propositions. Most of the remaining books contain definitions and propositions. A few books just contain propositions. Clicking on any definition, common notion, postulate or proposition will take you to explanatory material, including the relevant Java applet. Professor Joyce includes a Table of Contents and an Introduction that explains how to use the Java applets and provides additional information about Euclid.
The Elements covers the following topics:
- Book 1. The fundamentals of geometry: theories of triangles, parallels, and area.
- Book 2. Geometric algebra.
- Book 3. Theory of circles
- Book 4. Constructions for inscribed and circumscribed figures.
- Book 5. Theory of abstract proportions.
- Book 6. Similar figures and proportions in geometry.
- Book 7. Fundamentals of number theory.
- Book 8. Continued proportions in number theory.
- Book 9. Number theory.
- Book 10. Classification of incommensurables
- Book 11. Solid geometry.
- Book 12. Measurement of figures.
- Book 13. Regular solids.
Enjoy!