Euclid's Elements - A 2,500 Year History
Bob Gardner
East Tennessee State University
Department of Mathematics and Statistics
Johnson City, TN 37614
The Content of The Elements
Euclid in a close-up of Raphael's The School at Athens
Image from The MacTutor History of Mathematics archive.
Euclid's Elements of Geometry consists of 13 "books," which are better described in modern terms as 13 chapters.
- Plane geometry, Books I-VI
- Arithmetic, Books VII-X
- Solid geometry, Books XI-XIII
The size of the books varies between about 2.5% of the whole for the smallest, Book II, and 25% for Book X. Each of the others is roughly 5-8% of the total.
Euclid is known to have written several other works, including:
- The Data. This concerns elementary geometry and may be thought of as elementary exercises in analysis.
- The book On divisions (of figures). This work is lost in Greek but has been discovered in the Arabic.
- The Porisms. This contains 38 lemmas and 171 theorems. A "porism" is something between a theorem and a problem: it deals with something already existing, as a theorem does, but has to find it (eg. the center of a circle).
- The Conics. This is lost, but is said to have consisted of four books and was used by Apollonius.
- The Phaenomena. This is an astronomical work and is still extant.
- The Optics. Copies still exist.
- Elements of Music is a work credited to Euclid, but no longer exists.
[Heath, pages 8 to 17]
Go to the next section: Greek Commentaries on The Elements.
Last revised November 14, 2009.