Most of the theorems appearing in the Elements were not discovered by Euclid himself, but were the work of earlier Greek mathematicians such as Pythagoras (and his school), Hippocrates of Chios, Theaetetus of Athens, and Eudoxus of Cnidos. However, Euclid is generally credited with arranging these theorems in a logical manner, so as to demonstrate (admittedly, not always with the rigour demanded by modern mathematics) that they necessarily follow from five simple axioms. Euclid is also credited with devising a number of particularly ingenious proofs of previously discovered theorems: e.g., Theorem 48 in Book 1.

The geometrical constructions employed in the Elements are restricted to those that can be achieved using a straight-rule and a compass. Furthermore, empirical proofs by means of measurement are strictly forbidden: that is, any comparison of two magnitudes is restricted to saying that the magnitudes are either equal, or that one is greater than the other.

The Elements consists of thirteen books.

I have prepared a new edition of Euclid's Elements that presents the definitive (and completely out-of-print) Greek text - that is, the one edited by J.L. Heiberg (1883-1885) - accompanied by a modern English translation, as well as a Greek-English lexicon. Neither the spurious books 14 and 15, nor the extensive scholia which have added to the Elements over the centuries, are included in the edition. The aim of the translation is to make the mathematical argument as clear and unambiguous as possible, while still adhering closely to the meaning of the original Greek. Text within square parenthesis (in both Greek and English) indicates material identified by Heiberg as being later interpolations to the original text (some particularly obvious or unhelpful interpolations have been omitted altogether). Text within round parenthesis (in English) indicates material which is implied, but not actually present, in the Greek text.

My modern edition of Euclid's Elements is available in various formats:

- [PDF]
- A downloadable fully-bookmarked PDF document.
- [BOOK]
- A professionally-bound hardback print-on-demand book.
- [BOOK]
- A professionally-bound paperback print-on-demand book. This version is also available from Amazon.

*Euclidus Opera Ominia*, I.L. Heiberg & H. Menge (editors), Teubner (1883-1916).*Euclid in Greek, Book 1*, T.L. Heath (translator), Cambridge (1920).*Euclid's Elements*, T.L. Heath (translator), Dover (1956).*History of Greek Mathematics*, T.L. Heath, Dover (1981).

Richard Fitzpatrick Last modified: Tue Aug 26 21:02:48 CDT 2014