Euclid's Elements is the most famous mathematical work of classical antiquity, and has had a profound influence on the development of modern Mathematics and Physics. This volume contains the definitive Ancient Greek text of J.L. Heiberg 1883, together with an English translation. For ease of use, the Greek text and the corresponding English text are on facing pages. Moreover, the figures are drawn with both Greek and English symbols. Finally, a helpful GreekEnglish lexicon explaining Ancient Greek mathematical jargon is appended. Volume III contains Book 10, and covers incommensurable magnitudes.