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EUCLID’S ELEMENTS OF GEOMETRY The Greek text of J.L. Heiberg (1883–1885) from Euclidis Elementa, edidit et Latine interpretatus est I.L. Heiberg, in aedibus B.G. Teubneri, 1883–1885 edited, and provided with a modern English translation, by Richard Fitzpatrick c Richard Fitzpatrick, 2007. All rights reserved. ISBN Contents Introduction 4 Book 1 5 Book 2 49 Book 3 69 Book 4 109 Book 5 129 Book 6 155 Book 7 193 Book 8 227 Book 9 253 Book 10 281 Book 11 423 Book 12 471 Book 13 505 Greek-English Lexicon 539 Introduction Euclid’s Elements is by far the most famous mathematical work of classical antiquity, and also has the distinction of being the world’s oldest continuously used mathematical textbook. Little is known about the author, beyond the fact that he lived in Alexandria around 300 BCE. The main subjects of the work are geometry, proportion, and number theory. 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 which can be achieved using a straight-rule and a compass. F