Some remarks on The Elements

Definition 5 in Book V is the first rigorous definition of a real number. It was this very same idea that Dedekind spelled out so carefully centuries later. It is attributed to Eudoxus.

The Euclidean algorithm for finding the greatest common measure of two lengths is beautifully described in Proposition 3 of Book X. Unfortunately, there is no proof of the irrationality of the square root of a positive integer which is not a perfect square (attributed to Theaetetus-see Plato's dialogue titled Theaetetus). Socrates lived 469-399BC, whereas