Elements

The Elements of Euclid is the archetype of the axiomatic method. Book I moves from the point that has no part to the theorem of Pythagoras; the middle books develop areas, circles, and the theory of proportion of Eudoxus; Books VII–IX treat number, including the infinitude of primes; Book X classifies irrationals; and the solid books culminate in the five regular (Platonic) solids.

For the Platonic and Pythagorean tradition the work was more than mathematics: Proclus read its first principles as a descent of unity from the Monad into figure and number. It is given here in Thomas Heath’s translation, with the Greek of Heiberg alongside.