Euclid's Elements

Euclid's Elements are a series of mathematical and geometric treatises consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. They are a collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. The thirteen books cover Euclidean geometry and the ancient Greek version of elementary number theory.

Democritus Atomic Theory

Democritus' exact contributions are difficult to disentangle from his mentor Leucippus, as they are often mentioned together in texts. Their speculation on atoms, taken from Leucippus, bears a passing and partial resemblance to the nineteenth-century understanding of atomic structure that has led some to regard Democritus as more of a scientist than other Greek philosophers; nevertheless their ideas rested on very different bases.

Zeno's paradoxes

Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. It is usually assumed, based on Plato's Parmenides 128c-d, that Zeno took on the project of creating these paradoxes because other philosophers had created paradoxes against Parmenides's view.