AXIOM, a statement admitted without proof, as that if two equal quantities are added respectively to two equal quantities, the sums will be equal. The Greek philosophers recognized the existence of first principles "the truth of which," as Aristotle said, "it is not possible to prove." These were called axioms, and also "the common [things]" (rQ. Kowa, to koina) or "com mon opinions" (Kotvai SoE at, koinai doxai) . (See MATHEMATICS, FOUNDATIONS OF.)