It would be natural, and in some respects desirable, to call these foundations of geometry by the name "assumptions," since they are simply statements that are assumed to be true. The real foundation principles cannot be proved; they are the means by which we prove other statements. But as with most names of men or things, they have received certain titles that are time-honored, and that it is not worth the while to attempt to change. In English we call them axioms and postulates, and there is no more reason for attempting to change these terms than there is for attempting to change the names of geometry[42] and of algebra.[43] Since these terms are likely to continue, it is necessary to distinguish between them more carefully than is often done, and to consider what assumptions we are justified in including under each. In the first place, these names do not go back to Euclid, as is ordinarily supposed, although the ideas and the statements are his. "Postulate" is a Latin form of the Greek [Greek: aitema] (_aitema_), and appears only in late translations. Euclid stated in substance, "Let the following be assumed." "Axiom" ([Greek: axioma], _axioma_) dates perhaps only from Proclus (fifth century A.D.), Euclid using the words "common notions" ([Greek: koinai ennoiai], _koinai ennoiai_) for "axioms," as Aristotle before him had used "common things," "common principles," and "common opinions." The distinction between axiom and postulate was not clearly made by ancient writers. Probably what was in Euclid's mind was the Aristotelian distinction that an axiom was a principle common to all sciences, self-evident but incapable of proof, while the postulates were the assumptions necessary for building up the particular science under consideration, in this case geometry.[44]