Ăx'i-om, n.

(Synop., § 130), n. [Fr. axiome, Lat. axioma, Gr. ἀξίωμα, that which is thought worthy, that which is assumed, a basis of demonstration, a principle, from ἀξιόω, to think worthy, ἄξιος, worthy.]

1. (Math.) A self-evident and necessary truth, or a proposition whose truth is so evident at first sight, that no process of reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, “The whole is greater than a part;” “A thing can not, at the same time, be and not be.”
2. An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy.

Syn. — AXIOM, MAXIM, APHORISM, ADAGE. An axiom is a self-evident truth which is taken for granted as the basis of reasoning. A maxim is a guiding principle ever to be received and admitted, especially in the practical concerns of life. An aphorism is a detached sentence expressing some weighty truth or sentiment. An adage is a saying of long-established authority and of universal application.