Thē'o-rem, n.

n. [Fr. théorème, Sp. & It. teorema, Lat. theorema, Gr. θεώρημα, from θεωρεῖν, to look at, from θεωρός, a spectator.]

1Sense 1. That which is considered and established as a principle; hence, sometimes, a rule. “Not theories, but theorems (θεωρήματα), the intelligible products of contemplation, intellectual objects in the mind, and of and for the mind exclusively.” Coleridge.

By my theorems, Which your polite and terser gallants practice, I re-refine the court, and civilize Their barbarous natures. Massinger.

2Sense 2. (Math.) A statement of a principle to be demonstrated.

A theorem is something to be proved, and is thus distinguished from a problem, which is something to be solved. In analysis, the term is sometimes applied to a rule, especially a rule or statement of relations expressed in a formula or by symbols; as, the binomial theorem; Taylor’s theorem.

Negative theorem, a theorem which expresses the impossibility of any assertion.—Particular theorem, a theorem which extends only to a particular quantity.—Universal theorem, a theorem which extends to any quantity without restriction.