theorem

n. [ L. theorema, Gr. &unr_; a sight, speculation, theory, theorem, fr. &unr_; to look at, &unr_; a spectator: cf. F. théorème. See Theory. ] 1. That which is considered and established as a principle; hence, sometimes, a rule. [ 1913 Webster ]

Not theories, but theorems (&unr_;), the intelligible products of contemplation, intellectual objects in the mind, and of and for the mind exclusively. Coleridge. [ 1913 Webster ]

By the theorems,
Which your polite and terser gallants practice,
I re-refine the court, and civilize
Their barbarous natures. Massinger. [ 1913 Webster ]

2. (Math.) A statement of a principle to be demonstrated. [ 1913 Webster ]

☞ 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. See the Note under Proposition, n., 5. [ 1913 Webster ]

Binomial theorem. (Math.) See under Binomial. --
Negative theorem, a theorem which expresses the impossibility of any assertion. --
Particular theorem (Math.), a theorem which extends only to a particular quantity. --
Theorem of Pappus. (Math.) See Centrobaric method, under Centrobaric. --
Universal theorem (Math.), a theorem which extends to any quantity without restriction. [ 1913 Webster ]