### Theorem

**THE'OREM**, *noun* [Gr. to see.]

**1.** In mathematics, a proposition which terminates in theory, and which considers the properties of things already made or done; or it is a speculative proposition deduced from several definitions compared together.

A *theorem* is a proposition to be proved by a chain of reasoning. A *theorem* is something to be proved; a problem is something to be done.

**2.** In algebra or analysis, it is sometimes used to denote a rule, particularly when that rule is expressed by symbols.

A universal *theorem* extends to any quantity without restriction.

A particular *theorem* extends only to a particular quantity.

A negative *theorem* expresses the impossibility of any assertion.

A local *theorem* is that which relates to a surface.

A solid *theorem* is that which considers a space terminated by a solid, that is, by any of the three conic sections.