THE'OREM, n. [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.