Theorem
in geometry, a proposition to be proved; a statement of a principle to be demonstrated; that is, the truth of which is required to be made evident THEOREM by a course of reasoning called a demonstration. In the synthetical method of investigation, which is that for the most part employed in geometry, it is usual to state the principle to be proved before to be pro commencing the demonstration, which proceeds by a regular course of argumentation to the final conclusion, confirmatory of the principle enunciated. The principle being proved, it may properly be employed as a premise in the deduction of new truths. The principle, as enunciated before the demonstration, is the theorem; its statement after rule or demonstration constitutes a rule or formula, according as the statement is made in ordinary or in algebraic language. A theorem differs from a problem in this, that the latter is a statement of something to be done, the former of something to be proved .