Prŏb'lem, n.

n. [Fr. problème, Sp., It., & Lat. problema, from Gr. πρόβλημα, any thing thrown forward, a question proposed for solution, from προβάλλει, to throw or lay before, from πρό, before, forth, forward.] 1. A question proposed for solution; a matter stated for examination or proof; hence, a matter difficult of solution or settlement; a doubtful case; a question involving doubt. The problem is, whether a strong and constant belief that a thing will be helps any thing to the effecting of the thing. Bacon. 2. (Math.) Any thing which is required to be done; as, in geometry, to bisect a line, to draw a perpendicular, or, in algebra, to find an unknown quantity. Problem, in customary usage, differs from theorem in this, that a problem is something to be done, a theorem something to be proved; the former a specific thing to be effected, the latter a relation or identity to be shown or established;—a distinction not made by the ancients.