Problem

Prob"lem (?), n. [F. problème, L. problema, fr. Gr. ? anything thrown forward, a question proposed for solution, fr. ? to throw or lay before; ? before, forward + ? to throw. Cf. Parable. ]

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. Bacon.

2. (Math.) Anything 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 differs from theorem in this, that a problem is something to be done, as to bisect a triangle, to describe a circle, etc.; a theorem is something to be proved, as that all the angles of a triangle are equal to two right angles.

Plane problem (Geom.), a problem that can be solved by the use of the rule and compass. -- Solid problem (Geom.), a problem requiring in its geometric solution the use of a conic section or higher curve.