PROBLEM
, in Geometry, is a proposition in which some operation or construction is required. As, to bisect a line, to make a triangle, to raise a perpendicular, to draw a circle through three points, &c.
A Problem, according to Wolsius, consists of three parts: The proposition, which expresses what is to be done; the resolution, or solution, in which are orderly rehearsed the several steps of the process or operation; and the demonstration, in which it is shewn, that by doing the several things prescribed in the resolution, the thing required is obtained.
Problem, in Algebra, is a question or proposition which requires some unknown truth to be investigated or discovered; and the truth of the discovery demonstrated.
Problem, Kepler's. See Kepler's Problem.
Problem, Determinate, Diophantine, Indeterminate, Limited, Linear, Losal, Plane, Solid, Sursolid, and Unlimited. See the adjectives.
Deliacal Problem, in Geometry, is the doubling of a cube. This amounts to the same thing as the finding of two mean proportionals between two given lines: whence this also is called the Deliacal Problem. See Duplication.
