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From: Webster's Revised Unabridged Dictionary (1913)

 Plane a.  Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface.
 Note:In science, this word (instead of plain) is almost exclusively used to designate a flat or level surface.
 Plane angle, the angle included between two straight lines in a plane.
 Plane chart, Plane curve. See under Chart and Curve.
 Plane figure, a figure all points of which lie in the same plane. If bounded by straight lines it is a rectilinear plane figure, if by curved lines it is a curvilinear plane figure.
 Plane geometry, that part of geometry which treats of the relations and properties of plane figures.
 Plane problem, a problem which can be solved geometrically by the aid of the right line and circle only.
 Plane sailing Naut., the method of computing a ship's place and course on the supposition that the earth's surface is a plane.
 Plane scale Naut., a scale for the use of navigators, on which are graduated chords, sines, tangents, secants, rhumbs, geographical miles, etc.
 Plane surveying, surveying in which the curvature of the earth is disregarded; ordinary field and topographical surveying of tracts of moderate extent.
 Plane table, an instrument used for plotting the lines of a survey on paper in the field.
 Plane trigonometry, the branch of trigonometry in which its principles are applied to plane triangles.

From: Webster's Revised Unabridged Dictionary (1913)

 Prob·lem n.
 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.
 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.
 Note: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.