Plane \Plane\, a. [L. planus: cf. F. plan. See Plan, a.]

Without elevations or depressions; even; level; flat; lying in, or constituting, a plane; as, a plane surface. [1913 Webster]

Note: In science, this word (instead of plain) is almost exclusively used to designate a flat or level surface. [1913 Webster]

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. [1913 Webster]

Source: The Collaborative International Dictionary of English v.0.48
 

Problem \Prob"lem\, n. [F. probl[`e]me, L. problema, fr. Gr. ? anything thrown forward, a question proposed for solution, fr. ? to throw or lay before; ? before, forward + ? to throw. Cf. Parable. ] [1913 Webster]

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. [1913 Webster]

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. [1913 Webster]

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. [1913 Webster]

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. [1913 Webster] Problematic

Source: The Collaborative International Dictionary of English v.0.48
 

Plane \Plane\, a. [L. planus: cf. F. plan. See Plan, 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.

Source: Webster's Revised Unabridged Dictionary (1913)
 

Problem \Prob"lem\, n. [F. probl[`e]me, 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.

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.

Source: Webster's Revised Unabridged Dictionary (1913)