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.
   [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]

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