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]

WordNet (r) 3.0 (2006):

plane figure
    n 1: a two-dimensional shape [syn: plane figure, two-
         dimensional figure]