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:

Trigonometry \Trig`o*nom"e*try\, n.; pl. -tries. [Gr. ? a
   triangle + -metry: cf. F. trigonom['e]trie. See Trigon.]
   1. That branch of mathematics which treats of the relations
      of the sides and angles of triangles, which the methods of
      deducing from certain given parts other required parts,
      and also of the general relations which exist between the
      trigonometrical functions of arcs or angles.
      [1913 Webster]

   2. A treatise in this science.
      [1913 Webster]

   Analytical trigonometry, that branch of trigonometry which
      treats of the relations and properties of the
      trigonometrical functions.

   Plane trigonometry, and Spherical trigonometry, those
      branches of trigonometry in which its principles are
      applied to plane triangles and spherical triangles
      respectively.
      [1913 Webster]