Geometry

geometry
    n 1: the pure mathematics of points and lines and curves and
         surfaces
    

Geometry \Ge*om"e*try\, n.; pl. {Geometries}[F. g['e]om['e]trie,
   L. geometria, fr. Gr. ?, fr. ? to measure land; ge`a, gh^,
   the earth + ? to measure. So called because one of its
   earliest and most important applications was to the
   measurement of the earth's surface. See {Geometer}.]
   1. That branch of mathematics which investigates the
      relations, properties, and measurement of solids,
      surfaces, lines, and angles; the science which treats of
      the properties and relations of magnitudes; the science of
      the relations of space.
      [1913 Webster]

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

   {Analytical geometry}, or {Co["o]rdinate geometry}, that
      branch of mathematical analysis which has for its object
      the analytical investigation of the relations and
      properties of geometrical magnitudes.

   {Descriptive geometry}, that part of geometry which treats of
      the graphic solution of all problems involving three
      dimensions.

   {Elementary geometry}, that part of geometry which treats of
      the simple properties of straight lines, circles, plane
      surface, solids bounded by plane surfaces, the sphere, the
      cylinder, and the right cone.

   {Higher geometry}, that pert of geometry which treats of
      those properties of straight lines, circles, etc., which
      are less simple in their relations, and of curves and
      surfaces of the second and higher degrees.
      [1913 Webster]
    

Mathematics \Math`e*mat"ics\, n. [F. math['e]matiques, pl., L.
   mathematica, sing., Gr. ? (sc. ?) science. See {Mathematic},
   and {-ics}.]
   That science, or class of sciences, which treats of the exact
   relations existing between quantities or magnitudes, and of
   the methods by which, in accordance with these relations,
   quantities sought are deducible from other quantities known
   or supposed; the science of spatial and quantitative
   relations.
   [1913 Webster]

   Note: Mathematics embraces three departments, namely: 1.
         {Arithmetic}. 2. {Geometry}, including {Trigonometry}
         and {Conic Sections}. 3. {Analysis}, in which letters
         are used, including {Algebra}, {Analytical Geometry},
         and {Calculus}. Each of these divisions is divided into
         pure or abstract, which considers magnitude or quantity
         abstractly, without relation to matter; and mixed or
         applied, which treats of magnitude as subsisting in
         material bodies, and is consequently interwoven with
         physical considerations.
         [1913 Webster]