Geometries

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.
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   2. A treatise on this science.
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   {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.
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