From The Collaborative International Dictionary of English v.0.48 [gcide]:
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]
From The Collaborative International Dictionary of English v.0.48 [gcide]:
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]
From WordNet (r) 3.0 (2006) [wn]:
geometry
n 1: the pure mathematics of points and lines and curves and
surfaces
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