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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]


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.
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{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]