From The Collaborative International Dictionary of English v.0.48:

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
   [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 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
      [1913 Webster]
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