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.

2. A treatise in this science.

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.

Source: Webster's Revised Unabridged Dictionary (1913)
 

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.

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.

Source: Webster's Revised Unabridged Dictionary (1913)