Măth'e-măt'ics, n. sing.

n. sing. [Fr. mathématiques, pl., Lat. mathematica, sing., Gr. μαθηματική (sc. ἐπιστήμη), science.] 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.

☞ 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, which considers magnitude or quantity abstractly, without relation to matter; and mixed, which treats of magnitude as subsisting in material bodies, and is consequently interwoven with physical considerations.

☞ The names of sciences ending in ics, as mathematics, mechanics, metaphysics, optics, &c., are, with respect to their form, nouns in the plural number. Some of them are found in old English writers in the singular; as, mathematic (Chaucer), mechanic (Gower), metaphysic (Pope, Hobbes), &c. The plural form was probably introduced to mark the complex nature of such sciences; and it may have been in imitation of the use of the Greek plurals τὰ φυσικά, τὰ μετὰ τὰ φυσικά, τὰ ἀναλυτικά, τὰ ἠθικά, &c., to designate parts of Aristotle's writings. Previously to the present century, nouns ending in ics were construed with a verb or a pronoun in the plural; but it is now generally considered preferable to treat them as singular. In German we have die Mathematik, die Mechanik, &c., and in French la metaphysique, la optique, &c., corresponding to our mathematics, mechanics, metaphysics, optics, &c. In arithmetic, logic, magic, music, and rhetoric, — words entirely similar in origin and character, — we have ourselves preserved the singular form. The citations subjoined will serve as examples of the best present usage.

Ethics is the science of the laws which govern our actions as moral agents. Sir W. Hamilton.

All parts of knowledge have their origin in metaphysics, and finally, perhaps, revolve into it. De Quincey.

Mathematics has not a foot to stand upon which is not purely metaphysical. De Quincey.

Mechanics, like pure mathematics, may be geometrical, or may be analytical; that is, it may treat space either by a direct consideration of its properties, or by a symbolical representation. Whewell.

The Scotch metaphysics he [Carlyle] respects as being, in its day, a powerful protest against sensationalism. J. D. Morell.