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From The Collaborative International Dictionary of English v.0.48 [gcide]:
Mathematics \Math'e*mat"ics\, noun [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.
From The Collaborative International Dictionary of English v.0.48 [gcide]:
Algebra \Al"ge*bra\, noun [LL. algebra, fr. Ar. al-jebr reduction of parts to a whole, or fractions to whole numbers, fr. jabara to bind together, consolidate; al-jebr w'almuq[=a]balah reduction and comparison (by equations): cf. F. alg['e]bre, It. & Sp. algebra.]
1. (Math.) That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols. It is applicable to those relations that are true of every kind of magnitude.
2. A treatise on this science. Algebraic
From WordNet (r) 3.0 (2006) [wn]:
noun
1: the mathematics of generalized arithmetical operations
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