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:

Algebra \Al"ge*bra\, n. [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.
      [1913 Webster]

   2. A treatise on this science.
      [1913 Webster] Algebraic
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