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
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   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:

Arithmetic \A*rith"me*tic\, n. [OE. arsmetike, OF. arismetique,
   L. arithmetica, fr. Gr. ? (sc. ?), fr. ? arithmetical, fr. ?
   to number, fr. ? number, prob. fr. same root as E. arm, the
   idea of counting coming from that of fitting, attaching. See
   Arm. The modern Eng. and French forms are accommodated to
   the Greek.]
   1. The science of numbers; the art of computation by figures.
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   2. A book containing the principles of this science.
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   Arithmetic of sines, trigonometry.

   Political arithmetic, the application of the science of
      numbers to problems in civil government, political
      economy, and social science.

   Universal arithmetic, the name given by Sir Isaac Newton to
      [1913 Webster]
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