Definition: arithmetic

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Source: WordNet (r) 1.7 

arithmetic
     adj : relating to or involving arithmetic; "arithmetical
           computations" [syn: arithmetical]
     n : the branch of pure mathematics dealing with the theory of
         numerical calculations

Source: Webster's Revised Unabridged Dictionary (1913) 

Sexagesimal \Sex`a*ges"i*mal\, a. [Cf. F. sexag['e]simal.]
   Pertaining to, or founded on, the number sixty.

   Sexagesimal fractions or numbers (Arith. & Alg.), those
      fractions whose denominators are some power of sixty; as,
      1/60, 1/3600, 1/216000; -- called also astronomical
      fractions, because formerly there were no others used in
      astronomical calculations.

   Sexagesimal, or Sexagenary, arithmetic, the method of
      computing by the sexagenary scale, or by sixties.

   Sexagesimal scale (Math.), the sexagenary scale.
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.

   2. A book containing the principles of this science.

   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
      algebra.
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.