Source : Webster's Revised Unabridged Dictionary (1913)

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.

Source : WordNet®

arithmetic
     adj : relating to or involving arithmetic; "arithmetical
           computations" [syn: {arithmetical}]

arithmetic
     n : the branch of pure mathematics dealing with the theory of
         numerical calculations