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
   relations.
   [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]

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.
      [1913 Webster]

   2. A book containing the principles of this science.
      [1913 Webster]

   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.
      [1913 Webster]

WordNet (r) 3.0 (2006):

arithmetic
    adj 1: relating to or involving arithmetic; "arithmetical
           computations" [syn: arithmetical, arithmetic]
    n 1: the branch of pure mathematics dealing with the theory of
         numerical calculations

Moby Thesaurus II by Grady Ward, 1.0:

65 Moby Thesaurus words for "arithmetic":
   Boolean algebra, Euclidean geometry, Fourier analysis,
   Lagrangian function, algebra, algebraic geometry, analysis,
   analytic geometry, associative algebra, binary arithmetic,
   calculation, calculus, ciphering, circle geometry,
   descriptive geometry, differential calculus, division algebra,
   equivalent algebras, estimation, figuring, game theory, geodesy,
   geometry, graphic algebra, group theory, higher algebra,
   higher arithmetic, hyperbolic geometry, infinitesimal calculus,
   integral calculus, intuitional geometry, invariant subalgebra,
   inverse geometry, line geometry, linear algebra,
   mathematical physics, matrix algebra, metageometry,
   modular arithmetic, n-tuple linear algebra, natural geometry,
   nilpotent algebra, number theory, plane trigonometry,
   political arithmetic, projective geometry, proper subalgebra,
   quaternian algebra, reckoning, reducible algebra, set theory,
   simple algebra, solid geometry, speculative geometry,
   spherical trigonometry, statistics, subalgebra, systems analysis,
   topology, trig, trigonometry, universal algebra,
   universal geometry, vector algebra, zero algebra