The Collaborative International Dictionary of English v.0.48:

Dimension \Di*men"sion\, n. [L. dimensio, fr. dimensus, p. p. of
   dimetiri to measure out; di- = dis- + metiri to measure: cf.
   F. dimension. See Measure.]
   1. Measure in a single line, as length, breadth, height,
      thickness, or circumference; extension; measurement; --
      usually, in the plural, measure in length and breadth, or
      in length, breadth, and thickness; extent; size; as, the
      dimensions of a room, or of a ship; the dimensions of a
      farm, of a kingdom.
      [1913 Webster]

            Gentlemen of more than ordinary dimensions. --W.
                                                  Irving.
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   Space of dimension, extension that has length but no
      breadth or thickness; a straight or curved line.

   Space of two dimensions, extension which has length and
      breadth, but no thickness; a plane or curved surface.

   Space of three dimensions, extension which has length,
      breadth, and thickness; a solid.

   Space of four dimensions, as imaginary kind of extension,
      which is assumed to have length, breadth, thickness, and
      also a fourth imaginary dimension. Space of five or six,
      or more dimensions is also sometimes assumed in
      mathematics.
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   2. Extent; reach; scope; importance; as, a project of large
      dimensions.
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   3. (Math.) The degree of manifoldness of a quantity; as, time
      is quantity having one dimension; volume has three
      dimensions, relative to extension.
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   4. (Alg.) A literal factor, as numbered in characterizing a
      term. The term dimensions forms with the cardinal numbers
      a phrase equivalent to degree with the ordinal; thus,
      a^2b^2c is a term of five dimensions, or of the fifth
      degree.
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   5. pl. (Phys.) The manifoldness with which the fundamental
      units of time, length, and mass are involved in
      determining the units of other physical quantities.

   Note: Thus, since the unit of velocity varies directly as the
         unit of length and inversely as the unit of time, the
         dimensions of velocity are said to be length [divby]
         time; the dimensions of work are mass [times]
         (length)^2 [divby] (time)^2; the dimensions of
         density are mass [divby] (length)^3.

   Dimensional lumber, Dimension lumber, Dimension
   scantling, or Dimension stock (Carp.), lumber for
      building, etc., cut to the sizes usually in demand, or to
      special sizes as ordered.

   Dimension stone, stone delivered from the quarry rough, but
      brought to such sizes as are requisite for cutting to
      dimensions given.
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WordNet (r) 3.0 (2006):

dimension
    n 1: the magnitude of something in a particular direction
         (especially length or width or height)
    2: a construct whereby objects or individuals can be
       distinguished; "self-confidence is not an endearing property"
       [syn: property, attribute, dimension]
    3: one of three Cartesian coordinates that determine a position
       in space
    4: magnitude or extent; "a building of vast proportions" [syn:
       proportion, dimension]
    v 1: indicate the dimensions on; "These techniques permit us to
         dimension the human heart"
    2: shape or form to required dimensions

Moby Thesaurus II by Grady Ward, 1.0:

57 Moby Thesaurus words for "dimension":
   acreage, ambit, amplitude, area, bigness, body, breadth, bulk,
   caliber, circle, compass, confines, continuum, coverage, depth,
   diameter, dimensions, emptiness, empty space, expanse, expansion,
   extension, extent, field, galactic space, gauge, girth, greatness,
   height, infinite space, interstellar space, largeness, length,
   magnitude, mass, measure, measurement, nothingness, outer space,
   proportion, proportions, radius, range, reach, scale, scope, size,
   space, spatial extension, sphere, spread, superficial extension,
   surface, tract, void, volume, width