Gentlemen of more than ordinary dimensions. --W.
Irving.
{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.
2. Extent; reach; scope; importance; as, a project of large
dimensions.
3. (Math.) The degree of manifoldness of a quantity; as, time
is quantity having one dimension; volume has three
dimensions, relative to extension.
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^{2}b^{2}c is a term of five dimensions, or of the fifth
degree.
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}.