5. (Math.) (a) The equality or similarity of ratios, especially of
geometrical ratios; or a relation among quantities such that the
quotient of the first divided by the second is equal to that of the
third divided by the fourth; -- called also geometrical proportion, in
distinction from arithmetical proportion, or that in which the
difference of the first and second is equal to the difference of the
third and fourth.
Proportion in the mathematical sense differs from ratio. Ratio is the
relation of two quantities of the same kind, as the ratio of 5 to 10,
or the ratio of 8 to 16. Proportion is the sameness or likeness of two
such relations. Thus, 5 to 10 as 8 to 16; that is, 5 bears the same
relation to 10 as 8 does to 16. Hence, such numbers are said to be in
proportion. Proportion is expressed by symbols thus:
a:b::c:d, or a:b = c:d, or a/b = c/d.
(b) The rule of three, in arithmetic, in which the three given terms,
together with the one sought, are proportional.
Continued proportion, Inverse proportion, etc. See under Continued,
Inverse, etc. -- Harmonical, or Musical, proportion, a relation of
three or four quantities, such that the first is to the last as the
difference between the first two is to the difference between the last
two; thus, 2, 3, 6, are in harmonical proportion; for 2 is to 6 as 1 to
3. Thus, 24, 16, 12, 9, are harmonical, for 24:9::8:3. -- In
proportion, according as; to the degree that. "In proportion as they
are metaphysically true, they are morally and politically false."
Burke.
Pro*por"tion, v. t. [imp. & p. p. Proportioned (?); p. pr. & vb. n.
Proportioning.] [Cf. F. proportionner. Cf. Proportionate, v.] 1. To
adjust in a suitable proportion, as one thing or one part to another;
as, to proportion the size of a building to its height; to proportion
our expenditures to our income.
In the loss of an object we do not proportion our grief to the real
value . . . but to the value our fancies set upon it.
Addison.