Harmonical proportion

Proportion Pro*por"tion, n. [F., fr. L. proportio; pro before + portio part or share. See {Portion}.] [1913 Webster] 1. The relation or adaptation of one portion to another, or to the whole, as respect magnitude, quantity, or degree; comparative relation; ratio; as, the proportion of the parts of a building, or of the body. [1913 Webster]

The image of Christ, made after his own proportion. --Ridley. [1913 Webster]

Formed in the best proportions of her sex. --Sir W. Scott. [1913 Webster]

Documents are authentic and facts are true precisely in proportion to the support which they afford to his theory. --Macaulay. [1913 Webster]

2. Harmonic relation between parts, or between different things of the same kind; symmetrical arrangement or adjustment; symmetry; as, to be out of proportion. ``Let us prophesy according to the proportion of faith.'' --Rom. xii. 6. [1913 Webster]

3. The portion one receives when a whole is distributed by a rule or principle; equal or proper share; lot. [1913 Webster]

Let the women . . . do the same things in their proportions and capacities. --Jer. Taylor. [1913 Webster]

4. A part considered comparatively; a share. [1913 Webster]

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. [1913 Webster]

Note: 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: [1913 Webster] a:b::c:d, or a:b = c:d, or a/b = c/d. [1913 Webster] (b) The rule of three, in arithmetic, in which the three given terms, together with the one sought, are proportional. [1913 Webster]

{Continued proportion}, {Inverse proportion}, etc. See under {Continued}, {Inverse}, etc.

{Harmonical proportion} 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. [1913 Webster]