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1 definition found
for Harmonical proportion
From The Collaborative International Dictionary of English v.0.48 :
Proportion \Pro*por"tion\, n. [F., fr. L. proportio; pro before
+ portio part or share. See Portion.]
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.
The image of Christ, made after his own proportion.
Formed in the best proportions of her sex. --Sir W.
Documents are authentic and facts are true precisely
in proportion to the support which they afford to
his theory. --Macaulay.
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.
3. The portion one receives when a whole is distributed by a
rule or principle; equal or proper share; lot.
Let the women . . . do the same things in their
proportions and capacities. --Jer. Taylor.
4. A part considered comparatively; a share.
(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.
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.
(b) The rule of three, in arithmetic, in which the three
given terms, together with the one sought, are
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.
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