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