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Inverse proportion
(gcide) | Inverse \In*verse"\, a. [L. inversus, p. p. of invertere: cf. F.
inverse. See Invert.]
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1. Opposite in order, relation, or effect; reversed;
inverted; reciprocal; -- opposed to direct.
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2. (Bot.) Inverted; having a position or mode of attachment
the reverse of that which is usual.
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3. (Math.) Opposite in nature and effect; -- said with
reference to any two operations, which, when both are
performed in succession upon any quantity, reproduce that
quantity; as, multiplication is the inverse operation to
division. The symbol of an inverse operation is the symbol
of the direct operation with -1 as an index. Thus sin-1 x
means the arc or angle whose sine is x.
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Inverse figures (Geom.), two figures, such that each point
of either figure is inverse to a corresponding point in
the order figure.
Inverse points (Geom.), two points lying on a line drawn
from the center of a fixed circle or sphere, and so
related that the product of their distances from the
center of the circle or sphere is equal to the square of
the radius.
Inverse ratio, or Reciprocal ratio (Math.), the ratio of
the reciprocals of two quantities.
Inverse proportion, or Reciprocal proportion, an equality
between a direct ratio and a reciprocal ratio; thus, 4 : 2
: : 1/3 : 1/6, or 4 : 2 : : 3 : 6, inversely.
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Inverse 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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