catflap.org Online Dictionary Query

  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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