proportion


From The Collaborative International Dictionary of English v.0.48:

Geometric \Ge`o*met"ric\, Geometrical \Ge`o*met"ric*al\, a. [L.
   geometricus; Gr. ?: cf. F. g['e]om['e]trique.]
   1. Pertaining to, or according to the rules or principles of,
      geometry; determined by geometry; as, a geometrical
      solution of a problem.
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   2. (Art) characterized by simple geometric forms in design
      and decoration; as, a buffalo hide painted with red and
      black geometrical designs.

   Syn: geometric.
        [WordNet 1.5]

   Note: Geometric is often used, as opposed to algebraic, to
         include processes or solutions in which the
         propositions or principles of geometry are made use of
         rather than those of algebra.
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   Note: Geometrical is often used in a limited or strictly
         technical sense, as opposed to mechanical; thus, a
         construction or solution is geometrical which can be
         made by ruler and compasses, i. e., by means of right
         lines and circles. Every construction or solution which
         requires any other curve, or such motion of a line or
         circle as would generate any other curve, is not
         geometrical, but mechanical. By another distinction, a
         geometrical solution is one obtained by the rules of
         geometry, or processes of analysis, and hence is exact;
         while a mechanical solution is one obtained by trial,
         by actual measurements, with instruments, etc., and is
         only approximate and empirical.
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   Geometrical curve. Same as Algebraic curve; -- so called
      because their different points may be constructed by the
      operations of elementary geometry.

   Geometric lathe, an instrument for engraving bank notes,
      etc., with complicated patterns of interlacing lines; --
      called also cycloidal engine.

   Geometrical pace, a measure of five feet.

   Geometric pen, an instrument for drawing geometric curves,
      in which the movements of a pen or pencil attached to a
      revolving arm of adjustable length may be indefinitely
      varied by changing the toothed wheels which give motion to
      the arm.

   Geometrical plane (Persp.), the same as Ground plane .

   Geometrical progression, proportion, ratio. See under
      Progression, Proportion and Ratio.

   Geometrical radius, in gearing, the radius of the pitch
      circle of a cogwheel. --Knight.

   Geometric spider (Zool.), one of many species of spiders,
      which spin a geometrical web. They mostly belong to
      Epeira and allied genera, as the garden spider. See
      Garden spider.

   Geometric square, a portable instrument in the form of a
      square frame for ascertaining distances and heights by
      measuring angles.

   Geometrical staircase, one in which the stairs are
      supported by the wall at one end only.

   Geometrical tracery, in architecture and decoration,
      tracery arranged in geometrical figures.
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.

From The Collaborative International Dictionary of English v.0.48:

Proportion \Pro*por"tion\, v. t. [imp. & p. p. Proportioned;
   p. pr. & vb. n. Proportioning.] [Cf. F. proportionner. Cf.
   Proportionate, v.]
   1. To adjust in a suitable proportion, as one thing or one
      part to another; as, to proportion the size of a building
      to its height; to proportion our expenditures to our
      income.
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            In the loss of an object we do not proportion our
            grief to the real value . . . but to the value our
            fancies set upon it.                  --Addison.
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   2. To form with symmetry or suitableness, as the parts of the
      body.
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            Nature had proportioned her without any fault. --Sir
                                                  P. Sidney.
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   3. To divide into equal or just shares; to apportion.
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.

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.]
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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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