ratio


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.
      [1913 Webster]

   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.
         [1913 Webster]

   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.
         [1913 Webster]

   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.
      [1913 Webster]
.

From The Collaborative International Dictionary of English v.0.48:

Ratio \Ra"ti*o\ (r[=a]"sh[i^]*[-o] or r[=a]"sh[-o]), n. [L., fr.
   reri, ratus, to reckon, believe, think, judge. See Reason.]
   1. (Math.) The relation which one quantity or magnitude has
      to another of the same kind. It is expressed by the
      quotient of the division of the first by the second; thus,
      the ratio of 3 to 6 is expressed by 3/6 or 1/2; of a to b
      by a/b; or (less commonly) the second term is made the
      dividend; as, a:b = b/a.
      [1913 Webster]

   Note: Some writers consider ratio as the quotient itself,
         making ratio equivalent to a number.
         [1913 Webster] The term ratio is also sometimes applied
         to the difference of two quantities as well as to their
         quotient, in which case the former is called
         arithmetical ratio, the latter, geometrical ratio. The
         name ratio is sometimes given to the rule of three in
         arithmetic. See under Rule.
         [1913 Webster]

   2. Hence, fixed relation of number, quantity, or degree;
      rate; proportion; as, the ratio of representation in
      Congress.
      [1913 Webster]

   Compound ratio, Duplicate ratio, Inverse ratio, etc.
      See under Compound, Duplicate, etc.

   Ratio of a geometrical progression, the constant quantity
      by which each term is multiplied to produce the succeeding
      one.
      [1913 Webster]
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