geometrical pace

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.
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   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:

pace \pace\ (p[=a]s), n. [OE. pas, F. pas, from L. passus a
   step, pace, orig., a stretching out of the feet in walking;
   cf. pandere, passum, to spread, stretch; perh. akin to E.
   patent. Cf. Pas, Pass.]
   1. A single movement from one foot to the other in walking; a
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   2. The length of a step in walking or marching, reckoned from
      the heel of one foot to the heel of the other; -- used as
      a unit in measuring distances; as, he advanced fifty
      paces. "The height of sixty pace ." --Chaucer.
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   Note: Ordinarily the pace is estimated at two and one half
         linear feet; but in measuring distances be stepping,
         the pace is extended to three feet (one yard) or to
         three and three tenths feet (one fifth of a rod). The
         regulation marching pace in the English and United
         States armies is thirty inches for quick time, and
         thirty-six inches for double time. The Roman pace
         (passus) was from the heel of one foot to the heel of
         the same foot when it next touched the ground, five
         Roman feet.
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   3. Manner of stepping or moving; gait; walk; as, the walk,
      trot, canter, gallop, and amble are paces of the horse; a
      swaggering pace; a quick pace. --Chaucer.
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            To-morrow, and to-morrow, and to-morrow,
            Creeps in this petty pace from day to day. --Shak.
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            In the military schools of riding a variety of paces
            are taught.                           --Walsh.
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   4. A slow gait; a footpace. [Obs.] --Chucer.
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   5. Specifically, a kind of fast amble; a rack.
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   6. Any single movement, step, or procedure. [R.]
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            The first pace necessary for his majesty to make is
            to fall into confidence with Spain.   --Sir W.
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   7. (Arch.) A broad step or platform; any part of a floor
      slightly raised above the rest, as around an altar, or at
      the upper end of a hall.
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   8. (Weaving) A device in a loom, to maintain tension on the
      warp in pacing the web.
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   9. The rate of progress of any process or activity; as, the
      students ran at a rapid pace; the plants grew at a
      remarkable pace.

   Geometrical pace, the space from heel to heel between the
      spot where one foot is set down and that where the same
      foot is again set down, loosely estimated at five feet, or
      by some at four feet and two fifths. See Roman pace in
      the Note under def. 2. [Obs.]

   To keep pace with or To hold pace with, to keep up with;
      to go as fast as. "In intellect and attainments he kept
      pace with his age." --Southey.

   To put (someone) through one's paces to cause (someone) to
      perform an act so as to demonstrate his/her skill or
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