pace n.
 1. A single movement from one foot to the other in walking; a step.
 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 .”
 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.
 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.
 To-morrow, and to-morrow, and to-morrow,
 Creeps in this petty pace from day to day.   --Shak.
    In the military schools of riding a variety of paces are taught.   --Walsh.
 4. A slow gait; a footpace. [Obs.]
 5. Specifically, a kind of fast amble; a rack.
 6. Any single movement, step, or procedure. [R.]
    The first pace necessary for his majesty to make is to fall into confidence with Spain.   --Sir W. Temple.
 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.
 8. Weaving A device in a loom, to maintain tension on the warp in pacing the web.
 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 ability.

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 Ge·o·met·ric Ge·o·met·ric·al a.
 1. Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.
 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.
 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.
 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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