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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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
step.
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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.
Temple.
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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.
[PJC]
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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