{ Ge`o*met"ric (?), Ge`o*met"ric*al (?), } a. [L. geometricus; Gr. &?;:
cf. F. gÈomÈtrique.] Pertaining to, or according to the rules or
principles of, geometry; determined by geometry; as, a geometrical
solution of a problem.
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.
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 (Zoˆl.), 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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Ge`o*met"ric*al*ly (?), adv. According to the rules or laws of
geometry.
Ge*om`e*tri"cian (?), n. One skilled in geometry; a geometer; a
mathematician.
Ge*om"e*trid (?), a. (Zoˆl.) Pertaining or belonging to the GeometridÊ.
Ge*om"e*trid, n. (Zoˆl.) One of numerous genera and species of moths,
of the family GeometridÊ; -- so called because their larvÊ (called
loopers, measuring worms, spanworms, and inchworms) creep in a looping
manner, as if measuring. Many of the species are injurious to
agriculture, as the cankerworms.
Ge*om"e*trize (?), v. i. [imp. & p. p. Geometrized (?); p. pr. & vb. n.
Geometrizing (?).] To investigate or apprehend geometrical quantities
or laws; to make geometrical constructions; to proceed in accordance
with the principles of geometry.
Nature geometrizeth, and observeth order in all things.
Sir T. Browne.
Ge*om"e*try (?), n.; pl. Geometries (#) [F. gÈomÈtrie, L. geometria,
fr. Gr. &?;, fr. &?; to measure land; ge`a, gh^, the earth + &?; to
measure. So called because one of its earliest and most important
applications was to the measurement of the earth's surface. See
Geometer.] 1. That branch of mathematics which investigates the
relations, properties, and measurement of solids, surfaces, lines, and
angles; the science which treats of the properties and relations of
magnitudes; the science of the relations of space.