# Geometrical progression

Geometrical progression
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} (Zo["o]l.), 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]

The Collaborative International Dictionary of English. 2000.

### См. также в других словарях:

• Geometrical progression — Progression Pro*gres sion, n. [L. progressio: cf. F. progression.] [1913 Webster] 1. The act of moving forward; a proceeding in a course; motion onward. [1913 Webster] 2. Course; passage; lapse or process of time. [1913 Webster] I hope, in a… …   The Collaborative International Dictionary of English

• geometrical progression — geometric(al) progression noun A series of quantities each of which has the same ratio to its predecessor • • • Main Entry: ↑geometry * * * geometrical progression, = geometric progression. (Cf. ↑geometric progression) …   Useful english dictionary

• geometrical progression — noun see geometric progression …   New Collegiate Dictionary

• geometrical progression — series of numbers in which each number is multiplied by the same factor (Mathematics) …   English contemporary dictionary

• Ratio of a geometrical progression — 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… …   The Collaborative International Dictionary of English

• Progression — Pro*gres sion, n. [L. progressio: cf. F. progression.] [1913 Webster] 1. The act of moving forward; a proceeding in a course; motion onward. [1913 Webster] 2. Course; passage; lapse or process of time. [1913 Webster] I hope, in a short… …   The Collaborative International Dictionary of English

• Geometrical — 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.… …   The Collaborative International Dictionary of English

• Geometrical curve — 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.… …   The Collaborative International Dictionary of English

• Geometrical pace — 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.… …   The Collaborative International Dictionary of English

• Geometrical plane — 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.… …   The Collaborative International Dictionary of English

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