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The Collaborative International Dictionary
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.

  2. (Art) characterized by simple geometric forms in design and decoration; as, a buffalo hide painted with red and black geometrical designs.

    Syn: geometric.

    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 algebr

    1. 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 (Zo["o]l.), one of many species of spiders, which spin a geometrical we

    2. 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.

Geometrical progression

Progression \Pro*gres"sion\, n. [L. progressio: cf. F. progression.]

  1. The act of moving forward; a proceeding in a course; motion onward.

  2. Course; passage; lapse or process of time.

    I hope, in a short progression, you will be wholly immerged in the delices and joys of religion.
    --Evelyn.

  3. (Math.) Regular or proportional advance in increase or decrease of numbers; continued proportion, arithmetical, geometrical, or harmonic.

  4. (Mus.) A regular succession of tones or chords; the movement of the parts in harmony; the order of the modulations in a piece from key to key.

    Arithmetical progression, a progression in which the terms increase or decrease by equal differences, as the numbers [lbrace2]2, 4, 6, 8, 1010, 8, 6, 4, 2[rbrace2] by the difference 2.

    Geometrical progression, a progression in which the terms increase or decrease by equal ratios, as the numbers by a continual multiplication or division by 2.

    Harmonic progression, a progression in which the terms are the reciprocals of quantities in arithmetical progression, as 1/2, 1/4, 1/6, 1/8, 1/10.

Usage examples of "geometrical progression".

Only when we have admitted the conception of the infinitely small, and the resulting geometrical progression with a common ratio of one tenth, and have found the sum of this progression to infinity, do we reach a solution of the problem.

Had we multiplied by 2 and 8 we should get the regular geometrical progression, 1, 2, 4, 8, 16, 32, 64, 128, and 256, but I wish to avoid high numbers.

Not only does the process increase the number of our unknown quantities in Geometrical progression at every step, but we must ultimately arrive at a point where the definition of Z involves the term A.

A minute and imperceptible statistical advantage of the molecules that could copy themselves was soon transformed by the arithmetic of geometrical progression into the dominant process in the oceans.

But (especially after the passing of Tiphareth) the distance between grade and grade increases as it were by a geometrical progression with an enormously high factor, which itself progresses.

Another means of silently lessening the inequality of property is to exempt all from taxation below a certain point, and to tax the higher portions or property in geometrical progression as they rise.

Daily Alice liked cats, as her mother hadn't, and as Auberon grew up the number of cats in the house grew by geometrical progression.

It could have been caused by a single spore which has increased by geometrical progression.