**Ge`o*met"ric** (?), **Ge`o*met"ric*al** (?), a. [L. *geometricus*; Gr. : cf. F. *g'eom'etrique*.]

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 ajustable 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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*© Webster 1913.*