Ratio

From The Collaborative International Dictionary of English v.0.48 [gcide]:

Geometric \Ge'o*met"ric\, Geometrical \Ge'o*met"ric*al\, adjective [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.

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.

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} (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.

From The Collaborative International Dictionary of English v.0.48 [gcide]:

**Ratio** \Ra"ti*o\ (r[=a]"sh[i^]*[-o] or r[=a]"sh[-o]), noun [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 of the division of the first by the second; thus,
the **ratio** of 3 to 6 is expressed by 3/6 or 1/2; of a to b
by a/b; or (less commonly) the second term is made the
dividend; as, a:b = b/a.

Note: Some writers consider **ratio** as the quotient itself,
making **ratio** equivalent to a number.
The term **ratio** is also sometimes applied
to the difference of two quantities as well as to their
quotient, in which case the former is called
arithmetical **ratio**, the latter, geometrical **ratio**. The
name **ratio** is sometimes given to the rule of three in
arithmetic. See under {Rule}.

2. Hence, fixed relation of number, quantity, or degree;
rate; proportion; as, the **ratio** of representation in
Congress.

{Compound **ratio**}, {Duplicate **ratio**}, {Inverse **ratio**}, etc.
See under {Compound}, {Duplicate}, etc.

{**Ratio** of a geometrical progression}, the constant quantity
by which each term is multiplied to produce the succeeding
one.

From WordNet (r) 3.0 (2006) [wn]:

noun

1: the relative magnitudes of two quantities (usually expressed as a quotient)

2: the relation between things (or parts of things) with respect
to their comparative quantity, magnitude, or degree; "an
inordinate proportion of the book is given over to
quotations"; "a dry martini has a large proportion of gin"
[syn: {proportion}, {**ratio**}]

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