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The Collaborative International Dictionary of English v.0.48 (gcide)

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.
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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.
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{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.
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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 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.
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Note: Some writers consider ratio as the quotient itself,
making ratio equivalent to a number.
[1913 Webster] 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}.
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2. Hence, fixed relation of number, quantity, or degree;
rate; proportion; as, the ratio of representation in
Congress.
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{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.
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