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

Syn: geometric.
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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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Proportion \Pro*por"tion\, v. t. [imp. & p. p. {Proportioned};
p. pr. & vb. n. {Proportioning}.] [Cf. F. proportionner. Cf.
{Proportionate}, v.]
1. To adjust in a suitable proportion, as one thing or one
part to another; as, to proportion the size of a building
to its height; to proportion our expenditures to our
income.
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In the loss of an object we do not proportion our
grief to the real value . . . but to the value our
fancies set upon it. --Addison.
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2. To form with symmetry or suitableness, as the parts of the
body.
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Nature had proportioned her without any fault. --Sir
P. Sidney.
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3. To divide into equal or just shares; to apportion.
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Proportion \Pro*por"tion\, n. [F., fr. L. proportio; pro before
portio part or share. See {Portion}.]
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1. The relation or adaptation of one portion to another, or
to the whole, as respect magnitude, quantity, or degree;
comparative relation; ratio; as, the proportion of the
parts of a building, or of the body.
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The image of Christ, made after his own proportion.
--Ridley.
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Formed in the best proportions of her sex. --Sir W.
Scott.
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Documents are authentic and facts are true precisely
in proportion to the support which they afford to
his theory. --Macaulay.
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2. Harmonic relation between parts, or between different
things of the same kind; symmetrical arrangement or
adjustment; symmetry; as, to be out of proportion. "Let us
prophesy according to the proportion of faith." --Rom.
xii. 6.
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3. The portion one receives when a whole is distributed by a
rule or principle; equal or proper share; lot.
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Let the women . . . do the same things in their
proportions and capacities. --Jer. Taylor.
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4. A part considered comparatively; a share.
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5. (Math.)
(a) The equality or similarity of ratios, especially of
geometrical ratios; or a relation among quantities
such that the quotient of the first divided by the
second is equal to that of the third divided by the
fourth; -- called also {geometrical proportion}, in
distinction from arithmetical proportion, or that in
which the difference of the first and second is equal
to the difference of the third and fourth.
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Note: Proportion in the mathematical sense differs from
ratio. Ratio is the relation of two quantities of the
same kind, as the ratio of 5 to 10, or the ratio of 8
to 16. Proportion is the sameness or likeness of two
such relations. Thus, 5 to 10 as 8 to 16; that is, 5
bears the same relation to 10 as 8 does to 16. Hence,
such numbers are said to be in proportion. Proportion
is expressed by symbols thus:
[1913 Webster] a:b::c:d, or a:b = c:d, or a/b = c/d.
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(b) The rule of three, in arithmetic, in which the three
given terms, together with the one sought, are
proportional.
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{Continued proportion}, {Inverse proportion}, etc. See under
{Continued}, {Inverse}, etc.

{Harmonical proportion} or {Musical proportion}, a relation
of three or four quantities, such that the first is to the
last as the difference between the first two is to the
difference between the last two; thus, 2, 3, 6, are in
harmonical proportion; for 2 is to 6 as 1 to 3. Thus, 24,
16, 12, 9, are harmonical, for 24:9::8:3.

{In proportion}, according as; to the degree that. "In
proportion as they are metaphysically true, they are
morally and politically false." --Burke.
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