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# proportion

From *The Collaborative International Dictionary of English v.0.48*:

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. [1913 Webster] 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. [1913 Webster] 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. [1913 Webster] .

From *The Collaborative International Dictionary of English v.0.48*:

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. [1913 Webster] 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. [1913 Webster] 2. To form with symmetry or suitableness, as the parts of the body. [1913 Webster] Nature had proportioned her without any fault. --Sir P. Sidney. [1913 Webster] 3. To divide into equal or just shares; to apportion. [1913 Webster] .

From *The Collaborative International Dictionary of English v.0.48*:

Proportion \Pro*por"tion\, n. [F., fr. L. proportio; pro before + portio part or share. See Portion.] [1913 Webster] 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. [1913 Webster] The image of Christ, made after his own proportion. --Ridley. [1913 Webster] Formed in the best proportions of her sex. --Sir W. Scott. [1913 Webster] Documents are authentic and facts are true precisely in proportion to the support which they afford to his theory. --Macaulay. [1913 Webster] 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. [1913 Webster] 3. The portion one receives when a whole is distributed by a rule or principle; equal or proper share; lot. [1913 Webster] Let the women . . . do the same things in their proportions and capacities. --Jer. Taylor. [1913 Webster] 4. A part considered comparatively; a share. [1913 Webster] 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. [1913 Webster] 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. [1913 Webster] (b) The rule of three, in arithmetic, in which the three given terms, together with the one sought, are proportional. [1913 Webster] 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. [1913 Webster]