Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A part considered in relation to the whole.
 n. A relationship between things or parts of things with respect to comparative magnitude, quantity, or degree: the proper proportion between oil and vinegar in the dressing.
 n. A relationship between quantities such that if one varies then another varies in a manner dependent on the first: "We do not always find visible happiness in proportion to visible virtue” ( Samuel Johnson).
 n. Agreeable or harmonious relation of parts within a whole; balance or symmetry.
 n. Dimensions; size. Often used in the plural.
 n. Mathematics A statement of equality between two ratios. Four quantities, a, b, c, d, are said to be in proportion if a/b = c/d .
 transitive v. To adjust so that proper relations between parts are attained.
 transitive v. To form the parts of with balance or symmetry.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. A quantity of something that is part of the whole amount or number.
 n. Harmonious relation of parts to each other or to the whole.
 n. Proper or equal share.
 n. The relation of one part to another or to the whole with respect to magnitude, quantity, or degree.
 n. A statement of equality between two ratios.
 n. size
 v. To set or render in proportion.
from the GNU version of the Collaborative International Dictionary of English
 adj.
 n. The relation or adaptation of one portion to another, or to the whole, as respect magnitude, quantity, or degree; comparative relation; ratio.
 n. Harmonic relation between parts, or between different things of the same kind; symmetrical arrangement or adjustment; symmetry.
 n. The portion one receives when a whole is distributed by a rule or principle; equal or proper share; lot.
 n. A part considered comparatively; a share.
 n.
 n. 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.
 n. The rule of three, in arithmetic, in which the three given terms, together with the one sought, are proportional.
 transitive v. To adjust in a suitable proportion, as one thing or one part to another
 transitive v. To form with symmetry or suitableness, as the parts of the body.
 transitive v. To divide into equal or just shares; to apportion.
from The Century Dictionary and Cyclopedia
 To adjust in suitable relations; adapt harmoniously to something else as regards dimensions or extent: as, to proportion the size of a building to its height, or the thickness of a thing to its length; to proportion expenditure to income.
 To form with symmetry; give a symmetrical form to.
 To bear proportion or adequate relation to; correspond to.
 To divide into portions; allot; apportion.
 To compare; estimate the relative proportions of.
 In typemanuf., to adjust (a font of type) so that it shall contain the proper number of each letter, point, etc.
 n. The relation of one thing to another in respect to size, quantity, magnitude of corresponding parts, capacity, or degree.
 n. Specifically, the relation of one part to another or to the whole with respect to magnitude; the relative size and arrangement of parts: as, the proportion of the parts of an edifice, or of the human body. Commonly in the plural.
 n. Symmetrical arrangement, distribution, or adjustment; the proper relation of parts in a whole; symmetry or harmony.
 n. That which falls to one's lot when a whole is divided according to a rule or principle; just or proper share; in general, portion; lot.
 n. Form; shape; figure.
 n. In mathematics, the equality of ratios or relations; analogy.
 n. In music: The ratio between the vibrationnumbers of two tones.
 n. Same as rhythm or meter.
 n. In arithmetic, the rule of three; that rule which, according to the theory of proportion, enables us to find a fourth proportional to three given numbers — that is, a number to which the third bears the same ratio as the first does to the second.
 n. See mixed.
 n. Synonyms See symmetry.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. the quotient obtained when the magnitude of a part is divided by the magnitude of the whole
 n. harmonious arrangement or relation of parts or elements within a whole (as in a design)
 n. the relation between things (or parts of things) with respect to their comparative quantity, magnitude, or degree
 n. balance among the parts of something
 v. adjust in size relative to other things
 n. magnitude or extent
 v. give pleasant proportions to
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

When one proportion of a body is combined with two or more proportions of anotlier, it seems to enter with more difficulty into new combinations, than when it is combined wiUi one proportion*

The change in proportion is also moderated by the assumption that population growth is all in England but I want to err on the side of caution.

Although generally attributed to Leonardo Pisano, il Figlio di (son of) Bonacci, this proportion is also found in the measurements of the Ark of the Covenant (Exodus 25): 2.5 cubits long by 1.5 cubits wide and high (1.5/2.5 = 0.6).
Architecture and Memory: The Renaissance Studioli of Federico da Montefeltro

"It's only my sense o 'duty, an' o 'what you call proportion," said

There were no prehispanic “Filipinos” as a distinct cultural group, but instead a lot of separate tribes with their own cultures, the variation between which grows in proportion to their distance from each other.

No capitation, or other direct, tax shall be laid, unless in proportion to the census or enumeration herein before directed to be taken.

The requirements grow linearly, in proportion to the number of folk.

I understand this is a slippery slope, as in proportion to the United States most states look tiny.

I assumed that government payouts would fall in proportion with the loss in social security tax revenue i.e. responsibility for current government benefits due would go to the private firm or cease.
Quizzes, Arnold Kling  EconLog  Library of Economics and Liberty

Although ANCs provide some benefits to their shareholders, those benefits may not be in proportion to the potential for waste, fraud and abuse created by the ANCs 'contracting preferences.
A drumbeat of warnings about impropriety regarding Alaska native corporation contracts
PossibleUnderscore commented on the word proportion
Miss Bart was discerning enough to know that the inner vanity is generally in proportion to the outer selfdepreciation.
Edith Wharton, The House of Mirth
July 26, 2009