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Proportion definitions

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Webster's 1828 Dictionary

PROPORTION, n. [L.proportio; pro and portio, part or share. See Portion.]
1. The comparative relation of any one thing to another. Let a man's exertions be in proportion to his strength.
2. The identity or similitude of two ratios. Proportion differs from ratio. Ratio is the relation which determines the quantity of one thing from the quantity of another, without the intervention of a third. Thus the ratio of 5 and Isaiah 2; the ratio of 8 and 16 is 2. Proportion is the sameness or likeness of two such relations. Thus 5 is to 10, as 8 to 16, or A is to B, as C is to D; that is, 5 bears the same relation to 10, as 8 does to 16. Hence we say, such numbers are in proportion.
Proportion, in mathematics, an equality or ratios.
The term proportion is sometimes improperly used for ratio. The ratio between two quantities, is expressed by the quotient of one divided by the other; thus, the ratio of 10 to 5 is 2, and the ratio of 16 to 8 is 2. These two equal ratios constitute a proportion, which is expressed by saying, 10 is to 5 as 16 is to 8; or more concisely,
10:
5::
16: 8. [See Ratio.]
3. In arithmetic, a rule by which, when three numbers are given, a fourth number is found, which bears the same relation to the third as the second does to the first; or a fourth number is found, bearing the same relation to the second as the first does to the third. The former is called direct, and the latter, inverse proportion.
4. Symmetry; suitable adaptation of one part or thing to another; as the proportion of one limb to another in the human body; the proportion of the length and breadth of a room to its highth.
Harmony, with every grace,
Place in the fair proportions of her face.
5. Equal or just share; as, to ascertain the proportion of profit to which each partner in a company is entitled.
6. Form; size. [Little used.]
7. The relation between unequal things of the same kind, by which their several parts correspond to each other with an equal augmentation and diminution, as in reducing and enlarging figures.
[This more properly belongs to ratio.]
Harmonical or musical proportion, is when, of three numbers,the first is to the third as the difference of the first and second to the difference of the second and third. Thus 2.3.6. are in harmonical proportion; for 2 is to 6 as 1 to 3. So also four numbers are harmonical, when the first is to the fourth, as the difference of the first and second is to the difference of the third and fourth. Thus, 24.16.12.9. are harmonical, for 24 : 9 :: 8 : 3.
Arithmetical and geometrical proportion. [See Progression, No.4.]
Reciprocal proportion, an equality between a direct and a reciprocal ratio. Thus, 4 : 2 :: 1/3 : 1/6. [See Reciprocals, and Reciprocal ratio.]
PROPORTION, v.t. To adjust the comparative relation of one thing or one part to another; as, to proportion the size of a building to its highth, or the thickness of a thing to its length; to proportion our expenditures to our income.
In the loss of an object, we do not proportion our grief to its real value, but to the value our fancies set upon it.
1. To form with symmetry or suitableness, as the parts of the body.

WordNet (r) 3.0 (2005)

n
1: the quotient obtained when the magnitude of a part is divided by the magnitude of the whole
2: magnitude or extent; "a building of vast proportions" [syn: proportion, dimension]
3: balance among the parts of something [syn: symmetry, proportion] [ant: disproportion]
4: 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]
5: harmonious arrangement or relation of parts or elements within a whole (as in a design); "in all perfectly beautiful objects there is found the opposition of one part to another and a reciprocal balance"- John Ruskin [syn: proportion, proportionality, balance] v
1: give pleasant proportions to; "harmonize a building with those surrounding it"
2: adjust in size relative to other things

Merriam Webster's

I. noun Etymology: Middle English proporcion, from Anglo-French, from Latin proportion-, proportio, from pro for + portion-, portio portion — more at for Date: 14th century 1. harmonious relation of parts to each other or to the whole ; balance, symmetry 2. a. proper or equal share <each did her proportion of the work> b. quota, percentage 3. the relation of one part to another or to the whole with respect to magnitude, quantity, or degree ; ratio 4. size, dimension 5. a statement of equality between two ratios in which the first of the four terms divided by the second equals the third divided by the fourth (as in 4/2=10/5) — compare extreme 1b, mean 1c II. transitive verb (proportioned; proportioning) Date: 14th century 1. to adjust (a part or thing) in size relative to other parts or things 2. to make the parts of harmonious or symmetrical 3. apportion, allot

Oxford Reference Dictionary

n. & v. --n. 1 a a comparative part or share (a large proportion of the profits). b a comparative ratio (the proportion of births to deaths). 2 the correct or pleasing relation of things or parts of a thing (the house has fine proportions; exaggerated out of all proportion). 3 (in pl.) dimensions; size (large proportions). 4 Math. a an equality of ratios between two pairs of quantities, e.g.
3:5 and
9:15. b a set of such quantities. c Math. = rule of three; see also direct proportion, inverse proportion. --v.tr. (usu. foll. by to) make (a thing etc.) proportionate (must proportion the punishment to the crime). Phrases and idioms: in proportion 1 by the same factor. 2 without exaggerating (importance etc.) (must get the facts in proportion). Derivatives: proportioned adj. (also in comb.). proportionless adj. proportionment n. Etymology: ME f. OF proportion or L proportio (as PRO-(1), PORTION)

Webster's 1913 Dictionary

Inverse In*verse", a. [L. inversus, p. p. of invertere: cf. F. inverse. See Invert.] 1. Opposite in order, relation, or effect; reversed; inverted; reciprocal; -- opposed to direct. 2. (Bot.) Inverted; having a position or mode of attachment the reverse of that which is usual. 3. (Math.) Opposite in nature and effect; -- said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity; as, multiplication is the inverse operation to division. The symbol of an inverse operation is the symbol of the direct operation with -1 as an index. Thus sin-1 x means the arc whose sine is x. Inverse figures (Geom.), two figures, such that each point of either figure is inverse to a corresponding point in the order figure. Inverse points (Geom.), two points lying on a line drawn from the center of a fixed circle or sphere, and so related that the product of their distances from the center of the circle or sphere is equal to the square of the radius. Inverse, or Reciprocal, ratio (Math.), the ratio of the reciprocals of two quantities. Inverse, or Reciprocal, {proportion, an equality between a direct ratio and a reciprocal ratio; thus, 4 : 2 : : 1/3 : 1/6, or 4 : 2 : : 3 : 6, inversely.

Webster's 1913 Dictionary

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

Webster's 1913 Dictionary

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

Webster's 1913 Dictionary

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

Webster's 1913 Dictionary

Geometric Ge`o*met"ric, Geometrical Ge`o*met"ric*al, a. [L. geometricus; Gr. ?: cf. F. g['e]om['e]trique.] Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem. 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 (Zo["o]l.), 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.

Collin's Cobuild Dictionary

(proportions) Frequency: The word is one of the 3000 most common words in English. 1. A proportion of a group or an amount is a part of it. (FORMAL) A large proportion of the dolphins in that area will eventually die... A proportion of the rent is met by the city council. N-COUNT: usu sing, usu N of n 2. The proportion of one kind of person or thing in a group is the number of people or things of that kind compared to the total number of people or things in the group. The proportion of women in the profession had risen to 17.3%... N-COUNT: usu sing, usu N of n 3. The proportion of one amount to another is the relationship between the two amounts in terms of how much there is of each thing. Women's bodies tend to have a higher proportion of fat to water. = ratio N-COUNT: oft N of n to n 4. If you refer to the proportions of something, you are referring to its size, usually when this is extremely large. (WRITTEN) In the tropics plants grow to huge proportions. N-PLURAL: usu supp N 5. If one thing increases or decreases in proportion to another thing, it increases or decreases to the same degree as that thing. The pressure in the cylinders would go up in proportion to the boiler pressure. PREP-PHRASE 6. If something is small or large in proportion to something else, it is small or large when compared with that thing. Children tend to have relatively larger heads than adults in proportion to the rest of their body. PREP-PHRASE 7. If you say that something is out of all proportion to something else, you think that it is far greater or more serious than it should be. The punishment was out of all proportion to the crime. PREP-PHRASE: usu v-link PREP 8. If you get something out of proportion, you think it is more important or worrying than it really is. If you keep something in proportion, you have a realistic view of how important it is. Everything just got blown out of proportion... We've got to keep this in proportion. PHRASE: PHR after v

International Standard Bible Encyclopedia

pro-por'-shun: Occurs once in the sense of "space" as the translation of ma`-ar, "void or open space" (1Ki 7:36 the King James Version margin "Hebrew `nakedness,' " the Revised Version (British and American) "space"); once in the obsolete sense of "form" as the translation of `erekh, "array," or "row" (Job 41:12, the Revised Version (British and American) "frame"); and once in the sense of "measure" as the translation of analogia, "proportion" "equality" (Ro 12:6, "the proportion of faith," the Revised Version (British and American) "the proportion of our faith"). "Proportionally" occurs in The Wisdom of Solomon 13:5, analogos, the Revised Version (British and American) "in like proportion," margin "correspondently."

Soule's Dictionary of English Synonyms

I. n. 1. Arrangement, relation, adaptation (of parts). 2. Distribution, adjustment, symmetry, symmetrical, relation. 3. Share, lot, part, portion. II. v. a. 1. Adjust (in proper relations), regulate, graduate, put in proportion. 2. From, shape, with symmetry or suitableness. 3. Equal, bear proportion to.

Moby Thesaurus

accommodate, accord, acreage, adapt, addition, adjust, adjust to, agreement, allegory, allotment, allowance, amount, amplitude, analogousness, analogy, approximation, area, arithmetical proportion, arrangement, array, assimilate, attune, balance, balancing, beauty, big end, bigger half, bigness, bilateral symmetry, bit, bite, body, breadth, budget, bulk, caliber, cancel, capacity, change, chunk, coequality, coextension, commensurability, commission, comparability, comparableness, comparative anatomy, comparative degree, comparative grammar, comparative judgment, comparative linguistics, comparative literature, comparative method, comparativeness, compare, comparing, comparison, compass, compensate, concinnity, concord, conform, conformity, confrontation, confrontment, congruity, consistency, contingent, continued fraction, continuum, contrast, contrastiveness, coordinate, correlation, correspondence, counterbalance, counterpoise, countervail, coverage, cut, cut to, deal, degree, deployment, depth, destiny, diameter, differentiation, dimension, dimensions, disposal, disposition, distinction, distinctiveness, distribution, divide, dividend, division, dole, dynamic symmetry, emptiness, empty space, end, enlarge, equal share, equality, equalize, equate, equation, equilibrium, equipoise, equipollence, equiponderance, equity, equivalence, equivalency, euphony, eurythmics, eurythmy, even, even up, evenness, evolution, expanse, expansion, extension, extent, extrapolation, fate, field, finish, fit, fix, formation, fraction, galactic space, gauge, gear to, geometric ratio, girth, grade, graduate, greatness, group, half, halver, harmonic proportion, harmonize, harmony, height, helping, homologate, homologize, identity, improper fraction, infinite space, integrate, integration, interest, interpolation, interstellar space, interval, inversion, involution, justice, keeping, key to, largeness, layout, leap, length, level, levelness, likeness, likening, lineup, lot, magnitude, make plumb, make uniform, mark, marshaling, mass, match, matching, measure, measuredness, measurement, meed, mess, metaphor, modicum, modify, modulate, moiety, multilateral symmetry, multiplication, notation, notch, nothingness, nuance, opposing, opposition, order, orderedness, organization, outer space, par, parallelism, parity, part, pas, peace, peg, percent, percentage, period, piece, pitch, plane, plateau, point, poise, polarity, portion, practice, pro rata, proportionability, proportionality, proportionate, proportions, prorate, put in tune, quantum, quiet, quietude, quota, quotum, radius, rake-off, range, rank, rate, ratio, ration, reach, reconcile, rectify, reduction, regularity, regularize, regulate, relation, relationship, remove, rhythm, right, round, routine, rule of three, rung, scale, scope, segment, set, set right, setup, shade, shadow, shape, shapeliness, share, similarity, similarize, simile, similitude, size, slice, small share, sort, space, spatial extension, sphere, spread, square, stair, stake, standard, step, stint, stock, strike a balance, structure, subtraction, suitableness, superficial extension, surface, sweetness, symmetricalness, symmetry, sync, synchronize, system, tailor, tract, tranquillity, transformation, tread, trilateral symmetry, trim to, trope of comparison, true, true up, tune, uniformity, void, volume, weighing, width