Pro-pōr'tion1, n.
n. [Lat. proportio, from pro, before, and portio, part or share; Fr. proportion, Pr. proporcio, Sp. proporcion, It. proporzione. See PORTION.]
Sense 1. The arrangement of parts; the relation or adaptation of one portion to another, or to the whole, with relation to magnitude or quantity; as, the proportion of the parts of a building, or of the body.
They carried about the image of Christ, made after his own proportion. Ridley.
Formed in the best proportion of her sex, Rowena was tall of stature. W. Scott.
Sense 2. The portion which falls to one's lot when a whole is distributed by a rule or principle; equal or just share; lot.
Let the women . . . do the same things in their proportions and capacities. Bp. Taylor.
Sense 3. Harmonizing relation between parts, or between different things of the same kind; symmetrical arrangement, distribution, or adjustment; as, to be out of proportion.
Sense 4. (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.
☞ Proportion 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 is 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 (\frac{a}{b}=\frac{c}{d}).
(b.) The rule of three, in arithmetic, in which the three given terms, together with the one sought, are proportional.
Continued proportion, a succession of several equal ratios.—Harmonical or musical proportion, a relation of three or four quantities, such that the first is to the last as the difference between the two first is to the difference between the two last; 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.—Reciprocal or inverse proportion, an equality between a direct and a reciprocal ratio, or a proportion in which the first term is to the second as the fourth is to the third; thus, 4 : 2 :: ⅓ : ⅙, or 4 : 2 :: 3 : 6 inversely.—Rhythmical proportion (Mus.), the proportion in relation to time or measure, between the notes representing duration; thus, the semibreve to the minim is 2 : 1; the semibreve to the crotchet 4 : 1.