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#top Continued Proportion

From The Collaborative International Dictionary of English v.0.48 [gcide]:

Proportion \Pro*por"tion\, noun [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.

Formed in the best proportions of her sex. --Sir W. Scott.

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 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.

From The Collaborative International Dictionary of English v.0.48 [gcide]:

{Continued bass} (Mus.), a bass continued through an entire piece of music, while the other parts of the harmony are indicated by figures beneath the bass; the same as thorough bass or figured bass; basso continuo. [It.]

{Continued proportion} (Math.), a proportion composed of two or more equal ratios, in which the consequent of each preceding ratio is the same with the antecedent of the following one; as, 4 : 8 : 8 : 16 :: 16 : 32.