PROPORTION, the identity or similitude of two ratios. Hence quantities that have the same ratio between them are said to be proportional; e. gr. if A be to B as C to D, or 3 be to 4 as 30 to 15; A, B, C, D, and 3, 4, 30, and 15, are said to be in proportion, or are simply called proportionals. Proportion is frequently confounded with ratio; yet have the two in reality very different ideas, which ought by all means to be distinguished. Ratio is properly the relation or habitude
Proportion. tude of two things, which determines the quantity of one from the quantity of another, without the intervention of any third: thus we say the ratio of 5 and 10 is 2, the ratio of 12 and 24 is 2. Proportion is the sameness or likeness of two such relations; thus the relations between 5 and 10 and 12 and 24 being the same, or equal, the four terms are said to be in proportion. Hence ratio exists between two numbers, but proportion requires at least three. Proportion, in fine, is the habitude or relation of two ratios when compared together; as ratio is of two quantities. See ALGEBRA, ARITHMETIC and GEOMETRY.
Arithmetical and Geometrical PROPORTION. See PROGRESSION.