# DUPLE

, or Double Ratio, is that in which the antecedent term is double the consequent; or, where the exponent of the ratio is 2. Thus, 6 to 3 is in a duple ratio.

Sub-Duple Ratio, is that in which the consequent is double the antecedent; or, in which the exponent of the ratio is 1/2. As in 3 to 6, which is in subduple ratio.

DUPLICATE Ratio, is the square of a ratio, or the ratio of the squares of two quantities. Thus, the duplicate ratio of a to b, is the ratio of a2 to b2, or of the square of a to the square of b.—In a series of geometrical proportionals, the 1st term is to the 3d, in a duplicate ratio of the 1st to the 2d, or as the square of the first to the square of the 2d: Thus, in the geometricals 2, 4, 8, 16, &c, the ratio of 2 to 8, is the duplicate of that of 2 to 4, or as the square of 2 to the square of 4, that is, as 4 to 16. So that duplicate ratio is the ratio of the squares, as triplicate ratio is the ratio of the cubes, &c.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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