# 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 *a*^{2} to *b*^{2}, 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.