What is "duplicate proportion"

duplicate \du"pli*cate\, a. [L. duplicatus, p. p. of duplicare to double, fr. duplex double, twofold. See Duplex.] Double; twofold.

Duplicate proportion or Duplicate ratio (Math.), the proportion or ratio of squares. Thus, in geometrical proportion, the first term to the third is said to be in a duplicate ratio of the first to the second, or as its square is to the square of the second. Thus, in 2, 4, 8, 16, the ratio of 2 to 8 is a duplicate of that of 2 to 4, or as the square of 2 is to the square of 4.