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 for Duplicate proportion
From The Collaborative International Dictionary of English v.0.48 :

  duplicate \du"pli*cate\, a. [L. duplicatus, p. p. of duplicare
     to double, fr. duplex double, twofold. See Duplex.]
     Double; twofold.
     [1913 Webster]
     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.
        [1913 Webster]

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