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From: Webster's Revised Unabridged Dictionary (1913)

 du·pli·cate a.  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.
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