Ratio \Ra"ti*o\ (r[=a]"sh[i^]*[-o] or r[=a]"sh[-o]), n. [L., fr.
   reri, ratus, to reckon, believe, think, judge. See Reason.]
   1. (Math.) The relation which one quantity or magnitude has
      to another of the same kind. It is expressed by the
      quotient of the division of the first by the second; thus,
      the ratio of 3 to 6 is expressed by 3/6 or 1/2; of a to b
      by a/b; or (less commonly) the second term is made the
      dividend; as, a:b = b/a.
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   Note: Some writers consider ratio as the quotient itself,
         making ratio equivalent to a number.
         [1913 Webster] The term ratio is also sometimes applied
         to the difference of two quantities as well as to their
         quotient, in which case the former is called
         arithmetical ratio, the latter, geometrical ratio. The
         name ratio is sometimes given to the rule of three in
         arithmetic. See under Rule.
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   2. Hence, fixed relation of number, quantity, or degree;
      rate; proportion; as, the ratio of representation in
      Congress.
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   Compound ratio, Duplicate ratio, Inverse ratio, etc.
      See under Compound, Duplicate, etc.

   Ratio of a geometrical progression, the constant quantity
      by which each term is multiplied to produce the succeeding
      one.
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duplicate \du"pli*cate\, a. [L. duplicatus, p. p. of duplicare
   to double, fr. duplex double, twofold. See Duplex.]
   Double; twofold.
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   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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