**The Collaborative International Dictionary of English v.0.48:**

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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**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.
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