Definition of Ratio. Meaning of Ratio. Synonyms of Ratio
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Definition of Ratio
ratio Inverse In*verse", a. [L. inversus, p. p. of invertere: cf. F.
inverse. See Invert.]
1. Opposite in order, relation, or effect; reversed;
inverted; reciprocal; -- opposed to direct.
2. (Bot.) Inverted; having a position or mode of attachment
the reverse of that which is usual.
3. (Math.) Opposite in nature and effect; -- said with
reference to any two operations, which, when both are
performed in succession upon any quantity, reproduce that
quantity; as, multiplication is the inverse operation to
division. The symbol of an inverse operation is the symbol
of the direct operation with -1 as an index. Thus sin-1 x
means the arc whose sine is x.
Inverse figures (Geom.), two figures, such that each point
of either figure is inverse to a corresponding point in
the order figure.
Inverse points (Geom.), two points lying on a line drawn
from the center of a fixed circle or sphere, and so
related that the product of their distances from the
center of the circle or sphere is equal to the square of
the radius.
Inverse, or Reciprocal, ratio (Math.), the ratio of the
reciprocals of two quantities.
Inverse, or Reciprocal, proportion, an equality between
a direct ratio and a reciprocal ratio; thus, 4 : 2 : : 1/3
: 1/6, or 4 : 2 : : 3 : 6, inversely.
Ratio Ratio Ra"ti*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 is made the
dividend; as, a:b = b/a.
Note: Some writers consider ratio as the quotient itself,
making ratio equivalent to a number. 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.
2. Hence, fixed relation of number, quantity, or degree;
rate; proportion; as, the ratio of representation in
Congress.
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.
ratio Duplicate Du"pli*cate, a. [L. duplicatus, p. p. of duplicare
to double, fr. duplex double, twofold. See Duplex.]
Double; twofold.
Duplicate proportion or 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.
