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Webster 1913 Edition

Ratio

Ra′ti-o

(rā′shĭ-ō̍ or rā′shō̍)
,
Noun.
[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 ½; of a to b by
a/b
; or (less commonly) the second term is made the dividend; as,
a:b =
b/a
.
☞ 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.

Webster 1828 Edition

Ratio

RA'TIO

,
Noun.
ra'sho. [L. from ratus, reor, to think or suppose, to set, confirm or establish. Reor is contracted from redor or retor, and primarily signifies to throw, to thrust, hence to speak, to set in the mind, to think, like L. suppono; and setting gives the sense of a fixed rate or rule. See Reason.]
Proportion, or the relation of homogeneous things which determines the quantity of one from the quantity of another, without the intervention of a third.
The relation which one quantity has to another of the same kind, as expressed by the quotient of the one divided by the other. Thus the ratio of 4 to 2 is 4/2, or 2; and the ratio of 5 to 6 is 5/6. This is geometrical ratio, which is that signified when the term is used without distinction; but arithmetical ratio is the difference between two quantities. Thus the arithmetical ratio of 2 to 6 is 4.
Ratio respects magnitudes of the same kind only. One line may be compared with another line, but a line cannot be compared with a superficies, and hence between a line and a superficies there can be no ratio.

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