# Ratio of a geometrical progression

Ratio of a geometrical progression
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. [1913 Webster]

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}. [1913 Webster]

2. Hence, fixed relation of number, quantity, or degree; rate; proportion; as, the ratio of representation in Congress. [1913 Webster]

{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. [1913 Webster]

The Collaborative International Dictionary of English. 2000.

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• Geometrical progression — Geometric Ge o*met ric, Geometrical Ge o*met ric*al, a. [L. geometricus; Gr. ?: cf. F. g[ e]om[ e]trique.] 1. Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.… …   The Collaborative International Dictionary of English

• geometrical progression — geometric(al) progression noun A series of quantities each of which has the same ratio to its predecessor • • • Main Entry: ↑geometry * * * geometrical progression, = geometric progression. (Cf. ↑geometric progression) …   Useful english dictionary

• 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 …   The Collaborative International Dictionary of English

• ratio — Geometric Ge o*met ric, Geometrical Ge o*met ric*al, a. [L. geometricus; Gr. ?: cf. F. g[ e]om[ e]trique.] 1. Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.… …   The Collaborative International Dictionary of English

• Geometrical — Geometric Ge o*met ric, Geometrical Ge o*met ric*al, a. [L. geometricus; Gr. ?: cf. F. g[ e]om[ e]trique.] 1. Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.… …   The Collaborative International Dictionary of English

• Geometrical curve — Geometric Ge o*met ric, Geometrical Ge o*met ric*al, a. [L. geometricus; Gr. ?: cf. F. g[ e]om[ e]trique.] 1. Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.… …   The Collaborative International Dictionary of English

• Geometrical pace — Geometric Ge o*met ric, Geometrical Ge o*met ric*al, a. [L. geometricus; Gr. ?: cf. F. g[ e]om[ e]trique.] 1. Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.… …   The Collaborative International Dictionary of English

• Geometrical plane — Geometric Ge o*met ric, Geometrical Ge o*met ric*al, a. [L. geometricus; Gr. ?: cf. F. g[ e]om[ e]trique.] 1. Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.… …   The Collaborative International Dictionary of English

• Geometrical radius — Geometric Ge o*met ric, Geometrical Ge o*met ric*al, a. [L. geometricus; Gr. ?: cf. F. g[ e]om[ e]trique.] 1. Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.… …   The Collaborative International Dictionary of English

• Geometrical staircase — Geometric Ge o*met ric, Geometrical Ge o*met ric*al, a. [L. geometricus; Gr. ?: cf. F. g[ e]om[ e]trique.] 1. Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem.… …   The Collaborative International Dictionary of English