Adjacent Words

Ratio definitions

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Webster's 1828 Dictionary

RA'TIO, n. 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.

WordNet (r) 3.0 (2005)

n
1: the relative magnitudes of two quantities (usually expressed as a quotient)
2: the relation between things (or parts of things) with respect to their comparative quantity, magnitude, or degree; "an inordinate proportion of the book is given over to quotations"; "a dry martini has a large proportion of gin" [syn: proportion, ratio]

Merriam Webster's

noun (plural ratios) Etymology: Latin, computation, reason — more at reason Date: 1660 1. a. the indicated quotient of two mathematical expressions b. the relationship in quantity, amount, or size between two or more things ; proportion 2. the expression of the relative values of gold and silver as determined by a country's currency laws

Oxford Reference Dictionary

n. (pl. -os) the quantitative relation between two similar magnitudes determined by the number of times one contains the other integrally or fractionally (in the ratio of three to two; the ratios
1:5 and
20:100 are the same). Etymology: L (as RATE(1))

Webster's 1913 Dictionary

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.

Webster's 1913 Dictionary

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.

Webster's 1913 Dictionary

Anharmonic An`har*mon"ic, a. [F. anharmonique, fr. Gr. 'an priv. + ? harmonic.] (Math.) Not harmonic. The anharmonic function or ratio of four points abcd on a straight line is the quantity (ac/ad):(bc/bd), where the segments are to be regarded as plus or minus, according to the order of the letters.

Webster's 1913 Dictionary

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.

Webster's 1913 Dictionary

Geometric Ge`o*met"ric, Geometrical Ge`o*met"ric*al, a. [L. geometricus; Gr. ?: cf. F. g['e]om['e]trique.] Pertaining to, or according to the rules or principles of, geometry; determined by geometry; as, a geometrical solution of a problem. Note: Geometric is often used, as opposed to algebraic, to include processes or solutions in which the propositions or principles of geometry are made use of rather than those of algebra. Note: Geometrical is often used in a limited or strictly technical sense, as opposed to mechanical; thus, a construction or solution is geometrical which can be made by ruler and compasses, i. e., by means of right lines and circles. Every construction or solution which requires any other curve, or such motion of a line or circle as would generate any other curve, is not geometrical, but mechanical. By another distinction, a geometrical solution is one obtained by the rules of geometry, or processes of analysis, and hence is exact; while a mechanical solution is one obtained by trial, by actual measurements, with instruments, etc., and is only approximate and empirical. Geometrical curve. Same as Algebraic curve; -- so called because their different points may be constructed by the operations of elementary geometry. Geometric lathe, an instrument for engraving bank notes, etc., with complicated patterns of interlacing lines; -- called also cycloidal engine. Geometrical pace, a measure of five feet. Geometric pen, an instrument for drawing geometric curves, in which the movements of a pen or pencil attached to a revolving arm of adjustable length may be indefinitely varied by changing the toothed wheels which give motion to the arm. Geometrical plane (Persp.), the same as Ground plane . Geometrical progression, proportion, ratio. See under Progression, Proportion and Ratio. Geometrical radius, in gearing, the radius of the pitch circle of a cogwheel. --Knight. Geometric spider (Zo["o]l.), one of many species of spiders, which spin a geometrical web. They mostly belong to Epeira and allied genera, as the garden spider. See Garden spider. Geometric square, a portable instrument in the form of a square frame for ascertaining distances and heights by measuring angles. Geometrical staircase, one in which the stairs are supported by the wall at one end only. Geometrical tracery, in architecture and decoration, tracery arranged in geometrical figures.

Collin's Cobuild Dictionary

(ratios) A ratio is a relationship between two things when it is expressed in numbers or amounts. For example, if there are ten boys and thirty girls in a room, the ratio of boys to girls is
1:3, or one to three. The adult to child ratio is 1 to 6. N-COUNT: usu sing, oft N of n to n

Soule's Dictionary of English Synonyms

n. Proportion, rate, fixed relation.

Moby Thesaurus

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