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ratio |
6 definitions found From Webster's Revised Unabridged Dictionary (1913) [web1913]: 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. From Webster's Revised Unabridged Dictionary (1913) [web1913]: 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 From Webster's Revised Unabridged Dictionary (1913) [web1913]: 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. From Webster's Revised Unabridged Dictionary (1913) [web1913]: 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. From Webster's Revised Unabridged Dictionary (1913) [web1913]: 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. From WordNet r 1.6 [wn]: ratio n : the relative magnitudes of two quantities (usually expressed as a quotient)
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