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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.

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 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.

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.

- In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, if a bowl of...

- In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure...

- constant speed ratio. Features of gears and gear trains include: The ratio of the pitch circles of mating gears defines the speed ratio and the mechanical...

- In survival analysis, the hazard ratio (HR) is the ratio of the hazard rates corresponding to the conditions described by two levels of an explanatory...

- The aspect ratio of an image describes the proportional relationship between its width and its height. It is commonly expressed as two numbers separated...

- The odds ratio (OR) is a statistic defined as the ratio of the odds of A in the presence of B and the odds of A without the presence of B. This statistic...

- **** ratio is the ratio of males to females in a po****tion. More data is available for humans than for any other species, and the human **** ratio is more...

- Poisson's ratio, denoted by the Gr**** letter 'nu', ν {\displaystyle \nu } , and named after Siméon Poisson, is the negative of the ratio of (signed) transverse...

- In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance...

- attenuate. The damping ratio is a measure of describing how rapidly the oscillations decay from one bounce to the next. The damping ratio is a system parameter...

- In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure...

- constant speed ratio. Features of gears and gear trains include: The ratio of the pitch circles of mating gears defines the speed ratio and the mechanical...

- In survival analysis, the hazard ratio (HR) is the ratio of the hazard rates corresponding to the conditions described by two levels of an explanatory...

- The aspect ratio of an image describes the proportional relationship between its width and its height. It is commonly expressed as two numbers separated...

- The odds ratio (OR) is a statistic defined as the ratio of the odds of A in the presence of B and the odds of A without the presence of B. This statistic...

- **** ratio is the ratio of males to females in a po****tion. More data is available for humans than for any other species, and the human **** ratio is more...

- Poisson's ratio, denoted by the Gr**** letter 'nu', ν {\displaystyle \nu } , and named after Siméon Poisson, is the negative of the ratio of (signed) transverse...

- In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) is a way to examine the performance...

- attenuate. The damping ratio is a measure of describing how rapidly the oscillations decay from one bounce to the next. The damping ratio is a system parameter...

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