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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.

- these ratios are ratios of two integers and hence are rational, the limit of the sequence of these rational ratios is the irrational golden ratio. Similarly...

- many standard ratios used to try to evaluate the overall financial condition of a corporation or other organization. Financial ratios may be used by...

- cinema and video aspect ratios exist, but are used infrequently. In still camera photography, the most common aspect ratios are 4:3, 3:2, and more recently...

- witnessed birth **** ratios below 100, that is more girls are born than boys. Angola, Botswana and Namibia have reported birth **** ratios between 94 and 99...

- Sharpe ratio should be derived from the performance of the underlying ****ets rather than the fund returns. Sharpe ratios, along with Treynor ratios and Jensen's...

- transmit torque smoothly. The speed ratios of chain and belt drives are computed in the same way as gear ratios. See bicycle gearing. Gear teeth are...

- "Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates". British Medical Journal (Clinical Research Ed.)...

- 20 years, compression ratios are typically between 8:1 and 12:1. Several production engines have used higher compression ratios, including: Cars built...

- the rectangles representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and...

- each of the po****r aspect ratios. When overlapped with their center points aligned, he found that all of those aspect ratio rectangles fit within an outer...

- many standard ratios used to try to evaluate the overall financial condition of a corporation or other organization. Financial ratios may be used by...

- cinema and video aspect ratios exist, but are used infrequently. In still camera photography, the most common aspect ratios are 4:3, 3:2, and more recently...

- witnessed birth **** ratios below 100, that is more girls are born than boys. Angola, Botswana and Namibia have reported birth **** ratios between 94 and 99...

- Sharpe ratio should be derived from the performance of the underlying ****ets rather than the fund returns. Sharpe ratios, along with Treynor ratios and Jensen's...

- transmit torque smoothly. The speed ratios of chain and belt drives are computed in the same way as gear ratios. See bicycle gearing. Gear teeth are...

- "Calculating confidence intervals for relative risks (odds ratios) and standardised ratios and rates". British Medical Journal (Clinical Research Ed.)...

- 20 years, compression ratios are typically between 8:1 and 12:1. Several production engines have used higher compression ratios, including: Cars built...

- the rectangles representing these and other ratios (e.g. the 'golden cut'). The sole value of these ratios is that they are intellectually fruitful and...

- each of the po****r aspect ratios. When overlapped with their center points aligned, he found that all of those aspect ratio rectangles fit within an outer...

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