Ratio
in law, an account; a cause, or the giving judgment therein. In mathematics: (1) The measure of the relation which one quantity bears to another of the same kind; that is, it is the number of times that one quantity contains another regarded as a standard. This is found by dividing the one by the other. The quotient or ratio thus ob- RATIO tained is the proper measure of the relation of the two quantities. Some writers define the ratio of one quantity to another as the quotient of the first quantity divided by the second, while others define it as the quotient of the second divided by the first. Thus, the ratio of 2 to 4, or of a to b, may be taken either as 2÷4 or 4-2, and ab or ba. In every ratio there are two quantities compared, one of which is supposed known, and and is assumed as a standard; the other is to be determined in terms of this standard.
These quantities are called terms of the ratio; the first one, or that which is antecedently known, is called the antecedent, and that whose value is to be measured by the antecedent, is called the consequent. Ratios are compared by comparing the fractions; thus, the ratio of 8:5 is compared with the ratio of 9:6, by comparing the fractions % and 9%; these fractions are respectively equal to 48/30 and 45/30 and since 48/30 is greater than 45/30, the ratio of 8:5 is greater than that of 9:6. Ratios are compounded together by multiplying the their antecedents together for a new antecedent, and their consequents together for a new consequent; thus the ratio of a:b, compounded with that of c:d, is ac: bd. Proportion is the relation of equality subsisting between two ratios. See PROPORTION. (2) A name sometimes given to the rule of three in arithmetic.
Compound ratio: (a) The ratio of the product of the antecedents of two or more ratios to the product of the consequents: thus if 3:6:: 4 : 12, then 12:72 is the compound ratio. (b) When one quantity is connected with two others in such a manner that if the first is increased or diminished, the product of the other two is increased or diminished in the same proportion, then the first quantity is said to be in the compound ratio of the other two.
Direct ratio, two quantities are said to be in direct ratio when they both increase or decrease together, and in such a manner that their ratio is constant.
Duplicate ratio, when three quantities are in continued proportion, the first is said to have to the third the duplicate ratio of that which it has to the second, or the first is to the third as the square of the first to the square of the second.
Inverse ratio, two quantities or magnitudes are said to be in inverse ratio, when if the one increases the other necessarily decreases, and, vice versa, when the one decreases the other increases.
Mixed ratio or proportion: a ratio or proportion in which the sum of the antecedent and consequent is compared with the difference of the antecedent and consequent. Thus, if a:b::c:d, then a+b: RATION a-b::c+d:c-d is the mixed ratio or proportion.
Prime and ultimate ratios, a method of analysis, devised and first successfully, employed by Newton in his "Principia."
It is an extension and simplification of the method known among the ancients as the method of exhaustions. To conceive the idea of this method, let us suppose two variable quantities constantly ap- In general when two variable quantities, ratio of the two quantities equal to 1. assignable quantity; then is the ultimate their ratio continually approaches 1, and at last differs from 1 by less than any assignable quantity; then is the ultimate ratio of the two quantities equal to 1.
In general when two variable quantities, simultaneously approach two other quantities, which, under the same circumstances, remain fixed in value, the mate ratios, according as the ratio of fixed. They are called prime or ultities is the same as the ratio of the quantities whose values remain fixed. They are called prime or ultimate ratios, according as the ratio of called the method of limits. or approaching to the ratio of the limits.
This method of analysis is generally called the method of limits.
Extreme and mean ratio, in geometry, the ratio where a line is divided in such a manner that the greater segment is a mean proportional between the whole line and the lesser segment: that is, that Composition of ratios, the act of comas that greater segment is to the less. Composition of ratios, the act of compounding ratios. Ratio of a geometrical progression, the constant quantity by which each term is multiplied to produce the succeeding one. To find the ratio of a given progression, divide any term by the preceding one. Ratio of exchange, a phrase used in political economy to denote the proportion in which a quantity of one commodity exchanges for a given quantity of another. The expression can never be used with any degree of accuracy, except in those cases where the commodities are homogeneous in quality, and susceptible of weight or measurement, as in the exchange of gold for silver, copper, iron, etc., or that of wheat for barley, oats, etc.