Outlines of Mathematical Science for the School Room

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Their difference affords the true an- swer, and is the measure of their proportion.
PROPORTION AND RATIO. 99 In comparing numbers with respect to their quo- tient, the question is, how many times is one greater or less than the other? Their quotient or ratio, is the true answer, and is the measure of their proportion. Ten, for example, is nine greater than one, if we com- pare the numbers one and ten by their difference. But if we compare them by their quotient, ten is said to be ten times as g
...reat as one the language " ten times" having reference to the quotient, which is al- ways taken as the measure of the relative value of the two numbers so compared. Thus, when we say, that, the units of our common system of numbers increase in a tenfold ratio, we mean that they so in- crease that each succeeding unit shall contain the preceding, one ten times. This is a convenient lan- guage to express a particular relation of two num- bers, and is perfectly correct, when used in conformity to an accurate definition.

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