We have already seen the pomposity and verbosity displayed by Webster in the definition of number. These characteristics can be duplicated in the definitions of numerous other common words. Thus Webster states that the area of a surface is its "superficial contents": The Century defines area as "the superficies of an enclosed or defined surface space"! Webster defines a proportion as "the relation or adaptation of one portion to another or to the whole, as respects magnitude, quantity or degree." This definition (not intended, of course, as a mathematical one) is hazy enough to suit a mystic. He says equals means "exactly agreeing with respect to quantity," which is not bad aside from the fact that every word is Latin with the exception of the two prepositions. Webster defines ratio as the relation which one magnitude or quantity has to another of the same kind, and in a note distinguishes two kinds of ratio, arithmetical and geometrical. Now nine thousand nine hundred and ninety-nine times out of ten thousand, by the ratio of two numbers, is meant the geometric ratio or the quotient of one by the other, nearly always the first divided by the second. So far as the dictionary definitions go the reader would be likely to think one definition as important as the other.
The foregoing definitions from Webster are those in the Old International now in wide use over the country. It will be found interesting to compare them with those of the New International recently published which contains numerous new features. Looking for the word number we find instead of the four definitions given above, the following two: "The or a total, aggregate, or amount of units (whether of things, persons, or abstract units); arithmetical aggregate; as odd or even number." Now bad as the preceding definitions were, probably every one will say these are inferior in their crude awkwardness. Ideas, for instance, would hardly be included in the parenthesis list, and yet they can be counted when they exist. What the last phrase about odd and even means in its setting does not appear.
Fortunately the bad definition of number just referred to seems to be a very poor example by which to judge the new dictionary. The definitions of ratio and proportions, for instance, unlike in the old dictionary, are above reproach, with a single exception. Under ratio it is said that it is sometimes called the "rule of three." This is evidently a continuation of the old confusion of ratio and proportion. Ratio has only two terms, while rule of three has three, with a fourth implied. Under "proportion" one definition is, the rule of three, which is correct.
Under the word area are given the same old definitions which have been handed down from Dr. Johnson's time, hazy in meaning and oozing with Latin roots. Under the word volume, on the other hand, strangely enough, is found a simple and correct definition. Thus,
