MATHEMATICAL DEFINITIONS | 461 
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 mag- 
nitude, 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 thou- 
sand, 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 Inter- 
national now in wide use over the country. It will be found interesting 
to compare them with those of the New International recently pub- 
lished which contains numerous new features. Looking for the word 
number we find instead of the four definitions given above, the follow- 
ing 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 evi- 
dently 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, 
