Page:Blaise Pascal works.djvu/437

 us; and, nevertheless, something must be said of it, although it is impossible to practise it.

This true method, which would form demonstrations in the highest excellence, if it were possible to arrive at it, would consist in two principal things: the one, in employing no term the meaning of which had not first been clearly explained; the other, in never advancing any proposition which could not be demonstrated by truths already known; that is, in a word, in defining every term, and in proving every proposition. But to follow the same order that I am explaining, it is necessary that I should state what I mean by definition.

The only definitions recognized in geometry are what the logicians call definitions of name, that is, the arbitrary application of names to things which are clearly designated by terms perfectly known; and it is of these alone that I speak.

Their utility and use is to elucidate and abbreviate discourse, in expressing by the single name that has been imposed what could otherwise be only expressed by several terms; so that nevertheless the name imposed remains divested of all other meaning, if it has any, having no longer any than that for which it is alone designed. Here is an example:

If we are under the necessity of discriminating numbers that are divisible equally by two from those which are not, in order to avoid the frequent repetition of this condition, a