passes us; and, nevertheless, something must be said of it, although it is impossible to practise it.[1]
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
- ↑ After this paragraph occur in the MS. the following lines, written in a finer hand, and inclosed in parenthesis: "…is much more to succeed in the one than the other, and I have chosen this science to attain it only because it alone knows the true rules of reasoning, and, without stopping at the rules of syllogisms which are so natural that we cannot be ignorant of them, stops and establishes itself upon the true method of conducting reasoning in all things, which almost every one is ignorant of, and which it is so advantageous to know, that we see by experience that among equal minds and like circumstances, he who possesses geometry bears it away, and acquires a new vigor. "I wish, therefore, to explain what demonstrations are by the example of those of geometry, which is almost the only one of the human sciences that produces infallible ones, because she alone observes the true method, whilst all the others are, through a natural necessity, in a sort of confusion, which the geometricians alone know exceedingly well how to comprehend." On the margin of this fragment is in the MS. the following note: "That which is in small characters was hidden under a paper, the edges of which were glued, and upon which was written the article beginning: I cannot better explain, etc."—Faugère.
