which we make use; to prove them all by mentally substituting definitions in the place of things defined.
And here it seems to me proper to anticipate three principal objections which may be made:
1st, that this method has nothing new; 2d, that it is very easy to learn, it being unnecessary for this to study the elements of geometry, since it consists in these two words that are known at the first reading; and, 3d, that it is of little utility, since its use is almost confined to geometrical subjects alone.
It is necessary therefore to show that there is nothing so little known, nothing more difficult to practise, and nothing more useful or more universal.
As to the first objection, that these rules are common in the world, that it is necessary to define every thing and to prove every thing, and that logicians themselves have placed them among the principles of their art, I would that the thing were true and that it were so well known that I should not have the trouble of tracing with so much care the source of all the defects of reasonings which are truly so common. But so little is this the case, that, geometricians alone excepted, who are so few in number that they are single in a whole nation and long periods of time, we see no others who know it. It will be easy to make this understood by those who have perfectly comprehended the little that I have said; but if they have not fully comprehended this, I confess that they will learn nothing from it.
But if they have entered into the spirit of these rules, and if the rules have made sufficient impression on them to become rooted and established in their minds, they will feel how much difference there is between what is said here and what a few logicians may perhaps have written by chance approximating to it in a few passages of their works.
Those who have the spirit of discernment know how much difference there is between two similar words, according to their position, and the circumstances that accompany them. Will it be maintained, indeed, that two persons who have read the same book, and learned it by heart, have a like acquaintance with it, if the one comprehends it in such a manner that he knows all its principles, the force of its conclusions, the
