I do not speak of the first; I treat particularly of the second, and it includes the third. For if we know the method of proving the truth, we shall have, at the same time, that of discriminating it, since, in examining whether the proof that is given of it is in conformity with the rules that are understood, we shall know whether it is exactly demonstrated.

Geometry, which excels in these three methods, has explained the art of discovering unknown truths; this it is which is called *analysis*, and of which it would be useless to discourse after the many excellent works that have been written on it.

That of demonstrating truths already found, and of elucidating them in such a manner that the proof of them shall be irresistible, is the only one that I wish to give; and for this I have only to explain the method which geometry observes in it; for she teaches it perfectly by her examples, although she may produce no discourse on it. And since this art consists in two principal things, the one in proving each proposition by itself, the other in disposing all the propositions in the best order, I shall make of it two sections, of which the one will contain the rules for the conduct of geometrical, that is, methodical and perfect demonstrations; and the second will comprehend that of geometrical, that is, methodical and complete order: so that the two together will include all that will be necessary to direct reasoning, in proving and discriminating truths, which I design to give entire.

Section First—Of the method of geometrical, that is, of methodical and perfect demonstrations.

I cannot better explain the method that should be preserved to render demonstrations convincing, than by explaining that which is observed by geometry.

But it is first necessary that I should give the idea of a method still more eminent and more complete, but which mankind could never attain; for what exceeds geometry sur-