But apart from these, the rest of the terms that this science employs are to such a degree elucidated and defined that we have no need of a dictionary to understand any of them; so that in a word all these terms are perfectly intelligible, either by natural enlightenment or by the definitions that it gives of them.
This is the manner in which it avoids all the errors that may be encountered upon the first point, which consists in defining only the things that have need of it. It makes use of it in the same manner in respect to the other point, which consists in proving the propositions that are not evident.
For, when it has arrived at the first known truths, it pauses there and asks whether they are admitted, having nothing clearer whereby to prove them; so that all that is proposed by geometry is perfectly demonstrated, either by natural enlightenment or by proofs.
Hence it comes that if this science does not define and demonstrate every thing, it is for the simple reason that this is impossible.[1]
It will perhaps be found strange that geometry does not define any of the things that it has for its principal objects: for it can neither define motion, numbers, nor space; and nevertheless these three things are those of which it treats in particular, and according to the investigation of which it takes the three different names of mechanics, arithmetic, and geometry, this last name belonging to the genus and species.
But this will not surprise us if we remark that, this admirable science only attaching itself to the simplest things, this same quality which renders them worthy of being its objects renders them incapable of being defined; so that the lack of definition is a perfection rather than a defect, since it does not come from their obscurity, but on the contrary from their extreme obviousness, which is such that though it may not have the conviction of demonstrations, it has all their certainty. It supposes therefore that we know what is the thing that is understood by the words motion, number, space; and
