scientifically that which is demonstrable, is to possess demonstration, so that if there is demonstration in regard to things of this kind, there can evidently not be also definition of them, for a person might know by definition without demonstration, since nothing prevents the possession of it at one and the same time. A sufficient evidence of this is also derived from induction, for we have never known by definition, any of those which are inherent per se nor which are accidents; besides, if definition be a certain indication of substance, it is evident that such things are not substances.
Clearly then, there is not definition of every thing of which there is also demonstration, but what, is there then demonstration of every thing of which there is definition or not? there is one reason and the same also of this. For of one thing, so far as it is one, there is one science, so that if to know that which is demonstrable be to possess demonstration, an impossibility would happen, for he who possesses definition would know scientifically without demonstration. Besides, the principles of demonstration are definitions, of which it has been shown before, there will not be demonstrations, since either principles will be demonstrable, and principles of principles, and this would proceed to infinity, or the first (principles) will be indemonstrable definitions.
Yet if there are not of every thing and the same, may there not be definition and demonstration of a certain thing and the same? or is it impossible? since there is not demonstration of what there is definition. For definition is of what a thing is, and of substance, but all demonstrations appear to suppose and assume what a thing is, as mathematics, what is unity and what an odd number, and the rest in like manner. Moreover every demonstration shows something of somewhat, as that it is, or that it is not, but in definition one thing is not predicated of another, as neither animal of biped, nor this of animal, nor figure of superficies, for superficies is not figure, nor figure superficies. Again, it is one thing to show what a thing is, but another to show that it is, definition then shows what a thing is, but demonstration that this thing, either
