difference, neither will that which was mentioned, since it is divided oppositely to this.
Moreover (he errs), if he divides genus by negation, as those who define a line to be length without breadth, since this signifies nothing else than that it has no breadth; the genus then will happen to partake of the species, for every length is either with, or without breadth, since of every thing either affirmation or negation is verified, so that the genus of a line which is length, will either be without breadth, or will have breadth. But length without breadth is the definition of the species; likewise, length with breadth, for without breadth and with breadth are differences; but the definition of species is from the difference and the genus; so that genus would receive the definition of species; in like manner also, the definition of difference, since one of the above-named differences is necessarily predicated of genus. The place mentioned however is useful against those who assert that there are ideas, for if there is length itself, how will it be predicated of the genus that it has breadth or has it not, for it is necessary that one of these should be verified of every length, if it is to be verified of the genus. This however does not occur, since there are lengths without breadth, and those which have breadth, so that this place is useful against those only, who say that genus is one in number, and this they do who admit ideas, for they say that length itself and animal itself are genera.
Perhaps, indeed, in some cases it is necessary for a person when defining, to use negation, as in privations, for that thing is blind which has not sight when it is naturally adapted to have it. Still it makes no difference whether we divide genus by negation, or by such an affirmation, as to which it is necessary that negation should be oppositely divided; for instance, if length were defined to be that which has breadth, for to what has breadth that which
