last, (I call the first that which is indeed itself predicated of something else, but nothing else of it). If then these things are so, the progression must stop in negation, for the not being present is demonstrated triply, since either B is present with every individual with which C is, but A is present with none with which B is. In B C therefore, and always in the other proposition, it is necessary to proceed to immediates, for this proposition is affirmative. With regard to the other however it is clear, that if it is not present with something else prior, for instance, with D, it will be requisite that this (D) should be present with every B. Also if again it is not present with something else prior to D, it will require that to be present with every D, so that since the upward progression stops, the downward progression will also stop, and there will be something first with which it is not present. Moreover if B is with every A, but with no C, A will be with no C; again, if it is required to show this, it is evident, that it may be demonstrated either through the superior mode, or through this, or through the third, now the first has been spoken of, but the second shall be shown. Thus indeed it may demonstrate it, as, for instance, that D is present with every B, but with no C, if it is necessary that any thing should be with B, and, again, if this is not present with C, something else is present with D, which is not present with C, wherefore since the perpetually being present with something superior stops, the not being present will also stop. But the third mode was if A indeed is present with every B, but C is not present, C will not be present with every A; again,
