Chapter 20
That media cannot be infinite, if the predications, both downward and upward, stop, is evident: I call indeed the predication upward, which tends to the more universal, but the downward that which proceeds to the particular. For if when A is predicated of F, the media are infinite, that is B, it evidently may be possible that from A in a descending series, one thing may be predicated of another to infinity, (for before we arrive at F, there are infinite media,) and from F in an ascending series, there are infinite (attributes) before we arrive at A. Hence, if these things are impossible, it is also impossible that there should be infinite media between A and F; for it does not signify if a man should say that some things of A B F so mutually adhere, as that there is nothing intermediate, but that others cannot be assumed. For whatever I may assume of B, the media with reference to A or to F, will either be infinite or not, and it is of no consequence from what the infinites first begin, whether directly or not directly, for those which are posterior to them are infinite.
Chapter 21
It is apparent also, that in negative demonstration the progression will stop, if indeed in affirmative it is stopped in both (series), for let it be impossible to proceed to infinity upward from the last, (I call the last that which is itself not present with any thing else, but something else with it, for instance, F,) or from the first to the
