necessary; but when the presence with nothing is necessary, as to what it need not be present with, we must look to those which cannot be present with it; or on the contrary, (as regards that) with which it is necessary not to be present, we must look to those which cannot be with it, but as to what ought not to be present, to the consequents. For whichever of these are identical, it will happen that the one is in no other, since sometimes a syllogism arises in the first and at other times in the middle figure. If however the particular non-inesse (is to be proved), that with which it ought not to be present, and those which it follows, are to be looked to; but of that which ought not to be present, those must be considered, which it is impossible can be in it, for if any of these be identical the particular non-inesse is necessary. What has been said however will perhaps be more clear thus. Let the consequents to A be B, but let those to which it is consequent be C; those again which cannot be in it, D; again, let the things present with E be F, and those to which it is consequent, G; lastly, those which cannot be in it, H. Now if a certain C and a certain F are identical, it is necessary that A should be with every E, for F is present with every E, and A with every C, so that A is with every E; but if C and G are identical, A must necessarily be with a certain E, for A follows every C, and E every G. If however F and D are identical, A will be with no E from a pro-syllogism, for since a negative is convertible and F is identical with D, A will be with no F, but F is with every E; again, if B and H are the same, A will be with no E, for B is with every A, but with no E, for it was the same as H, and H was with no E. If D and G are identical, A will not be with a certain E, for A will not be with G, since it is not present with D, but G is under E, so that neither will it be with a certain E. Moreover if B is identical with G there will be an inverse syllogism, for G will be with every A, (since B is with A,) and E with B (for B is the same as G); still it is not necessary that A should be with every E, but it is neces-
