Chapter 22
When the extremes are converted, the middle must necessarily be converted with both. For if A is present with C through B, if it is converted, and C is with whatever A is, B also is converted with A, and with whatever A is present, B also is through the middle C, and C is converted with B through the middle A. The same will occur with negatives, as if B is with C, but A is not with B, neither will A be with C, if then B is converted with A, C also will be converted with A. For let B not be with A, neither then will C be with A, since B was with every C, and if C is converted with B, (the latter) is also converted with A; for of whatever B is predicated, C also is, and if C is converted with A, B also is converted with A, for with whatever B is present, C also is, but C is not present with what A is. This also alone begins from the conclusion, (but the others not similarly,) as in the case of an affirmative syllogism. Again, if A and B are converted, and C and D likewise; but A or C must necessarily be present with every individual; B and D also will so subsist, as that one of them will be present with every individual. For since B is present with whatever A is, and D with what ever C is, but A or C with every individual, and not both at the same time, it is evident that B or D is with every individual, and not both of them at the same time; for two syllogisms are conjoined. Again, if A or B is with every individual and C or D, but they are not present at the same time, if A and C are converted B also and D are converted, since if B is not present with a certain thing with which D is, it is evident that A is present
