It appears then, that not the contrary, but the contradictory must be supposed in all syllogisms, for thus there will be a necessary (consequence), and a probable axiom, for if of every thing affirmation or negation (is true), when it is shown that negation is not, affirmation must necessarily be true. Again, except it is admitted that affirmation is true, it is fitting to admit negation; but it is in neither way fitting to admit the contrary, for neither, if the being present with no one is false, is the being present with every one necessarily true, nor is it probable that if the one is false the other is true.
It is palpable, therefore, that in the first figure, all other problems are demonstrated through the impossible; but that the universal affirmative is not demonstrated.
Chapter 12
In the middle, however, and last figure, this also is demonstrated. For let A be supposed not present with every B, but let A be supposed present with every C, therefore if it is not present with every B, but is with every C, C is not with every B, but this is impossible, for let it be manifest that C is with every B, wherefore what was supposed is false, and the being present with every individual is true. If however the contrary be supposed, there will be a syllogism, and the impossible, yet the proposition is not demonstrated. For if A is present with no B, but with every C, C will be with no B, but this is impossible, hence that A
