present with every B, the proposition is not demonstrated, but in order to its not being present with every, this hypothesis must be taken. For if A is with every B, and C with a certain B, A is with a certain C, but this was not so, hence it is false that it is with every one, and if thus, it is true that it is not with every B, and if it is supposed present with a certain B, there will be the same things as in the syllogisms above mentioned.
It appears then that in all syllogisms through the impossible the contradictory must be supposed, and it is apparent that in the middle figure the affirmative is in a certain way demonstrated, and the universal in the last figure.
Chapter 14
A Demonstration to the impossible differs from an ostensive, in that it admits what it wishes to subvert, leading to an acknowledged falsehood, but the ostensive commences from confessed theses. Both therefore assume two allowed propositions, but the one assumes those from which the syllogism is formed, and the other one of these, and the contradictory of the conclusion. In the one case also the conclusion need not be known, nor previously assumed that it is, or that it is not, but in the other it is necessary (previously to assume) that it is not; it is of no consequence however whether the conclusion is affirmative or
