is with no B is false. Still it does not follow, that if this is false, the being present with every B is true, but when A is with a certain B, let A be supposed present with no B, but with every C, therefore it is necessary that C should be with no B, so that if this is impossible A must necessarily be present with a certain B. Still if it is supposed not present with a certain one, there will be the same as in the first figure. Again, let A be supposed present with a certain B, but let it be with no C, it is necessary then that C should not be with a certain B, but it was with every, so that the supposition is false, A then will be with no B. When however A is not with every B, let it be supposed present with every B, but with no C, therefore it is necessary that C should be with no B, and this is impossible, wherefore it is true that A is not with every B. Evidently then all syllogisms are produced through the middle figure.
Chapter 13
Through the last figure also, (it will be concluded) in a similar way. For let A be supposed not present with a certain B, but C present with every B, A then is not with a certain C, and if this is impossible, it is false that A is not with a certain B, wherefore that it is present with every B is true. If, again, it should be supposed present with none, there will be a syllogism, and the impossible, but the proposition is not proved, for if the contrary is supposed there will be the same as in the former (syllogisms). But in order to conclude that it is present with a certain one, this hypothesis must be assumed, for if A is with no B, but C with a certain B, A will not be with every C, if then this is false, it is true that A is with a certain B. But when A is with no B, let it be supposed present with a certain one, and let C be assumed present with every B, wherefore it is necessary that A should be with a certain C, but it was with no C, so that it is false that A is with a certain B. If however A is supposed
