monstrated per impossibile, (there will be still the first figure,) because the false being assumed, a syllogism arises in the first figure. For example, in the last figure, if A and B are present with every C, it can be shown that A is present with some B, for if A is present with no B, but B is present with every C, A will be present with no C; but it was supposed that A was present with every C, and in like manner it will happen in other instances.
It is also possible to reduce all syllogisms to universal syllogisms in the first figure. For those in the second, it is evident, are completed through these, yet not all in like manner, but the universal by conversion of the negative, and each of the particular, by deduction per impossibile. Now, particular syllogisms in the first figure are completed through themselves, but may in the second figure be demonstrated by deduction to the impossible. For example, if A is present with every B, but B with a certain C, it can be shown that A will be present with a certain C, for if A is present with no C, but is present with every B, B will be present with no C, for we know this by the second figure. So also will the demonstration be in the case of a negative, for if A is present with no B, but B is present with a certain C, A will not be present with a certain C, since if A is present with every C, and with no B, B will be present with no C, and this was the middle figure. Wherefore, as all syllogisms in the middle figure are reduced to universal syllogisms in the first figure, but particular in the first are reduced to those in the middle figure, it is clear that particular will be reduced to universal syllogisms in the first figure. Those, however, in the third, when the terms are universal, are immediately completed through those syllogisms; but when particular (terms) are assumed (they are completed) through particular syllogisms in the first figure; but these have been reduced to those, so that also particular syllogisms in the third figure (are reducible to the same). Wherefore, it is evident that all can be reduced to universal syllogisms in the first figure; and we have therefore shown how syllogisms de inesse and de non inesse
