deduction to the impossible, (for it is demonstrated by syllogism,) but the other we cannot, for it is concluded from hypothesis. They differ nevertheless from the before-named, because we must in them indeed have admitted some thing previously, if we are about to consent, as if, for example, one power of contraries should have been shown, and that there was the same science of them, now here they admit, what they had not allowed previously on account of the evident falsity, as if the diameter of a square having been admitted commensurable with the side, odd things should be equal to even.
Many others also are concluded from hypothesis, which it is requisite to consider, and clearly explain; what then are the differences of these, and in how many ways an hypothetical syllogism is produced, we will show hereafter; at present, let only so much be evident to us, that we cannot resolve such syllogisms into figures; for what reason we have shown.
Chapter 45
As many problems as are demonstrated in many figures, if they are proved in one syllogism, may be referred to another, e.g. a negative in the first may be referred to the second, and one in the middle to the first, still not all, but some only. This will appear from the following: if A is with no B, but B with every C, A is with no C, thus the first figure arises; but if the negative is converted, there will be the middle, for B will be with no A, and with every C. In the same manner, if the syllogism be not universal, but particular, as if A is with no B, but B is with a certain C, for the negative being converted there will be the middle figure.
