is present with no A, and A is contingent with every C, and the first figure is produced; the same would also occur if the negation belongs to C. But if both propositions be affirmative, there will not be a syllogism, clearly not of the non-inesse, nor of the necessary non-inesse, because a negative premise is not assumed, neither in the simple, nor in the necessary inesse. Neither, again, will there be a syllogism of the contingent non-inesse, for necessary terms being assumed, B will not be present with C, e.g. if A be assumed "white," B "a swan," and C "man;" nor will there be from opposite affirmations, since B has been shown necessarily not present with C, in short, therefore, a syllogism will not be produced. It will happen the same in particular syllogisms, for when the negative is universal and necessary, there will always be a syllogism of the contingent, and of the non-inesse, but the demonstration will be by conversion; still, when the affirmative (is necessary), there will never be a syllogism, and this may be shown in the same way as in the universals, and by the same terms. Nor when both premises are assumed affirmative, for of this there is the same demonstration as before, but when both are negative, and that which signifies the non-inesse is universal, and necessary; the necessary will not be concluded through the propositions, but the contingent being converted, there will be a syllogism as before. If however both propositions are laid down indefinite, or particular, there will not be a syllogism, and the demonstration is the same, and by the same terms.
It appears then, from what we have said, that an universal, and necessary negative being assumed, there is always a syllogism, not only of the contingent, but also of the simple non-inesse; but with a necessary affirmative, there will never be a syllogism; also that when the terms subsist in the same manner, in necessary, as in simple propositions, there is, and is not, a syllogism; lastly, that all these syllogisms are incomplete, and that they are completed through the above-mentioned figures.
