[363] It will be found that it comes to just the same thing if the minor premiss is stated first.

It follows that in figure 4 the number of valid syllogisms must be some multiple of three. The number is, as we know, six. There are, therefore, two equivalent trios; and they will be found to be as follows: 335

[Bramantip, AEO, Fesapo;]
Camenes, Fresison, Dimaris.

The equivalent antilogisms are [AAE,] AEI. Comparing this result with that obtained in the preceding section, we see that the only valid antilogistic combinations are AAO and AEI, with the addition of AAE (in which one of the three propositions is unnecessarily strengthened).[364]

[364] This result might be inferred from the rules given in section [214].

268. Equivalence of the Special Rules of the First Three Figures.—Let the following be a valid syllogism in figure 1,—

(minor)S ⎯ M,(1)
(major)M ⎯ P,(2)
(conclusion)∴ (S ⎯ P)ʹ. (3)

Then the corresponding valid syllogism in figure 2 will be

(major) M ⎯ P, (2)
(minor) S ⎯ P, contradictory of (3)
(conclusion) ∴(S ⎯ M)ʹ; contradictory of (1)

and the corresponding valid syllogism in figure 3 will be