It will be seen that (2) is in figure 2, and (3) in figure 3.
Next, let P, Q, ∴ Rʹ be in figure 2, the major premiss being stated first. We then have for our three syllogisms,—
| P ⎯ M, S ⎯ M, ∴ (S ⎯ P)ʹ; | (1) |
| S ⎯ M, S ⎯ P, ∴ (P ⎯ M)ʹ; | (2) |
| S ⎯ P, P ⎯ M, ∴ (S ⎯ M)ʹ. | (3) |
Here (2) is in figure 3, (3) in figure 1.
Finally, let P, Q, ∴ Rʹ be in figure 3, the major premiss being stated first. We have
| M ⎯ P, M ⎯ S, ∴ (S ⎯ P)ʹ; | (1) |
| M ⎯ S, S ⎯ P, ∴ (M ⎯ P)ʹ; | (2) |
| S ⎯ P, M ⎯ P, ∴ (M ⎯ S)ʹ. | (3) |
Here (2) is in figure 1, (3) in figure 2.
Hence we see that, starting with a syllogism in any one of the first three figures (the minor premiss preceding the major in figure 1, but following it in figures 2 and 3), and taking the 334 propositions in the above cyclic order, then the figures will always recur in the cyclic order 1, 2, 3.[361]
[361] If we were to start with a syllogism in figure 1, the major premiss being stated first, then the cyclic order of figures would be 1, 3, 2, and in figures 2 and 3 the minor premiss would precede the major.
It follows that (as we already know to be the case) there must be an equal number of valid syllogisms in each of the first three figures, and that they may be arranged in sets of equivalent trios. These equivalent trios will be found to be as follows (sets containing strengthened premisses or weakened conclusions being enclosed in square brackets);