§ 626. The first of the eleven moods, AAA, is excluded by the rule that the conclusion cannot be a universal affirmative.
Two more moods, namely AOO and OAO, are excluded by the rule that neither of the premisses can be a particular negative.
AII violates the rule that when the major premiss is affirmative, the minor must be universal.
EAE violates the rule that, when the minor premiss is affirmative, the conclusion must be particular. Thus we are left with six moods which are valid in the fourth figure, namely,
AAI. AEE. IAI. EAO. EIO. AEO.
§ 627. Thus the 256 possible forms of syllogism have been reduced to two dozen legitimate combinations of mood and figure, six moods being valid in each of the four figures.