(1) One way is to begin by finding what Moods of Figure I. conform to the Dictum.  Now, the Dictum requires that, in the major premise, P be predicated of a term distributed, from which it follows that no Mood can be valid whose major premise is particular, as in I.A.I. or O.A.O.  Again, the Dictum requires that the minor premise be affirmative ("with which term another is identified"); so that no Mood can be valid whose minor premise is negative, as in A.E.E. or A.O.O.  By such considerations we find that in Figure I., out of 64 Moods possible, only six are valid, namely, those above-mentioned in Sec. 3, including the two subalterns.  The second step of this method is to test the Moods of the Second, Third, and Fourth Figures, by trying whether they can be reduced to one or other of the four Moods of the First (as briefly illustrated in Sec. 1, and to be further explained in Sec. 6).

(2) Another way is to take the above six General or Common Canons, and to deduce from them Special Canons for testing each Figure:  an interesting method, which, on account of its length, will be treated of separately in the next section.

(3) Direct application of the Common Canons is, perhaps, the simplest plan.  First write out the 64 Moods that are possible without regard to Figure, and then cross out those which violate any of the Canons or Corollaries, thus: 

[Transcriber’s Note:  Moods surrounded with square brackets were crossed out in the original text.]

AAA, [AAE] (6th Can. b).  AAI. [AAO] (6th Can. b). [AEA] (6th Can. a) AEE, [AEI] (6th Can. a) AEO, [AIA] (Cor. ii.) [AIE] (6th Can. b) AII, [AIO] (6th Can. b) [AOA] (6th Can. a) [AOE] (Cor. ii.) [AOI] (6th Can. a) AOO.

Whoever has the patience to go through the remaining 48 Moods will discover that of the whole 64 only 11 are valid, namely: 

A.A.A., A.A.I., A.E.E., A.E.O., A.I.I., A.O.O.,
E.A.E., E.A.O., E.I.O., I.A.I., O.A.O.

These 11 Moods have next to be examined in each Figure, and if valid in every Figure there will still be 44 moods in all.  We find, however, that in the First Figure, A.E.E., A.E.O., A.O.O. involve illicit process of the major term (3rd Can.); I.A.I., O.A.O. involve undistributed Middle (4th Can.); and A.A.I., E.A.O. are subalterns.  In the Second Figure all the affirmative Moods, A.A.A., A.A.I., A.I.I., I.A.I., involve undistributed Middle; O.A.O. gives illicit process of the major term; and A.E.O., E.A.O. are subalterns.  In the Third Figure, A.A.A., E.A.E., involve illicit process of the minor term (3rd Can.); A.E.E., A.E.O., A.O.O., illicit process of the major term.  In the Fourth Figure, A.A.A. and E.A.E. involve illicit process of the minor term; A.I.I., A.O.O., undistributed Middle; O.A.O. involves illicit process of the major term; and A.E.O. is subaltern.

Those moods of each Figure which, when tried by these tests, are not rejected, are valid, namely: