§ 612. Proof of Rule 3.—The major premiss must be universal.
The conclusion being negative, the major term will there be distributed. But the major term is subject in the major premiss. Therefore the major premiss must be universal (by Rule 4).
FIGURE III.
§ 613. Proof of Rule 1.—The minor premiss must be affirmative.
B—A B—C C—A
The proof of this rule is the same as in the first figure, the two figures being alike so far as the major term is concerned.
§ 614. Proof of Rule 2.—The conclusion must be particular.
The minor premiss being affirmative, the minor term, which is its predicate, will be undistributed there. Hence it must be undistributed in the conclusion (by Rule 4). Therefore the conclusion must be particular.
FIGURE IV.
§ 615. Proof of Rule I.—When the major premiss is affirmative, the minor must be universal.