The commentary uses reductio ad absurdum (khalf). Assume both premises true and the intended conclusion false. If this forces the contradiction of a premise, the assumed falsity of the conclusion must be rejected.
Example:
All cats are animals.
No stone is an animal.
Target: No cat is a stone.
If that target were false, some cats would be stones. Those cats would be animals by the minor and non-animals by the major—an outright contradiction. Thus the negative conclusion follows.
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The Second Figure: Conditions of Validity and Four Productive Moods
The commentary uses reductio ad absurdum (khalf). Assume both premises true and the intended conclusion false. If this forces the contradiction of a premise, the assumed falsity of the conclusion must be rejected.
Example:
All cats are animals.
No stone is an animal.
Target: No cat is a stone.
If that target were false, some cats would be stones. Those cats would be animals by the minor and non-animals by the major—an outright contradiction. Thus the negative conclusion follows.