The commentary also uses conversion of the minor followed by conversion of the conclusion to show this mood's validity.
Original minor: No C is B.
Its converse: No B is C.
Original major: All A are B.
First-figure result: No A is C.
Converse of that result: No C is A.
Converting the negative minor produces an appropriate first-figure argument. Converting its universal negative conclusion gives exactly the original intended conclusion.
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The Second Figure: Conditions of Validity and Four Productive Moods
The commentary also uses conversion of the minor followed by conversion of the conclusion to show this mood's validity.
Original minor: No C is B.
Its converse: No B is C.
Original major: All A are B.
First-figure result: No A is C.
Converse of that result: No C is A.
Converting the negative minor produces an appropriate first-figure argument. Converting its universal negative conclusion gives exactly the original intended conclusion.