 Buridan uses four methods to prove the valid syllogistic moods. All first figure moods are proved by the rules of class inclusion, that is, the dici de omni and dici de nullo rules. The second and third figure moods are proved using three different methods: either by conversion — that is, by (8:3), (8:4), (8:5) or (8:6) — by reductio ad impossibile, or by expository syllogism. Proof by impossibility is used on a few occasions, but Buridan’s approach here differs in no way from Aristotle’s. This fourth way is frequently used to prove the valid third figure moods. Since the number of possible combinations of premises and conclusions in modal syllogistic is quite extensive, he limits himself to discussing those moods whose assertoric counterparts are valid, but even so he manages to discuss a large number of valid and invalid syllogisms (see Hughes 1989, Lagerlund 2000, Thom 2003, Klima 2008, and Dutilh Novaes 2008).