The book analyzes reductio through two syllogisms. The first connects two hypothetical conditionals and concludes that if the contradictory of the claim holds, an impossibility follows.
The second is an exceptive syllogism. It takes that conditional conclusion and adds that the impossible consequence does not hold; denying the consequent then rejects the contradictory assumption.
The progression is:
1. Assume the contradictory.
2. Establish that it entails an impossibility.
3. Deny the impossibility, thereby rejecting the assumption.
4. Affirm the original claim.