Between Aristotle and the later Middle Ages, I've assigned only Hamblin's single paragraph on Cicero. That's because Hamblin will refer to his distinction between intrinsic and extrinsic arguments at a few points later.
The main focus of this assignment is a form of disputation that Hamblin refers to as the "Game of Obligation." Although disputations were a standard sort of formal discourse in medieval universities, these were usually of another form ("quodlibetal disputations"—roughly, "free-choice disputations"). People are not sure exactly what function the rules of Obligation served, but they describe a form of disputation that is closer to the elenchus that Aristotle was concerned with than were quodlibetal disputations.
The interest of these is less as a context for traditional fallacies (though some will appear) than as a more definite set of rules governing dialogue than we had for elenchus exchanges. So think through the rules both in their own right and in application to examples.
Here's a key to (or reminder of) some of the logical terminology that shows up in the example on p. 128. A conditional is an if ... then sentence. Its antecedent is the subordinate clause (the if-clause), and its consequent is the main clause (the then-clause). A disjunction is a sentence formed by joining two sentences with or, and a conjunction is a sentence formed similarly with and (so the logical use of conjunction is narrower than its grammatical use).