Alexander of Aphrodisias, Commentaries on Aristotle's Topica 9.9-20 Wallies, cf. the English translation in On Aristotle, Topics I by J.M. Van Ophuijsen (2001) p.11.9-18.
[1] See Aristotle, Rhetoric 1356b4-5: "I call a rhetorical syllogism an enthymeme". The enthymeme is a type of argument especially used by rhetoricians; it is a kind of argument which excites the louder aplause from the audience (Rhetoric 1356b24-25; see also Problemata 916b25ff.). The syllogism (or "deductive argument"; syllogismos) is defined by Aristotle as "an argument in which, certain things being established, something different from the supposed things turns out to be of necessity through them" (Topica 100a25-27). But this is the scientific or demonstrative syllogism, i.e the one which starts from what is primary and true (Topica 100a27-29). By contrast, the enthymeme is related to what Aristotle calls "dialectical syllogism", i.e. that syllogism whose premises are plausible or probable (endoxa) but neither primary nor necessarily true. An enthymeme is concerned with what, for the most part, can be otherwise (Rhetoric 1357a13-15). it is a "sort" of dialectical argument insofar as its premises are just plausible. But it is not the same thing because in rhetoric the argument must be clear to the hearers who do not have expertise in logic (see Rhetoric 1395b21-27). For a clear explanation of the plausible, probable or "reputable" premises in the dialectical syllogisms see Evans (below) 77-85. See also Burnyeat (below). In the practice of Cicero and other orators, enthymeme is particularly applied to arguments that avoid spelling out a socially or politically unacceptable belief by suppressing as if obvious that premise of the argument, e.g., under a tyrant, one does not articulate as premise that all tyrants deserve death.