This paper is chiefly aimed at individuating some deep, but as yet almost unnoticed, similarities between Aristotle's syllogistic and the Stoic doctrine of conditionals, notably between Aristotle's metasyllogistic equimodality condition and truth-conditions for third type conditionals. In fact, as is shown in §1, Aristotle's condition amounts to introducing in his metasyllogistic a non-truthfunctional implicational arrow '', the truth-conditions of which turn out to be logically equivalent to truth-conditions of third type conditionals, according to which only the impossible follows from the (...) impossible. Moreover, Aristotle is given precisely this non-Scotian conditional logic in two so far overlooked passages of Themistius' Paraphrasis of De Caelo. Some further consequences of Aristotle's equimodality condition on his logic, and notably on his syllogistic, are pointed out and discussed at length. A extension of Aristotle's condition is also discussed, along with a full characterization of truth-conditions of fourth type conditionals. (shrink)