Parmi les écrits consacrés à la réflexion des rayons « visuels» et solaires sur les différents miroirs, il en existe deux, qui ont précédé bien d'autres, et qui occupent une position centrale dans l'histoire de la catoptrique : l'un est attribué à Euclide, l'autre à Ptolémée. À ces deux noms, on en ajoute un troisième jusqu'ici inconnu, Thiasos. Dans cet article, nous reprenons l'histoire textuelle et conceptuelle de cette tradition de recherche catoptrique.

In his analysis of the hypothetical (šarṭīyya) connected (muttaṣila) and disjunctive (munfaṣila) propositions (Al-qiyās, section V), Ibn Sīnā suggests that they can be quantified and presents in section VI a hypothetical system containing the conditional ones, which is exactly parallel to categorical syllogistic and makes use of the same conversion rules and the same proofs. In section VII, he provides four lists of hypothetical quantified propositions whose clauses are themselves quantified and says that the relations of the Aristotelian square of opposition hold for them. In addition, he says that some conditional universal affirmative propositions are equivalent to some universal negative ones with opposed consequents, and to some quantified disjunctive ones. The problem is that these claims are incompatible with each other, since they require two different readings of the universal affirmative conditional proposition, which Ibn Sīnā does not distinguish clearly. In this paper we solve the problem by distinguishing explicitly between these two readings and showing that the first one satisfies the conversion rule of the universal affirmative and the relations of the logical square, and validates all the admitted moods, while the second one satisfies the contraposition rule and the equivalences stated by Ibn Sīnā. This accounts for all Ibn Sīnā’s claims and makes the system coherent.

In the fresh reading proposed here of the still not satisfactorily interpreted passages in Metaphysics Ε2-3, Aristotle emerges as making a case against determinism based on a robust notion of the accident. Accidental beings are uncaused causes and have their rightful place in Aristotle's ontology. The resulting physical indeterminism is here used as a litmus test for the exegetical practice of the great Commentator, Averroes, whose self-proclaimed, and later proverbial, loyalty to Aristotle's text will be shown to give way to idiosyncratic interpretations at times. His explanations of Metaphysics Ε2-3 are sparse and no less obscure than Aristotle's text. It is only when read together with his commentaries on the Physics, to which he explicitly refers twice in his Long commentary on Metaphysics Ε2-3, that a surprising picture emerges. Averroes recycles the notion of the accident, now reconceptualised in cosmological terms, and – putting it to the opposite use of Aristotle's – weaves it into an original theory of motion that integrates both supra- and sublunar realms into a deterministic framework of uninterrupted causal chains, thus safeguarding the principle of Divine providence.