ArgumentA Catoptrica attributed to Euclid appears in manuscripts amongst treatises dealing with elementary astronomy. Despite this textual background, the treatise has always been read literally as a theory of mirrors, and its astronomical significance has gone unnoticed. However, optics, catoptrics, and astronomy appear strongly intermingled in sources such as, amongst others, Geminus, Theon of Smyrna, Plutarch and Cleomedes. If one compares the optical reasoning put forward in these sources to account for the formation of moonlight with arguments of Catoptrica, one (...) is able to shed new light on several principles and propositions of Catoptrica, some of which had been deemed corrupt, meaningless, and obscure. Moreover, the present analysis offers a glimpse at the context of a specific stage in the evolution of ancient catoptrics: Whether literally or by analogy, several of its results appear to have been set against a wider astronomical background, which explains the inclusion of Catoptrica in the group of texts loosely defined as “little astronomy.”. (shrink)

There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and (...) continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous. (shrink)