Euclid's Optics and Geometrical Astronomy

This paper seeks to demonstrate that propositions 23-27 of the Euclidian Optics originated in the context of geometrical astronomy. These entries, which deal with the geometry of spheres and rays, present material that overlaps considerably with propositions 1-3 of Aristarchus of Samos' On the Sizes and Distances of the Sun and the Moon. While all these theorems deal with material that could conceivably be native to celestial illumination, the proofs do not work for binocular vision. It therefore seems probable that the proofs were borrowed from Aristarchus or, more likely, some common astronomical predecessor. As an extension of this observation, this paper argues that the Optics displays a far less unified purpose than has typically been assumed. Instead, it reflects a conglomerate of concerns, goals and dependencies, insofar as it presents multiple proofs that emerge from a set of geometrical concerns not directly related to vision as a physical phenomenon. These entries complicate the idea that the Optics is about explaining light, sight or false appearances in any straightforward sense. Instead, the text is oriented toward a somewhat more diffuse goal: simply to articulate the geometry of vision and rays. Optics as a discipline should should therefore be understood not as a purely mathematical explanation of vision, but as a target-field of explanation constituted by features and boundaries derived from extra-visual geometric concerns.