Abstract
Aristotle is aware of the mathematical treatment of natural phenomena constitutive of Greek astronomy, optics, harmonics, and mechanics. Here I provide an account of Aristotle's understanding of these 'subordinate sciences', drawing on both his methodological discussions and his optical treatment of the rainbow in Meteorology III 5. This account sheds light on the de Caelo, in which Aristotle undertakes a natural investigation of the heavens distinct from, but closely related to, astronomical (thus mathematical) investigations. Although Aristotle insists that such subordinate sciences belong to mathematical and not natural science, he sees them as essential to complete scientific knowledge of the sensible world.