Chapter Summary. In this chapter and the next I explore the ways in which Aristotle uses the results of one natural inquiry as starting points for inquiry in another area. This is a practice in which Aristotle routinely indulges, and yet there is, at least prima facie, a problem with him doing so, given his views about how we arrive at first principles and the propriety of those principles to specific domains. In APo. i.7–13, he allows that geometric and arithmetic premises can be used in a range of fields of inquiry he refers to as ‘subalternate’ branches of mathematics, which he elsewhere describes as ‘the more natural of the mathematical sciences’ (i.e., optics, astronomy, mechanics, and harmonics). However, whether and, if so, how this practice might apply within the science of nature is never explicitly addressed. In this chapter, I address this question by exploring the dependence of Aristotle’s discussion of the application of the concepts ‘right’ and ‘left’ to the motions of the heavens on his discussion of directional dimensions in De incessu animalium.