This paper explores Aristotle's remarks in Posterior Analytics on certain special disciplines that are subordinate to pure mathematical sciences. Optics, harmonics and mechanics prove their own contents by means of premises belonging to arithmetic or geometry. Even though subaltern sciences are exceptions to the prohibition on kind crossing, the premises to their demonstrations are legitimately appropriate to the relative conclusions. In order to delineate the demonstrative structure of subordinate sciences, Aristotle introduces the distinction between knowledge of a fact and knowledge (...) of the reason for it. In his view, these two different levels of knowledge, characterizing respectively empirical and theoretical approaches, are closely related. Nautical astronomy, for instance, deals with the observation and recording of the astral motions, which are made intelligible by mathematical astronomy. The Aristotelian ideal of an explanatory connection between appearances and mathematical principles seems to be the main aspect in the treatment of subordinate sciences in Posterior Analytics. (shrink)