Astronomical Images : Proof that no finite mover can cause motion that occupies infinite time

Aristotle

Astronomical Images

<p style='text-align: justify;'>This work comprises Aristotle's <i>Physics</i> and Thomas Aquinas's commentary edited by the Augustinian, Timoteo Maffei of Verona (d. 1470). Aristotle discussed the nature of motion in the latter books of <i>Physics</i>, often referring to figures to elucidate his points. These figures were not always illustrated, and there was no traditional stock of figures like the wind diagrams or concentric circles associated with the Aristotelian analysis of motion. This edition makes an effort to supply such figures. In <i>Physics</i>, book 8, chapter 10, Aristotle seeks to show that the Prime Mover is without parts or magnitude. He first shows that no finite mover can cause a motion that will occupy an unlimited time. The first woodcut shows two hands A as the mover, circle B as the thing moved and C as infinite time supposed to be taken by A to move B any given distance. The second woodcut shows one hand D as part of A, moving a half-circle E (thus half of B) the same distance. The time it takes, Z, cannot be as great as the unlimited time C, for it will take D a longer time to move the greater quantity (any larger fraction of B). Thus, time Z is not unlimited. By taking the work done piecemeal, a fraction at a time, by adding one D to another, the finite A will be exhausted, and by adding one E to another, B will be exhausted. But the time will not be exhausted by deducting from it a corresponding length for each such addition since it is time unlimited. Thus the whole of A will take only a finite period of time C to move the whole of B. So an unlimited motion cannot be imparted to anything by a finite mover. Therefore, a finite mover cannot cause a motion during unlimited time. (Aristotle, <i>Physics</i> VIII.10.266a10-26, trans. Wicksteed and Cornford.)</p>