 It is clear that Kilvington’s belief that mathematics is the legitimate method of describing natural phenomena also allowed him to formulate a new rule of local motion. Kilvington agrees that the proper way of measuring the speed of motion is to describe variations of proportion of forces to resistances. He was aware that Aristotle’s and Averroes’s rules of motion, given in Physics VII, were not universally applicable, and was convinced that the correct calculus of proportions was formulated by Euclid in his Elements. As a consequence, he noticed that the proper understanding of Euclid’s definition of operations on proportions necessitates a new interpretation of Aristotle’s and Averroes’s theory of motion. On the one hand, Euclid’s and Archimedes’s theory of operations on proportions concludes that doubling a ratio corresponds to squaring the fraction which we form from the ratio. On the other hand, Aristotle’s and Averroes’s statements clearly indicate that speed is proportional to the proportion of an active power to resistance, which is not squared but simply multiplied by two. Having noticed the inconsistency between these two views, Kilvington first presented two main arguments against the Aristotelian proposition and finally concluded that, when talking about a power moving one half of a mobile (that is, something moveable), Aristotle means precisely a double ratio between F and R; when talking about a power moving a mobile twice as heavy, he means taking the square root of the ratio of F : R. The new mathematical rule describing the speed of motion is in accord with those of Aristotle only in one case: if the ratio of the power of the mover to that of its mobile is 2 : 1, the same power will move half the mobile with exactly twice the speed. Kilvington’s reinterpretation of Aristotle’s and Averroes’s rules of motion reveals that the speed cannot be described by multiplication alone. Kilvington’s calculus provides values of the ratio of F to R greater than 1 : 1 for any speed down to zero, since any root of a ratio greater than 1 : 1 is always a ratio greater than 1 : 1. And, with his additional assumption that any excess, however small, of an active power over resistance is sufficient to initiate and continue motion, he may have described a very slow motion with a speed greater than 0 and less than 1 (0 &gt; v &lt; 1). Hence, he avoids a serious weakness of Aristotle’s theory, which cannot explain the mathematical relation of F and R in very slow motions, at speeds less than 1 (Jung 2022a: 76–77).