Oresme's proof of the density of rotations of a circle through an irrational angle

One of the theorems of Nicole Oresme's (ca. 1320-1382) says that, for two points moving uniformly but incommensurably along a circle, “no sector of a circle is so small that two such mobiles could not conjunct in it at some future time, and could not have conjuncted in it at some time.” A detailed study of his proof of this and related theorems shows that he was in the possession of all the arguments needed for the proof to be conclusive