Oresme is known, among other things, for having developed in his Questions on Euclid's Geometry a “series theory”, including the nature and summation of geometric series and the divergence of the harmonic series. The present paper aims, on the one hand, to see in what sense Oresme really developed a series theory, by situating this theory within the framework of medieval mathematics, and, on the other hand, to show that this theory can be seen as a deeper investigation, at the mathematical level, of the Aristotelian notions of the infinite by division and the infinite by addition. It closes with a discussion of the question of the degree of generality which Oresme accorded his results.