Abstract
This article aims at clarifying some issues raised by a recent book of Daniel W. Graham about the Presocratic cosmology. It particularly intends to shed some light on the understanding of Anaxagoras’ universe by suggesting some reasons why, despite Graham’s opinion, it is still possible to think that the stars were flat according to him. Another goal is highlighting the importance of the comprehensive physical theory of Anaxagoras, based on a circular motion called perichoresis, which would explain diverse phenomena in a consistent way by introducing simplicity in his cosmology.