We attempt to grasp the mathematics behind the planetary theories of the Syrian astronomer Ibn al-Shatir (1304-1375) in his treatise Nihayat al-Sul. Following the Maragha school of astronomers, by composing circular movements with constant angular velocity, Ibn al-Shatir attains two goals. He eliminates the need of excentrics and equant points in astronomy; but he also describes longitudes and latitudes with a unique method, with no more orbs than what is strictly necessary to the longitudes. A better understanding of rotation as a spatial transformation enables this ultimate economy of thought. In our commentary, we take Venus as an example offering an interesting problem about the latitudes. It is the opportunity to give the edition of the chapter of the Nihayat al-Sul dedicated to the latitudes of Mercury and Venus.
Comment: 32 pages, in French, 10 figures. Added journal reference
free text keywords: [MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO], Mathematics - History and Overview, History and Philosophy of Science, Philosophy, History, Venus, biology.organism_classification, biology, Spatial transformation, Astronomy, Equant, Critical edition, Astronomer