  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.
