  This book is a critical edition of a treatise of astronomy by the Syrian
scholar Ibn al-\v{S}\=atir (1304-1375). The Arabic text has been established on
the basis of several manuscript copies, and it has been translated into French;
a bilingual index is also provided. This treatise is one of the latest and one
of the most elaborate medieval work on theoretical astronomy; it is famous
today for having provided the first viable lunar model in terms of the distance
Moon-Earth. Although demonstrations have been consigned to another manuscript
which is now lost, we reconstruct the physical models in our mathematical
commentary, and we attempt at a better historical understanding of the nascent
concepts of space transformations, solid reference frames, trajectory, etc.
Predictions of the models are to be compared to observations and to other
contemporary models, as well as theoretical premises; in turn, when records of
observations are missing, those have to be recalculated by modern means. Part
of our commentary is devoted to the latitudinal movement of the five planets:
Ibn al-\v{S}\=atir's work on this problem belongs to a tradition initiated by
Ibn al-Haytham three centuries before. Ibn al-\v{S}\=atir addresses a clever
criticism to the work of his predecessor Nas\=ir al-D\=in al-T\=us\=i on this
problem, thus revealing a better understanding of affine rotations in space.
Many other criticisms by Ibn al-\v{S}\=atir, especially to the astronomers
working at Mar\=a\.ga during the 13th century, also contribute to a better
knowledge of their own work.
