We attempt to grasp the mathematics behind the planetary theories of the Syrian astronomer Ibn al-Šāṭir (1304–1375) in his treatise Nihāyat al-Sūl. Following the astronomers of the Marāgha school, by composing circular movements with constant angular velocity, Ibn al-Šāṭir 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 for 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. This is an opportunity to give a critical edition of the chapter of the Nihāyat al-Sūl dedicated to the latitudes of Mercury and Venus., RésuméNous avons tenté de restituer ici les mathématiques qui président aux théories planétaires exposées par l'astronome syrien Ibn al-Šāṭir (1304–1375) dans son ouvrage Nihāyat al-Sūl. Dans la lignée des astronomes de l’école de Marāgha, en composant des mouvements de rotation à vitesse angulaire constante, Ibn al-Šāṭir atteint deux objectifs. Non seulement il élimine tout recours aux excentriques et aux points équants; mais il décrit aussi longitudes et latitudes planétaires par une méthode unique, sans adjoindre aucun orbe en sus des orbes nécessaires à la description des seuls mouvements en longitude. Une meilleure compréhension des rotations comme transformations spatiales lui permet cette grande économie de moyens. Dans notre commentaire, nous prenons pour exemple la planète Vénus dont les latitudes posent un problème intéressant. C'est aussi l'occasion d'offrir l’édition critique d'un chapitre de la Nihāyat al-Sūl consacré aux mouvements en latitude de Mercure et Vénus.
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