V\'enus selon Ibn al-Shatir

TL;DR

This paper analyzes Ibn al-Shatir's planetary theories, highlighting his innovative geometric methods that eliminate the need for excentrics and equants, and discusses his approach to planetary latitudes using Venus as a case study.

Contribution

It provides a detailed mathematical interpretation of Ibn al-Shatir's planetary models, emphasizing their geometric economy and novel treatment of latitudes.

Findings

Ibn al-Shatir's models eliminate excentrics and equants.

He describes planetary latitudes with minimal celestial spheres.

The paper offers an edition of the relevant chapters on Venus and Mercury.

Abstract

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.