As early as the ninth century, Muslim astronomers started refining the Ptolemaic astronomy which, by this time, had been fully adopted as the framework of their research. Already, in the early part of this century, refinements were based on improved observational techniques, and included a variety of phenomena such as the length of the seasons, the solar equation, mean motion parameters, and many others.

In this article we study the development of the mathematical theorem, now known as the Tūsī Couple, and discuss the difference between its plane and spherical applications. Dans cet article, nous étudions le développement du théorème mathématique, connu maintenant sous le nom de ‘couple d'al-Tūsī’; et nous discutons la différence entre son application plane et son application sphérique.

The undoubted truth is that there exist for the planetary motions true and constant configurations from which no impossibilities or contradictions follow; they are not the same as the configurations asserted by Ptolemy; and Ptolemy neither grasped them nor did his understanding get to imagine what they truly are.

A passage in Copernicus's De Revolutionibus regarding the rotation of the Earth provides evidence that he was aware, whether directly or indirectly, of an Islamic tradition dealing with this problem that goes back to Na[sdotu]īr al-Dīn al-[Tdotu]ūsī. The most striking similarity is the use of comets by both astronomers to discredit Ptolemy's “proofs” in the Almagest that depended upon observational evidence. The manner in which this question was dealt with by Copernicus, as an astronomical rather than natural philosophical matter, also (...) argues for his being within the tradition of late medieval Islamic astronomy, more so than that of medieval Latin scholasticism. This of course is bolstered by his use of non-Ptolemaic models, such as the [Tdotu]ūsī couple, that have a long history in Islam but virtually none in medieval Europe. Finally, al-Qūshjī, who was in Istanbul just before Copernicus was born, entertained the possibility of the Earth's rotation; this also opens up the possibility of non-textual transmission. (shrink)

In this article we study the development of the mathematical theorem, now known as the T Couple, and discuss the difference between its plane and spherical applications.