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.

In this article the author analyzes a fifteenth-century Arabic reform of the Ptolemaic model for Mercury. The author of the reform was the Central Asian Al al-D who, in his youth, had been instructed in the mathematical sciences by none other than the famous Central Asian monarch Ulugh Beg (1394 has been yet identified to have produced a theoretical text devoted to the criticism, let alone the reform, of the Ptolemaic mathematical planetary models. The present article on Qushji's reform of (...) the Ptolemaic model for Mercury includes a critical first edition of Qushji's Arabic text, an English translation, and a historical and technical commentary. (shrink)