Coming after Muʾayyad al-Dīn al-ʿUrḍī and Naṣīr al-Dīn al-Ṭūsī, Quṭb al-Dīn al-Shīrāzī, a leading figure of the so-called Marāgha school in astronomy, presents his predecessors’ non-Ptolemaic models and criticizes them in his threehayʾabooks. Since his own new models inNihāyat al-idrāk andIkhtiyārāt muẓaffarī are not without difficulties, in his latest book onhayʾa,al-Tuḥfa al-shāhiyya he puts forward his modified models inspired from Ṭūsī’s and ʿUrḍī’s models and produces a series of new models for Mercury and the oscillation of the spheres. Nevertheless, in (...) spite of all his attempts, the tradition of non-Ptolemaic modeling after him never converged to a series of standard models.RésuméVenu après Muʾayyad al-Dīn al-ʿUrḍī et Naṣīr al-Dīn al-Ṭūsī, Quṭb al-Dīn al-Shīrāzī, éminente figure de l’école dite de Marāgha en astronomie, présente, dans ses trois ouvrages dehayʾa, les modèles de ses prédécesseurs tout en les critiquant. Puisque ses propres nouveaux modèles, présentés dansNihāyat al-idrāk etIkhtiyārāt muẓaffarī, ne sont pas sans difficulté, il présente, dans son dernier ouvrage dehayʾa,al-Tuḥfa al-shāhiyya, d'autres modèles inspirés de ceux d'al-Tūsī et d'al-ʿUrḍī, et produit un ensemble de nouveaux modèles pour Mercure et l'oscillation des sphères. Or, en dépit de tous ces efforts, la tradition des modèles non ptolémaïques, telle qu'elle se développa après lui, ne convergea pas vers un ensemble standard de modèles. (shrink)

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.

Duhem has generally been understood to have maintained that the major Greek astronomers were instrumentalists. This view has emerged mainly from a reading of his 1908 publication To Save the Phenomena. In it he sharply contrasted a sophisticated Greek interpretation of astronomical models (for Duhem this was that they were mathematical contrivances) with a naive insistence of the Arabs on their concrete reality. But in Le Système du monde, which began to appear in 1913, Duhem modified his views on Greek (...) astronomy considerably; his more subtle understanding included the recognition that many Greeks subordinated mathematical astronomy to physical theory. But he could not completely repudiate his earlier views about Greek astronomy in part because his extreme nineteenth century prejudices led him to continue to insist on a clear-cut demarcation between Greek and Arabic astronomy. The inevitable result is a certain unevenness in the Système and some glaring inconsistencies. (shrink)

This paper analyses a kinematic model for the solar motion by Quṭb al-Dīn al-Shīrāzī, a thirteenth-century Iranian astronomer at the Marāgha observatory in northwestern Iran. The purpose of this model is to account for the continuous decrease of the obliquity of the ecliptic and the solar eccentricity since the time of Ptolemy. Shīrāzī puts forward different versions of the model in his three major cosmographical works. In the final version, in his Tuḥfa, the mean ecliptic is defined by an eccentric (...) of fixed mean eccentricity and a mean obliquity fixed with respect to the celestial equator, and the center of the epicycle, which is inclined to the eccentric, moves on the eccentric with an annual period. By an additional slow motion of the sun on the epicycle, the true eccentricity of the solar deferent, defined by the annual motion of the sun, and the sun’s extreme declination from the equator change, accounting for the reduction of the eccentricity and the obliquity of the ecliptic since the time of Ptolemy. (shrink)

This article is an attempt to analyze and criticize, both positively and negatively. Whitehead's concept of progress. Whitehead's progressive cosmology is critically examined, as is the relationship between technology and moral progress. The fragility of progress is emphasized.