Aristotle’s Topics, and especially, as far as the subject of this study is concerned, their central books (II-VII), played a role of central importance both in the medieval Latin and in the Arabic logical tradition. This did not occur without transformations, which affected the nature and the function of the loci of which these books set forth the theory. One of the most visible signposts of this tradition of re-elaboration of the Topics is represented by Themistius (ob. c. 388), to whom both Boethius and Averroes refer. Yet no work by Themistius on the Topics has come down to us in Greek. With a view to reconstructing the work(s) of this author, we have here collected and translated the passages that are attributed to him explicitly (with the exception of one of them) in Averroes’ Middle Commentary on the Topics, comparing them, where necessary, to the testimonies collected by Boethius in his De topicis differentiis. In addition – and this is a new element added to the file – we show that the Themistian classification of loci was taken up by Abū al-Barakāt al-Baġādī (ob. after 1164), author of a philosophical summa entitled al-Kitāb al-mu‘tabar (The meditated book). These three testimonies are all the more precious in that they are independent of one another. The study of the chapter in the logical part of al-Kitāb al-mu‘tabar, containing the Themistian classification of loci, of which a corrected text with translation is offered, shows that one finds in it some of the most singular aspects of this classification, as it appears in Boethius. Abū al-Barakāt al-Baġādī thus reveals himself to be closer than Averroes to the testimony of Boethius. This suggests the idea of a double redaction by Themistius of the classification of loci: one, more concentrated, comes from an introduction to the paraphrase of the central books of the Topics, which may have inspired Averroes; the other, more extensive, which will have been part of an original work, and inspired the classifications of Boethius and of Abū al-Barakāt al-Baġādī.

After having reformulated optics, Ibn al-Haytham conceived of an analogous project for astronomy. This has just been revealed by an important book by the mathematician which has never been studied until now. Ibn al-Haytham's reform consists in excluding all cosmology, and in developing a systematic study of a celestial kinematics that has been completely geometrized. In turn, the realization of such a reform demanded innovative research in infinitesimal geometry. In this article, an attempt is made to present this new geometry, as well as the mathematical means invented to elaborate it.

This paper investigates the objections that were raised by the philosopher ‘Abd al-Laṭīf al-Baghdādī (d. ca. 1231 CE) against al-Ḥasan ibn al-Haytham’s (Alhazen; d. after 1041 CE) geometrisation of place. In this line of enquiry, I contrast the philosophical propositions that were advanced by al-Baghdādī in his tract: Fī al-Radd ‘alā Ibn al-Haytham fī al-makān (A refutation of Ibn al-Haytham’s place), with the geometrical demonstrations that Ibn al-Haytham presented in his groundbreaking treatise: Qawl fī al-Makān (Discourse on place). In examining the particulars of al-Baghdādī’s fragile defence of Aristotle’s definition of topos as delineated in Book IV of the Physics, which was rejected on mathematical grounds by Ibn al-Haytham, a special attention is also given to highlighting the systemic distinctions between the entities that are studied within the speculative physical doctrines of common sense and immediate experience, and the postulated ‘objects’ of scientific and mathematical research.

In this paper, my aim is to offer some comments on the study of Mu‘tazilite kalām, framed around the study of a particular episode in the Mu‘tazilite dispute about man (‘mā huwa al-insān’) – a question with a deceptively Aristotelian cadence that is not too difficult to dispel. Within this episode, my focus is on one of the major arguments used by the late Baṣrans to hold up their side of the dispute (a side heavily indebted to Abū Hāshim’s ontological innovations), and on the relationship between the mental and the physical (or the subjective and objective) which emerges from it. The most interesting – and most surprising – aspect of this relationship is that the mental and the physical do not seem to be treated as distinct terms, thus creating the space for questions about how the two relate. The first person perspective seems to be identified with the physical body. My interest then is in the response of the reader to this surprising presentation – or rather, in a certain kind of reader response, and thus a certain kind of interpretive mode, whose value and viability it is part of my aim to help clarify.

Until the end of the 14th century, the sources of Hebrew mathematical writings were almost exclusively in Arabic. This was particularly true of texts that contained elements of algebra or algebraic developments. The testimonies we present and analyze here are due to Jewish authors living in Italy, primarily in the 15th century, who made use of the most varied sources, in addition to Arabic: in Castilian, in Italian, and perhaps in Latin. These testimonies constitute both an indication, and a product, of the circulation of Arab algebraic traditions in Renaissance Italy. Simon Moṭoṭ’s book on The Calculation of Algebra stems from the Italian tradition of ‘‘treatises on the abacus’’. Mordekhay Finzi of Mantua is the author of a Hebrew version of the great work on algebra by Abū Kāmil (9th century), as well as of a version, distinct from the preceding, of the Arabic scholar’s introductory exposition. Beginning in 1473, Finzi also translated from Italian to Hebrew the important treatise on algebra by Maestro Dardi of Pisa (1344). We also indicate some 16th century continuations of Hebrew mathematical production, which contain algebraic developments.

The perfect compass, used by al-Qūhī, al-Sijzī and his successors for the continuous drawing of conic sections, reappeared after a long eclipse in the works of Renaissance mathematicians like Francesco Barozzi in Venice. The resurgence of this instrument seems to have depended on its interest to solve new optico-perspective problems. Having reviewed the various instruments designed for the drawing of conic sections, the article is focused on the sole conic compass. Theoretical and empirical applications are detailed. Contrarily to the common thesis of an independant discovery, various elements suggest a direct descent between the birkār al-tāmm of the Arabic mathematical tradition and the Italian conic compass. Then we present the most probable transmission hypothesis involving: 1° Ibn Yūnus and his disciples of Mosul, 2° Sultan Malik al-Kāmil in Damas, 3° Master Theodore and Frederick II at the court of Sicily, 4° Andalò di Negro and Robert of Anjou in Naples, 5° Lorenzo della Volpaia, Vinci, Sangallo and Michelangelo in Florence, 6° Ausonio, Contarini, Thiene and Francesco Barozzi in Venice.