In his Sphaerica, Menelaus did not prove Proposition III.5 which is particularly important. He only gave an outline of a proof. Once the Sphaerica were translated into Arabic, mathematicians, starting from the end of the 9th century on, took up this proof. That was made possible to Ibn ʿIrāq thanks to the development of spherical geometry. A first paper contained the history of his contribution. Two other mathematicians, from the 13th century – Naṣīr al-Dīn al-Ṭūsī and Ibn Abī Jarrāda – worked out again the proof of the proposition with the help of Menelaus' book and of the new acquisitions of Ibn ʿIrāq. This is the subject of this second paper.

This article aims to reconstruct part of Book IV of Galen's lost treatise On Demonstration. This reconstruction is based on testimonies transmitted by Abū Bakr al-Rāzī (d. 925) in the Doubts About Galen, as well as on a source that until now has never been studied, namely the Solution to the Doubts About Galen of Abū al-ʿAlāʾ ibn Zuhr (d. 1131). This paper argues that, in Book IV, Galen maintains that no one can reach any certain conclusion regarding the eternity of the world, and that he consequently criticizes Aristotle's treatment of the subject in On the Heavens. Galen approves only of one of the arguments used by Aristotle in On the Heavens I, 3 (270b12–17), because it is based on empirical evidence. Al-Rāzī focuses on Galen's commentary on this passage. Our hypothesized reconstruction resolves some of the contradictions between the fragments of Book IV that are transmitted in al-Rāzī's report and Philoponus’ Against Proclus On the Eternity of the World. Finally, this article shows that al-Rāzī's interest in this passage from On Demonstration can be explained with reference to his own philosophical-theological goals. As my examination will make clear, al-Rāzī objects to Galen's arguments because he considers that Galen's teleology is based on a framework where the world is eternal (although Galen does not state this view explicitly), and that this framework does not allow Galen to understand that theodicy is prior to both cosmology and biology.

This paper provides an analysis and translation of a previously edited, but otherwise unstudied work by Miskawayh (d. 1030) entitled On Pleasures and Pains (Fī al-Laḏḏāt wa-al-ālām). After a brief orientation regarding the Aristotelian account of pleasure in the Nicomachean Ethics, which is Miskawayh's main source, the theory of pleasure set out in On Pleasures and Pains is compared to the discussion of pleasure in Miskawayh's better known Refinement of Character (Tahḏīb al-aḫlāq). Despite considerable harmony between the two texts, their treatments of pleasure differ in that the Refinement accepts, whereas On Pleasures and Pains rejects, the “restoration” theory of pleasure of Plato's Timaeus.

Galen's On the Elements according to Hippocrates is an important source for physical doctrines circulating in late antiquity. The variety of atomistic doctrines that Galen brings into the discussion, as well as his arguments aimed at refuting them, were closely studied by the early kalām atomists. Of particular interest are the summaries of this text, which seem to have been written many centuries after Galen; some of them are products of early Islamicate culture. In this paper, we present an edition, translation, and study of a hitherto unknown summary, extent in a unique manuscript where it is attributed to Ḥunayn ibn Isḥāq. Like the other summaries, it presents a doxography of physical doctrines, not always repeating precisely what Galen says, but rather reflecting the discourse of its period.

Kalām atomism stood in opposition to the Aristotelian natural philosophy of the falāsifa. In the Physics of the Shifā', Ibn Sīnā undertook a detailed refutation of kalām atomism through several arguments. These arguments elicited a muted response from al-Ghazālī, whose commitment to kalām was minimal at best. A more forceful response seems to have been offered by al-Shahrastānī but its details remain sketchy due to the lack of surviving sources. Fakhr al-Dīn al-Rāzī, whose intellectual development went through a phase of commitment to Avicennism and thereby a vigorous endorsement of Ibn Sīnā's anti-atomist arguments followed by a phase of a critical engagement with Avicennism, provides a detailed rebuttal to Ibn Sīnā's arguments in addition to constructing novel arguments in defense of kalām atomism.

Ever since the rediscovery of Ibn Khaldūn's Muqaddima in modern times, debates have been ongoing regarding his identity as a scholar: was he a revolutionary thinker in the modern sense of the word, breaking away from classical and medieval modes of thinking, or was he in fact a conservative Muslim scholar who did not venture far from his traditional Muslim horizons? Through a careful examination of the preface to the Muqaddima, this article shows what he thought about the nature of his project and why he thought it necessary. Accordingly, it builds the case that Ibn Khaldūn is indeed a revolutionary – but not in the modern sense of the word – who did not shy away from challenging tradition in order to reform society's moral and political horizons. An examination of the preface alone will not provide a definitive answer to the question of Ibn Khaldūn's radical vs. conservative thought, but it does put his conservatism (apparent and real) in context.

In an article published in Arabic Sciences and Philosophy 22 (2012), pp. 217–87, by Gad Freudenthal and Mauro Zonta, “Avicenna among Medieval Jews: the reception of Avicenna's philosophical, scientific and medical writings in Jewish cultures, East and West,” the authors promise to present “a preliminary but comprehensive picture of Avicenna's reception by medieval Jewish cultures.” As such, it seemed to offer the “comprehensive study” referred to as a desideratum by Zonta at the conclusion of his groundbreaking and very important survey, “Avicenna in medieval Jewish philosophy” (2002). Zonta explained that such a future “comprehensive study of the many and different interpretations given to his doctrines by Jewish thinkers would allow us to evaluate the real role played by [Avicenna] in medieval thought.” Surprisingly, the recent article adds little that is new to the previous studies of Zonta and others on the subject, and omits useful information found in them. The main point of the present notes is to try to correct several oversimplifications, questionable assumptions, and misleading statements in the article under consideration. Its purpose is to help readers of the article to attain a fuller and more accurate – although certainly not comprehensive – picture of the reception of Avicenna among medieval Jews.

The extant manuscript tradition of the Kitāb al-Kašf provides evidences of three phases of redaction and revision of the treatise. This study aims to illustrate the relations between the two Arabic versions and the anonymous fourteenth century Hebrew translation, taking into account the additions and modifications that differentiate them. I conclude that the Hebrew translation represents an intermediate stage of reworking, attesting important additions to the text as well as philosophical changes, especially in arguments concerning the creation of the world at the beginning of the treatise. However, it precedes the next revision phase of the text, which leaded to the modifications of the last Arabic version, in the chapters dealing with the thorny questions of divine corporeality and direction. The analysis of additions and arguments in the matter of content, context and reasoning helps to understand the redaction phases' history and the way the treatise was transmitted.

In the Planisphaerium, Ptolemy deals with a method of representing a sphere onto a plane, according to principles which were compatible with the stereographic projection. But this projection will only become a real mathematical concept in the 9th century, when al-Farghānī will demonstrate the fundamental property of this projection. It is only in the 10th century that the first general theory of projections of spheres was worked out by al-Qūhī and Ibn Sahl. This paper addresses the reasons which allow to claim that Ptolemy did not conceive of projection and that this conception was based on the Apollonius' definition of the conical surface.

The notion of a “World of Images” located somewhere between the immaterial and the material world was a mainstay of eschatological speculation in late medieval Islam. As has been recognised before, the concept was launched by al-Suhrawardī (d. 1191). However, its more properly philosophical underpinnings, in particular the notion of “suspended” images – images which somehow have an objective, rather than just a mental or subjective, status – merit further clarification, which this article attempts to provide. Since the concept of “suspended forms”, while applied to eschatological matters in the last treatise of the Philosophy of Illumination, makes its first appearance in a discussion of mirror vision, I examine in some detail Avicenna's understanding of mirror vision as presented in the Shifāʾ, to which al-Suhrawardī reacts. I then undertake a detailed reconstructive analysis of two paragraphs of the Philosophy of Illumination, paying particular attention to the question of the ontological status of “suspended” or “self-subsistent” images as well as to the idea that mirrors serve, not as loci in which images inhere, but as loci at which they become manifest (singular maẓhar).