The mathematician al-Māhānī (9th century AD) is the author of one of the first commentaries on the fifth Book of Euclid's Elements which have been handed down to us. In this commentary, al-Māhānī intends to justify Definitions V. 5 and V. 7 of the Elements, which deal with the identity of ratios and with greater ratio, by starting from an anthyphairetic conception of ratio, and by proving the equivalence of the Euclidean and the anthyphairetic points of view. We will try in this paper to describe in detail the content of al-Māhānī's commentary, basing ourselves on a thorough examination of most of the extant manuscripts of the Arabic text. The reader will also find in the appendices a mathematical commentary, an English translation, and a critical edition of al-Māhānī's commentary.

The development of geometrical analysis in the 10th century was partly inspired by the reception of the works of Apollonius, which Arab mathematicians translated as early as the preceding century. Al-Qūhī contributed to this development by writing several collections of problems dealing with Apollonian themes and solved by the method of analysis; however, it seems that they do not all occupy the same place in his work. The author gives here the edition, translation, and mathematical commentary of a short work, entitled The determination of two straight lines from a point along a known angle, which presents the particularity of providing problems as geometrical lemmas to other studies. Indeed, al-Qūhī uses two of these lemmas in more complex constructions which belong to his Treatise on the art of the astrolabe. In this same treatise on the astrolabe, as well as in his Treatise on the perfect compass, this scholar also uses as lemmas several problems solved in another of his works, entitled The generation of points on straight lines according to ratios of which the terms are surfaces. This work is unfortunately lost, and all that remains of it are the traces which subsist in other treatises in which it has been used. This study seems to be necessary if one wishes to understand the organization of the work of al-Qūhī, a mathematician of the first rank who was representative of his time.

At the basis of Ghazali's criticisms of Ash'arite kalām is the thesis that its primary function is the defence of traditional Islamic belief, the 'aqida, against the distortions of heretical innovations (al-bida'). Kalām is not an end in itself and it is error to think that the mere engagement in it constitutes the experientially religious. In the I[hdotu]yā' he maintains in effect that when it is pursued as an end in itself, its dogmas can constitute a veil preventive of the attainment of gnosis (ma'rifa). On the other hand, Ash'arite kalām when not pursued as an end in itself can be an aid in the quest after gnosis. This is implicit in his reference (in Kitāb al-Arba'īn) to his own major work of Ash'arite kalām, the Iqti[sdotu]ād fī al-i'tiqād, where he states that “it goes deeper in ascertaining [the truth] and is closer to knocking at the doors of gnosis than the official discourse encountered in the books of the mutakallimīn.” The I[hdotu]yā' abounds with homilies, guides for the pious, particularly for those seeking mystical knowledge. Ash'arism pervades such homilies. Thus in Kitāb al-Tawba, Ghazali formulates, analyzes and defends the concept of human choice in Ash'arite terms. He thus argues that each of the ingredients of this concept - knowledge, power, the decisive will, as well as the ensuing choice - is individually the direct creation of God. Not that the argument for this concept yields experiential knowledge of its meaning within the cosmic scheme of things. For Ghazali such knowledge is only attained through mystical vision. But the Ash'arite argument, when not pursued as an end in itself, can be an aid to the seekers of gnosis. It can bring them closer to knocking at its doors.

How do the variegated forms of sublunar substances (the elements, homoeomerous substances, plants, animals) arise in prime matter? Averroes throughout his life believed that “a principle from without” was involved, but changed his mind over its identity. While in an early period of his life he maintained that all forms emanate from the active intellect, he later discarded that metaphysical notion and sought to develop a more naturalistic, astrologically inspired account, which identified the heavenly bodies as the source of sublunar forms. Comparing different versions of Averroean texts, this paper seeks to spell out how, in Averroes' view, the heavenly bodies generate forms in matter. Averroes claims that this is brought about by means of their “heats,” an answer that is however problematic seeing that in the Aristotelian cosmology the celestial realm is quality-less. The paper examines Averroes' ideas on the relationship between light and heat, concluding that the Commentator was unable to integrate the postulate that the heavenly bodies inform matter within his Aristotelian theory of matter.

The present article is devoted to two issues. The first is the identification of lead and tin in medieval Arabic alchemy. The second is the investigation of whether Arabic alchemists differentiate between these problematic substances or not. These two issues are investigated in the light of a comparison which is made between the facts that are stated about the two problematic substances in the original Arabic alchemical works and those stated in modern chemical literature. It is proved that Arabic alchemists made a sharp distinction between lead and tin. Also, it becomes clear that these two metals were used in a satisfactory purity in the era of medieval Arabic alchemy. As a consequence of the present study, some conclusions are drawn about the existence of some categories of ‘derivatives’ of fusible bodies in Arabic alchemy which are degenerate to modern categories of oxides, carbonates, etc.

The aim of this work is to end the debate about the widespread acceptance among specialists, that the 6th century Byzantium treatise by Cassianus reached Muslim scholars by means of two routes: a “direct” translation from Greek into Arabic (Filā[hdotu]a rūmiyya attributed to Qus[tdotu]ūs) and the other “indirect” translation by means of a Persian translation (Filā[hdotu]a fārisiyya attributed to either Kasīnūs or Qus[tdotu]ūs). Thanks to a comparison of the texts, one can prove beyond all doubt that there was only a secondary translation route into Arabic from the Persian version. Additionally, this work highlights the significant influence of the Filā[hdotu]a rūmiyya on the Andalusian agronomy. The most influenced subjects are pointed out and those agronomic sources derived from this treatise and the 10th century Greek Geoponica (based on Cassianus) are studied. This study allows us to conclude that the later work was never translated into Arabic, therefore, the Andalusian agronomists only had access to the Arabic versions of Anatolius and Cassianus to which the Pseudo-Qus[tdotu]ūs' work was later added.