Al-Qūhī, mathematician of the 10th century, examines critically two arguments in the 6th book of the Aristotelian Physics. This critic does not follow the method of the philosophers, with doctrinal amendments, but with a mathematical and experimental style. For understanding of this critical examination and its influence, it is necessary to situate it in the mathesis of al-Qūhī and to produce its mechanical presuppositions. This is the purpose of the author of this paper.

Albert of Saxony, master of Arts at Paris from 1351 until 1361/62, has left two commentaries on the Physics of Aristotle. Since he was well aware of the tradition, his writings may serve for an analysis of the transmision of ideas from the ancient and Arabic philosophers into the fourteenth century. In this paper, this is exemplified by the problems of place and space, especially by those of the definition of place and of the immobility of place, of natural place and of the location of the last and outermost sphere. As a result, four modes emerge how an author of the fourteenth century may have been influenced by tradition. Ancient Greek or Pre-Socratic philosophers were mainly known through Aristotle, and thus their opinions were mostly refuted; the same holds true for later ancient or Arabic authors known through the commentaries of Averroes; the influence of the authors of the thirteenth century was present though their texts may not have been directly consulted; and, finally, the contemporary authors were known, but nearly never quoted. Thus, though there was a line of tradition from Aristotle into the fourteenth century, there was also room for proper “medieval” solutions.

Scholars working in the field of Graeco-Arabic Neoplatonism often discuss the role Porphyry, the editor of Plotinus, must be credited with in the formation of the Arabic Plotinian corpus. A note in this corpus apparently suggests that Porphyry provided a commentary to the so-called Theology of Aristotle, i.e., parts of some treatises of Enneads IV-VI. Consequently, Porphyry has been considered as responsible for the (sometimes relevant) doctrinal shifts which affect the Arabic Plotinian paraphrase with respect to the original text. This article aims at submitting this hypothesis to trial on a specific doctrinal point where Porphyry parts company with Plotinus: the relationship between the Demiurgic Intellect and World Soul. The ancient doxographical sources testify that Porphyry, in his conviction to be in agreement with Plotinus, in fact parted company with him in so far as he merged the World Soul into the Demiurgic Intellect, while Plotinus always kept them apart. There are in the Enneads some baffling passages where the role of Intellect as the Demiurge of the sensible world is not clearly distinguishable from the role of World Soul. Notwithstanding that, these passages in the Arabic paraphrase do not bear any trace of the characteristically Porphyrian merging of World Soul into Intellect. The Arabic paraphrase of Plotinus’ writings never confuses Intellect and World Soul, as Porphyry did. This fact seems to disprove, at least on this point, the hypothesis of Porphyry's intervention as the explanation for the doctrinal differences between the original Plotinus’ text and its Arabic tradition.

This paper presents the first edition, translation and analyse of al-Māhānī’s commentary of the Book X of Euclid’s Elements (9th century, the most ancient to have reached us) and of an anonymous’ one (prior to 968, among the first algebraic commentaries). For the first time, irrational numbers are defined and classified. The algebraisation of Elements’ X-91 to 102, on the basis of al-Khwārizmī’s Algebra, shows irrational numbers as solution to algebraic quadratic equations. The algebraic calculus makes here the first steps. On this occasion, negative numbers and their calculation rules appears. Simplifications imposed by the algebraic writings are sometimes in opposition with the conclusions of propositions conceived in a purely geometrical framework, revealing a contradiction between geometrical and algebraic goals. It will be resolved by the independant way algebra will take with mathematicians belonging to the tradition of al-Karajī and al-Samaw’al from the 11th-12th centuries on.