From Euclid to the second half of the 17th century, mathematicians as well as philosophers continued to raise the question of the angle of contact and, generally, of the concept of angle. This article is the first essay devoted to this subject in Arabic mathematics. It deals with Greek writings translated into Arabic on the one hand, and contributions of Arabic mathematicians on the other hand: al-Nayrīzī, Ibn al-Haytham, al-Samawʾal, al-Shīrāzī, al-Fārisī, al-Qūshjī, among others. Most of these contributions are hitherto unknown.

What is the function of logic in al-Kindī's corpus? What kind of relation does it have with mathematics? This article tackles these questions by examining al-Kindī's theory of categories as it was presented in his epistle On the Number of Aristotle's Books (Fī Kammiyyat kutub Arisṭū), from which we can learn about his special attitude towards Aristotle theory of categories and his interpretation, as well. Al-Kindī treats the Categories as a logical book, but in a manner different from that of the classical Aristotelian tradition. He ascribes a special status to the categories Quantity (kammiyya) and Quality (kayfiyya), whereas the rest of the categories are thought to be no more than different combinations of these two categories with the category Substance. The discussion will pay special attention to the function of the categories of Quantity and Quality as mediators between logic and mathematics.

In the thirteenth century, the influential logician Afḍal al-Dīn al-Khūnajī (d. 1248) departed from the Avicennan view that the subject matter of logic is “second intentions”. For al-Khūnajī, the subject matter of logic is “the objects of conception and assent”. His departure elicited intense and sometimes abstruse discussions in the course of subsequent centuries. Prominent supporters of Khūnajī's view on the subject matter of logic included Kātibī (d. 1277), Ibn Wāṣil (d. 1298) and Taftāzānī (d. 1390). Defenders of Avicenna's view included Ṭūsī (d. 1274), Samarqandī (d. 1303) and Quṭb al-Dīn al-Rāzī (d. 1365). This article presents the outline of the development of this discussion down to the end of the fourteenth century and attempts to reconstruct the major arguments of both sides.

The article aims at demonstrating that in attributing the creatio ex nihilo to both Plato and Aristotle as their unanimous philosophical conviction the Treatise on the Harmony between the Two Sages deeply depends upon the Neoplatonic reading of those two philosophers. The main obstacles for such a view in the works of the two sages are Plato's assumption of a precosmic chaos in the Timaeus and Aristotle's denial of any efficient causality to the unmoved mover in the Metaphysics. Both of these points had been, however, done away with by the Neoplatonist commentators already, especially by Ammonius in his lost treatise on efficient and final causality in Aristotle the use of which in the Harmony is shown by a comparison with Simplicius. Christian and Muslim readers just had to transfer those arguments and hermeneutical techniques into an anti-eternalist context in order to make the two philosophers agree with one of the basic tenents of their face, a hermeneutical technique considerably different from the one employed by al-Fārābī in his exposition of Plato's and Aristotle's philosophy which is compared to the Harmony in a briefly sketched concluding section.

Once Apollonius' Conics had been translated from Greek into Arabic, they became a main reference and the principal tool in studying solid problems, algebraic equations of 3rd and 4th degrees, infinitesimal mathematics, etc. Mathematicians of the 9th–10th centuries also studied the conic sections' constructions, as well as their continuous drawing and their drawing by points. Ibrāhīm ibn Sinān (909–946), as his grandfather Thābit ibn Qurra (826–901), was one of the most active and inventive mathematicians in these fields. Late Hélène Bellosta examined in this article Ibn Sinān's contribution.

During the second half of the twentieth century an attention of historians of mathematics shifted to mathematics of the Late Antiquity and its subsequent development by mathematicians of the Arabic world. Many critical editions of works of mathematicians of the Hellenistic era have made their appearance, giving rise to a new, more detailed historical picture. Among these are the critical editions of the works of Diophantus, Apollonius, Archimedes, Pappus, Diocles, and others.