First century Chinese, fifth century Indian, and Arabic documents from the 9th century onwards, contain similar tabular procedures to extract square and cube roots on place-value numeration systems. Moreover, an 11th century Chinese astronomer, Jia Xian, as well as al-Samaw'al, a 12th century Arab mathematician, extracted roots of higher order with the so-called Ruffini-Horner procedure. This article attempts to define a textual method to organize this corpus, by distinguishing relevant criteria for identifying similarities and differences from a historical as well as conceptual point of view. The first part analyses three different states of the descriptions of algorithms in China between the 1st and the 11th centuries, all of which exhibit a definite historical stability. The rewriting which allows one to proceed progressively from one state to the next shows a uniformity in the components of the algorithm, which culminates in procedures of the type Ruffini-Horner. Textual criteria demonstrate a greater affinity of certain algorithms, such as those described by Kūshyār ibn Labbān (ca 1000) with Chinese rather than with Indian texts, which are in turn closer to algorithms described by al-Khwārizmī. Criteria of the same kind link the algorithms of Jia Xian and al-Samaw'al on the one hand, and those of Kūshyār and al-Samaw'al on the other.

Some of the short pieces attributed in various Arabic manuscripts to Alexander of Aphrodisias in fact derive from Proclus's Elements of Theology. Twenty such pieces were published in 1973 by G. Endress, who traced the unnamed translator to the circle of Kindi. Another such piece is here identified, published, and assigned to the same translator. Its beginning and end seem to have been revised by a later transmitter. Section II of the article adduces a parallel case where the original Arabic version still exists. Section III surveys a number of related pieces that would also appear to have been changed in transmission. Section IV argues that most if not all were once united in a single collection of Proclus and Alexander. Section V argues that since certain changes of detail were evidently made during or soon after translation, the general arrangement of the Kindi-circle Alexander, as of the Kindi-circle Liber de Causis and the Kindi-circle “Theology of Aristotle”, is also likely to be peculiar to the Arabic tradition. The text from which Proclus Arabus was first translated need not have differed substantially from the transmitted Greek.

This treatise of medicine by Yühannā ibn Sarābiyūn, written in Syriac in the 8th century, translated into Arabic in the 10th century and then into Latin in the 12th century, is a typical example of the transmission of Hippocratic medicine from the Arabic East to the Latin West in the Middle Ages. However, while the complete Latin translation of Gerard of Cremona has reached us, we have only fragments of the Arabic text, dispersed in five manuscripts preserved in four European libraries.

In the first part we shall try to establish the biographical information about the author and the four translators of his treatise from Syriac to Arabic. In the second part we shall study the Arabic fragments of the Paris manuscript and the two Escorial manuscripts, first by examining their language, and then by comparing them to the Latin translation.

In this paper, are included new data about three treatises ascribed in Arabic to Alexander of Aphrodisias. These treatises were thought to have no Greek correspondent. The author shows that one of them, (D.8a), is an adapted version – following the norms of “al-Kindi circle” – of Quaestio I 21, along with the later and more exact version of this Quaestio by Abū ‘Uṭmān al-Dimašqi (d. 900). He shows also that the two other treatises (D.9 and D.16) are, in contradistinction to the first, adapted versions of passages belonging in the De Aeternitate mundi contra Proclum of John Philoponus: respectively IV, 4–6 and IX, 11. Philoponus’ book was known to have been translated, into Arabic. But, except for some short fragments in al-Bīrūnī (d. 1048), it seems that it is the first time that important adapted extracts of it are put in light. Some points are made about the historical position of the epitomator of these passages. In Appendix II, another treatise ascribed to Alexander (D.27g) appears – provisionally – as a composite text, mixing elements coming from Philoponus and others from neoplatonic texts in Arabic. In Appendix III is analysed the use of D.16 by Miskawayh (d. 1030), and the use of D.27g by ‘Abdallaṭīf al-Baġdādī (d. 1231).

Ṯābit b. Qurra is especially known as a mathematician, but his work in astronomy is also important. This article reviews his eight surviving astronomical treatises, as well as relevant fragments of his lost works cited by later authors in Arabic and Latin. We conclude that, as an active participant in the scientific movement of 9th-century Baghdad, Ṯābit played a crucial role in the establishment of astronomy as an exact science. The argument is based on an assessment of his contribution in three areas: the relationship between observation and theory, the “mathematization” of astronomy, and the relationship between “mathematical” astronomy and “physical” astronomy.

The theological foundations of Ghazali's causal theory are fully expressed in the chapter on the attribute of divine power in his al-Iqtiṣād fi al-I'tiqād (Moderation in Belief). The basic doctrine which he proclaims and argues for is that divine power, an attribute additional to the divine essence, is one and pervasive. It does not consist of a multiplicity of powers that produce a multiplicity of effects, but is a unitary direct cause of each and every created existent. In a defense of the doctrine of kasb (acquisition), Ghazali argues (a) that power in all animate creatures is created directly (i.e. without intermediaries) by God and (b) that there is created with it the object of power, normally, but erroneously regarded as its effect: the object of power is in fact directly created by God. It exists with the created power, but not by it. In his critique of the Mu'tazilite theory of the generated act he again denies that created power has any causal efficacy and denies that inanimate things have any causal efficacy. What one normally regards as the effects of inanimate causes are in reality their concomitants, directly caused by divine power.

The discussion of kasb, the longest in the chapter, includes Ghazali's spirited defense of it against possible objections. The defense, however, as will be shown, is not immune against criticism. At the same time, the discussion of kasb, central as it is, has to be understood in the context of the chapter as a whole, whose intricate arguments remain integrated and unified. Hence a brief exposition of the chapter's arguments will first be given, followed by a critical comment on some aspects of Ghazali's defense of kasb. This is then followed by an annotated translation of the entire chapter, a chapter so very basic for the study of Ghazali's position on causality.

In a departure from the tradition of the Neoplatonic commentators of the Organon, the sequence of summaries in the “Bratislava series” insert two treatises between the Prior Analytics and the Posterior Analytics, namely the Resolution (kitāb al-Taḥlīl) and the Sophistical Refutations. And even though the Taḥlīl is concerned with Book 2 of the Topics, it does not deal with dialectic. Instead, it comments on the summary of the Topics that belongs to the Prior Analytics (I, 27–30), while “completing” it. The contents of kitāb al-Taḥlīl and the different titles that the fahāris give it (e.g., fīiktisăb al-muqaddimāt), lead one to realize that it is an addition to the Prior Analytics offering a theory concerning the generation of the premisses of the syllogism, something that may have appeared to Alfarabi as missing from Kitāb al-Qiyās.

The scholastic doctrine of transcendentals is inherited from Arabic philosophy to a certain extent. This dependance is clearly illustrated in the construction of the problematic of the transcendental one, which is identical with being, and of the numerical one, which is not. The scholastic discussion as a whole reproduces the major themes of Avicenna's position, then of Averroes' criticism of Avicenna. This article attempts to reconstruct the complex of questions, topics, and arguments which constitute this problematic by tracing its evolution through the analysis of anonymous sophismata and of texts by Nicholas of Paris, Roger Bacon, Albert the Great, and James of Viterbo. Two stages are distinguished: the first is centered on the distinction between the transcendental and numerical one; the second, essentially German (Dietrich of Freiberg and Berthold of Moosburg), is centered on the subordination of the Aristotelian to the Platonic concept of the transcendental one. Along the way, it is shown that, with the exception of the German philosophers, the understanding of Avicenna's position is constantly filtered through Averroes' interpretation.

Euclid's definition of proportional magnitudes in the Fifth Book of the Elements gave rise to many commentaries. We examine closely two of these commentaries, one by al-Jayyānī (11th century) and the other by Saunderson (18th century). Both al-Jayyānī and Saunderson attempted to defend Euclid's definition by making explicit what Euclid had only implied. We show that the two authors explain Euclid's position in a virtually identical manner.