This article takes up the adventure of the Arabic version of the Elements published in Rome at the Typographia Medicea in 1594 at the point where the first installment (Cassinet, Revue française d’histoire du livre 78–79:5–51, 1993) ended. In this new installment of the adventure, we situate the Rome edition within a stemma of connected Arabic copies spanning some four centuries. We show that the text of the Rome edition was typeset from Biblioteca Medicea Laurenziana, Or. 20 and that Or. (...) 20 in turn was copied from Or. 50. We show that a manuscript (Tehran, Sipahsalar 540) was later copied from the printed edition and that still later the text of the Rome edition was reissued in lithograph form in Fez. The story is important because the Rome edition influenced the development of non-Euclidean geometry in European mathematics and because the mistaken identity of its author has led to persistent errors in the history of mathematics. (shrink)

The ArgumentThe development of autonomous theoretical science is often considered a “Greek miracle.” It is argued in the present paper that another “miracle,” necessary for the creation of modern science, took place for the first time in the Islamic Middle Ages, viz. the integration of theory and practice.The discussion focuses on the mathematical disciplines. It starts by investigating the plurality of traditions which were integrated into Islamic mathematics during its formation, emphasizing practitioners' “sub-scientific” traditions, and shows how these were synthesized (...) in a way virtually unknown in earlier cultures. A discussion of the sociocultural roots of this specific synthesis concludes that a major role was played in the earlier period by the combination of fundamentalist convictions characteristic of Islam – that the most humble daily activity is directly responsible to the highest ontological level, while conversely this highest level is concerned with the humblest ranks of daily existence – with the absence of an institutionalized “Church” able to monopolize the interpretation of the mutual bond of the divine and the everyday levels.As the institutions of learning crystallized around the turn of the millennium, the integrative attitude to theory and practice was fixated institutionally; the latter process is discussed, first with the example of the madrasah institution as the carrier of an arithmetical textbook tradition, and second with that of the bond between astronomy and theoretical geometry. (shrink)

The historian Agathias (Hist. II 30.3-31.4) relates that under the Emperor Justinian seven philosophers (Damascius, Simplicius, Eulamius, Priscianus, Hermeias, Diogenes, and Isidorus) sought refuge in Persia because of their own country's anti-pagan laws but that they ultimately returned in 532 to the Roman Empire. There have been many hypotheses about the fate of these philosophers after their return. Most recently M. Tardieu has argued that these philosophers went to Harran, a town that was located on the Persian frontier and that (...) remained mostly pagan until the tenth century. This hypothesis, which M. Tardieu had backed with a number of arguments, has found many echoes, both positive and negative, in subsequent secondary literature. Yet the complexity of the issue has never really been faced by Tardieu's critics. For example, the fact that, according to Arab sources, Simplicius could found a famous school of mathematics has been completely neglected, as has the fact that details of the dogmas of Manicheanism, which he obtained through his encounter with a member of that sect, enable one to envision a Mesopotamian locale for this encounter. The present study aims at taking stock of the elements of this controversy, beginning with a detailed article by D. Watts and a review by C. Luna. Watts mostly bases his criticisms of M. Tardieu and me on Luna's summary. In the conclusion (pages 58-59), I summarize the main points that seem to me to confirm M. Tardieu's hypothesis. (shrink)

Euclid discusses the ex aequali relationship twice in the Elements. The first is in Book V, during his discussion of arithmetical relations between mathematical magnitudes in general. The second is in Books VIIIX, he was not much troubled by the differences between his treatment of ex aequali ratios in these two contexts. Later generations of mathematicians, however, found these differences less acceptable and tried to minimize them in various ways. This paper summarizes Euclid's use of the ex aequali relation in (...) developing his mathematics. The paper then outlines the fate of the post-Theonine Greek attempts to the Euclidean discussion when the Elements entered the Arabic/Islamic intellectual tradition. The study concludes with the attempts by Ibn al-Hayam and Ibn al-Sarī to improve the parallelism between the discussions of ex aequali ratios in Book V and Book VII. (shrink)

In this paper, I explore general features of the “architecture” (relations of white space, diagram, and text on the page) of medieval manuscripts and early printed editions of Euclidean geometry. My focus is primarily on diagrams in the Arabic transmission, although I use some examples from both Byzantine Greek and medieval Latin manuscripts as a foil to throw light on distinctive features of the Arabic transmission. My investigations suggest that the “architecture” often takes shape against the backdrop of an educational (...) landscape. The constraints of the economic marketplace and cultural aesthetic ideals also appear to play a role in determining the “architecture” of both manuscripts and early printed editions. (shrink)