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)

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)

"Are those who know equal to those who do not know?". In the Hadith similar sentiments are expressed; "The seeking of knowledge is obligatory upon every Muslim". These demands to attain knowledge have been deeply inscribed on the hearts of pious Muslims everywhere. Nevertheless, there have been discussions historically over whether every statement claiming to be valid knowledge should be accepted under such injunctions. Knowledge of nature is one such area of concern. Should the results of natural philosophy or science (...) be accepted uncritically as valid knowledge? This question is especially acute in cases where the sciences appear to contradict the overt content of the divine Qur'anic revelation, whose veracity cannot be questioned. Some have argued that all knowledge is valid, while others have claimed that some knowledge is not acceptable and should either be reformulated in an appropriate way or be excluded from the repertoire of the sincere Muslim. (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)