In Proclus' penetrating exposition of Euclid's method's and principles, the only one of its kind extant, we are afforded a unique vantage point for understanding the structure and strenght of the Euclidean system. A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere.

This paper investigates the affiliation of Book I of the Latin translation of Euclid's Elements attributed to Hermann of Carinthia with the Arabic transmission of the Greek mathematical work. It argues that it is a translation of a text of the Arabic secondary transmission, that is, of an Arabic edition mixed with comments. Two methodological claims are made in the paper. The first insists that the determination of a text whose transmission was as multifaceted and complex as the Euclidean Elements (...) needs to be based on a systematic investigation of entire books rather than on selected theorems or diagrams of global, mostly structural relevance. The second claim starts from the experience that almost all results regarding the place of a particular document in a chain of transmission are conjectural. It acknowledges that individual results are more or less persuasive, depending upon the qualitative status of the argument. It suggests that the quantitative accumulation of similarities, differences, errors, regularities, or peculiarities allows one to recognize patterns and thus improves the reliability of judgment. (shrink)

The "Text" and the "Commentary" mentioned in the title of this essay are, respectively, the "Kitāb al-Manāẓir", or "Optics", of al-Ḥasan ibn al-Haytham, composed in the first half of the fifth/eleventh century, and the "Tanqīḥ al-Manāẓir li-dhawī l-abṣār wa l-baṣā'ir", written by Abū l-Ḥasan (or al-Ḥasan) Kamāl al-Dīn al-Fārisī in the second half of the seventh/thirteenth century. It is known that, so far, only the first five of the seven "maqālāt"/Books that make up the Arabic text of IH's "Optics" have (...) been published, and that the "Tanqīḥ" was published in two volumes. I shall be concerned with certain episodes in the lives of these two works, my aim being to shed light on their transmission within the Islamic Arabic and Persian worlds. -/- . (shrink)