Observations on Hermann of Carinthia’s Version of the Elements and its Relation to the Arabic Transmission Sonja Brentjes Max Planck Institute for the History of Science, Berlin* Argument 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. The Arabic transmission of the Elements was a complex phenomenon where linguistic, mathematical, and cultural aspects intermingle. Its decipherment may yield insights into the complexity of Muslim interests in ancient Greek scientific works. There were at least two Arabic translations of Books I–XIII. One was made before 805 by al- ˙ Hajj¯ aj ibn Y¯ usuf ibn Ma ˙ tar (fl. between 786–833). A second was made by Is ˙ h¯ aq ibn ˙ Hunayn (d. 910/11), probably during the last third of the ninth century. Both translations were reworked at least once. Al- ˙ Hajj¯ aj reworked his own translation during the reign of caliph al-Ma  m¯ un (813–833). The two versions of his work constitute the first Arabic tradition of the Elements, the so-called ˙ Hajj¯ aj tradition. Is ˙ h¯ aq’s translation was edited by Th¯ abit ibn Qurra (d. 901). These two texts constitute the second Arabic tradition of the Elements, the so-called Is ˙ h¯ aq/Th¯ abit tradition. These two traditions will be called the Arabic primary transmission of the Elements. * I thank the Humboldt Foundation, Bonn and the Institute for Advanced Study, Princeton for sponsoring the research on the Arabic transmission of Euclid’s Elements, Books I-IV. This paper is a revised form of a contribution to a conference held in honor of Boris A. Rosenfeld in 1994 at Pennsylvania State University. I thank M. Folkerts, P. Kunitzsch, and R. Lorch for their help. Science in Context 14(1/2), 39–84 (2001). Copyright © Cambridge University Press DOI: 10.1017/0269889701000035 Printed in the United Kingdom