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)

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)

ArgumentThis article is the sequel to an article published in the previous issue ofScience in Contextthat dealt with homeomeric lines (Acerbi 2010). The present article deals with foundational issues in Greek mathematics. It considers two key characters in the study of mathematical homeomery, namely, Apollonius and Geminus, and analyzes in detail their approaches to foundational themes as they are attested in ancient sources. The main historiographical result of this paper is to show thatthere wasa well-establishedmathematicalfield of discourse in “foundations of (...) mathematics,” a fact that is by no means obvious. The paper argues that the authors involved in this field of discourse set up a variety of philosophical, scholarly, and mathematical tools that they used in developing their investigations. (shrink)