The Development of Mathematics in Medieval Europe: The Arabs, Euclid, Regiomontanus

This is Menso Folkerts' second Variorum volume.The first was published in 2003 [see Høyrup 2007b for a review]; it contained papers dealing with the properly Latin tradition in European mathematics, that is, the kind of mathematics which developed (mainly on the basis of agrimensor mathematics and the surviving fragments of Boethius' translation of the Elements) before the 12th-century Arabo-Latin and Greco-Latin translations.This second volume deals with aspects of the development which took place after this decisive divide, from ca 1100 to ca 1500.Few scholars, if any, know more than Folkerts about medieval Latin mathematical manuscripts.It is, therefore, natural that the perspective on mathematics applied in the papers of this volume is on mathematics as a body of knowledge, in particular, as it is transmitted in and between manuscripts.To the extent that mathematics as an activity is an independent topic, it mostly remains peripheral, being dealt with through references to the existing literature-exceptions are the investigations of what Regiomontanus and Pacioli do with their Euclid [in articles VII and XI]-or it is undocumented, as when it is said that Jordanus de Nemore's De numeris datis was 'probably used as a university textbook for algebra' [VIII.413].There should be no need to argue, however, that familiarity with the body of mathematical knowledge is fundamental for the study of mathematics from any perspective: whoever is interested in medieval Latin mathematics can therefore learn from this book.It is more questionable that Folkerts tends to describe the mathematics which he refers to through their modern interpretation.To say, for instance, that the Liber augmentis et diminutionis shows