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

Menso Folkerts
Publication Date: 
Number of Pages: 
Variorum Collected Studies
[Reviewed by
Fernando Q. Gouvêa
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Three years ago, I reviewed an earlier volume by Menso Folkerts in the same Variorum Collected Studies Series. Entitled Essays on Early Medieval Mathematics, it collected several of Folkerts' papers on that topic. This volume is clearly a continuation of the other, focusing this time on "The Arabs, Euclid, and Regiomontanus" (and therefore on a slightly later part of the Medieval period).

The goal of the Variorum series is to bring together papers originally published in various journals and books in order to make them easily accessible to scholars. To that end, papers are usually published exactly as originally published, even to the extent of retaining their original pagination. The Development of Mathematics in Medieval Europe breaks with that tradition in various ways, for good reasons and with good results. First of all, two of the papers have been translated into English, reflecting, perhaps, the realities of today's academic world. Two essays are described as "completely revised." One essay is listed as "to appear" in a conference proceedings volume. Finally, one article is published here for the first time. The result is that even a library that already has all of the books and journals where most of these articles originally appeared will want to get a copy of this book.

Euclid is a dominant presence in the essays collected here. In focus is the enormous impact of the Elements on the mathematicians of the late middle ages, from Leonardo Fibonacci to Pacioli, Piero della Francesca, and Regiomontanus. Since the latter also played a crucial role with respect to the transmission of the work of other Greek mathematicians, he gets a starring role in five of the papers. Finally, Greek mathematics originally arrived in Europe after being translated, digested, internalized, improved upon, and transformed by mathematicians writing in Arabic, and the first two essays trace that influence and impact.

The final essay, published here for the first time, deals with algebra in 15th century Germany, a topic that usually receives very little attention in history books. Regiomontanus is the link here, of course. But the German Rechenmeister deserve as much historical attention as the Italian maestri d'abbaco; this essay ably summarizes what is known about them.

As I pointed out in my review of the earlier collection, Folkerts is writing about a period that tends to receive very little attention from the standard compendia on the history of mathematics. A couple of essays taken from these volumes would therefore be very useful as supplementary reading in an introductory history of mathematics course.

It would be very nice to see more such collections of papers on the history of mathematics in the Variorum series. For now, anyone interested in the subject should make sure their library gets a copy of this one.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College.

 Preface; Arabic mathematics in the West; Early texts on Hindu-Arabic calculation; Euclid in Medieval Europe; Probleme der Euklidinterpretation und ihre Bedeutung für die Entwicklung der Mathematik; Die mathematischen Studien Regiomontans in seiner Wiener Zeit; Regiomontanus' role in the transmission and transformation of Greek mathematics; Regiomontanus' approach to Euclid; Regiomontanus' role in the transmission of mathematical problems; Leonardo Fibonacci's knowledge of Euclid's Elements and of other mathematical texts; Piero della Francesca and Euclid; Luca Pacioli and Euclid; Algebra in Germany in the 15th century; Indexes.