In 1953 Marshall Clagett presented a preliminary scheme of the medieval Latin versions of Euclid'sElements. Since then a considerable body of these texts has become available in critical editions, thanks to Clagett's labours on the Archimedean tradition and H. L. L. Busard's work on the Euclidean versions. Further, Busard, M. Folkerts, R. Lorch and C. Burnett have scrutinized the pivotal ‘second’ version of Adelard of Bath, and have thereby exposed a diversity of text forms that spells real complications for the (...) effort to establish its provenance and use. In his recent overview of the medieval Euclidean tradition, Folkerts displays not only how these studies have filled out and expanded upon Clagett's initial framework, but also how they have compelled rethinking of some basic issues, such as on the source relations and authorship of the various versions. (shrink)

When ancient mathematical treatises lack expositions of numerical techniques, what purposes could ancient mathematical theories be expected to serve? Ancient writers only rarely address questions of this sort directly. Possible answers are suggested by surveying geometry, mechanics, optics, and spherics to discover how the mathematical treatments imply positions on this issue. This survey shows the ways in which these ancient theoretical inquiries reflect practical activity in their fields. This account, in turn, suggests that the authors may have intended their theorems (...) not to predict, but to explain phenomena. We may then consider what kind of explanations they were seeking. (shrink)

In two articles published in 1881 and 1884, the young academics, Martin Klamroth and Johan L. Heiberg, engaged in a brief debate on the textual choices that should govern the publication of a new critical edition of Euclid's Elements. This short debate seemed to settle the problem in Heiberg's favor as to what should be taken as the definitive text of Euclid's Elements. But the issue ought to be considered once again for there are good reasons for the claim that (...) Klamroth was right, and that Heiberg was wrong. If so, we have been consulting, and continue to consult, the wrong text in our efforts to interpret the Euclidean tradition. In order to substantiate this claim, the textual issue debated by Klamroth and Heiberg is rehearsed again, and the principal reasons brought forth by Heiberg against Klamroth's position are reconstructed. Specimens from three broad areas of evidence – structural, linguistic, and technical – will be considered. They reveal how the medieval tradition of the text advocated by Klamroth displays textual superiority to the Greek tradition promoted by Heiberg. Such a reorientation of the texts has the potential to change significantly our understanding of ancient mathematics. (shrink)