To justify certain steps of the computation developed in his Sand-Reckoner, Archimedes cites the following inequalities relative to the sides of right triangles: if of two right-angled triangles, the sides about the right angle are equal , while the other sides are unequal, the greater angle of those toward [sc. next to] the unequal sides has to the lesser a greater ratio than the greater line of those subtending the right angle to the lesser, but a lesser than the greater (...) line of those about the right angle to the lesser. That is, with reference to the two right triangles ABG, DEZ , where AG equals DZ and the angle at B is greater than that at E, ZE:GB < angle B:angle E < DE:AB. (shrink)

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)

To justify certain steps of the computation developed in his Sand-Reckoner, Archimedes cites the following inequalities relative to the sides of right triangles: if of two right-angled triangles, the sides about the right angle are equal, while the other sides are unequal, the greater angle of those toward [sc. next to] the unequal sides has to the lesser a greater ratio than the greater line of those subtending the right angle to the lesser, but a lesser than the greater line (...) of those about the right angle to the lesser. That is, with reference to the two right triangles ABG, DEZ, where AG equals DZ and the angle at B is greater than that at E, ZE:GB < angle B:angle E < DE:AB. (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)

The anthropological approach is the central focus of this study. Laboratories are looked upon with the innocent eye of the traveller in exotic lands, and the societies found in these places are observed with the objective yet compassionate eye of the visitor from a quite other cultural milieu. There are many surprises that await us if we enter a laboratory in this frame of mind... This study is a realistic enterprise, an attempt to truly represent the social order of life (...) in laboratories and institutes of research, just as they are. By bringing the philosophical issues to the surface as matters not of prejudgement but as matters of concern, Karin Knorr-Cetina has developed the first really positive challenge to the philosophy of science since the days of paradigms and internal definitions of meanings. (shrink)

This volume offers a selection of the most interesting and important work from recent years in the philosophy of mathematics, which has always been closely linked to, and has exerted a significant influence upon, the main stream of analytical philosophy. The issues discussed are of interest throughout philosophy, and no mathematical expertise is required of the reader. Contributors include W.V. Quine, W.D. Hart, Michael Dummett, Charles Parsons, Paul Benacerraf, Penelope Maddy, W.W. Tait, Hilary Putnam, George Boolos, Daniel Isaacson, Stewart Shapiro, (...) and Hartry Field. (shrink)

How does science create knowledge? Epistemic cultures, shaped by affinity, necessity, and historical coincidence, determine how we know what we know. In this book, Karin Knorr Cetina compares two of the most important and intriguing epistemic cultures of our day, those in high energy physics and molecular biology. The first ethnographic study to systematically compare two different scientific laboratory cultures, this book sharpens our focus on epistemic cultures as the basis of the knowledge society.