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)

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)

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)

This book provides an exciting and diverse philosophical exploration of the role of practice and practices in human activity. It contains original essays and critiques of this philosophical and sociological attempt to move beyond current problematic ways of thinking in the humanities and social sciences. It will be useful across many disciplines, including philosophy, sociology, science, cultural theory, history and anthropology.

This book constitutes the outcome of an international conference held at the Otto-Mobes-Volkswirtschaftsschule, Graz-Stifting( Austria), from June 16 to 22, 1974. The conference was initiated by a project group working on determinants and controls of social science development at the In stitute for Advanced Studies and Scientific Research in Vienna and or ganized by the editors of this volume. It was held under the auspices of the Austrian Ministry of Science and Research. The main topics of the conference were those (...) at the forefront of the 'state of argumentation' (to borrow from one of our contributors) in philosophy and sociology of science ever since the controversy between Thomas S. Kuhn and Sir Karl R. Popper has sharpened our awareness for the methodological and substantial presuppositions involved with questions of growth and development in science. Let us give two examples of those topics. The borderline between sociology of science and philo sophy of science has become more and more unclear; while the work of at least some philosophers of science comes to have an empirical flavour, sociologists of science are increasingly apt to include logical and methodo logical components of the research process as their objects of examina tion. Papers included in this volume testify to both tendencies. (shrink)

Descartes' place in history, by L. J. Lafleur.--A central ambiguity in Descartes, by S. Rosen.--Doubt, common sense and affirmation in Descartes and Hume, by H. J. Allen.--Some remarks on logic and the cogito, by R. N. Beck.--The cogito, an ambiguous performance, by J. B. Wilbur.--The modalities of Descartes' proofs for the existence of God, by B. Magnus.--Descartes and the phenomenological problem of the embodiment of consciousness, by J. M. Edie.--The person and his body: critique of existentialist responses to Descartes, (...) by P. A. Bertocci. (shrink)