Dissertation/Thesis Abstract

Conjugate diameters: Apollonius of Perga and Eutocius of Ascalon
by McKinney, Colin Bryan Powell, Ph.D., The University of Iowa, 2010, 189; 3422241
Abstract (Summary)

The Conics of Apollonius remains a central work of Greek mathematics to this day. Despite this, much recent scholarship has neglected the Conics in favor of works of Archimedes. While these are no less important in their own right, a full understanding of the Greek mathematical corpus cannot be bereft of systematic studies of the Conics. However, recent scholarship on Archimedes has revealed that the role of secondary commentaries is also important. In this thesis, I provide a translation of Eutocius' commentary on the Conics, demonstrating the interplay between the two works and their authors as what I call conjugate. I also give a treatment on the duplication problem and on compound ratios, topics which are tightly linked to the Conics and the rest of the Greek mathematical corpus. My discussion of the duplication problem also includes two computer programs useful for visualizing Archytas' and Eratosthenes' solutions.

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Indexing (document details)
Advisor: Anderson, Daniel D.
Commitee: Gibson, Craig A., Jorgensen, Palle E. T., Kutzko, Philip C., Muhly, Paul S.
School: The University of Iowa
Department: Mathematics
School Location: United States -- Iowa
Source: DAI-B 71/10, Dissertation Abstracts International
Subjects: Mathematics, Classical Studies, Science history
Keywords: Apollonius, Archimedes, Conic sections, Conics, Conjugate diameters, Eutocius, Greek mathematics
Publication Number: 3422241
ISBN: 9781124209500
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