Date of Degree

2010

Document Type

PhD diss.

Degree Name

PhD (Doctor of Philosophy)

Department

Mathematics

First Advisor

Daniel D. Anderson

Abstract

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.

Pages

ix, 176

Bibliography

175-176

Copyright

Copyright 2010 Colin Bryan Powell McKinney

archytas.pde (5 kB)
Archytas solution visualization program

eratosthenes.pde (1 kB)
Eratosthenes solution visualization program

Additional Files

archytas.pde (5 kB)
Archytas solution visualization program

eratosthenes.pde (1 kB)
Eratosthenes solution visualization program

Included in

Mathematics Commons

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