Date of Degree
PhD (Doctor of Philosophy)
Daniel D. Anderson
First Committee Member
Craig A. Gibson
Second Committee Member
Paul S. Muhly
Third Committee Member
Palle E. T. Jorgensen
Fourth Committee Member
Philip C. Kutzko
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.
Apollonius, Archimedes, conic sections, Conics, Eutocius, Greek mathematics
ix, 176 pages
Includes bibliographical references (pages 175-176).
Copyright 2010 Colin Bryan Powell McKinney
McKinney, Colin Bryan Powell. "Conjugate diameters: Apollonius of Perga and Eutocius of Ascalon." PhD (Doctor of Philosophy) thesis, University of Iowa, 2010.
Additional Filesarchytas.pde (5 kB)
Archytas solution visualization program
eratosthenes.pde (1 kB)
Eratosthenes solution visualization program