Document Type


Date of Degree

Summer 2010

Degree Name

PhD (Doctor of Philosophy)

Degree In


First Advisor

Anderson, Daniel D

First Committee Member

Gibson, Craig A

Second Committee Member

Muhly, Paul S

Third Committee Member

Jorgensen, Palle E T

Fourth Committee Member

Kutzko, Philip C


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

Additional Files

archytas.pde (5 kB)
Archytas solution visualization program

eratosthenes.pde (1 kB)
Eratosthenes solution visualization program

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Mathematics Commons