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Conjugate diameters : Apollonius of Perga and Eutocius of Ascalon

Author: Colin Bryan Powell McKinney; Eutocius, of Ascalon.; Daniel D Anderson; University of Iowa. Department of Mathematics.
Publisher: [Iowa City, Iowa] : University of Iowa, 2010.
Dissertation: Ph. D. thesis University of Iowa 2010.
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : eBook   Computer File : English
Database:WorldCat
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  Read more...
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Named Person: Archimedes.; Apollonius, of Perga.; Eutocius, of Ascalon.; Apollonius, of Perga.; Archimedes.; Eutocius, of Ascalon.
Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Colin Bryan Powell McKinney; Eutocius, of Ascalon.; Daniel D Anderson; University of Iowa. Department of Mathematics.
OCLC Number: 678634416
Language Note: Includes Eustocius's commentary on Apollonius's work on conics in both original Greek and English translation.
Notes: Thesis supervisor: Daniel D. Anderson.
Description: ix, 176 pages : illustrations
Details: Mode of access: World Wide Web.; System requirements: Adobe Reader.
Responsibility: by Colin Bryan Powell McKinney.
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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.

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