A mathematical translation of Apollonius of Perga's Conics IV

by 1952- Rhodes, Diana L.

Apollonius of Perga was one of the greatest mathematicians of the ancient world. He is most famous for his work on the curves obtained from the intersection of a plane and a cone, written in eight books: Conics. This is an English translation of the fourth book of that work, which examines the intersections and tangencies of these curves. Ungari and Fried’s recently published book on Apollonius’ Conics criticized the use of anachronistic mathematical concepts and techniques in the interpretation and analysis of ancient texts. Mindful of that, the drawings herein illustrating each proposition were created using only the meeting point formulas and constructions found in, or directly obtainable from, the works of Apollonius himself or Euclid’s Elements. The first chapter provides a brief context for Apollonius and his work, as well as an introduction to the methods used in the translation and the computer-generated drawings. The second chapter outlines the key elements of the ancient mathematical foundations upon which Conics was written. The combination of ancient mathematical formulas and constructs with modern computer mathematical software led to a deeper analysis of the work itself; this analysis is detailed in the third chapter. The few constructions which were not immediately supplied by ancient texts are also presented here. Since Conics IV is a mathematical text, it builds on an already established logical framework. This framework is no longer well-known to the modern world. Therefore the setting-out and diagrams of earlier propositions required to support the given proofs are supplied in an appendix. In addition, the appendix contains an English translation of the alternate proofs given by Eutocius. A small list of defined terms and a short glossary of Greek words are also supplied. iii