By Michael N. Fried
Apollonius’s Conics was once one of many maximum works of complicated arithmetic in antiquity. The paintings comprised 8 books, of which 4 have come right down to us of their unique Greek and 3 in Arabic. by the point the Arabic translations have been produced, the 8th ebook had already been misplaced. In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an version of the Greek textual content of the Conics of Books I-IV, a translation into Latin from the Arabic models of Books V-VII, and a reconstruction of ebook VIII.
The current paintings offers the 1st whole English translation of Halley’s reconstruction of booklet VIII with supplementary notes at the textual content. It additionally includes 1) an advent discussing points of Apollonius’s Conics 2) an research of Edmond Halley's figuring out of the character of his enterprise into old arithmetic, and three) an appendices giving a short account of Apollonius’s method of conic sections and his mathematical techniques.
This publication could be of curiosity to scholars and researchers drawn to the historical past of historical Greek arithmetic and arithmetic within the early smooth period.
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Additional resources for Edmond Halley’s Reconstruction of the Lost Book of Apollonius’s Conics: Translation and Commentary
41 Similarly, Savilian astronomy professors were to give due attention to classical texts; they were, for example, required to teach Ptolemy’s Almagest. So when Henry Aldrich, Dean of Christ Church College Oxford, persuaded the newly elected Savilian professor of geometry, namely, Halley, to work with David Gregory on an edition of Apollonius, he was not only acting out of a keen interest in mathematics—Aldrich was a deeply interested and well-informed reader of mathematics, especially of classical mathematics42—but also out of an understanding of the requirements of Halley’s position.
And one could even accept this identity as a historian without denying Halley’s identity as a mathematician. For, certainly, while his reconstruction demanded a considerable degree of mathematical ingenuity, such as one might expect from the new Savilian professor of geometry, one need not assume the reconstruction was only a pretense for Halley to exhibit his mathematical prowess or to explore new mathematical themes, Apollonian or not, that might flow from Conics, Book VII. Yet the fact remains that Halley did come to the project as a mathematician and scientist and did so willingly, as I have already stressed.
My own parenthetical remarks, additions, and clarifications are contained by square parentheses. There are two deviations from this. ” In the text itself this appears thus: “Propositio I. ” (2) I have included the original Latin word or phrase in rounded parentheses where it seemed to me that the English translation did not catch entirely the nuances of Halley’s Latin. As for the diagrams, except for the extra smoothness and straightness one can achieve with modern technology, the diagrams below were meant to be entirely faithful to those in the 1710 edition.