Edmond Halley’s Reconstruction of the Lost Book of by Michael N. Fried

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 all the way 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 variation 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 publication 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 comprises 1) an creation discussing elements of Apollonius’s Conics 2) an research of Edmond Halley's realizing of the character of his enterprise into historic arithmetic, and three) an appendices giving a quick account of Apollonius’s method of conic sections and his mathematical techniques.

This ebook may be of curiosity to scholars and researchers attracted to the historical past of historic Greek arithmetic and arithmetic within the early sleek period.

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Additional info for Edmond Halley’s Reconstruction of the Lost Book of Apollonius’s Conics: Translation and Commentary

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Suttle (1940). E. G. W. Bill (1988) also points out Aldrich’s interest in classical mathematics and stresses that this was a pattern at Christ Church: “Perhaps above all the Deans of Christ Church encouraged the study of mathematics. John Fell, though not generally reputed a mathematician, contributed a preface in 1676 to John Wallis’s edition of Archimedes and Eutocius in which he spoke of the disappointing reception of the proposal to issue an edition of Veteres Mathematici. His successor Aldrich was described when a tutor as ’a great mathematician of our house’, and at the time of his death had an edition of Euclid in the press.

It is apparent that Halley saw these formulations, which I have translated, respectively, as “the square on the sum of the given diameters” and “the square of the sum,” as interchangeable. The Greek phrase unambiguously refers to a geometrical situation where a square is conceived as built on a certain line. Thus, while the Greek phrase may be much abbreviated, the word apo is always present. N. 71 On this reading, one might conclude that, despite Halley’s general sensitivity to the difference between the Greek geometrical thinking and the modern algebraic thinking, his own modern mind sometimes got the better of him.

The latter does not seem very likely. Halley’s approach to the works of Apollonius then was truly his own, even if it was in perfect sympathy with Gregory’s. 68 In particular, concerning the positions of the bright stars Aldebaran, Sirius, and Arcturus. 66 5 Halley’s Dialogue with the Past 31 and of course in his cometary work. Even here, though, the seriousness with which Halley used historical data shows the seriousness with which he viewed the collectors of those data. But the past, for Halley, was not only a repository of data or, as it might have been for an earlier figure such as Ibn al-Haytham, a source of lost knowledge: it was also a font of intelligent treatments of problems and ideas by thoughtful people.

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