By Michael N. Fried

Apollonius’s Conics was once one of many maximum works of complex 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 e-book 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 comprises 1) an advent discussing facets of Apollonius’s Conics 2) an research of Edmond Halley's figuring out of the character of his enterprise into historical arithmetic, and three) an appendices giving a short account of Apollonius’s method of conic sections and his mathematical techniques.

This publication might be of curiosity to scholars and researchers attracted to the background of historical 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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In the preface to the reconstruction, Halley recounts Aldrich’s observation that “. in Pappus’ Mathematical Collection, [Pappus] himself passed on lemmas serving [what] was to be demonstrated in the seventh and the eighth book of the Conics at the same time; whereas in the other books, different [lemmas] to the different [books] are provided. ” Surely, by the time Halley wrote this, he would have known the connection between the contents of Books VII and VIII which Apollonius himself points out in the preface to Book VII, as described above.

38 The story of Golius and the Ban¯ u M¯us¯a text is told in greater detail by Toomer (op. , pp. 113–117. Golius’s manuscript of the Ban¯u M¯us¯a text is now in the Bodleian Library, Oxford shelved as Marsh 667, after Narcissus Marsh who sponsored its purchase in Leiden in 1696 and who left it to the Bodleian Library as part of his bequest (see Toomer, op. , pp. lxxxv–lxxxvii). N. 1007/978-1-4614-0146-9 3, © Springer Science+Business Media, LLC 2011 13 14 3 The Path to Halley at Oxford (1673–1691), made a copy of the manuscript in 1668 and took some initial steps to translate the text.

He was, as I have said, a mediator between the ancient and the modern mathematical world, giving the former all its historical mathematical due. 69 That is, a sight used with the naked eye. Later Halley’s relations with Hevelius soured somewhat as did Halley’s enthusiasm for Hevelius’s techniques. See Ronan (1969), chap. 4, and Cook (1998), chap. 4 for detailed accounts of this chapter in Halley’s career. Some of Halley’s correspondence with Hevelius can be found in MacPike (1932). 70 Chapter 6 A Note on the Translation Someone remarked to me once that Ver Eecke’s French translations of Apollonius, Pappus, and Diophantus are so well done the original Greek text can almost be reconstructed from them.

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