Edmond Halley’s Reconstruction of the Lost Book of Apollonius’s Conics: Translation and Commentary (Sources and Studies in the History of Mathematics and Physical Sciences)

Apollonius’s Conics was one of the greatest works of advanced mathematics in antiquity. The work comprised eight books, of which four have come down to us in their original Greek and three in Arabic. By the time the Arabic translations were produced, the eighth book had already been lost. In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an edition of the Greek text of the Conics of Books I-IV, a translation into Latin from the Arabic versions of Books V-VII, and a reconstruction of Book VIII. The present work provides the first complete English translation of Halley’s reconstruction of Book VIII with supplementary notes on the text. It also contains 1) an introduction discussing aspects of Apollonius’s Conics 2) an investigation of Edmond Halley's understanding of the nature of his venture into ancient mathematics, and 3) an appendices giving a brief account of Apollonius’s approach to conic sections and his mathematical techniques. This book will be of interest to students and researchers interested in the history of ancient Greek mathematics and mathematics in the early modern period. Apollonius's Conics Was One Of The Greatest Works Of Advanced Mathematics In Antiquity. The Work Comprised Eight Books, Four Of Which Have Come Down To Us In Their Original Greek And Three In Arabic. By The Time The Arabic Translations Were Produced, The Eighth Book Had Already Been Lost. In 1710, Edmond Halley, Then Savilian Professor Of Geometry At Oxford, Produced An Edition Of The Greek Text Of The Conics Of Books I-iv, A Translation Into Latin From The Arabic Versions Of Books V-vii, And A Reconstruction Of Book Viii. Motivated By Such Questions As What Role Did Halley's Reconstruction Play In The Mathematical World Of The Late 17th And Early 18th Century? And What Did Halley See Himself Learning From Engaging With Mathematicians Such As Apollonius?, Michael Fried's Work Provides The First Complete english Translation Of Halley's Reconstruction Of Book Viii With supplementary Notes On The Text. the Volume Also Contains An Introduction Discussing Aspects Of Apollonius's Conics, An Investigation Of Edmond Halley's Understanding Of the Nature Of His Venture Into Ancient Mathematics, And Appendices Giving Brief Accounts Of Apollonius's Approach To Conic Sections And His Mathematical Techniques. This Book Will Be Of Great Interest To Students And Researchers Interested In The History Of ancient greek mathematics And Mathematics In The Early Modern Period. I. Introduction -- 1. Edmond Halley: Ancient And Modern -- 2. Apollonius's Conics -- 3. The Path To Halley -- 4. Halley's General Strategy For Reconstructing Conics, Book Viii -- 5. Halley's Dialogue With The Past.-6. A Note On The Translation-ii. Apollonius Of Perga's On Conics: Book Eight Restored -- Iii.synopsis And Appendices.-synopsis Of The Contents Of Halley's Conics, Book Viii.-appendix 1: Terminology And Notions From Greek Mathematics.-appendix 2: Hippocrates' First Quadrature Of A Lune.-references.-index. Michael N. Fried. Includes Bibliographical References (p. 127-129) And Index. Apollonius ́ s Conics was one of the greatest works of advanced mathematics in antiquity.℗ The work comprised eight books, four of which have come down to us in their original Greek and three in Arabic.℗ By the time the Arabic translations were produced, the eighth book had already been lost. In 1710, Edmond Halley, then Savilian Professor of Geometry at Oxford, produced an edition of the Greek text of the Conics of Books I-IV, a translation into Latin from the Arabic versions of Books V-VII, and a reconstruction of Book VIII.℗ ℗ Motivated by such questions as what role did Halley's reconstruction play in the mathematical world of the late 17th and early 18th century? and what did Halley see himself learning from engaging with mathematicians such as Apollonius?, Michael Fried ́ s work provides the first complete℗ English translation of Halley ́ s reconstruction of Book VIII with℗ supplementary notes on the text. ℗ The volume also contains an introduction discussing aspects of Apollonius ́ s Conics, an investigation of Edmond Halley's understanding of℗ the nature of his venture into ancient mathematics, and appendices giving brief accounts of Apollonius ́ s approach to conic sections and his mathematical techniques. This book will be of great interest to students and researchers interested in the history of℗ ancient℗ Greek℗ mathematics and mathematics in the early modern period.℗ Front Matter....Pages i-x Front Matter....Pages 1-1 Chapter 1 Edmond Halley: Ancient and Modern....Pages 3-6 Chapter 2 Apollonius’s Conics ....Pages 7-11 Chapter 3 The Path to Halley....Pages 13-15 Chapter 4 Halley’s General Strategy for Reconstructing Conics , Book VIII....Pages 17-21 Chapter 5 Halley’s Dialogue with the Past....Pages 23-31 Chapter 6 A Note on the Translation....Pages 33-34 Front Matter....Pages 35-35 Apollonius of Perga’s on Conics : Book Eight Restored or the Book on Determinate Problems Conjectured....Pages 37-113 Front Matter....Pages 115-115 Synopsis of the Contents of Halley’s Conics , Book VIII....Pages 117-126 Back Matter....Pages 127-132 Comprised of eight books, Apollonius's Conics was one of the greatest works of advanced mathematics in antiquity. This volume provides the first complete English translation of Edmond Halley's reconstruction of Book VIII with supplementary notes on the text.