This is the first edition of the original text of the advanced part of the most important work on conic sections written in antiquity and one of the most influential works in mathematics. It is also the first literal English translation of it ever to be published. The purpose of the work is to make available, to those interested in the history of science and to mathematicians, a version of the work as close to the original as possible. This part of Apollonius' Conics is lost in the original Greek, and only an Arabic translation made in the 9th century survives. This text has never been published previously, and all "editions" of this part of Apollonius' work are based on the Latin translation from the Arabic published by Edmund Halley in 1710, which suffers from Halley's insufficient knowledge of Arabic and his use of a single manuscript. The present edition is based on all known manuscripts. Its other improvements over Halley's edition are: 1) the Arabic text with a full critical apparatus; 2) an accurate English translation (until now only a loose paraphrase, based on Halley's translation, has been available in English); 3) a commentary to elucidate both mathematical and historical difficulties. This book will replace Halley's edition and all its derivatives as the standard edition of this part of Apollonius' work.
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4 Mathematical Summary
5 The Ancient Mathematical Background
6 other sections not shown
angles Apollonius axes Banu Musa Book closer cone conic section Conies conjugate diameters constructed on KB corr curve diameter KB diameter to latus draw line drawn from point ellipse equals the ratio figure constructed Furthermore H supp half the latus Halley hence hyperbola ibn al-Haytham J^JI J&JI j£iJI Jaill JiiJI jJJI jLaJI JLiJI JLill join line JSjJI latera latus rec latus rectum less LiJI line AA line equal major axis minima drawn minimum line drawn minor axis parabola parallel to line perpendicular Proof propositions proven in Prop quadrant ratio of AP ratio of transverse rectangle constructed rectangle mentioned section ABr segment sides similar structed tangent theorem transverse diameter triangles vertex