Menelaus' ›Spherics‹ : Early Translation and Al-Māhānī / Al-Harawī's Version

Despite Its Importance In The History Of Ancient Science, Menelaus’ Spherics Is Still By And Large Unknown. This Treatise, Which Lies At The Foundation Of Spherical Geometry, Is Lost In Greek But Has Been Preserved In Its Arabic Versions. The Reader Will Find Here, For The First Time Edited And Translated Into English, The Essentials Of This Tradition, Namely: A Fragment Of An Early Arabic Translation And The First Arabic Redaction Of The Spherics Composed By Al-māhānī /al-harawī, Together With A Historical And Mathematical Study Of Menelaus’ Treatise. With This Book, A New And Important Part Of The Greek And Arabic Legacy To The History Of Mathematics Comes To Light. This Book Will Be An Indispensable Acquisition For Any Reader Interested In The History Of Ancient Geometry And Science And, More Generally, In Greek And Arabic Science And Culture.-- Menelaus And His Writings -- The Redaction Of The Spherics By Al-māhānī And Al-harawī -- An Eleventh Century Witness Of The Translations Of The Spherics: Ibn Hūd-- Edition And Translation Of Menelaus' Propositions Quoted In Ibn Hūd's Encyclopedia -- The Mathematical Content Of The Spherics -- The Propositions -- The Spherics: A Fragment Of An Ancient Translation -- The Spherics: The Version Of Al-māhānī And Al-harawī -- Postface: Spherical Geometry: A Few Markers -- Bibliography -- Arabic-english Glossary. By Roshdi Rashed And Athanase Papadopoulos. Includes Bibliographical References (pages 827-838) And Indexes. Arabic Text With English Translation On Facing Pages; Critical Matter In English.

Despite its importance in the history of Ancient science, Menelaus’ Spherics is still by and large unknown. This treatise, which lies at the foundation of spherical geometry, is lost in Greek but has been preserved in its Arabic versions. The reader will find here, for the first time edited and translated into English, the essentials of this tradition, namely: a fragment of an early Arabic translation and the first Arabic redaction of the Spherics composed by al-Māhānī /al-Harawī, together with a historical and mathematical study of Menelaus’ treatise. With this book, a new and important part of the Greek and Arabic legacy to the history of mathematics comes to light. This book will be an indispensable acquisition for any reader interested in the history of Ancient geometry and science and, more generally, in Greek and Arabic science and culture.

FOREWORD 5 TABLE OF CONTENTS 7 INTRODUCTION 11 PART I 17 CHAPTER 1: MENELAUS AND HIS WRITINGS 17 CHAPTER 2: THE REDACTION OF THE SPHERICS BY AL-MĀHĀNĪ AND AL-HARAWĪ 37 CHAPTER 3: AN ELEVENTH-CENTURY WITNESS OF THE TRANSLATIONS OF THE SPHERICS: IBN HŪD 87 EDITION AND TRANSLATION OF MENELAUS’ PROPOSITIONS QUOTED IN IBN HŪD’S ENCYCLOPEDIA 105 PART II: MATHEMATICAL COMMENTARY 139 CHAPTER 1: THE MATHEMATICAL CONTENT OF THE SPHERICS 139 CHAPTER 2: THE PROPOSITIONS 153 PART III: TEXTS AND TRANSLATIONS 413 CHAPTER 1: THE SPHERICS: A FRAGMENT OF AN ANCIENT TRANSLATION 413 TEXT AND TRANSLATION: Menelaus’ Treatise on the Spherics 499 CHAPTER 2: THE SPHERICS: THE VERSION OF AL-MĀHĀNĪ AND AL-HARAWĪ 499 TEXT AND TRANSLATION: The Treatise of Menelaus on the Spherical Figures 793 POSTFACE: SPHERICAL GEOMETRY: A FEW MARKERS 793 BIBLIOGRAPHY 841 ARABIC-ENGLISH GLOSSARY 853 INDEXES 879 "....Menelaus' treatise, the Spherics, is a landmark in the history of classical mathematics. Before the Greek original was lost, this work, which is at the foundations of spherical geometry, and in fact, the first work on non-Euclidean geometry, was translated several times into Arabic, between the 9th and the 10th century....Starting from the 11th century, the Arabic translations of the Spherics became the subject of rectifications and commentaries by several mathematicians. Thus, al-Māhānī (fl. 853-66) rectified the second Arabic translation which was probably due to Isḥāq ibn Ḥunayb (d. 910-11), a rectification which was revised in the following century by al-Harawī."--Foreword, p. [v] English translation of early text on mathematics of spheres, from approximately the 2nd century. Based on Arabic translations by al-Mahani, and al-Harawi