Textual Studies in Ancient and Medieval Geometry

Introduction: Philologist, Heal Thy Text.- I Ancient Texts on Geometric Problems.- 1 The Hero-Apollonius Method of Cube Duplication.- 2 The Hero-Apollonius Lemma in Nicomedes and Euclid.- 3 The Philonian Method of Cube Duplication.- Appendix: Philoponus' Account of Cube Duplication.- 4 Pappus' Texts on Cube Duplication.- 5 Eutocius' Anthology of Cube Duplications.- The Platonic Construction.- The Methods of Hero, Philo, and Apollonius.- The Method of Diodes.- The Methods of Pappus and Sporus.- The Method of Menaechmus.- The Method of Archytas.- The Methods of Eratosthenes and Nicomedes.- Summary.- 6 Eutocius' Text of Eratosthenes: A Thesis of U. von Wilamowitz.- Appendix: Two Accounts of Eratosthenes' Method.- 7 On Eutocius: A Thesis of J. Mogenet.- Appendix: Four Texts on Compound Ratio.- 8 Angle Trisections in Pappus and Arabic Parallels.- 9 The Ancient Commentators and Their Methods: Pappus and Eutocius.- II Arabic Geometric Texts and Their Ancient Sources.- A The Cube Duplication by Abû Bakr al-Harawî.- B The Angle Trisection by Ahmad ibn Mûsâ.- C The Angle Trisection by Thâbit ibn Qurra.- D The Angle Trisection by al-Sijzî.- E The Cube Duplication and Angle Trisection by Abû Sahl al-Qûhî.- F The Cube Duplication by Abû Jacfar in the Manner of Nicomedes.- Appendix: Texts in Transcription.- Facsimile.- III The Textual Tradition of Archimedes': Dimension of the Circle.- 1 Versions in the Ancient Commentators.- Appendix I. Archimedes' Circle Theorem in Pappus and Theon: Translations and Facsimiles.- II. Pappus' Text of the Sector Theorem: Translation and Facsimile.- 2 Origin of the Extant Text of the Dimension of the Circle.- Appendix I. The Extant Greek Text of Dimension of the Circle: Translation and Facsimile.- II. Theon's Lemma to the Circle Theorem: Translation and Facsimile.- 3 The Medieval Tradition of Dimension of the Circle, Prop. 1.- Appendix I. Translation from the Arabic Text.- II. Variant Readings.- III. On the Arabic and Hebrew Translators.- Facsimiles of the Arabic, Hebrew and Latin Texts.- 4 Versions of Dimension of the Circle, Props. 2 and 3.- Appendix I. The Ancient and Medieval Texts of Props. 2 and 3.- II. Variants in the Medieval Versions.- 5 Lost Propositions of the Archimedean Prototype.- 6 Eutocius' Text of Dimension of the Circle.- Appendix: Extracts from Eutocius and Theon.- 7 Arabic Elaborations of the Dimension of the Circle.- Banu Musa.- Abu '1-Rashid.- Al-Tusi.- I. The Version of Abu 'l-Rashid: Translation and Facsimile.- II. The Version of al-Tusi: Translation and Facsimile.- 8 The Latin Tradition: De curvis superficiebus.- 9 The Latin Tradition: De quadratura circuli.- The Florence Version.- The Cambridge Version.- The Naples Version.- The Gordanus Version.- The Munich Version.- The Vatican, or ps.-Bradwardine, Version.- The Abbreviated Version.- The Version by Albert of Saxony.- The Corpus Christi Version.- The Glasgow Version.- Synthesis.- 10 The Anonymous Tract On Isoperimetric Figures.- Appendix: Propositions of the Anonymous Tract.- 11 On Hypatia of Alexandria.- Appendix I. Four Accounts of Division from Theon's Commentary on Ptolemy.- II. Pappus' Method of Long Division.- Facsimiles from Theon.- 12 The History of a Text: Tradition, Time and Opportunity.