Textual Studies in Ancient and Medieval Geometry

For textual studies relating to the ancient mathematical corpus the efforts by the Danish philologist, 1. L. Heiberg (1854-1928), are especially significant. Beginning with his doctoral dissertation, Quaestiones Archimedeae (Copen­ hagen, 1879), Heiberg produced an astonishing series of editions and critical studies that remain the foundation of scholarship on Greek mathematical 4 science. For comprehensiveness and accuracy, his editions are exemplary. In his textual studies, as also in the prolegomena to his editions, he carefully described the extant evidence, organized the manuscripts into stemmata, and drew out the implications for the state of the text. 5 With regard to his Archimedean work, Heiberg sometimes betrayed signs of the philologist's occupational disease - the tendency to rewrite a text deemed on subjective grounds to be unworthy. 6 But he did so less often than his prominent 7 contemporaries, and not as to detract appreciably from the value of his editions. In examining textual questions bearing on the Archimedean corpus, he attempted to exploit as much as possible evidence from the ancient commentators, and in some instances from the medieval translations. It is here that opportunities abound for new work, extending, and in some instances superseding, Heiberg's findings. For at his time the availability of the medieval materials was limited. In recent years Marshall Clagett has completed a mammoth critical edition of the medieval Latin tradition of Archimedes,8 while the bibliographical instruments for the Arabic tradition are in good order thanks to the work of Fuat Sezgin.

Table of Contents:
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.- 4 Pappus’ Texts on Cube Duplication.- 5 Eutocius’ Anthology of Cube Duplications.- 6 Eutocius’ Text of Eratosthenes: A Thesis of U. von Wilamowitz.- 7 On Eutocius: A Thesis of J. Mogenet.- 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.- III The Textual Tradition of Archimedes’: Dimension of the Circle.- 1 Versions in the Ancient Commentators.- 2 Origin of the Extant Text of the Dimension of the Circle.- 3 The Medieval Tradition of Dimension of the Circle, Prop. 1.- 4 Versions of Dimension of the Circle, Props. 2 and 3.- 5 Lost Propositions of the Archimedean Prototype.- 6 Eutocius’ Text of Dimension of the Circle.- 7 Arabic Elaborations of the Dimension of the Circle.- 8 The Latin Tradition: De curvis superficiebus.- 9 The Latin Tradition: De quadratura circuli.- 10 The Anonymous Tract On Isoperimetric Figures.- 11 On Hypatia of Alexandria.- 12 The History of a Text: Tradition, Time and Opportunity.