Ebook: 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.

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Content:
Front Matter....Pages i-xvii
Introduction: Philologist, Heal Thy Text....Pages 1-8
Front Matter....Pages 9-9
The Hero-Apollonius Method of Cube Duplication....Pages 11-28
The Hero–Apollonius Lemma in Nicomedes and Euclid....Pages 29-40
The Philonian Method of Cube Duplication....Pages 41-61
Pappus’ Texts on Cube Duplication....Pages 63-76
Eutocius’ Anthology of Cube Duplications....Pages 77-129
Eutocius’ Text of Eratosthenes: A Thesis of U. von Wilamowitz....Pages 131-153
On Eutocius: A Thesis of J. Mogenet....Pages 155-211
Angle Trisections in Pappus and Arabic Parallels....Pages 213-224
The Ancient Commentators and Their Methods: Pappus and Eutocius....Pages 225-245
Front Matter....Pages 247-249
The Cube Duplication by Ab? Bakr al-Haraw?....Pages 251-265
The Angle Trisection by Ahmad ibn M?s?....Pages 267-275
The Angle Trisection by Th?bit ibn Qurra....Pages 277-291
The Angle Trisection by al-Sijz?....Pages 293-300
The Cube Duplication and Angle Trisection by Ab? Sahl al-Q?h?....Pages 301-309
The Cube Duplication by Ab? Jacfar in the Manner of Nicomedes....Pages 311-372
Front Matter....Pages 373-373
Versions in the Ancient Commentators....Pages 375-400
The Medieval Tradition of Dimension of the Circle, Prop. 1....Pages 401-419
Versions of Dimension of the Circle, Props. 2 and 3....Pages 421-475
Front Matter....Pages 477-494
Lost Propositions of the Archimedean Prototype....Pages 373-373
On Hypatia of Alexandria....Pages 495-512
The History of a Text: Tradition, Time and Opportunity....Pages 513-534
Back Matter....Pages 535-594
....Pages 595-615