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Textual Studies in Ancient and Medieval Geometry

  • Book
  • © 1989

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Authors:
  1. Wilbur Richard Knorr

    1. Program in the History of Science, Stanford University, Stanford, USA

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Table of contents (28 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Introduction: Philologist, Heal Thy Text

    1. Introduction: Philologist, Heal Thy Text

      • Wilbur Richard Knorr
      Pages 1-8

  3. Ancient Texts on Geometric Problems

    1. Front Matter

      Pages 9-9
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    2. The Hero-Apollonius Method of Cube Duplication

      • Wilbur Richard Knorr
      Pages 11-28

    3. The Hero–Apollonius Lemma in Nicomedes and Euclid

      • Wilbur Richard Knorr
      Pages 29-40

    4. The Philonian Method of Cube Duplication

      • Wilbur Richard Knorr
      Pages 41-61

    5. Pappus’ Texts on Cube Duplication

      • Wilbur Richard Knorr
      Pages 63-76

    6. Eutocius’ Anthology of Cube Duplications

      • Wilbur Richard Knorr
      Pages 77-129

    7. Eutocius’ Text of Eratosthenes: A Thesis of U. von Wilamowitz

      • Wilbur Richard Knorr
      Pages 131-153

    8. On Eutocius: A Thesis of J. Mogenet

      • Wilbur Richard Knorr
      Pages 155-211

    9. Angle Trisections in Pappus and Arabic Parallels

      • Wilbur Richard Knorr
      Pages 213-224

    10. The Ancient Commentators and Their Methods: Pappus and Eutocius

      • Wilbur Richard Knorr
      Pages 225-245

  4. Arabic Geometric Texts and Their Ancient Sources

    1. Front Matter

      Pages 247-249
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    2. The Cube Duplication by Abū Bakr al-Harawī

      • Wilbur Richard Knorr
      Pages 251-265

    3. The Angle Trisection by Ahmad ibn Müsä

      • Wilbur Richard Knorr
      Pages 267-275

    4. The Angle Trisection by Thābit ibn Qurra

      • Wilbur Richard Knorr
      Pages 277-291

    5. The Angle Trisection by al-Sijzī

      • Wilbur Richard Knorr
      Pages 293-300

    6. The Cube Duplication and Angle Trisection by Abū Sahl al-Qūhī

      • Wilbur Richard Knorr
      Pages 301-309

    7. The Cube Duplication by Abū Jacfar in the Manner of Nicomedes

      • Wilbur Richard Knorr
      Pages 311-372

  5. The Textual Tradition of Archimedes’

    1. Front Matter

      Pages 373-373
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Keywords

About this book

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.

Authors and Affiliations

  • Program in the History of Science, Stanford University, Stanford, USA

    Wilbur Richard Knorr

Bibliographic Information

  • Book Title: Textual Studies in Ancient and Medieval Geometry

  • Authors: Wilbur Richard Knorr

  • DOI: https://doi.org/10.1007/978-1-4612-3690-0

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1989

  • Softcover ISBN: 978-1-4612-8213-6Published: 30 September 2011

  • eBook ISBN: 978-1-4612-3690-0Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: 864

  • Topics: Geometry, History of Mathematical Sciences

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