Archive for History of Exact Sciences

, Volume 35, Issue 4, pp 281–324 | Cite as

Archimedes' dimension of the circle: A view of the genesis of the extant text

  • Wilbur R. Knorr
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Bibliography of works cited

  1. Archimedes, Opera, ed. J. L. Heiberg, Leipzig, 2. ed., 3 vol., 1910–1915 (repr. Stuttgart, 1972)Google Scholar
  2. Becker, O., “Eudoxos-Studien I: Eine voreudoxische Proportionenlehre und ihre Spuren bei Aristoteles und Euklid,” Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, 1936, 3, Abt. B, pp. 311–333Google Scholar
  3. Becker, O., “Eudoxos-Studien IV: Das Prinzip des ausgeschlossenen Dritten in der griechischen Mathematik,” Quellen und Studien, 1936, 3, Abt. B, pp. 370–388Google Scholar
  4. M. Clagett, Archimedes in the Middle Ages, I: The Arabo-Latin Tradition, Madison, Wisc., 1964Google Scholar
  5. Dijksterhuis, E. J., Archimedes, Copenhagen, 1956 (New York, 1957)Google Scholar
  6. Euclid, Opera, ed. J. L. Heiberg, I–IV: Elemente, Leipzig, 1883–1885; V: “Prolegomena critica” and Scholia, 1888 (rev. ed., ed. E. S. Stamatis, Stuttgart, 5 vol., 1969–77)Google Scholar
  7. Eutocius, In Archimedem (see: Archimedes, Opera, vol. III)Google Scholar
  8. Heath, T. L., Apollonius of Perga: Treatise on Conic Sections, Cambridge, 1896Google Scholar
  9. Heath, T. L., A History of Greek Mathematics, 2 vol., Oxford, 1921Google Scholar
  10. Heath, T. L., The Thirteen Books of Euclid's Elements, 2. ed., 3 vol., Cambridge, 1926Google Scholar
  11. Heath, T. L., The Works of Archimedes ... with a Supplement, The Method of Archimedes, New York, n.d. (repr. of Cambridge ed. of 1897 with the supplement of 1912)Google Scholar
  12. Heiberg, J. L., “Philologische Studien zu griechischen Mathematikern, II: Ueber die Restitution der zwei Bücher des Archimedes πɛρι σϕαιρας και κυλινδρου”, Jahrbücher für classische Philologie, 1880, Suppl. 11, pp. 384–398Google Scholar
  13. Heiberg, J. L., “Philologische Studien ..., V: Interpolationen in den Schriften des Archimedes,” Jahrbücher ..., 1883, Suppl. 13, pp. 566–577Google Scholar
  14. Heiberg, J. L., “Prolegomena critica” to the Archimedean corpus (see Archimedes, Opera, vol. III)Google Scholar
  15. Heiberg, J. L., “Prolegomena critica” to the text of Euclid's Elements (see Euclid, Opera, vol. V)Google Scholar
  16. Heiberg, J. L., Quaestiones Archimedeae, Copenhagen, 1879Google Scholar
  17. Hero of Alexandria, Opera, III: Metrica, ed. H. Schöne, Leipzig, 1903Google Scholar
  18. Knorr, W. R., “Archimedes and the Elements: Proposal for a Revised Chronological Ordering of the Archimedean Corpus,” Archive for History of Exact Sciences, 1978, 19, pp. 211–290Google Scholar
  19. Knorr, W. R., “Archimedes and the Measurement of the Circle: A New Interpretation,” Archive for History of Exact Sciences, 1976, 15, pp. 125–140Google Scholar
  20. Knorr, W. R., “Archimedes and the pre-Euclidean Proportion Theory,” Archives internationales d'histoire des sciences, 1978, 28, pp. 183–244Google Scholar
  21. Knorr, W. R., “The Hyperbola-Construction in the Conics, Book II: Variations on a Theorem of Apollonius,” Centaurus, 1982, 25, pp. 253–291Google Scholar
  22. Knorr, W. R., “Infinity and Continuity: The Interaction of Mathematics and Philosophy in Antiquity,” in N. Kretzmann (ed.), Infinity and Continuity in Ancient and Medieval Thought, Ithaca, N.Y./London, 1982, pp. 112–145Google Scholar
  23. Kramer, E., “Hypatia,” Dictionary of Scientific Biography, ed. C. C. Gillispie, New York, VI, 1972, pp. 615–616Google Scholar
  24. Mogenet, J., l'Introduction à l'Almageste, Brussels, 1956Google Scholar
  25. Pappus, Collectionis quae supersunt, ed. F. Hultsch, 3 vol., Berlin, 1876–78Google Scholar
  26. Pappus, Commentary on Ptolemy's Book VI (see Rome, vol. 1)Google Scholar
  27. Proclus, In Primum Euclidis Elementorum Librum Commentarii, ed. G. Friedlein, Leipzig, 1873Google Scholar
  28. Rome, A., ed., Commentaires de Pappus et de Théon d'Alexandrie sur l'Almageste, 3 vol., (Studi e Testi, vol. 54, 72, 106), Rome and Vatican City, 1931/36/43Google Scholar
  29. Sato, T., “Archimedes' On the Measurement of a Circle, Proposition 1: An Attempt at a Reconstruction,” Japanese Studies in the History of Science, 1979, 18, pp. 83–99Google Scholar
  30. Schneider, I., Archimedes: Ingenieur, Naturwissenschaftler und Mathematiker, Darmstadt, 1979Google Scholar
  31. Simplicius, In Aristotelis de Caelo, ed. J. L. Heiberg, (Commentaria in Aristotelem Graeca, vol. VII), Berlin, 1894Google Scholar
  32. Theon, In Claudii Ptolemaei Magnam Constructionem Commentariorum Lib. XI, ap. J. Walder, Basel, 1538Google Scholar
  33. Theon, Commentary on Ptolemy's Book I (see Rome, vol. II)Google Scholar
  34. Toomer, G. J., ed. Diocles: On Burning Mirrors, Berlin/Heidelberg/New York, 1976Google Scholar
  35. Toomer, G. J., “The Mathematician Zenodorus,” Greek, Roman and Byzantine Studies, 1972, 13, pp. 177–192Google Scholar
  36. Toomer, G. J., “Theon of Alexandria,” in Dictionary of Scientific Biography, ed. C. C. Gillispie, New York, XIII, 1976, pp. 321–325Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Wilbur R. Knorr
    • 1
  1. 1.Program in the History of ScienceStanford University

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