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The Cube Duplication by Abū Jacfar in the Manner of Nicomedes

In: Textual Studies in Ancient and Medieval Geometry

Author

Listed:
  • Wilbur Richard Knorr

    (Stanford University, Program in the History of Science)

Abstract

The text of the cube duplication by Abū Jacfar (here denoted as F) is taken from Bibl. nat. ms. arab. (Slane) 2457, no. 47 (f. 198v–199r). As the author asserts, the construction in its opening section is based on the method of Nicomedes, as reported by Eutocius; the latter had already been rendered into Arabic by Thabit ibn Qurra, as part of his translation of Archimedes’ Sphere and Cylinder and Eutocius’ commentary on that work. For comparison’s sake, I insert after this section of Abū Jacfar’s text the analogous portions of Eutocius’ text, first in the version of Thābit (taken from Escorial ms. 960, f. 30r–31r; denoted here as F2), then directly from the Greek (Arehimedis Opera, ed. Heiberg, III, pp. 104–106; denoted as F3). In the following section of his text, Abū Jacfar shows how a method via hyperbola effects the neusis that Nicomedes works out via the conchoid; this may be compared with the auxiliary conic construction introduced in the angle trisections by Pappus and Thābit (see chaps. B and C). Abū Jacfar closes with the demonstration of the cube duplication; I here display this in parallel with the comparable portion of the Arabic version of Eutocius (F2), differing in only trivial respects from the Greek (F3).

Suggested Citation

  • Wilbur Richard Knorr, 1989. "The Cube Duplication by Abū Jacfar in the Manner of Nicomedes," Springer Books, in: Textual Studies in Ancient and Medieval Geometry, chapter 0, pages 311-372, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3690-0_16
    DOI: 10.1007/978-1-4612-3690-0_16
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