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Angle Trisections in Pappus and Arabic Parallels

In: Textual Studies in Ancient and Medieval Geometry

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  • Wilbur Richard Knorr

    (Stanford University, Program in the History of Science)

Abstract

In Book IV of the Collection Pappus presents a series of methods for trisecting the given angle. In several respects this is a correlate to his survey of cube duplications in Book III. Both sections begin with the same preface on the tripartite classification of problems, although the two accounts diverge on certain interpolated details.1 Most notably, in the version in Book III (chap. 7) the “ancient (palaioi) geometers” were not able to solve the cube duplication “geometrically” (geometrikôi logôi) because it is a solid problem, and they had difficulty drawing the conic sections in a plane; but they met success by resorting to mechanical means.2 In Book IV (chap. 36) the “former (proteroi) geometers” could not solve the angle trisection “by means of planes” (dia tôn epipedôn), because it is a solid problem and they were not well versed in the conic sections; but later they found solutions by means of conics.3

Suggested Citation

  • Wilbur Richard Knorr, 1989. "Angle Trisections in Pappus and Arabic Parallels," Springer Books, in: Textual Studies in Ancient and Medieval Geometry, chapter 0, pages 213-224, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3690-0_9
    DOI: 10.1007/978-1-4612-3690-0_9
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