The proof of Proposition 9 in Archimedes' On the Sphere and the Cylinder, Book i, contains an unproved statement that has been referred to as a lacuna. Most editors and experts in Archimedean texts have agreed on the existence of this gap and have offered different proofs for the statement, some of them with incomplete or even incorrect arguments. In this paper, I offer arguments of a mathematical, historical, and textual nature that show that it is not necessary to assume the presence of any gap in the text.
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Euclid, ;
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Examen des traités Sur la section du cylindre et Sur la section du cône de Sérénos d'Antinoé à la lumière de la tradition de l'optique géométrique ancienne
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The Treatise “On the Section of a Cylinder” of Serenus of Antinoeia and the Apollonian Tradition
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Netz, Reviel;
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Zhao, Ji-wei;
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On the orientation of Archimedes' method for mathematical discovery
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Cuomo, Serafina;
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Arithmetic and Geometry in Ancient Rome: Surveyors, Intellectuals, and Poets
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Reviel Netz;
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Archimedes, ;
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Lee, Alexander;
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Goals and Scope of the Archimedes Palimpsest Transcriptions
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Netz, Reviel;
Saito, Ken;
Tchernetska, Natalie;
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A New Reading of Method Proposition 14: Preliminary Evidence from the Archimedes Palimpsest (Part 1)
(/isis/citation/CBB000102363/)
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Netz, Reviel;
Saito, Ken;
Tchernetska, Natalie;
(2002)
A New Reading of Method Proposition 14: Preliminary Evidence from the Archimedes Palimpsest (Part 2)
(/isis/citation/CBB000202126/)
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