Article ID: CBB001022152

A “Lacuna” in Proposition 9 of Archimedes' On the Sphere and the Cylinder, Book I (2010)

unapi

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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Authors & Contributors
Netz, Reviel
Saito, Ken
Nikolantonakis, Konstantinos
Archimedes
Zhao, Jiwei
Unguru, Sabetai
Journals
Sciamvs: Sources and Commentaries in Exact Sciences
Sudhoffs Archiv: Zeitschrift fuer Wissenschaftsgeschichte
Studies in History and Philosophy of Science
Nuncius: Annali di Storia della Scienza
Notices of the American Mathematical Society
Journal of Dialectics of Nature
Publishers
Walter de Gruyter
Presses Universitaires de France
Kyoritsushuppan
Fundació Bernat Metge
Da Capo Press
Real Sociedad Matemática Española
Concepts
Mathematics
Geometry
Solid geometry
Translations
Arab/Islamic world, civilization and culture
Spherical geometry
People
Archimedes
Euclid
Apollonius, of Perga
Serenus, Antinoensis
Theodosius
Ptolemy, Claudius
Time Periods
Ancient
Medieval
Neolithic period
Renaissance
3rd century
Places
Greece
Rome (Italy)
Scotland
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