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
Archimedes
Nikolantonakis, Konstantinos
Saito, Ken
Tchernetska, Natalie
Acerbi, Fabio
Journals
Sciamvs: Sources and Commentaries in Exact Sciences
British Society for the History of Mathematics Bulletin
Actes d’Història de la Ciència i de la Tècnica
Apeiron: Journal for Ancient Philosophy and Science
Archive for History of Exact Sciences
Archives Internationales d'Histoire des Sciences
Publishers
Cambridge University Press
Fundació Bernat Metge
Presses Universitaires de France
Published for the Walters Art Museum by Cambridge University Press
Walter de Gruyter
Concepts
Mathematics
Geometry
Solid geometry
Translations
Arab/Islamic world, civilization and culture
Spherical geometry
People
Archimedes
Apollonius, of Perga
Euclid
Menelaos of Alexandria
Serenus, Antinoensis
Archytas of Tarentum
Time Periods
Ancient
Medieval
3rd century
Renaissance
Neolithic period
Places
Greece
Rome (Italy)
Scotland
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