Transcription of folios 0000-100v of the Archimedes Palimpsest. (= Archimedes folio Arch53r, Sphere and Cylinder) Archimedes Sponsor The Owner of the Archimedes Palimpsest Responsible for primary transcription (Dublin Core creator) Reviel Netz Responsible for primary transcription (Dublin Core creator) Nigel Wilson Contributor Mike Toth Contributor William Noel Contributor Doug Emery Contributor Alexander Lee Contributor Neel Smith Contributor Christopher Blackwell Contributor Jennifer Adams Contributor Jennifer Curtin Contributor Christopher D'Alessandro Contributor William Dolan Contributor Scott Dubè Contributor Michael Kinney Contributor Stephanie Wheeler Contributor Joshua Whelan Contributor Alana L. Bates Contributor Mary Katherine Benson Contributor Edwin Ranier Brenegar Contributor Harry Briggs Contributor Andrew P. Cannon Contributor Katie Elizabeth Crumpton Contributor Katelyn Marie Ellis Contributor Matthew David Goodson Contributor Bryan Alton Keller Contributor Bethanie V. Kemper Contributor Claire Chamberlyn Kitchens Contributor Adam Charles Race Contributor Peter Eric Soder Contributor Charles David Stolper Contributor Jiayang Wu 5516 Owner of the Archimedes Palimpsest 2008

Licensed for use under Creative Commons Attribution 3.0 Unported, license http://creativecommons.org/licenses/by/3.0/legalcode.

It is requested that copies of any published articles based on the information in this data set be sent to The Curator of Manuscripts, The Walters Art Museum, 600 North Charles Street, Baltimore MD 21201.

 Privately owned parchment codex: "The Archimedes Palimpsest". Multispectral Digital Image Product of the Archimedes Palimpsest (The Owner of the Archimedes Palimpsest, 2008). Heiberg, J. L., Archimedis Opera omnia cum commentariis Eutocii (Leipzig: Teubner, 1910–15; reprinted 1972). Christie’s New York, 29th October 1998 Sale, no. 9058, The Archimedes Palimpsest. A. Papadopoulos-Kerameus, Hierosolymitike Bibliotheke, vol. 4 (St Petersburg, 1899), 329–331, MS 355. 10th Century Manuscript 13th Century Manuscript Archimedes Palimpsest Byzantine Manuscript Content: Against Diondas Content: Against Timandros Content: Archimedes Content: Aristotle Content: Categories Content: Hyperides Content: J. L. Heiberg Content: Method Content: On Floating Bodies Content: On Spiral Lines Content: On the Equilibrium of Planes Content: On the Measurement of the Circle Content: On the Sphere and Cylinder Content: Stomachion Foliation scheme: Undertext foliation, ordered by sequence of undertext Foliation scheme: Undertext foliation, ordered by sequence of columnar undertext Greek Manuscript J. L. Heiberg Parchment Manuscript Private Collection accented ancient Greek in Unicode-C Greek characters English Content: Archimedes Content: On the Sphere and Cylinder Archimedes Palimpsest Greek Manuscript Byzantine Manuscript Parchment Manuscript 13th Century Manuscript 10th Century Manuscript Private Collection Foliation scheme: Undertext foliation, ordered by sequence of columnar undertext
τὸ ὕψος αὐτοῦ τὸ ΝΟ. ἐπεὶ οὖν ἡ ΝΟ τῆι ΑΔ ἴση, ἔστιν ἄρα ὡς ἡ ΝΟ πρὸς ΔΕ, οὕτως ἡ ΑΔ πρὸς ΔΕ. ἀλλ’ ὡς μὲν ἡ ΑΔ πρὸς ΔΕ, οὕτως ὁ ΑΒΓΔ ῥόμβος πρὸς τὸν ΒΓΔ κῶ νον, ὡς δὲ ἡ ΝΟ πρὸς τὴν ΔΕ, οὕτως ὁ ΜΝΞ κῶνος πρὸς τὸν ΒΓΔ κῶνον διὰ τὸ τὰς βάσεις αὐτῶν εἶναι ἴσας· ὡς ἄρα ὁ ΜΝΞ κῶνος πρὸς τὸν ΒΓΔ κῶνον, οὕτως ὁ ΑΒΓ ῥόμβος πρὸς τὸν ΒΓΔ κῶνον· ἴσος ἄρα ἐστὶν ὁ ΜΝΞ τῶι ΑΒΓΔ ῥόμβωι. καὶ ἐπεὶ ἡ ἐπιφά νεια τοῦ ΑΒΓ ἴση ἐστὶν τῆι βάσει τοῦ ΗΘΚ, ὡς ἄρα ἡ ἐπιφάνεια τοῦ ΑΒΓ πρὸς τ τὴν ἰδίαν βάσιν, οὕτως ἡ βάσις τ τῆς ΗΘΚ πρὸς τὴν βάσιν τοῦ ΜΝΞ· ἡ γὰρ βάσις τοῦ ΑΒΓ ἴση ἐστὶ τῆι βάσει τοῦ ΜΝΞ πρὸς τὴν βάσιν. ὡς δὲ ἡ ἐπι φάνεια τοῦ ΑΒΓ πρὸς τὴν ἰδίαν βάσι βάσιν Κ Ἐὰν κῶνος ἰσοσκελὴς ἐπιπέδωι τμηθῆι παραλλήλωι τῆι βάσει, ἀπὸ δὲ τοῦ γενομένου κύκλου κῶ νος ἀναγραφῆι κορυφὴν ἔχον τὸ κέντρον τῆς βάσεως, ὁ δὲ γενόμε νος ῥόμβος ἀφαιρεθῆ ἀπὸ τοῦ ὅλου κώνου, τῶι περιλείμματι ἴσος ἔσται κῶνος ὁ βάσιν μὲν ἔχων ἴσην τῆι ἐπιφανείαι τοῦ κώνου τῆι μεταξὺ τῶν παραλλή λων ἐπιπέδων, ὕψος δὲ ἴσον τῆι ἀπὸ τοῦ κέντρου τῆς βάσεως ἐπὶ μίαν τοῦ κώνου καθέτω ἠγμένηι. ἔστω κῶνος ἰσοσκελὴς ὁ ΑΒΓ καὶ τετμήσθω ἐπιπέδωι παραλλήλωι