Transcription of folios 004v-005r of the Archimedes Palimpsest. (= Archimedes folio Arch47v, 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 5524 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
ΑΗ τουτ τουτέστι τῆς ΜΛ διπλάσιον τῶν ΕΔΗ ΔΗΖ ΕΗΖ τρίγωνον. ἔστι δὲ καὶ τὸ ὑπὸ τῶν ΘΚ ΛΜ διπλάσιον τοῦ ΛΚΘ τριγώνου· διὰ τοῦτο δὴ ἴση ἐστὶν ἡ ἐπιφάνεια τῆς πυραμίδος χωρὶς τῆς βάσεως τριγώνωι βάσιν μ μὲν ἔχοντι ἴσην τῆι περιμέτρωι τοῦ ΔΕΖ, ὕψος δὲ τὴν πλευρὰν τοῦ κών κώνου . ἐξ ἐξῆς τὸ σχᾶμα Ι Ἐὰν κώνου τινὸς ἰσοσκέλους εἰς τὸν κύκλον, ὅς ἐστι βάσις τοῦ κώνου, εὐ θεῖα γραμμὴ ἐμπέσηι, ἀπὸ δὲ τῶν περάτων αὐτῆς εὐθεῖαι γραμμαὶ ἀχθῶσιν ἐπὶ τὴν κορυφὴν τοῦ κώ νου, τὸ περιληφθὲν τρίγωνον ὑπό τε τῆς ἐμπεσούσης καὶ τῶν ἐπι ζευχθεισῶν ἐπὶ τὴν κορυφὴν ἐλάσ σων ἔσται τῆς ἐπιφανείας τοῦ κώνου τῆν μεταξὺ τῶν ἐπὶ τὴν κορυφὴν ἐπιζευχθεισῶν. ἔστω κώ νου ἰσοσκελοῦς βάσις ὁ ΑΒΓ κύ κλος, κορυφὴ δὲ τὸ Δ, καὶ διήχθω τις εἰς αὐτὸν εὐθεῖα ἡ ΑΓ, καὶ ἀπὸ τῆς κορυφῆς ἐπὶ τὰ ΑΓ ἐπεζεύ χθωσαν αἱ ΑΔ ΔΓ· λέγω ὅτι τὸ ΑΔΓ τρίγωνον ἔλασσόν ἐστιν τῆς ἐπι φανείας τῆς κωνικῆς τῆς με ταξὺ τῶν ΑΔΓ. τετμήσθω ἡ ΑΒΓ περιφέρεια δίχα κατὰ τὸ Β, καὶ ἐπεζεύχθωσαν αἱ ΑΒ ΓΒ ΔΒ· ἔστ ἔσται δὴ τὰ ΑΒΔ ΒΓΔ τρίγωνα μείζο να τοῦ ΑΔΓ τριγώνου. ὧι δὴ ὑ περέχει τὰ εἰρημένα τρίγωνα τοῦ ΑΔΓ τριγώνου, ἔστω τὸ Θ. τὸ δὴ Θ ἤτοι τῶν ΑΒ ΒΓ τμημάτων ἔλασσόν ἐστιν ἢ οὔ. ἔστω μὴ ἔλασσον πρότερον. ἐπεὶ οὖν δύο εἰσὶν ἐπιφά νειαι ἥ τε κωνικὴ ἡ μεταξὺ τῶν ΑΔΒ μετὰ τοῦ ΑΕΒ τμήματος καὶ ἡ τοῦ ΑΔΒ τριγώνου τὸ αὐτὸ πέρ πέρας ἔχουσαι τὴν περίμετρον τοῦ τρι γώνου τοῦ ΑΒΔ, μείζων ἔσται ἡ περιλαμβάνουσα τῆς περιλαμ βανομένης· μείζων ἄρα ἐστὶν ἡ κωνικὴ ἐπιφάνεια ἡ μεταξὺ τῶν ΑΔΒ μετὰ τοῦ ΑΕΒ τμήματος τοῦ ΑΒΔ τριγώνου. ὁμοίως δὲ καὶ ἡ μεταξὺ τοῦ ΔΒΓ τριγώνου μετὰ τοῦ ΓΒ τμήματος μείζων ἐστὶν τοῦ ΒΔΓ· ὅλη ἄρα ἡ κωνικὴ ἐπιφάνεια μετὰ τοῦ Θ χωρίου μείζων ἐστὶ τῶν εἰρημένων τριγώνων. τὰ δὲ εἰρη μένα τρίγωνα ἴσα ἐστὶν τῶ τε ΑΔΓ τριγώνωι καὶ τῶι Θ χωρίωι. κοινὸν ἀφηιρήσθω τὸ Θ χωρίον· λοιπὴ ἄρα ἡ κωνικὴ ἐπιφάνεια ἡ μεταξὺ τῶν ΑΒΓ μείζων ἐστὶν τοῦ ΑΔΓ τριγώνου. ἔστω δὴ τὸ Θ ἔλασ ἔλασσον τῶν ΑΒ ΒΓ τμημάτων τέμνον τες δὴ τὰς ΑΒ ΒΓ περιφεριφε ρείας δίχα καὶ τὰς ἡμισείας