Transcription of folios 034v-029r of the Archimedes Palimpsest. (= Archimedes folio Arch52v, 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 5538 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
καὶ τῶι ΜΝΞ γνώμονι, ὅς ἐστιν ἴσος τῶι ὑπὸ ΔΑ καὶ συναμφοτέρου τῆς ΑΗ ΔΖ. οἱ κῶνοι οἱ ἴσον ὕψος ἔχτες ἔχοντες τὸν αὐτὸν ἔχουσι λόγον ταῖς βάσε σιν· καὶ οἱ ἴσας ἔχοντες βάσεις τὸν αὐτὸν ἔχουσι λόγον τοῖς ὕψεσι ὕψεσιν . ἐὰν κύλινδρος ἐπιπέδωι τμηθῆι π παρὰ τὴν βάσιν, ἔστιν , ὧι ὁ κύλινδρος πρὸς τὸ τὸν κύλινδρον, ὁ ἄξων πρὸς τὸν ἄξονα. τοῖς δὲ κυλίνδροις ἐν τῶι αὐτῶι λόγωι εἰσὶν οἱ κῶνοι οἱ ἔχοντες τὰς αὐτὰς βάσεις τοῖς κυλίνδροις. καὶ τῶν ἴσων κώνων ἀντιπεπόν θασιν αἱ βάσεις τοῖς ὕψεσιν· καὶ ὧν ἀντιπεπόνθασιν αἱ βάσεις τοῖς ὕψεσιν, ἴσοι εἰσίν . καὶ οἱ κῶνοι, ὧ ὧν αἱ διάμετροι τῶν βάσεων τὸν αὐτὸν λόγον ἔχουσιν τοῖς ἄξοσι τουτέστι τουτέστιν τοῖς ὕψεσι, πρὸς ἀλλήλους ἐν τριπλα σίονι λόγωι εἰσὶν τῶν ἐν ταῖς βάσε σιν διαμέτρων. ταῦτα δὲ πρότερο πρότερον πάντα ὑπὸ Εὐκλείδς Εὐκλείδους ἀπεδεί χθη. ΙΗ ἐὰν ὦσι δύο κῶνοι ἰσοσκελεῖς, ἡ δὲ τοῦ ἑτέρου κώνου ἐπιφάνεια ἴση ἦ τῆι τοῦ ἑτέρου βάσει, ἡ δὲ ἀπὸ τοῦ κέντρου τῆς βάσεως ἐπὶ τὴν πλευ ρὰν τοῦ κώνου κάθετος ἀγομένη τῶι ὕψει ἴση ἦ, ἴσοι ἔσονται οἱ κῶ νοι. ἔστωσαν δύο κῶνοι ἰσοσκε λεῖς οἱ ΑΒΓ ΔΕΖ, καὶ τοῦ ΑΒΓ ἡ μὲν βάσις ἴση ἔστω τῆι ἐπιφανείαι τ τοῦ ΔΕΖ, τὸ δὲ ὕψος τὸ ΔΗ ἴσον ἔστω τῆι ἀπὸ τοῦ κέντρου τῆς βάσεως τ τοῦ Θ ἐπὶ μίαν πλευρὰν τοῦ κώνου, οἷον ἐπὶ τὴν ΔΕ, καθέτωι ἠγμένη τῆι ΚΘ· λέγω ὅτι ἴσοι εἰσὶν οἱ κῶνοι. ἐπεὶ γὰρ ἴση ἐστὶν ἡ βάσις τοῦ ΑΒΓ τῆι ἐπιφανείαι τοῦ ΔΕΖ, τὰ δὲ ἴσα πρὸς τὸ αὐτὸ τὸν αὐ τὸν ἔχει λόγον, ὡς ἄρα ἡ τοῦ ΒΑΓ βά σις πρὸς τὴν τοῦ ΔΕΖ βάσιν, οὕτως ἡ ἐπιφάνεια τοῦ ΔΕΖ πρὸς τὴν βάσιν τοῦ ΔΕΖ. ἀλλ’ ὡς ἡ ἐπιφάνεια πρὸς τ τὴν ἰδίαν βάσιν, οὕτως ἡ ΕΘ πρὸς τ τὴν ΘΚ· ἐδεί χθη γὰρ τοῦτο, ὅτι παντὸς κώνου ἰ σοσκελοῦς ἡ ἐπιφάνεια πρὸς τὴν βά σιν τὸν αὐτὸν λόγον ἔχει, ὃν ἡ πλευ ρὰ τοῦ κώνου πρὸς τὴν ἐκ τοῦ κέντρ κέντρου τῆς βάσεως, ἡ ΔΕ τουτ τουτέστι πρὸς ΔΘ. ὡς δὲ ἡ ΕΔ πρὸς ΘΔ, οὕτως ἡ ΕΘ πρὸς ΘΚ· ἰσο γώνια γάρ ἐστι τὰ τρίγωνα. ἴση δέ ἐστιν ἡ ΘΚ τῆι ΑΗ· ὡς ἄρα ἡ βάσις τ τοῦ ΒΑΓ πρὸς τὴν βάσιν τοῦ ΔΕΖ, οὕτως τὸ ὕψος τ τοῦ ΔΕΖ πρὸς τὸ ὕψος τοῦ ΑΒΓ. τῶν ΑΒΓ ΔΕΖ ἄρα ἀντιπεπόνθασιν αἱ βάσεις τοῖς ὕψεσιν· ἴσος ἄρα ἐστὶν ὁ ΒΑΓ τῶι ΔΕΖ κώ νωι. ἑξ ἑξῆς τὸ ΣΧΗΜΑ. ΙΘ Παντὶ ῥόμβωι ἐξ ἰσοσκελῶν κών κώνων συγκειμένωι ἴσος ἐστὶ κῶνος ὁ βά σιν μὲν ἔχων ἴσην τῆι ἐπιφα νείαι τοῦ ἑτέρου κώνου τῶν περιε χόντων τὸν ῥόμβον, ὕψος δὲ ἴσον τῆι ἀπὸ τῆς κορυφῆς τοῦ ἑτέρ ἑτέρου κώνου καθέτωι ἀγομένη ἐπὶ μία μίαν