Transcription of folios 002v-001r of the Archimedes Palimpsest. (= Archimedes folio Arch13v, On Floating Bodies) 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 5520 Owner of the Archimedes Palimpsest 2008

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 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 Floating Bodies 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
εὐθεῖαν κατὰ τὸ Η. δειχθήσεται δὲ ἡ ΠΥ διπλῆ τῆς ΥΙ, καθάπερ δέδει κται καὶ ἡ ΓΟ τῆς ΓΠ. ἤχθω δὲ καὶ ἡ μὲν ΠΩ ἐφαπτομένη τῆς ΑΠ ΟΛ κατὰ τὸ Τ, τῆι δὲ ΠΕ κάθετος ἐπὶ τὴ τὴν ΒΔ, καὶ ἡ ΥΑ ἐπιζευχθεῖσα διήχθω ἐπὶ τὸ Χ· ἔσται δὴ ἥ τε αι τῆι ΙΧ καὶ ἡ ΑΧ τῆι ΠΩ παράλληλος. δεικτέο δεικτέον δή, ἔστιν τὸ τμῆμα ἀφεθὲν ἐς τὸ ὑ γρὸν καὶ τεθὲν κεκλιμένον οὕτως, ὥστε τὴν βάσιν αὐτοῦ μὴ ἅπτεσθαι τοῦ ὑγροῦ, οὕτως, ὥστε τὸν ἄξονα αὐτοῦ κεκλιμένον καταστήσεται πρὸς τὴν ἐπιφάνειαν τοῦ ὑγροῦ ποιεῖν γωνίαν ἐλάσσονα τῆς Φ, τὴν δὲ βάσιν αὐτοῦ μηδὲ καθ’ ἓν ἅπτεσθαι τῆς τοῦ ὑγροῦ ἐπιφα νείας. ἀφείσθω οὖν εἰς τὸ ὑγρὸν
καὶ καθεστηκέτω, ὥστε τὴν βάσιν αὐτοῦ καθ’ ἓν σημεῖον ἅπτεσθαι τῆς τοῦ ὑγροῦ ἐπιφανείας, τμη θέντος δὴ τοῦ τμήματος ἐπιπέ δωι ὀρθῶι πρὸς τὴν τοῦ ὑγροῦ ἐπιφά νειαν διὰ τοῦ ἄξονος τομῆς, ὥστε τῆς μὲν τοῦ τμήματος ἐπιφα νείας ἡ ΑΗΒΛ ὀρθογωνίου κών κώνου τομή, τῆς δὲ τοῦ ὑγροῦ ἡ ΑΖ, ἄξων δὲ τοῦ τμήματος καὶ διάμετρος τῆς τομῆς ἡ ΒΔ, καὶ τετμήσθω ἡ ΒΔ κατὰ τὰ ΚΡ ὁμοίως τοῖς ἐπά νω, ἤχθω δὲ καὶ ἡ ΗΑ παρὰ τὴν ΑΖ ἐφαπτομένη τῆς τοῦ κώνου τομῆς κατὰ τὸ Η, ἡ δὲ ΗΘ παρὰ τὴν ΒΔ, ἡ δὲ ΗΘ κάθετος ἐπὶ τὴ τὴν ΒΔ. ἔπει οὖν τὸ τμῆμα τῶι βάρει πρὸς τὸ ὑγρὸν τοῦτον ἔχει τὸν λόγον, ὃν ἔχει τὸ ἀπὸ τῆς Ψ τετράγωνον πρὸς τὸ ἀπὸ τῆς ΒΔ, ὃν δὲ λόγον ἔχει τὸ τμῆμα τῶι βάρει πρὸς τὸ ὑγρόν, τοῦτον ἔχει τὸ ἀπὸ τῆς ΗΘ τετράγωνον πρὸς τὸ ἀπὸ τ τῆς ΒΔ διὰ τὰ αὐτὰ τοῖς πρότερον, ὅτι ἴση ἐστὶ ἡ ΗΘ τῆι Ψ, ὥστε ἴσα ἐστὶ καὶ τὰ ΑΗΖ ΑΠΧ τμήματα. καὶ ἐπὶ οις ἴσοις καὶ ὁμοίοις τμήμασι τοῖς Π ΓΑ ΒΔ ΒΑ ἀπ’ ἄκρων τῶν βάσεων. ἠγμέναι εἰσὶ αἱ ΑΧ ΑΖ ΑΖ ἴσα τμήματα ἀφαιροῦσαι· δῆλον ὅτι ἴσας ποιοῦσι γωνίας πρὸς τοῖς διαμέτροις τῶν τμημά των. τῶν ἐπὶ δὲ τῶν ΗΙΤ ΡΩΕ τρι γώνων ἴσαι εἰσὶ αἱ πρὸς τοῖς ΙΩ ἴσα