Transcription of folios 002r-001v of the Archimedes Palimpsest. (= Archimedes folio Arch13r, 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 5519 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
πλασία τῆς ϠΘΕ. ὡς τῶι ΟΥΝ ἡ ΠΗ διπλασία τῆς ΗΘ, καὶ ἐπε ζεύχθω ἡ ΗΚ καὶ ἐκβεβλήσθω ἐπὶ τὸ Ω. ἔσται δὴ τοῦ μὲν ὅλου τμή ματος κέντρον τοῦ βάρους τὸ Κ, τοῦ δ’ ἐν τῶι ὑγρῶι τὸ Η, τοῦ δ’ ἐκτ ἐκτὸς ἐπὶ τῆς ΚΩ· ἔσται τὸ Ω. δειχθή σεται δὴ ὁμοίως ἥ τε ΚΤ κά θετος ἐπὶ τὴν τοῦ ὑγροῦ ἐπιφά νειαν καὶ διὰ τῶν ΝΩ ἔσται π παρὰ τὴν ΚϠ. φανερόν, ὅτι οὐ μένει τὸ τμῆμα, ἀλλ’ ἐπικλίνει, ἕως ἂν ἡ βάσις αὐτοῦ ἅπτηται κα θ’ ἓν σημεῖον τῆς τοῦ ὑγροῦ ἐπι φανείας, καθάπερ ἐδείκνυ το ἐν τῶι ἑτέρωι τμήματι, ὡς ἐχεῖ ἐπὶ τοῦ τρίτου, καὶ μενεῖ οὕ τως τὸ τμῆμα καθεστηκός. ἐ ν ἴσοις γὰρ τμήμασι τοῖς ΑΠΟ ΑΟΘΛ. ἠγμέναι ἔσονται ἀπ’ ἄκρων τῶν βάσεων αἱ ΑΧ ΑΟ ἴσας ἀφαιροῦσαι· δειχθήσεται γὰρ αὐτῶι τῶι ΑΠΟ ὁμοίως τοῖς πρό τερον. ἴσας οὖν ποιήσει τὰς γω νίας ὀξείας αἱ ΑΟ ΑΧ πρὸς τὰς τῶν τμημάτων διαμέτρ διαμέτρους , ἐπεὶ δ’ ἴσαι εἰσὶν πρὸς τοῖς ΝΥ γω νίαι καὶ αἱ ΒΟ ΒΤ ἴσαι εἰσὶν, ὥσ τε καὶ ΟΡ ΡΤ καὶ αἱ ΟΥ ΠϠ ἴσ αι ΥΞ ΘϠ. δίπλη οὖν ἐστι τῆς ϠΘ, ἐπιζευχθείσης δὲ τῆς ϠΚ ἐκβληθείσης ἐπὶ τὸ Ω ἔσται τοῦ παντὸς τμήματος κέντρου βά ρους τοῦ Κ, τοῦ δ’ ἐν τῶι ὑγρῶι τὸ Ϡ, τοῦ δ’ ἐκτὸς ἐπὶ τῆς ΚΩ ἔστω τὸ Ω. καὶ ἡ ΚϠ κάθετός ἐστιν ἐπὶ τὴν τοῦ ὑγροῦ ἐπιφάνειαν. κατὰ τὰς αὐτὰς οὖν εὐθείας τώ τ’ ἐν τῶι ὑγρῶι ἀνε νεχθήσεται καὶ τὸ ἐκτὸς τοῦ ὑγροῦ κατενεχθήσεται· μενεῖ τὸ τμῆμα, καὶ ἥ τε βάσις καθ’ ἓν σημεῖον ἅ ψεται τῆς τοῦ ὑγροῦ ἐπιφανείας, καὶ ὁ ἄξων τοῦ τμήματος πρὸς τὴν ἐπιφάνειαν τοῦ ὑγροῦ ποιήσει γω νίαν ἴσην τῆι προγεγραμμένηι. ὁμοίως δὲ δειχθήσεται, καὶ ἐὰν τὸ τμῆμα τῶι βάρει πρὸς τὸ ὑγρὸν λό γον ἔχη τὸν αὐτὸν, τὸ ἀπὸ τῆς ΜΠ τετράγωνον πρὸς τὸ ἀπὸ τῆς ΒΔ, ὅτι ἀφεθὲν ἐς τὸ ὑγρὸν, ὥστε τὴν βάσιν αὐ τοῦ μὴ ἅπτεσθαι τῆς τοῦ ὑγροῦ ἐπι φανείας, κατατήσεται κεκλιμέ νον οὕτως, ὥστε τὴν βάσιν αὐτοῦ καθ’ ἓν σημεῖον ἅπτεσθαι τῆς τοῦ ὑγροῦ ἐπιφανείας καὶ τὸν ἄξονα αὐτοῦ πρὸς τὴν ἐπιφάνειαν τοῦ ὑ γροῦ γωνίαν ἴσην πρὸς τῆι Φ. Ε ΕΞΗΣ ΑΙ ΚΑΤΑΓΡΑΦΑΙ. Ἐχέτω δὴ πάλιν τμῆμα τῶι βάρει πρὸς τὸ ὑγρόν σημεῖον λόγον ἢ ὃν ἔχει τὸ ἀπὸ τῆς ΝΤ πρὸς τὸ ἀπὸ ΒΔ, ὃν λόγον ἔχει τὸ τμῆμα τῶι βά ρει πρὸς τὸ ὑγρόν, τοῦτον εχέτω τὸ ἀπὸ τ τῆς Ψ τετράγωνον· ἐλάσσων δὴ οὖν ἐστιν ἡ Ψ τῆς ΟΝ. πάλιν δὴ οὖν ἐνηρμόσθω τις μεταξὺ τῶν ΑΜ ΔΑ ΠΟΛ τεμῶν τὴν ΨΣ ΗΠ παρὰ τὴν ΒΔ ἠγμένη. ἴση δ’ ἡ ΡΗ ΗΨ. τέ μνει δὴ αὐτὴ τὴν μεταξὺ τοῦ κώ νου τομὴν κατὰ τοῦ, τὴν δὲ τὴν ΞΡ