Transcription of folios 028r-021v of the Archimedes Palimpsest. (= Archimedes folio Arch08r, 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 5531 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 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
Ρ, ὥστε καὶ ΟΡ τῆς ΡΝ διπλῆν εἶναι· ἔσται δὴ τοῦ μείζονος ὅ λου τμάματος τοῦ στερεοῦ κέν τρον τοῦ βάρους τὸ Ρ, τοῦ δὲ κατὰ τὴν ΙΠΟΣ τὸ Β· δέδεικται γὰρ ἐν ταῖς ἰσορροπείαις, ὅτι παν τὸς ὀρθογωνίου κώνου εἴδς εἴδους τμάματος τὸ κέντρον τοῦ βά ρους ἐστὶν ἐπὶ τοῦ ἄξονος διη ρήσθω οὕτως, ὥστε τὸ πρὸς τῆι κορυφῆι τοῦ ἄξονος τμᾶμα διπλάσιον εἶμεν τοῦ λοιποῦ. ἀ φαιρεθέντος δὲ τοῦ κατὰ τὴν ΙΠΟΣ τμάματος στερεοῦ ἀ πὸ τοῦ ὅλου τοῦ λοιποῦ κέν τρου ἔσται τοῦ βάρους ὁ ἐπὶ τ τῆς ΒΓ εὐθείας· δέδεικται γὰρ τοῦ το ἐν τοῖς στοιχείοις τῶν μηχα νικῶν, ὅτι , ἐὰν ἀπό τινος μεγέ θους ἀφειρηθη τι μέγεθος τὸ αὐτὸ κέντρον ἔχον τοῦ βάρους τῶι ὅλωι μεγέθει, τοῦ λοιποῦ τὸ κέντρον ἔσται τοῦ βάρους ἐπὶ τῆς εὐθείας τῆς ἐπιζευγνούσης τὰ κέντρα τοῦ τε ὅλου μεγέθεος καὶ τοῦ ἀφηρημένου ἐπὶ τὰ αὐτά, ἐφ’ οὗ τὸ κέντρον τοῦ ὅλου μεγέ θους ἐστίν . ἐκβεβλήσθω δὴ ἡ ΒΡ ἐπὶ τὸ Γ, καὶ ἔστω τὸ Γ τοῦ βάρους τοῦ λοιποῦ μεγέθους. ἐπεὶ οὖν ἡ ΝΟ τῆς μὲν ΟΡ η μη δια τις δὲ μέχρι τοῦ ἄξονος οὐ μεῖζον εἰ ἡμιολί α, δῆλον, ὅτι ἡ ΡΟ τῆς μέχρι τοῦ ἄξονος οὐκ ἔστι μείζων· ἡ ΠΡ ἄρα πρὸς τὴν ΚΩ γωνίας ἀνίσους ποιεῖ, καὶ ἡ ὑπὸ τῶν ΡΠΩ γίνετ γίνεται ὀξείη· ἀπὸ τοῦ Ρ ἄρα κάθετος ἐπὶ τὴν ΠΩ ἀγομένη μεταξὺ πεσεῖτ πεσεῖται τῶν ΠΩ. πιπτέτω ὡς ἡ ΡΘ· ἡ ΡΘ ἄρα ὀρθή ἐστι καὶ πρὸς τὸ τοῦ ὕδα τος ἐπίπεδον, ἐν ὧι ἐστιν ἡ ΣΙ, ὅ ἐστιν ἡ ἐπὶ τῆς ἐπιφανείας τοῦ ὑγροῦ. ἤχθωσαν δέ τινες ἀπὸ τῶ τῶν ΒΓ παρὰ τὰν ΡΘ· ἐνεχθήσεται δὴ τὸ μὲν ἐκτὸς τοῦ ὑγροῦ οὗ μεγέ θους εἰς τὸ κάτω κατὰ τὴν διὰ τοῦ Γ ἀγομένην κάθετον· ὑπόκειται ἕκαστον τῶν βαρέων εἴς τε κάτω φέρεσθαι κατὰ τὴν κάθετον τὴν διὰ τοῦ κέντρου ἀγομένην· τὸ δὲ ἐν τῶι ὑγρῶι μέγεθος, ἐπὶ κουφό τερον γίνεται τοῦ ὑγροῦ, ἐνεχθή σεται εἰς τὸ ἄνω κατὰ τὴν κάθε τον τὴν διὰ τοῦ Β ἀγομένην. ἐπι πέδου κατὰ τὴν αὐτὴν κάθετο κάθετον ἀλλὰ ἀλλήλοις ἀντιθλίβονται, δῆλον, ὡς οὐ μενεῖ τὸ τμᾶμα ἐν τῶι ὑγρῶι ἀλλὰ τὰ μὲν κατὰ τὸ Α εἰς τὸ ἄνω ἐνεχθήσεται, τὰ δὲ κατὰ τὸ Λ εἰς τὸ κάτω, ἀεὶ ἔστε ἔστεν , ἕως ἂν ὀρθὸν ἀποκατασταθῆι. ΕΞΗΣ ΤΟ ΣΧΗΜΑ
Γ Ὀρθὸν τμᾶμα τοῦ ὀρθογωνίου κω νοειδοῦς, ὅταν τὸν ἄξονα ἔχη μὴ μείζονα ἡμιόλιον τῆς μέχρι τοὺς ἄξονας, πάντα λόγον ἔχον πρὸς τὸ ὑγρὸν τῶι βάρει, ἀφεθὲν εἰς τὸ ὑγρὸν οὕτως, ὥστε τὴν βάσιν