Stomachion Archimedes Sponsor The Owner of the Archimedes Palimpsest Responsible for primary transcription (Dublin Core creator) Johan Ludvig Heiberg Contributor Alexander Lee Contributor Mike Toth Contributor William Noel Contributor Doug Emery Owner of the Archimedes Palimpsest 2008

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 This transcription is a reconstrunction of Heiberg's reading of Archimedes' Codex C, based on the apparatus criticus in his 1910–1915 edition of Archimedes' work, with use of the Netz-Wilson transcription of Codex C. Heiberg, J. L., Archimedis Opera omnia cum commentariis Eutocii (Leipzig: Teubner, 1910–15; reprinted 1972). Archimedes, Stomachion (digital transcription), edited by Reviel Netz and Nigel Wilson (2008). 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: Stomachion 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 J. L. Heiberg Content: J. L. Heiberg Ἀρχιμήδους Στομά χιον τοῦ λεγομένου Στομαχίου ποικί λαν ἔχοντος τᾶς ἐξ ὧν συνέστακε σχημάτων μεταθέσεως θεωρίαν ἀναγκαῖον ἡγησάμην πράττον του ρῶν ἐκθέσθαι, εἴς τε ἃ διαιρεῖται, ἕκαστόν τε αὐτῶν τίνι ἐστὶν ὁμοιού μενον, ἔτι δὲ καὶ ποῖαι γωνίαι σύ νδοιο λαμβανόμεναι καὶ θάς, εἴρηται πρὸς τὸ τὰς ἐναρμόσεις τῶν ἐξ αὐτῶν γεννωμένων σχα μάτων γιγνώσκεσθαι, εἴτε ἐπ’ εὐ θείας εἰσὶν αἱ γεννώμεναι ἐν τοῖς σχάμασι πλευραί, εἴτε καὶ μικρῶς λιποῦσαι τᾷ θεωρίᾳ λανθά νουσιν· τὰ γὰρ τοιαῦτα φιλότεχνα· καὶ ἐὰν ἐλάχιστον μὲν λίπηται, τᾷ δὲ θεωρίᾳ λανθάνῃ, οὐ παρὰ τοῦ τ’ ἐστὶν ἔκβλητα ἃ συνίσταται. ἔστι μὲν οὖν ἐξ αὐτῶν οὐκ ὀλίγων σχημάτων ο διὰ τὸ ντον εἶναι εἰς ἕτερον τόπου τοῦ ἴσου καὶ ἰσο γωνίου σχάματος μετατιθεμε καὶ ἑτέ λαμβάνοντας. ἐνιό τε δὲ καὶ δύο σχήματα συνάμφω ἑνὶ σχήματι ἴσων ὄντων καὶ ὁμοί ων τῷ ἑνὶ σχήματι ἢ καὶ δύο σχη μάτων συνάμφω ἴσων τε καὶ ὁμοί ων ὄντων δυσὶ σχήμασι συνάμφω πλείονα σχήματα συνίσταται ἐ κ τῆς μεταθέσεως. προγραφόμε νον οὖν τι θεώρημα εἰς αὐτὸ συντεῖ νον. ἔστω γὰρ παραλληλόγραμ μον ὀρθογώνιον τὸ ΖΓ, καὶ δειω ἡ ΕΖ τῷ Κ, καὶ διήχθωσαν ἀπὸ τῶν Γ, Β αἱ ΓΚ, ΒΕ ειων τῶν Γ ἐκβεβλή σθωσαν αἱ ΓΚ, ΒΖ καὶ συμπιπτέ τωσαν κατὰ τὸ Δ ἡ ΓΗ. ἐπεὶ ἴση ἐστὶν ἡ ΕΚ τῇ ΚΖ, ἴση καὶ ἡ ΓΕ, τουτέστιν ἡ ΒΖ, τῇ ΖΔ· ὥστε μείζων ἡ ΓΖ τῆς ΖΔ· καὶ γωνία ἄρα ἡ ὑπὸ τῶν ΖΔΓ τῆς ὑπὸ τῶν ΖΓΔ μείζων. ἴσαι δέ εἰσιν αἱ ὑπὸ ΗΒΔ, ΖΓΒ· ἡμίσεια γὰρ ὀρθῆς ἑκατέρα· μεί ζων ἄρα καὶ ἡ ὑπὸ τῶν ΓΗΒ, ἐπεὶ ἡ ὑπὸ ΓΗΒ ἴση δυσὶ ταῖς ἐντὸς καὶ ἀπεναντίον ταῖς ὑπὸ ΗΒΔ, ΗΔΒ, τῆς ὑπὸ τῶν ΗΓΒ· ὥστε μείζων ἐστὶν ἡ ΓΒ τῆς ΒΗ. ἐὰν ἄρα δίχα τμη θῇ ἡ ΓΗ κατὰ Χ, ἔσται ἀμβλεῖα μὲν ἡ ὑπὸ ΓΧΒ· ἐπεὶ γὰρ ἴση ἡ ΓΧ τῇ ΧΗ, καὶ κοινὴ ἡ ΧΒ, δύο δυσὶν ἴσαι· καὶ βάσεις ἡ ΓΒ τῆς ΒΗ μείζων· καὶ ἡ γωνία ἄρα τῆς γωνίας μεί ζων. ἀμβλεῖα μὲν ἄρα ἡ ὑπὸ ΓΧΒ, ὀξεῖα δὲ ἡ ἐφεξῆς. ἡμίσεια δὲ ὀρθῆς ἡ ὑπὸ ΓΒΗ· τοῦτο γάρ ἐστιν ὑποκείμε νον τοῦ παραλληλογράμμου· ὀξεῖ α δὲ ἡ ὑπὸ ΒΧΗ. καὶ τι δὴ ἴση ἡ λοιπαὶ ΓΒΗ καὶ συνίσταται καὶ διαιρεῖται τοῦτο ἐπ ον τον βάσιος τι αστα ἄρα ο ΑΒ ανο τὴν ΓΑ νῶν έχον τὸ ἐπίλοιπ δύνασθαι ἀρξειν ἐκ τῶν τομῶν τῶν τάξιν ἐχοντ. τε τμήσθω ἡ ΓΑ δίχα κατὰ τὸ Ε, καὶ διὰ τοῦ Ε τῇ ΒΓ παράλληλος ἤχθω ἡ ΕΖ· ἔστιν οὖν τετράγωνα τὰ ΓΖ, ΖΑ. ἤχθωσαν διάμετροι αἱ ΓΔ, ΒΕ, ΕΔ, καὶ τετμήσθωσαν δίχα αἱ ΓΗ, ΕΔ κατὰ τὰ Θ, Χ, καὶ ἐπεζεύχθωσαν αἱ ΒΘ, ΧΖ, καὶ διὰ τῶν , Κ τῇ ΒΔ πα ράλληλοι ἤχθωσαν αἱ Κ, Ξ. διὰ τὸ προκείμενον ἄρα θεώρημα τοῦ ΒΓΘ τριγώνου ἡ πρὸς τῷ Θ γωνία ἀμβλεῖα, ἡ δὲ λοιπὴ ὀξεῖα. νερὸν φανερὸν δὲ ει