# Quadratura parabolae ιβ΄.

Archimède, Quadratura parabolae, ιβ΄.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/archimede/quadratura-parabolae/%CE%B9%CE%B2%CE%84.

Ἔστω πάλιν τὸ μὲν ΑΓ ζύγιον, μέσον δὲ αὐτοῦ τὸ Β, τὸ δὲ △ΕΚΗ τραπέζιον ἔστω τὰς μὲν ποτὶ τοῖς Ε, Η σαμείοις γωνίας ὀρθὰς ἔχον, τὰς δὲ Κ△, ΕΗ γραμμὰς ποτὶ τὸ Γ νευούσας, καὶ ὃν μὲν λόγον ἔχει ἁ ΑΒ ποτὶ τὰν ΒΗ, τοῦτον ἐχέτω τὸ △ΚΕΗ τραπέζιον ποτὶ τὸ Μ, ὃν δὲ λόγον ἔχει ἁ ΑΒ ποτὶ τὰν ΒΕ, τοῦτον τὸν λόγον ἐχέτω τὸ △ΚΕΗ τραπέζιον ποτὶ τὸ Λ, κρεμάσθω δὲ τὸ △ΚΕΗ τραπέζιον ἐκ τοῦ ζυγοῦ κατὰ τὰ Ε, Η, τὸ δὲ Ζ χωρίον κρεμάσθω κατὰ τὸ Α, καὶ ἰσορροπείτω τῷ τραπεζίῳ οὕτως ἔχοντι ὡς νῦν ὑπόκειται. Θαμὶ δὴ τὸ Ζ τοῦ μὲν Λ μεῖζον εἶμεν, τοῦ δὲ Μ ἔλασσον. Ἔλαβον γὰρ τοῦ △ΚΕΗ τραπεζίου τὸ κέντρον τοῦ βάρεος, ἔστω δὲ τὸ Θ λαφθήσεται δὲ ὁμοίως τῷ πρότερον καὶ ἄγω τὰν ΘΙ παρὰ τὰν △Ε. Ἂν οὖν τὸ τραπέζιον ἐκ τοῦ ζυγοῦ κρεμασθῇ κατὰ τὸ Ι, ἀπὸ δὲ τῶν Ε, Η λυθῇ, μενεῖ τὰν αὐτὰν ἔχον κατάστασιν καὶ ἰσορροπήσει τῷ Ζ διὰ τὰ αὐτὰ τοῖς πρότερον. Ἐπεὶ δὲ ἰσορροπεῖ τὸ τραπέζιον κρεμάμενον κατὰ τὸ Ι τῷ Ζ κρεμαμένῳ κατὰ τὸ Α, τὸν αὐτὸν ἕξει λόγον τὸ τραπέζιον ποτὶ τὸ Ζ, ὃν ἁ ΑΒ ποτὶ τὰν ΒΙ· δῆλον οὖν ὅτι τὸ △ΚΕΗ ποτὶ μὲν τὸ Λ μείζονα λόγον ἔχει ἢ ποτὶ τὸ Ζ, ποτὶ δὲ τὸ Μ ἐλάσσονα ἢ ποτὶ τὸ Ζ ὥστε τὸ Ζ τοῦ μὲν Λ μεῖζόν ἐστι, τοῦ δὲ Μ ἔλασσον.

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Archimède, Quadratura parabolae, ed. Charles Mugler. Text: The Greek Library, from the Perseus Digital Library and other open sources, CC BY-SA 4.0. Changes: apostrophes normalised and the text divided into reading sections by Interlinea.
License: CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/). Source: https://thegreeklibrary.pages.lisn.upsaclay.fr/works/tlg0552.tlg007.local001/.