# Quadratura parabolae η΄.

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/archimede/quadratura-parabolae/%CE%B7%CE%84.

Ἔστω ζυγὸς ὁ ΑΒΓ, μέσον δὲ αὐτοῦ τὸ Β, καὶ κρεμάσθω κατὰ τὸ Β, τὸ δὲ Γ△Ε τρίγωνον ὀρθογώνιον ὀρθὰν ἔχον τὰν ποτὶ τῷ Ε γωνίαν, καὶ κρεμάσθω ἐκ τοῦ ζυγοῦ κατὰ τὰ Γ, Ε, τὸ δὲ Ζ χωρίον κρεμάσθω κατὰ τὸ Α καὶ ἰσορροπείτω τῷ Γ△Ε οὕτως ἔχοντι, ὡς νῦν κεῖται, ὃν δὲ λόγον ἔχει ἁ ΑΒ ποτὶ τὰν ΒΕ, τοῦτον ἐχέτω τὸ Γ△Ε τρίγωνον ποτὶ τὸ Κ χωρίον. Θαμὶ δὴ τὸ Ζ χωρίον τοῦ μὲν Γ△Ε τριγώνου ἔλασσον εἶμεν, τοῦ δὲ Κ μεῖζον. Λελάφθω γὰρ τοῦ △ΕΓ τριγώνου τὸ κέντρον τοῦ βάρεος καὶ ἔστω τὸ Θ, καὶ ἁ ΘΗ ἄχθω παρὰ τὰν △Ε. Ἐπεὶ οὖν ἰσορροπεῖ τὸ Γ△Ε τρίγωνον τῷ Ζ χωρίῳ, τὸν αὐτὸν ἔχει λόγον τὸ Γ△Ε χωρίον ποτὶ τὸ Ζ, ὃν ἁ ΑΒ ποτὶ τὰν ΒΗ· ὥστε ἔλασσόν ἐστι τὸ Ζ τοῦ Γ△Ε. Καὶ ἐπεὶ τὸ Γ△Ε τρίγωνον ποτὶ μὲν τὸ Ζ τοῦτον ἔχει τὸν λόγον, ὃν ἁ ΒΑ ποτὶ τὰν ΒΗ, ποτὶ δὲ τὸ Κ ὃν ἁ ΒΑ ποτὶ τὰν ΒΕ, δῆλον ὡς μείζονα λόγον ἔχει τὸ Γ△Ε τρίγωνον ποτὶ τὸ Κ ἢ ποτὶ τὸ Ζ ὥστε μεῖζόν ἐστι τὸ Ζ τοῦ Κ.

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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/.