# Metrica 27

Hero of Alexandria, Metrica, ΗΡΩΝΟΣ ΜΕΤΡΙΚΩΝ Α. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/hero-of-alexandria/metrica/27

κζ. Εἰς δὲ τὴν τοῦ τμήματος μέτρησιν προγράψομεν ταῦτα. ἔστω ὁσαδηποτοῦν μεγέθη τετραπλάσια ἀλλήλων τὰ Α, Β, Γ, ∠ ἢ καὶ πλείονα ἀρχόμενα ἀπὸ μεγίστου τοῦ Α· λέγω ὅτι τὸ γ΄ τοῦ Α ἴσον ἐστὶν τοῖς ΒΓ∠ καὶ τῷ γ΄ τοῦ ∠· ἐπεὶ γὰρ τὸ Α τετραπλάσιόν ἐστι τοῦ Β, τὸ Α ἄρα ἴσον ἐστὶ τέτταρσι τοῖς Β. τὸ ἄρα τρίτον τοῦ Α ἴσον ἐστὶ τῷ Β καὶ τῷ γ΄ τοῦ Β. διὰ τὰ αὐτὰ δὴ καὶ τὸ γ΄ τοῦ Β ἴσον ἐστὶν τῷ Γ καὶ τῷ γ΄ τοῦ Γ. ὁμοίως δὴ καὶ τοῦ Γ τὸ γ΄ ἴσον ἐστὶ τῷ ∠ καὶ τῷ γ΄ τοῦ ∠. ὥστε τὸ γ΄ τοῦ Ἂ ἴσον ἐστι τοῖς ΒΓ∠ καὶ τῷ γ΄ τοῦ ∠.

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Hero of Alexandria, Metrica, ed. Hermann Schöne. 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/tlg0559.tlg006.local001/.