# Metrica 3-3

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/hero-of-alexandria/metrica/3-3

γ. Ἔστω δὴ τὸ δοθὲν τρίγωνον τὸ ΑΒΓ ἔχου τὴμ μὲν ΑΒ μονάδων ιγ, τὴν δὴ ΒΓ μονάδων ιδ, τὴν δὲ ΓΑ μονάδων ιε. καὶ ἀπειλήφθω ἡ Α∠, εἰ τύχοι, μονάδων ιβ. καὶ δέον ἔστω ἀπὸ τοῦ ∠ διαγαγεῖν τὴν ∠Ε διαιροῦσαυ τὸ ΑΒΓ πρίγωνον ἐν λόχῳ τῷ δοθάντι. ἔσπω δὴ ὁ λόγος, ὃν ἔχει τὰ ε πρὸς τὰ β. ἤχθωσαν ἀπὸ τῶν Β, ∠ ἐπὶ τὴν ΑΓ κάθετον αἱ ΒΖ ∠Η. ἔσται δὴ ἡ ΒΖ κάθετος, ὡς ἐμάθομεν, μονάδων ια ε΄. καὶ ἐπεί ἐστιν ὡς ἡ ΒΑ πρὸς Α∠, τουτέστιν ὡς ιγ πρὸς ιβ, οὕτως ἡ ΒΖ πρὸς ∠Η, καὶ ἔστιυ ἡ ΒΖ ια εʹ, ἡ ἄρα ∠Η ἔσται μονάδων ι καὶ κβ καὶ ἐπεὶ τὸ ΑΒΓ τρίγωνον πρὸς τὸ Α∠Ε λόγον ἔχει, ὃν ε πρὸς γ, καὶ ἔστι τὸ ΑΒΓ τρίγωνον μονάδων πδ, τὸ ἄρα Α∠Ε τρίγωνον ἔσται μονάδων ν καὶ β. τοῦ δὲ Α∠Ε τριγώνου διπλάσιόν ἐσυι τὸ ὑπὸ τῶν ΑΕ ∠Η τὸ ἄρα ὑπὸ τῶν ΑΕ ∠Η ἔσται μονάδων ρ καὶ δ. καὶ ἔστιν ἡ ∠Η μονάδων ι καὶ κβ· ἡ ἄρα ΑΕ ἔσπαι μονάδων θU+2220δ΄. κἂν ἐπιζεύξωμεν τὴν ∠Ε, ἔσται τὸ προκείμενον. ἔστι δὲ ἡ μέθοδος τοιαύτη· ἐπεὶ ἡ ΒΖ κάθετός ἐστιν, ια ε΄ ἐπὶ τὰ ιβ· | καὶ τὰ γενόμενα μέρισον εἰς τὸν ιγ· γίνονται μονάδες ι καὶ κβ, καὶ ἐπεὶ λόγος, ἐν ᾧ διαιρεῖται, ὁ τῶν γ πρὸς τὰ β, σύνθες γ καὶ. β· γίγνεται ε· καὶ πολλαπλασίασον τὸν γ ἐπὶ τὸ ἐμβαδὸν τοῦ τριγώνου, τουτέστιν ἐπὶ τὰ πδ· γίχνεται σνβ. ταῦτα μέρισον εἰς τὸν ε· γίγνεται νβοέ. ταῦτα δίς· γίγνεται ρ καὶ δ. μέρισον ταῦτα παρὰ τὸν ι καὶ κβ· γίγνονται μονάδες θ∠δ΄. τοσούτου ἀπολαβὼν τὴν ΑΕ ἐπίζευξον τὴν ∠Ε· καὶ ἔσται τὸ προκείμενον.

---

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/.