# Metrica 5

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

Canonical: https://interlinea.aeterna-institute.org/library/greek/hero-of-alexandria/metrica/5

ε. Ἔστω τρίγωνον ὀξυγώνιον τὸ ΑΒΓ ἔχον τὴν μὲν ΑΒ μονάδων ιγ, τὴν δὲ ΒΓ μονάδων ιδ, τὴν δὲ ΑΓ μονάδων ιε. εὑρεῖν αὐτοῦ τὸ ἐμβαδόν. φανερὸν ὅτι ὀξεῖά ἐστιν ἡ πρὸς τῷ Β γωνία· τὸ γὰρ ἀπὸ τῆς ΑΓ τετράγωνον ἔλασσον ἐστὶ τῶν ἀπὸ τῶν ΑΒ ΒΓ τετραγώνων. κάθετος ἤχθω ἐπὶ τὴν ΒΓ ἡ Α∠. τὸ ἄρα ἀπὸ τῆς ΑΓ τῷ δὶς ὑπὸ τῶν ΓΒ Β∠ ἔλασσόν ἐστι τῶν ἀπὸ τῶν ΑΒ ΒΓ ὡς δέδεικται. καὶ ἔστι τὰ μὲν ἀπὸ τῶν ΑΒ ΒΓ μονάδων τξε, τὸ δὲ ἀπὸ τῆς ΑΓ μονάδων σκε· λοιπὸν ἄρα τὸ δὶς ὑπὸ τῶν ΓΒ Β∠ μονάδων ρμ· τὸ ἄρα ἅπαξ ὑπὸ τῶν ΓΒ Β∠ ἔσται μονάδων ο. καὶ ἔστιν ἡ ΒΓ μονάδων ιδ· ἡ ἄρα Β∠ ἔσται μονάδων ε. καὶ ἐπεὶ τὸ ἀπὸ τῆς ΑΒ ἴσον ἐστὶ τοῖς ἀπὸ τῶν Α∠ ∠Β· καὶ ἔστι τὸ μὲν ἀπὸ τῆς ΑΒ μονάδων ρξθ|, τὸ δὲ ἀπὸ τῆς Β∠ μονάδων κε· λοιπὸν ἄρα τὸ ἀπὸ τῆς Α∠ ἔσται μονάδων ρμδ. αὐτὴ ἄρα ἡ Α∠ ἔσται μονάδων ιβ. ἔστι δὲ καὶ ἡ ΒΓ μονάδων ιδ· τὸ ἄρα ὑπὸ τῶν ΒΓΑ∠ ἔσται μονάδων ρξη. καὶ ἔστι τοῦ ΑΒΓ τριγώνου διπλάσιον· τὸ ἄρα ΑΒΓ τρίγωνον ἔσται μονάδων πδ. ἡ δὲ μέθοδος ἔσται τοιαύτη· τὰ ιγ ἐφʼ ἑαυτά· γίγνεται ρξθ· καὶ τὰ ιδ ἐφʼ ἑαυτά· γίγνεται ρ𝔮ϛ· καὶ τὰ ιε ἐφʼ ἑαυτὰ· γίγνεται σκε· σύνθες τὰ ρξθ καὶ τὰ ρ𝔮ϛ· γίγνεται τξε· ἀπὸ τούτων ἄφελε τὰ σκε· γίγνεται λοιπὰ ρμ· τούτων τὸ ἥμισυ· γίγνεται ο· παράβαλε παρὰ τὸν ιδ· γίγνεται ε· καὶ τὰ ιγ ἐφʼ ἑαυτά· γίγνεται ρξθ. ἀφʼ ὧν ἄφελε τὰ ε ἐφʼ ἐαυτά· λοιπὰ ρμδ. τούτων πλευρὰ γίγνεται ιβ· τοσούτου ἔσται ἡ κάθετος. ταῦτα πολυπλασίασον ἐπὶ τὸν ιδ· γίγνεται ρξη· τούτων τὸ ἥμισυ πδ· τοσούτου ἔσται τὸ ἐμβαδόν.

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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/.