# Geodaesia [Sp.] 12.2

Hero of Alexandria, Geodaesia [Sp.], Chapter 12. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/hero-of-alexandria/geodaesia-sp/12.2

Οἷον ὡς ἐν ὑποδείγματι ἔστω τρίγωνον, οὗ αἱ πλευραὶ γ δ ε, ὅπερ καὶ ὀρθογώνιον τρίγωνόν ἐστιν. ὁ ἐκ τῶν τριῶν πλευρῶν συντιθέμενος ἀριθμὸς γίνεται ιβ· γ γὰρ καὶ δ ζ, καὶ ζ καὶ ε ιβ· τούτων τὸ U+2220ʹ ϛ· ὧν ἀφαιρουμένης ἑκάστης πλευρᾶς καταλείπονται μιᾶς ἑκάστης πλευρᾶς τῆς μὲν γ, τῆς δὲ β, τῆς δὲ ᾱ. τούτων ὁ μὲν γ πολλαπλασιασθεὶς ἐπὶ τὸν ϛ ποιεῖ τὸν ιη, ὁ δὲ β ἐπὶ τὸν ιη ποιεῖ τὸν λϛ, ἡ δὲ μονὰς ἐπὶ τὸν λϛ ποιεῖ πάλιν τὸν αὐτὸν λϛ. τούτων πλευρὰ τετράγωνος ὁ ϛ· καὶ ἔστι τὸ ἐμβαδὸν τοῦ τοιούτου τριγώνου ϛ. καὶ τοῦτο δῆλον καὶ ἀπὸ τῆς ἑτέρας μεθόδου τῆς περὶ τῶν ὀρθογωνίων τριγώνων· τὰ γὰρ γ τῆς καθέτου ἐπὶ τὰ ἡμίση τῆς βάσεως, τουτέστι τὰ β, πολλαπλασιαζόμενα ποιοῦσι τὸν ϛ. πεπείραται δὲ αὕτη ἡ μέθοδος καὶ ἐν τοῖς λοιποῖς πᾶσι τριγώνοις καὶ ἔστιν ἀσφαλεστάτη.

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Hero of Alexandria, Geodaesia [Sp.], ed. Johan Ludvig Heiberg. 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.tlg015.local001/.