# Scholia in Euclidis Data Ad prop. XXIV.

Scholia in Euclidem, Scholia in Euclidis Data, SCHOLIA.. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/scholia-in-euclidem/scholia-in-euclidis-data/Ad%20prop.%20XXIV.

77. Εἰλήφθω τῶν ∠, Ζ p. 44, 20] δύο δοθεισῶν εὐθειῶν μέσην ἀνάλογον προσευρεῖν. 78. Δοθὲν δὲ τὸ ὑπὸ τῶν ∠, Ζ p. 44, 22] ἐπεὶ γὰρ ἐμάθομεν ἐν τοῖς ὅροις, ὅτι εὐθύγραμμα σχήματα τῷ εἴδει δεδόσθαι λέγεται, ὧν αἵ τε γωνίαι δεδομέναι εἰσὶ κατὰ μίαν καὶ οἱ λόγοι τῶν πλευρῶν πρὸς ἀλλήλας δεδομένοι, ἐὰν ποιήσωμεν ὀρθογώνιον παραλληλόγραμμον τὸ ΑΒΓ∠ ἔχον ἴσην τῇ μὲν ∠ τὴν ΑΒ, τῇ δὲ Ζ ἴσην τὴν ΒΓ. ἔχομεν τῶν μὲν γω- νιῶν ἑκάστην δεδομένην διὰ τὸ ὀρθὴν εἶναι· πᾶσα γὰρ ὀρθὴ δέδοται· ὀρθὴ γὰρ ὀρθῆς οὐ διαφέρει. καὶ δῆλον, ὅτι καὶ οἱ λόγοι τῶν πλευρῶν δεδομένοι εἰσίν· ὁ γὰρ τῆς ΑΒ πρὸς ΒΓ λόγος δέδοται, ἐπεὶ καὶ ὁ τῆς ∠ πρὸς Ζ λόγος δέδοται. καὶ διὰ τοῦτο δέδοται τὸ ὑπὸ τῶν ∠, Ζ. 79. Δοθεῖσα ἄρα ἐστὶν ἡ Ε p. 44, 24] εἰ γὰρ δέδοταί μοι τὸ τετράγωνον, ἐπεὶ καὶ τὸ ἴσον αὐτῷ παραλληλόγραμμον τὸ ΑΓ, δέδοται καὶ ἡ εὐθεῖα ἡ ποιοῦσα αὐτό. καὶ ἄλλως· ἐπεὶ ἕσαι εἰσὶν αἱ δ πλευραὶ τοῦ τετραγώύνου, δῆλον, ὅτι δέδοται ἡ ποιοῦσα αὐτὸ εὐθεῖα· ἴσαι γὰρ αὐταὶ ἐπορίσθησαν· ὤστε δέδοται ἡ Ε. 80. Καὶ τὸ ἀντιστρόφιον αὐτοῦ ἀληθές.

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Scholia in Euclidem, Scholia in Euclidis Data, ed. Heinrich Menge. 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/tlg5022.tlg002.local001/.