# Scholia in Euclidis Data Ad prop. LXXIV.

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.%20LXXIV.

154. Ἀντιστρόφιον τῷ πρὸ αὐτοῦ. 155. Τὸ οδ΄ θεώρημα καθολικώτερον τοῦ νς΄. 156. Ἔστιν ἄρα ὡς ἡ ΓΒ p. 144, 14] διὰ τὸ νῦν πρῶτον δειχθὲν τοῦ οδ΄. 157. Ὅτι δέ ἐστιν ὡς ἡ ΓΒ πρὸς ΖΗ, οὕτως ἡ ΕΖ πρὸς ἣν ἡ ΑΓ πάλιν λόγον ἔχει δεδομένον, ἀντὶ τοῦ πρὸς τὴν ἴσην ἑαυτῇ, δείξομεν οὕτως. παρα- βεβλήσθω γὰρ ὁμοίως τῷ ἐπάνω παρὰ τὴν ΓΒ τῷ ΕΗ ἴσον παραλληλόγραμμον τὸ ΓΞ καὶ κείσθω, ὥστε ἐπʼ εὐθείας εἶναι τὴν ΓΝ τῇ ΛΓ· ἐπʼ εὐθείας ἄρα ἐστὶ καὶ ἡ ΜΒ τῃ ΒΞ. καὶ ἐπεὶ τοῦ ΑΒ πρὸς τὸ ΕΗ λόγος ἐστὶ δοθείς· ὑπόκειται γάρ· ἀλλὰ τὸ μὲν ΑΒ τῷ ΓΜ ἐστιν ἴσον, τὸ δὲ ΕΗ τῷ ΓΞ, καὶ τοῦ ΓΜ ἄρα πρὸς ΓΞ λόγος ἐστὶ δοθείς· ὥστε καὶ τῆς ΓΛ πρὸς ΓΝ λόγος ἐστὶ δοθείς· τῆς δὲ ΓΑ πρὸς ΓΛ λόγος ἐστὶ δοθεὶς διὰ τὸ δεδόσθαι τὸ ΑΓΛ τρίγωνον· καὶ τῆς ΑΓ ἄρα πρὸς ΓΝ λόγος ἐστὶ δοθείς. καὶ ἐπεὶ ἴσον ἐστὶ τὸ ΓΞ τῷ ΕΗ, ἔστι δὲ καὶ ἰσογώνιον, ἔστιν ἄρα ὡς ἡ ΓΒ πρὸς ΖΗ, οὕτως ἡ ΕΖ πρὸς ΓΝ. ἔστι δὲ καὶ ὡς ἡ ΓΒ πρὸς ΖΗ, οὕτως ἡ ΕΖ πρὸς ἣν ἡ ΛΓ λόγον ἔχει δεδομένον, τουτέστι πρὸς τὴν ΑΓ, διὰ τὸ νῦν πρῶτον δειχθὲν τοῦ οδ΄. ἔστιν ἄρα ὡς ἡ ΓΒ πρὸς ΖΗ, οὕτως ἡ ΕΖ πρὸς ἑκατέραν τῶν ΑΓ, ΓΝ· ἴση ἄρα ἡ ΑΓ τῇ ΓΝ.

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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/.