# Scholia in Euclidis Data Ad prop. LXXIX.

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.%20LXXIX.

163. Τὸ ἀντιστρόφιον τούτου ἀληθέστατον, καὶ ἐχρήσατο αὐτῷ κατιών. 164. Ἔστιν ἄρα ὡς ἡ ΑΓ p. 154, 8] ὅτι καθόλου ἐπὶ ὁμοίου τριγώνου τοῦτο συμβαίνει. ἔστω τρίγωνον τὸ ΒΑΓ, καὶ ἀπὸ τοῦ Β ἐπὶ τὴν ΑΓ κάθετος ἤχθω ἡ Β∠, καὶ διὰ τοῦ Θ τῇ ΑΓ παράλληλος ἤχθω ἡ ΘΕ. ἔστιν ἄρα ὡς ἡ ΑΓ πρὸς ΓΒ, ἡ ΘΕ πρὸς ΕΒ, καὶ ἐναλλὰξ ὡς ἡ ΑΓ πρὸς ΘΕ, ἡ ΓΒ πρὸς ΒΕ. ἔστι δὲ καὶ ὡς ἡ ΓΒ πρὸς ΒΕ, ἡ ΔΒ πρὸς ΒΜ, καὶ διʼ ἴσου ὡς ἡ ΑΓ πρὸς ΘΕ, ἡ ∠Β πρὸς ΒΜ, καὶ ἐναλλὰξ ὡς ἡ ΑΓ πρὸς ∠Ε, ἡ ΘΕ πρὸς ΜΒ. 165. Οὕτως ἡ ΗΘ πρὸς ΜΛ [p. 154, 8]. ἰσογώνια γὰρ τὰ τρίγωνα, καὶ ὁμόλογοι αἱ ὑπὸ τὰς ἴσας γωνίας πλευραί. ὁμόλογος δέ ἐστιν ἡ μὲν ΑΓ τῇ ΘΗ· ἴσας γὰρ γωνίας ὑποτείνουσι τὰς ὑπὸ ΑΒΓ, ΘΛΗ· ἡ δὲ Β∠ ἴση τῇ ΛΜ· ὁμόλογοι γὰρ καὶ αὗται ἴσας γωνίας ὑποτείνουσιν. 166. Ὅπως ἡ ΖΚ τῇ ΛΜ ἐστιν ἴση; ἐπεὶ ὑπό- κειται ὡς ἡ ΑΓ πρὸς Β∠, οὕτως ἡ ΘΗ πρὸς ΖΚ, ὡς δὲ ἡ ΑΓ πρὸς ∠Β, οὕτως ἡ ΘΗ πρὸς ΜΛ, καὶ ὡς ἄρα ἡ ΘΗ πρὸς ΜΛ, οὕτως αὐτὴ ἡ ΘΗ πρὸς ΖΚ. τὰ δὲ πρὸς τὸ αὐτὸ τὸν αὐτὸν ἔχοντα λόγον ἴσα ἀλλή- λοις ἐστίν· ἴση ἄρα ἡ ΛΜ τῇ ΚΖ.

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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/.