# Scholia in Euclidis Data Ad prop. LXI.

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.%20LXI.

118. Ἐπεὶ δοθεῖσά ἐστιν ἡ ὑπὸ ΖΓΒ γωνία p. 110,22] δεδομένον γὰρ τῷ εἴδει ὑπόκειται τὸ ΑΖΓΒ. 119. Δοθὲν ἄρα τὸ ΖΒ παραλληλόγραμμον p.110,23] ὅτι δέδοται τὸ ΖΒ παραλληλόγραμμον, δῆλον. ἐπεὶ γὰρ δέδοται ἡ ΖΓΒ γωνία, δέδοται ἄρα καὶ ἡ ΓΖΒ γωνία· εἰς γὰρ παραλλήλους τὰς ΖΒ, ΓΒ εὐθεῖα ἐμ- πέπτωκεν ἡ ΓΖ ποιοῦσα τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη δυσὶν ὀρθαῖς ἴσας, ὧν ἡ ὑπὸ ΖΓΒ δέδοται· καὶ λοιπὴ ἄρα ἡ ὑπὸ ΓΖΗ δέδοται· ὥστε καὶ αἱ λοιπαὶ δύο δεδομέναι εἰσίν. καὶ ἐπεὶ δέδοται ὁ τῆς ΓΖ πρὸς τὴν ΓΒ λόγος, ἴση δὲ ἡ μὲν ΖΓ τῇ ΗΒ, ἡ δὲ ΓΒ τῇ ΖΗ, καὶ ὁ λόγος τῶν πλευρῶν δέδοται. 120. Τοῦ δὲ ΖΒ πρὸς τὸ Γ∠ λόγος ἐστὶ δοθείς p. 112, 3–4] ἐπεὶ γὰρ τοῦ ΖΒ παραλληλογράμμου πρὸς τὸ ΑΖΒΓ εἶδος λόγος ἐστὶ δοθείς, τοῦ δὲ ΑΖΒΓ εἴδους πρὸς τὸ Γ∠ λόγος ἐστὶ δοθείς, καὶ διʼ ἴσου τοῦ ΖΒ πρὸς τὸ Γ∠ λόγος ἐστὶ δοθείς. 121. Ἴση γὰρ τῇ ὑπὸ ΚΓΒ p. 112, 14] ἐπεὶ γὰρ παράλληλος ἡ ΓΒ τῇ ΛΘ, καὶ εἰς αὐτὰς ἐμπέπτωκεν εὐθεῖα ἡ ΓΚ, αἱ ἐναλλὰξ γωνίαι ἴσαι ἀλλήλαις εἰσίν.

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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/.