νζ΄.
ἐπὶ τὰ Δ, Θ. καὶ ἐπεὶ δοθέν ἐστιν ἑκάτερον τῶν ΕΒ, ΑΗ, λόγος ἄρα τοῦ ΕΒ πρὸς τὸ ΑΗ δοθείς. ἴσον δὲ τὸ ΗΑ τῷ ΑΘ· λόγος ἄρα καὶ τοῦ ΕΒ πρὸς τὸ ΑΘ δοθείς· ὥστε καὶ τῆς ΕΑ πρὸς τὴν ΑΔ λόγος ἐστὶ δοθείς. ἴση δὲ ἡ ΕΑ τῇ ΑΒ· λόγος ἄρα καὶ τῆς
ΒΑ πρὸς ΑΔ δοθείς. καὶ ἐπεὶ δοθεῖσά ἐστιν ἡ ὑπὸ 1 2 τῶν ΓΑΒ, ὧν ἡ ὑπὸ ΔΑΒ δοθεῖσά ἐστιν, λοιπὴ ἄρα ἡ ὑπὸ τῶν ΓΑΔ ἐστι δοθεῖσα. ἔστι δὲ καὶ ἡ ὑπὸ τῶν ΓΔΑ δοθεῖσα· ὀρθὴ γάρ· λοιπὴ ἄρα ἡ ὑπὸ τῶν ΑΓΔ δοθεῖσά ἐστιν· δέδοται ἄρα τὸ ΑΓΔ τρίγωνον
τῷ εἴδει· λόγος ἄρα ἐστὶ τῆς ΓΑ πρὸς τὴν ΑΔ δοθείς. τῆς δὲ ΔΑ πρὸς τὴν ΑΒ λόγος ἐστὶ δοθείς· καὶ τῆς ΓΑ ἄρα πρὸς τὴν ΑΒ λόγος ἐστὶ δοθείς. καί ἐστι δοθεῖσα ἡ ΒΑ· δοθεῖσα ἄρα καὶ ἡ ΑΓ. καί ἐστι τὸ πλάτος τοῦ παραβλήματος.
Data. Euclid. ed. Johan Ludvig Heiberg, ed. Heinrich Menge. United States. 2016.
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