ξε΄.
τοῦ Α ἐπὶ τὴν ΒΓ κάθετος ἡ ΑΔ· λέγω, ὅτι, ᾧ ἔλασ- σόν ἐστι τὸ ἀπὸ τῆς ΑΓ τῶν ἀπὸ τῶν ΑΒ, ΒΓ τουτ- έστι τὸ δὶς ὑπὸ τῶν ΓΒ, ΒΔ πρὸς τὸ ΑΒΓ τρίγωνον λόγον ἔχει δεδομένον.
ἔστι δὲ καὶ ἡ ὑπὸ τῶν ΑΔΒ δοθεῖσα, καὶ λοιπὴ ἄρα ἡ ὑπὸ τῶν ΕΑΔ ἐστι δοθεῖσα· δέδοται ἄρα τὸ ΑΒΔ τρίγωνον τῷ εἴδει· λόγος ἄρα τῆς ΒΔ πρὸς τὴν ΔΑ δοθείς· ὥστε καὶ τοῦ ὑπὸ τῶν ΓΒΔ πρὸς τὸ ὑπὸ τῶν ΓΒ, ΑΔ λόγος ἐστὶ δοθείς· καὶ τοῦ δὶς ὑπὸ τῶν
ΓΒ, ΒΔ ἄρα. ἀλλὰ τοῦ ὑπὸ τῶν ΒΓ, ΑΔ πρὸς τὸ ΑΒΓ λόγος ἐστὶ δοθείς· καὶ τοῦ δὶς ὑπὸ τῶν ΓΒ, ΒΔ ἄρα πρὸς τὸ ΑΒΓ τρίγωνον λόγος ἐστὶ δοθείς. καί ἐστι τὸ δὶς ὑπὸ τῶν ΓΒ, ΒΔ, ᾧ ἔλασσόν ἐστι τὸ ἀπὸ τῆς ΑΓ τῶν ἀπὸ τῶν ΑΒ, ΒΓ· ᾧ ἄρα ἔλασσόν ἐστι
τὸ ἀπὸ τῆς ΑΓ τῶν ἀπὸ τῶν ΑΒ, ΒΓ, ἐκεῖνο τὸ χωορίον πρὸς τὸ ΑΒΓ τρίγωνον λόγον ἔχει δεδομένον.
Data. Euclid. ed. Johan Ludvig Heiberg, ed. Heinrich Menge. United States. 2016.
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