ιγ΄.
λόγῳ, ἀφῃρήσθω τὸ δοθὲν μέγεθος τὸ ΓΖ· λοιποῦ. 1 2 ἄρα τοῦ ΔΖ πρὸς τὸ Ε λόγος ἐστὶ δοθείς. καὶ ἐπεὶ λόγος ἐστὶ δοθεὶς τοῦ ΑΒ πρὸς τὸ ΓΔ, ὁ αὐτὸς αὐτῷ γεγονέτω ὁ τοῦ ΑΒ πρὸς τὸ ΓΖ. λόγος ἄρα καὶ τοῦ AH πρὸς τὸ ΓΖ δοθείς. δοθὲν δὲ τὸ ΓΖ δοῦὲν
ἄρα καὶ τὸ ΑΗ· καὶ λοιποῦ τοῦ ΗΒ πρὸς λοιπὸν τὸ ΔΖ λόγος ἐστὶ δοθείς. τοῦ δὲ ΔΖ πρὸς τὸ Ε λόγος ἐστὶ δοθείς· καὶ τοῦ ΗΒ ἄρα πρὸς τὸ Ε λόγος ἐστὶ δοθείς. καί ἐστὶ δοθὲν τὸ ΑΗ· τὸ ΑΒ ἄρα τοῦ Ε δοθέντι μεῖζόν ἐστιν ἢ ἐν λόγῳ.
Data. Euclid. ed. Johan Ludvig Heiberg, ed. Heinrich Menge. United States. 2016.
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