Ancient Greek
Book 3
Pappus Alexandrinus, Synagoge 3.22
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22 Λέγω δὴ ὅτι καὶ τὸ ὑπὸ ΚΕΛ ἴσον ἐστὶν τῷ ἀπὸ EΒ. Ἔπεὶ γὰρ ὡς ἡ ΑΕ πρὸς ΕΓ, οὕτως ἡ ΑΒ πρὸς ΒΓ, τουτέστιν πρὸς ΓΖ, ἔσται καὶ ἡ λοιπὴ ἡ ΒΕ πρὸς λοιπὴν τὴν ΕΖ ὡς ἡ ΑΕ πρὸς ΕΓ, τουτέστιν ὡς ἡ ΚΕ πρὸς Κ ∠. ἀλλʼ ὡς μὲν ἡ ΚΕ πρὸς Ε ∠,οὕτως τὸ ὑπὸ ΚΕΛ πρὸς τὸ ὑπὸ ΛΕ Ε ∠,ὡς δὲ ἡ ΒΕ πρὸς EΖ, οὕτως τὸ ἀπὸ τῆς ΒΕ πρὸς τὸ ὑπὸ BΕΖ, καὶ ἔστιν ἴσον τὸ ὑπὸ ΛΕ Ε ∠τῷ ὑπὸ ΒΕ ΕΖ· ἴσον ἄρα καὶ τὸ ὑπὸ ΚΕΛ τῷ ἀπὸ EΒ.