Chapter 6

κη΄. Κύκλου τοῦ ΑΒΓ ἐφαπτέσθωσαν αἱ Α∠, ∠Γ, καὶ ἐπεζεύχθω ἡ ΑΓ. καὶ διήχθω τυχοῦσα ἡ ∠Β· ὅτι γίνεται, ὡς ἡ Β∠ πρὸς τὴν ∠Ε, οὕτως ἡ Β πρὸς τὴν ΖΕ. ἐπεὶ γὰρ ἴση ἐστὶν ἡ Α∠ τῇ ∠Γ, τὸ ἄρα ὑπὸ ΑΖΓ μετὰ τοῦ ἀπὸ Ζ∠ ἴσον ἐστὶν τῷ ἀπὸ ∠Α. ἀλλὰ τὸ μὲν ὑπὸ ΑΖΓ ἴσον ἐστὶν τῷ ὑπὸ ΒΖΕ, τὸ δὲ ἀπὸ ∠Α. ἐστιν τὸ ὑπὸ Β∠Ε· τὸ ἄρα ὑπὸ ΒΖΕ μετὰ τοῦ ἀπὸ ∠Ζ ἴσον ἐστὶν τῷ ὑπὸ Β∠Ε. ἐὰν δὲ τοῦτο, γίνεται, ὡς ἡ Β∠ πρὸς τὴν ∠Ε, οὕτως ἡ ΒΖ πρὸς τὴν ΖΕ.