Εἰς τὸ ιϚ΄.

Καὶ ἐπεὶ τὸ ὑπὸ τῶν ΒΑ, ΑΗ ἴσον ἐστὶ τῷ ὑπὸ τῶν Β △Ζ καὶ τῷ ὑπὸ τῆς Α △καὶ συναμφοτέρου τῆς △Ζ, ΑΗ διὰ τὸ παράλληλον εἶναι τὴν △Ζ τῇ ΑΗ |Ἐπεὶ γὰρ παράλληλός ἐστιν ἡ △Ζ τῇ ΑΗ, ἔστιν ὡς ἡ ΒΑ πρὸς ΑΗ, ἡ Β△ πρὸς △Ζ· καὶ διὰ τοῦτο τὸ ὑπὸ τῶν ἄκρων τῶν ΒΑ, △Ζ ἴσον ἐστὶ τῷ ὑπὸ τῶν μέσων τῶν Β△, ΑΗ. Ἀλλὰ τὸ ὑπὸ τῶν ΒΑ, △Ζ ἴσον ἐστὶ τῷ ὑπὸ τῶν Β△, △Ζ καὶ τῷ ὑπὸ τῶν Α△, △Ζ διὰ τὸ πρῶτον θεώρημα τοῦ β΄ βιβλίου τῆς Στοιχειώσεως· καὶ τὸ ὑπὸ τῶν Β∠, ΑΗ ἄρα ἴσον ἐστὶ τῷ τε ὑπὸ Β△, △Ζ καὶ τῷ ὑπὸ Α△, △Ζ. Κοινὸν προσκείσθω τὸ ὑπὸ △Α, ΑΗ· τὸ ἄρα ὑπὸ Β△, ΑΗ μετὰ τοῦ ὑπὸ △Α, ΑΗ, ὅπερ ἐστὶν τὸ ὑπὸ ΒΑ, ΑΗ, ἴσον ἐστὶ τῷ ὑπὸ Β∠, ∠Ζ καὶ τῷ ὑπὸ Α△, △Ζ καὶ ἔτι τῷ ὑπὸ Α△, ΑΗ.