Commentarii in libros de sphaera et cylindro (11)

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.