Ancient Greek
SCHOLIA.
Scholia in Euclidem, Scholia in Euclidis Data Ad prop. XIV.
Not analysed yet
64. P. 26, 17] κἄν τε ἴσα ᾖ τὰ ΑΕ, ΓΖ κἄν τε ἄνισα. 65. Λόγος ἄρα τοῦ ΕΑ p. 26, 21–22] τῶν γὰρ δεδομένων μεγεθῶν ὁ λόγος πρὸς ἄλληλα δέδοται. 66. Λόγος ἄρα καὶ τοῦ ΗΒ p. 28, 6–7] διὰ τὸ ιβ΄ τοῦ ε΄ καὶ διὰ τὸ ἀντιστρόφιον τοῦ ὅρου. ἐπεὶ δέδοται ὁ τοῦ ΑΒ πρὸς Γ∠ λόγος καί ἐστιν ὁ αὐτὸς ὁ τοῦ ΗΑ πρὸς ΖΓ. δέδοται καὶ οὕτως ὁ τοῦ ΗΒ πρὸς Ζ∠. 67. Ἐὰν δὲ ποιήσωμεν ὡς τὸ ΑΒ πρὸς τὸ Γ∠, οὕτως τὸ ΑΕ πρὸς τὸ ἀπὸ τοῦ Γ ὡς ἐπὶ τὸ Ζ, εὑρε- θήσεται τὸ Ζ∠ τοῦ ΕΒ δοθέντι μεῖζον ἢ ἐν λόγῳ. Ad prop. XV. 68. Τοῦτο ἀντιστρόφιόν πως τοῦ πρὸ αὐτοῦ. δείξας γάρ, ὅτι ἐὰν προστεθῇ δεδομένα μεγέθη τοῖς δεδο- μένον ἔχουσι λόγον, νῦν καὶ ἀφαιρῶν τὰ αὐτὰ τῶν αὐτῶν δείκνυσι τὸ αὐτό.