[118] 118 αἱ μέσαι ἀνὰ λόγον εἰσὶν αἱ ΑΖ, ΓΗ· καὶ πρώτης οὔσηςω τῆς ΑΒ, δευτέρα μὲν ἔσται ἡ ΑΖ, τρίτη δὲ ἡ ΓΗ, τετάρτη δὲ ἡ ΒΓ. ἐπεὶ γὰρ ἴση ἐστὶν ἡ ΑΕ τῇ Ε∠ καὶ διῆκται ἡ ΕΖ, τὸ ἄρα ὑπὸ ∠ΖΑ μετὰ τοῦ
ἀπὸΑΕ ἴσον
1
ἐστὶ τῷ ἀπὸ τοῦ ΕΖ. διὰ τὰ αὐτὰ δὴ καὶ τὸ ὑπὸ ∠ΗΓ μετὰ τοῦ ἀπὸ ΓΕ ἴσον
ἐστὶ τῷ ἀπὸ ΕΗ· καί ἐστιν ἴση ἡ μὲν ΑΕ τῇ ΕΓ, ἡ δὲ ΕΖ τῇ ΕΗ. ἔσται ἄρα καὶ τὸ ὑπὸ ∠ΖΑ ἴσον τῷ ὑπὸ ∠ΗΓ. ὡς ἄρα ἡ Η∠ πρὸς ∠Ζ, οὕτως ἐστὶν ἡ ΑΖ πρὸς ΓΗ. ἀλλ᾿ ὡς ἡ Η∠ πρὸς ∠Ζ, ἥ τε ΑΒ πρὸς ΑΖ, καὶ ἡ ΖΑ: πρὸς ΓΗ, καὶ ἡ ΗΓ πρὸς |
ἐστὶ τῷ ἀπὸ ΕΗ· καί ἐστιν ἴση ἡ μὲν ΑΕ τῇ ΕΓ, ἡ δὲ ΕΖ τῇ ΕΗ. ἔσται ἄρα καὶ τὸ ὑπὸ ∠ΖΑ ἴσον τῷ ὑπὸ ∠ΗΓ. ὡς ἄρα ἡ Η∠ πρὸς ∠Ζ, οὕτως ἐστὶν ἡ ΑΖ πρὸς ΓΗ. ἀλλ᾿ ὡς ἡ Η∠ πρὸς ∠Ζ, ἥ τε ΑΒ πρὸς ΑΖ, καὶ ἡ ΖΑ: πρὸς ΓΗ, καὶ ἡ ΗΓ πρὸς |
Belopoeica. Hero of Alexandria. ed. E. W. Marsden. United States. 2018.
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