Belopoeica
Hero of Alexandria
Hero of Alexandria. Greek and Roman Artillery: Technical Treatises. Marsden, Eric William, editor. Oxford: Clarendon Press, 1971
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 [*](114. 4 〈οὕτως〉 Wescher 7 τοσούτων H. Schöne, τούτων MPV, καὶ οὕτω τούτων F)
42
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 |