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ἐὰν τέσσαρες εὐθεῖαι ἀνάλογον ὦσιν, δύνηται δὲ πρώτη τῆς δευτέρας μεῖζον τῷ ἀπὸ συμμέτρου ἑαυτῇ
μήκει, καὶ τρίτη τῆς τετάρτης μεῖζον δυνήσεται τῷ ἀπὸ συμμέτρου ἑαυτῇ μήκει. καὶ ἐὰν πρώτη τῆς
5δευτέρας μεῖζον δύνηται τῷ ἀπὸ ἀσυμμέτρου ἑαυτῇ μήκει, καὶ τρίτη τῆς τετάρτης μεῖζον δυνήσεται τῷ ἀπὸ ἀσυμμέτρου ἑαυτῇ μήκει.

ἔστωσαν τέσσαρες εὐθεῖαι ἀνάλογον αἱ Α, Β, Γ, Δ, ὡς Α πρὸς τὴν Β, οὕτως Γ πρὸς τὴν Δ, καὶ Α μὲν τῆς
10β μεῖζον δυνάσθω τῷ ἀπὸ τῆς Ε, δὲ Γ τῆς Δ μεῖζον δυνάσθω τῷ ἀπὸ τῆς Ζ: λέγω, ὅτι, εἴτε σύμμετρός ἐστιν Α τῇ Ε, σύμμετρός ἐστι καὶ Γ τῇ Ζ, εἴτε ἀσύμμετρός ἐστιν Α τῇ Ε, ἀσύμμετρός ἐστι καὶ Γ τῇ Ζ.

ἐπεὶ γάρ ἐστιν ὡς Α πρὸς τὴν Β,
15οὕτως Γ πρὸς τὴν Δ, ἔστιν ἄρα καὶ ὡς τὸ ἀπὸ τῆς Α πρὸς τὸ ἀπὸ τῆς Β, οὕτως τὸ ἀπὸ τῆς Γ πρὸς τὸ ἀπὸ τῆς Δ. ἀλλὰ τῷ μὲν ἀπὸ τῆς Α ἴσα ἐστὶ τὰ ἀπὸ τῶν Ε, Β, τῷ δὲ ἀπὸ τῆς Γ
20ἴσα ἐστὶ τὰ ἀπὸ τῶν Δ, Ζ. ἔστιν ἄρα ὡς τὰ ἀπὸ τῶν Ε, Β πρὸς τὸ ἀπὸ τῆς Β, οὕτως τὰ ἀπὸ τῶν Δ, Ζ πρὸς τὸ ἀπὸ τῆς Δ: διελόντι ἄρα ἐστὶν ὡς τὸ ἀπὸ τῆς Ε πρὸς τὸ ἀπὸ τῆς Β, οὕτως τὸ ἀπὸ τῆς Ζ πρὸς τὸ ἀπὸ τῆς Δ: ἔστιν ἄρα καὶ ὡς
25 Ε πρὸς τὴν Β, οὕτως Ζ πρὸς τὴν Δ: ἀνάπαλιν ἄρα ἐστὶν ὡς Β πρὸς τὴν Ε, οὕτως Δ πρὸς τὴν Ζ. ἔστι δὲ καὶ ὡς Α πρὸς τὴν Β, οὕτως Γ πρὸς τὴν Δ: δι᾽ ἴσου ἄρα ἐστὶν ὡς Α πρὸς τὴν Ε, οὕτως Γ πρὸς τὴν Ζ. εἴτε οὖν σύμμετρός ἐστιν Α τῇ Ε, σύμμετρός ἐστι καὶ
30 Γ τῇ Ζ, εἴτε ἀσύμμετρός ἐστιν Α τῇ Ε, ἀσύμμετρός ἐστι καὶ Γ τῇ Ζ.

ἐὰν ἄρα, καὶ τὰ ἑξῆς.

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load focus English (Thomas L. Heath, Sir Thomas Little Heath, 1956)
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