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ἐὰν κύβος ἀριθμὸς κύβον ἀριθμὸν μετρῇ, καὶ πλευρὰ τὴν πλευρὰν μετρήσει: καὶ ἐὰν πλευρὰ τὴν πλευρὰν μετρῇ, καὶ κύβος τὸν κύβον μετρήσει.

κύβος γὰρ ἀριθμὸς Α κύβον τὸν Β μετρείτω, καὶ
5τοῦ μὲν Α πλευρὰ ἔστω Γ, τοῦ δὲ Β Δ: λέγω, ὅτι Γ τὸν Δ μετρεῖ.

Γ γὰρ ἑαυτὸν πολλαπλασιάσας τὸν Ε ποιείτω, δὲ Δ ἑαυτὸν πολλαπλασιάσας τὸν Η ποιείτω, καὶ ἔτι Γ τὸν Δ πολλαπλασιάσας τὸν Ζ ποιείτω, ἑκάτερος δὲ
10τῶν Γ, Δ τὸν Ζ πολλαπλασιάσας ἑκάτερον τῶν Θ, Κ ποιείτω. φανερὸν δή, ὅτι οἱ Ε, Ζ, Η καὶ οἱ Α, Θ, Κ, Β ἑξῆς ἀνάλογόν εἰσιν ἐν τῷ τοῦ Γ πρὸς τὸν Δ λόγῳ. καὶ ἐπεὶ οἱ Α, Θ,
15κ, Β ἑξῆς ἀνάλογόν εἰσιν, καὶ μετρεῖ Α τὸν Β, μετρεῖ ἄρα καὶ τὸν Θ. καί ἐστιν ὡς Α πρὸς τὸν Θ, οὕτως Γ πρὸς τὸν Δ: μετρεῖ ἄρα καὶ Γ τὸν Δ.

ἀλλὰ δὴ μετρείτω Γ τὸν Δ: λέγω, ὅτι καὶ Α τὸν Β μετρήσει.

τῶν γὰρ αὐτῶν κατασκευασθέντων ὁμοίως δὴ δείξομεν, ὅτι οἱ Α, Θ, Κ, Β ἑξῆς ἀνάλογόν εἰσιν ἐν τῷ τοῦ Γ πρὸς τὸν Δ λόγῳ. καὶ ἐπεὶ Γ τὸν Δ μετρεῖ, καί ἐστιν ὡς
25 Γ πρὸς τὸν Δ, οὕτως Α πρὸς τὸν Θ, καὶ Α ἄρα τὸν Θ μετρεῖ: ὥστε καὶ τὸν Β μετρεῖ Α: ὅπερ ἔδει δεῖξαι.

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