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ἐὰν κύβος ἀριθμὸς κύβον ἀριθμὸν μὴ μετρῇ, οὐδὲ ἡ πλευρὰ τὴν πλευρὰν μετρήσει: κἂν ἡ πλευρὰ τὴν πλευρὰν μὴ μετρῇ, οὐδὲ ὁ κύβος τὸν κύβον μετρήσει. κύβος γὰρ ἀριθμὸς ὁ Α κύβον
5ἀριθμὸν τὸν Β μὴ μετρείτω, καὶ τοῦ μὲν Α πλευρὰ ἔστω ὁ Γ, τοῦ δὲ Β ὁ Δ: λέγω, ὅτι ὁ Γ τὸν Δ οὐ μετρήσει. εἰ γὰρ μετρεῖ ὁ Γ τὸν Δ, καὶ ὁ Α τὸν Β μετρήσει. οὐ
10μετρεῖ δὲ ὁ Α τὸν Β: οὐδ᾽ ἄρα ὁ Γ τὸν Δ μετρεῖ. ἀλλὰ δὴ μὴ μετρείτω ὁ Γ τὸν Δ: λέγω, ὅτι οὐδὲ ὁ Α τὸν Β μετρήσει. εἰ γὰρ ὁ Α τὸν Β μετρεῖ, καὶ ὁ Γ τὸν Δ μετρήσει. οὐ μετρεῖ δὲ ὁ Γ τὸν Δ: οὐδ᾽ ἄρα ὁ Α τὸν Β μετρήσει:
15ὅπερ ἔδει δεῖξαι.
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