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τῶν πρὸς τὸ αὐτὸ λόγον ἐχόντων τὸ μείζονα λόγον ἔχον ἐκεῖνο μεῖζόν ἐστιν: πρὸς δὲ τὸ αὐτὸ μείζονα λόγον ἔχει, ἐκεῖνο ἔλαττόν ἐστιν.

ἐχέτω γὰρ τὸ Α πρὸς τὸ Γ μείζονα
5λόγον ἤπερ τὸ Β πρὸς τὸ Γ: λέγω, ὅτι μεῖζόν ἐστι τὸ Α τοῦ Β.

εἰ γὰρ μή, ἤτοι ἴσον ἐστὶ τὸ Α τῷ Β ἔλασσον. ἴσον μὲν οὖν οὔκ ἐστι τὸ Α τῷ Β: ἑκάτερον γὰρ ἂν τῶν Α, Β πρὸς τὸ Γ τὸν αὐτὸν εἶχε λόγον. οὐκ ἔχει δέ: οὐκ ἄρα
10ἴσον ἐστὶ τὸ Α τῷ Β. οὐδὲ μὴν ἔλασσόν ἐστι τὸ Α τοῦ Β: τὸ Α γὰρ ἂν πρὸς τὸ Γ ἐλάσσονα λόγον εἶχεν ἤπερ τὸ Β πρὸς τὸ Γ. οὐκ ἔχει δέ: οὐκ ἄρα ἔλασσόν ἐστι τὸ Α τοῦ Β. ἐδείχθη δὲ οὐδὲ ἴσον: μεῖζον ἄρα ἐστὶ τὸ Α τοῦ Β.

ἐχέτω δὴ πάλιν τὸ Γ πρὸς τὸ Β μείζονα λόγον ἤπερ
15τὸ Γ πρὸς τὸ Α: λέγω, ὅτι ἔλασσόν ἐστι τὸ Β τοῦ Α.

εἰ γὰρ μή, ἤτοι ἴσον ἐστὶν μεῖζον. ἴσον μὲν οὖν οὔκ ἐστι τὸ Β τῷ Α: τὸ Γ γὰρ ἂν πρὸς ἑκάτερον τῶν Α, Β τὸν αὐτὸν εἶχε λόγον. οὐκ ἔχει δέ: οὐκ ἄρα ἴσον ἐστὶ τὸ Α τῷ Β. οὐδὲ μὴν μεῖζόν ἐστι τὸ Β τοῦ Α: τὸ Γ γὰρ ἂν πρὸς
20τὸ Β ἐλάσσονα λόγον εἶχεν ἤπερ πρὸς τὸ Α. οὐκ ἔχει δέ: οὐκ ἄρα μεῖζόν ἐστι τὸ Β τοῦ Α. ἐδείχθη δέ, ὅτι οὐδὲ ἴσον: ἔλαττον ἄρα ἐστὶ τὸ Β τοῦ Α.

τῶν ἄρα πρὸς τὸ αὐτὸ λόγον ἐχόντων τὸ μείζονα λόγον ἔχον μεῖζόν ἐστιν: καὶ πρὸς τὸ αὐτὸ μείζονα λόγον ἔχει,
25ἐκεῖνο ἔλαττόν ἐστιν: ὅπερ ἔδει δεῖξαι.

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