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ἐὰν ἀπὸ μονάδος ὁποσοιοῦν ἀριθμοὶ ἑξῆς ἀνάλογον ὦσιν, ἐλάττων τὸν μείζονα μετρεῖ κατά τινα τῶν ὑπαρχόντων ἐν τοῖς ἀνάλογον ἀριθμοῖς.

ἔστωσαν ἀπὸ μονάδος τῆς Α ὁποσοιοῦν ἀριθμοὶ ἑξῆς
5ἀνάλογον οἱ Β, Γ, Δ, Ε: λέγω, ὅτι τῶν Β, Γ, Δ, Ε ἐλάχιστος Β τὸν Ε μετρεῖ κατά τινα τῶν Γ, Δ.

ἐπεὶ γάρ ἐστιν ὡς Α μονὰς πρὸς τὸν Β, οὕτως Δ πρὸς τὸν Ε, ἰσάκις ἄρα Α μονὰς τὸν Β ἀριθμὸν
10μετρεῖ καὶ Δ τὸν Ε: ἐναλλὰξ ἄρα ἰσάκις Α μονὰς τὸν Δ μετρεῖ καὶ Β τὸν Ε. δὲ Α μονὰς τὸν Δ μετρεῖ κατὰ τὰς ἐν αὐτῷ μονάδας: καὶ Β ἄρα τὸν Ε μετρεῖ κατὰ τὰς ἐν τῷ Δ μονάδας: ὥστε
15ἐλάσσων Β τὸν μείζονα τὸν Ε μετρεῖ κατά τινα ἀριθμὸν τῶν ὑπαρχόντων ἐν τοῖς ἀνάλογον ἀριθμοῖς.

Πόρισμα Καὶ φανερόν, ὅτι ἣν ἔχει τάξιν μετρῶν ἀπὸ μονάδος, τὴν αὐτὴν ἔχει καὶ καθ᾽ ὃν μετρεῖ ἀπὸ τοῦ μετρουμένου
20ἐπὶ τὸ πρὸ αὐτοῦ. _ὅπερ ἔδει δεῖξαι.

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