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ἐὰν ἄρτιοι ἀριθμοὶ ὁποσοιοῦν συντεθῶσιν, ὁ ὅλος ἄρτιός ἐστιν. Συγκείσθωσαν γὰρ ἄρτιοι ἀριθμοὶ ὁποσοιοῦν οἱ ΑΒ, ΒΓ, ΓΔ, ΔΕ: λέγω, ὅτι ὅλος ὁ ΑΕ ἄρτιός ἐστιν.
5ἐπεὶ γὰρ ἕκαστος τῶν ΑΒ, ΒΓ, ΓΔ, ΔΕ ἄρτιός ἐστιν, ἔχει μέρος ἥμισυ: ὥστε καὶ ὅλος ὁ ΑΕ ἔχει μέρος ἥμισυ. ἄρτιος δὲ ἀριθμός ἐστιν ὁ δίχα διαιρούμενος: ἄρτιος ἄρα ἐστὶν ὁ ΑΕ: ὅπερ ἔδει δεῖξαι.
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