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ἐὰν τέσσαρα μεγέθη ἀνάλογον , τὸ δὲ πρῶτον τῷ δευτέρῳ σύμμετρον , καὶ τὸ τρίτον τῷ τετάρτῳ σύμμετρον ἔσται: κἂν τὸ πρῶτον τῷ δευτέρῳ ἀσύμμετρον , καὶ τὸ τρίτον τῷ τετάρτῳ ἀσύμμετρον ἔσται.
5

ἔστωσαν τέσσαρα μεγέθη ἀνάλογον τὰ Α, Β, Γ, Δ, ὡς τὸ Α πρὸς τὸ Β, οὕτως τὸ Γ πρὸς τὸ Δ, τὸ Α δὲ τῷ Β σύμμετρον ἔστω: λέγω, ὅτι καὶ τὸ Γ τῷ Δ σύμμετρον ἔσται.

ἐπεὶ γὰρ σύμμετρόν ἐστι τὸ Α τῷ Β, τὸ Α ἄρα πρὸς
10τὸ Β λόγον ἔχει, ὃν ἀριθμὸς πρὸς ἀριθμόν. καί ἐστιν ὡς τὸ Α πρὸς τὸ Β, οὕτως τὸ Γ πρὸς τὸ Δ: καὶ τὸ Γ ἄρα πρὸς τὸ Δ λόγον ἔχει, ὃν ἀριθμὸς πρὸς ἀριθμόν: σύμμετρον ἄρα ἐστὶ τὸ Γ τῷ Δ.

ἀλλὰ δὴ τὸ Α τῷ Β ἀσύμμετρον ἔστω: λέγω, ὅτι καὶ
15τὸ Γ τῷ Δ ἀσύμμετρον ἔσται. ἐπεὶ γὰρ ἀσύμμετρόν ἐστι τὸ Α τῷ Β, τὸ Α ἄρα πρὸς τὸ Β λόγον οὐκ ἔχει, ὃν ἀριθμὸς πρὸς ἀριθμόν. καί ἐστιν ὡς τὸ Α πρὸς τὸ Β, οὕτως τὸ Γ πρὸς τὸ Δ: οὐδὲ τὸ Γ ἄρα πρὸς τὸ Δ λόγον ἔχει, ὃν ἀριθμὸς πρὸς ἀριθμόν: ἀσύμμετρον ἄρα ἐστὶ τὸ Γ
20τῷ Δ.

ἐὰν ἄρα τέσσαρα μεγέθη, καὶ τὰ ἑξῆς.

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