The Republic · ¶266

But though agreeing with Dr. Donaldson thus far, I see no reason for supposing, as he does, that the first or perfect number is the world, the human or imperfect number the state; nor has he given any proof that the second harmony is a cube. Nor do I think that ἀῤῥήτων δὲ δυεῖν can mean ‘two incommensurables,’ which he arbitrarily assumes to be 2 and 3, but rather, as the preceding clause implies, δυεῖν ἀριθμοῖν ἀπὸ ἀῤῥήτων διαμέτρων πεμπάδος, i.e. two square numbers based upon irrational diameters of a figure the side of which is 5 = 50 × 2.

Plato · translated by Benjamin Jowett · composite transcription based on the 1888 third edition
Benjamin Jowett, revised third edition (1888), with Stephanus numbering from the 1908 edition; composite transcription, Project Gutenberg #55201
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