[L]et us assign the figures that have come into being in our theory to fire and earth and water and air. To earth let us give the cubical form; for earth is least mobile of the four and most plastic of bodies: and that substance must possess this nature in the highest degree which has its bases most stable. Now of the triangles which we assumed as our starting-point that with equal sides is more stable than that with unequal; and of the surfaces composed of the two triangles the equilateral quadrangle necessarily is more stable than the equilateral triangle... Now among all these that which has the fewest bases must naturally in all respects be the most cutting and keen of all, and also the most nimble, seeing it is composed of the smallest number of similar parts... Let it be determined then... that the solid body which has taken the form of the pyramid [tetrahedron] is the element and seed of fire; and the second in order of generation let [octahedron] us say to be that of air, and the third [icosahedron] that of water. Now all these bodies we must conceive as being so small that each single body in the several kinds cannot for its smallness be seen by us at all; but when many are heaped together, their united mass is seen...

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The society we have described can never grow into a reality or see the light of day, and there will be no end to the troubles of states, or indeed, my dear Glaucon, of humanity itself, till philosophers become rulers in this world, or till those we now call kings and rulers really and truly become philosophers, and political power and philosophy thus come into the same hands.

Evil is the vulgar lover who loves the body rather than the soul, inasmuch as he is not even stable, because he loves a thing which is in itself unstable, and therefore when the bloom of youth which he was desiring is over, he takes wing and flies away, in spite of all his words and promises; whereas the love of the noble disposition is life-long, for it becomes one with the everlasting.

τοῖς μὲν οὖν τότε, ἅτε οὐκ οὖσι σοφοῖς ὥσπερ ὑμεῖς οἱ νέοι, ἀπέχρη δρυὸς καὶ πέτρας ἀκούειν ὑπ᾽ εὐηθείας, εἰ μόνον ἀληθῆ λέγοιεν: σοὶ δ᾽ ἴσως διαφέρει τίς ὁ λέγων καὶ ποδαπός.