And if there is truth in what has preceded, he will be wedded to an image of pleasure which is thrice removed as to truth from the pleasure of the oligarch? He will. And the oligarch is third from the royal; since we count as one royal and aristocratical? Yes, he is third. Then the tyrant is removed from true pleasure by the space of a number which is three times three? Manifestly. The shadow then of tyrannical pleasure determined by the number of length will be a plane figure. Certainly. And if you raise the power and make the plane a solid, there is no difficulty in seeing how vast is the interval by which the tyrant is parted from the king. Yes; the arithmetician will easily do the sum. Or if some person begins at the other end and measures the interval by which the king is parted from the tyrant in truth of pleasure, he will find him, when the multiplication is complete, living 729 times more pleasantly, and the tyrant more painfully by this same interval. What a wonderful calculation! And how enormous is the distance which separates the just from the unjust in regard to pleasure and pain! Yet a true calculation, I said, and a number which nearly concerns human life, if human beings are concerned with days and nights and months and years. Yes, he said, human life is certainly concerned with them. Then if the good and just man be thus superior in pleasure to the evil and unjust, his superiority will be infinitely greater in propriety of life and in beauty and virtue? Immeasurably greater. Well, I said, and now having arrived at this stage of the argument, we may revert to the words which brought us hither: Was not some one saying that injustice was a gain to the perfectly unjust who was reputed to be just? Yes, that was said. Now then, having determined the power and quality of justice and injustice, let us have a little conversation with him. What shall we say to him? Let us make an image of the soul, that he may have his own words presented before his eyes. Of what sort? An ideal image of the soul, like the composite creations of ancient mythology, such as the Chimera or Scylla or Cerberus, and there are many others in which two or more different natures are said to grow into one. There are said of have been such unions. Then do you now model the form of a multitudinous, many-headed monster, having a ring of heads of all manner of beasts, tame and wild, which he is able to generate and metamorphose at will. You suppose marvellous powers in the artist; but, as language is more pliable than wax or any similar substance, let there be such a model as you propose. Suppose now that you make a second form as of a lion, and a third of a man, the second smaller than the first, and the third smaller than the second. That, he said, is an easier task; and I have made them as you say. And now join them, and let the three grow into one. That has been accomplished.