Thus much of the dances which are appropriate to fair forms and noble souls. Comedy, which is the opposite of them, remains to be considered. For the serious implies the ludicrous, and opposites cannot be understood without opposites. But a man of repute will desire to avoid doing what is ludicrous. He should leave such performances to slaves,--they are not fit for freemen; and there should be some element of novelty in them. Concerning tragedy, let our law be as follows: When the inspired poet comes to us with a request to be admitted into our state, we will reply in courteous words--We also are tragedians and your rivals; and the drama which we enact is the best and noblest, being the imitation of the truest and noblest life, with a view to which our state is ordered. And we cannot allow you to pitch your stage in the agora, and make your voices to be heard above ours, or suffer you to address our women and children and the common people on opposite principles to our own. Come then, ye children of the Lydian Muse, and present yourselves first to the magistrates, and if they decide that your hymns are as good or better than ours, you shall have your chorus; but if not, not. There remain three kinds of knowledge which should be learnt by freemen--arithmetic, geometry of surfaces and of solids, and thirdly, astronomy. Few need make an accurate study of such sciences; and of special students we will speak at another time. But most persons must be content with the study of them which is absolutely necessary, and may be said to be a necessity of that nature against which God himself is unable to contend. 'What are these divine necessities of knowledge?' Necessities of a knowledge without which neither gods, nor demigods, can govern mankind. And far is he from being a divine man who cannot distinguish one, two, odd and even; who cannot number day and night, and is ignorant of the revolutions of the sun and stars; for to every higher knowledge a knowledge of number is necessary--a fool may see this; how much, is a matter requiring more careful consideration. 'Very true.' But the legislator cannot enter into such details, and therefore we must defer the more careful consideration of these matters to another occasion. 'You seem to fear our habitual want of training in these subjects.' Still more do I fear the danger of bad training, which is often worse than none at all. 'Very true.' I think that a gentleman and a freeman may be expected to know as much as an Egyptian child. In Egypt, arithmetic is taught to children in their sports by a distribution of apples or garlands among a greater or less number of people; or a calculation is made of the various combinations which are possible among a set of boxers or wrestlers; or they distribute cups among the children, sometimes of gold, brass, and silver intermingled, sometimes of one metal only. The knowledge of arithmetic which is thus acquired is a great help, either to the general or to the manager of