in your words; but I am of opinion that, in matters which are not present but future, he who exhibits a pattern of that at which he aims, should in nothing fall short of the fairest and truest; and that if he finds any part of this work impossible of execution he should avoid and not execute it, but he should contrive to carry out that which is nearest and most akin to it; you must allow the legislator to perfect his design, and when it is perfected, you should join with him in considering what part of his legislation is expedient and what will arouse opposition; for surely the artist who is to be deemed worthy of any regard at all, ought always to make his work self-consistent.’

Having determined that there is to be a distribution into twelve parts, let us now see in what way this may be accomplished.  There is no difficulty in perceiving that the twelve parts admit of the greatest number of divisions of that which they include, or in seeing the other numbers which are consequent upon them, and are produced out of them up to 5040; wherefore the law ought to order phratries and demes and villages, and also military ranks and movements, as well as coins and measures, dry and liquid, and weights, so as to be commensurable and agreeable to one another.  Nor should we fear the appearance of minuteness, if the law commands that all the vessels which a man possesses should have a common measure, when we consider generally that the divisions and variations of numbers have a use in respect of all the variations of which they are susceptible, both in themselves and as measures of height and depth, and in all sounds, and in motions, as well those which proceed in a straight direction, upwards or downwards, as in those which go round and round.  The legislator is to consider all these things and to bid the citizens, as far as possible, not to lose sight of numerical order; for no single instrument of youthful education has such mighty power, both as regards domestic economy and politics, and in the arts, as the study of arithmetic.  Above all, arithmetic stirs up him who is by nature sleepy and dull, and makes him quick to learn, retentive, shrewd, and aided by art divine he makes progress quite beyond his natural powers (compare Republic).  All such things, if only the legislator, by other laws and institutions, can banish meanness and covetousness from the souls of men, so that they can use them properly and to their own good, will be excellent and suitable instruments of education.  But if he cannot, he will unintentionally create in them, instead of wisdom, the habit of craft, which evil tendency may be observed in the Egyptians and Phoenicians, and many other races, through the general vulgarity of their pursuits and acquisitions, whether some unworthy legislator of theirs has been the cause, or some impediment of chance or nature.  For we must not fail to observe, O Megillus and Cleinias, that there is a difference in places, and that some beget better men and others worse; and