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