How then can we rightly order the distribution of the land? In the first place, the number of the citizens has to be determined, and also the number and size of the divisions into which they will have to be formed; and the land and the houses will then have to be apportioned by us as fairly as we can. The number of citizens can only be estimated satisfactorily in relation to the territory and the neighbouring states. The territory must be sufficient to maintain a certain number of inhabitants in a moderate way of life--more than this is not required; and the number of citizens should be sufficient to defend themselves against the injustice of their neighbours, and also to give them the power of rendering efficient aid to their neighbours when they are wronged. After having taken a survey of their's and their neighbours' territory, we will determine the limits of them in fact as well as in theory. And now, let us proceed to legislate with a view to perfecting the form and outline of our state. The number of our citizens shall be 5040--this will be a convenient number; and these shall be owners of the land and protectors of the allotment. The houses and the land will be divided in the same way, so that every man may correspond to a lot. Let the whole number be first divided into two parts, and then into three; and the number is further capable of being divided into four or five parts, or any number of parts up to ten. Every legislator ought to know so much arithmetic as to be able to tell what number is most likely to be useful to all cities; and we are going to take that number which contains the greatest and most regular and unbroken series of divisions. The whole of number has every possible division, and the number 5040 can be divided by exactly fifty-nine divisors, and ten of these proceed without interval from one to ten: this will furnish numbers for war and peace, and for all contracts and dealings, including taxes and divisions of the land. These properties of number should be ascertained at leisure by those who are bound by law to know them; for they are true, and should be proclaimed at the foundation of the city, with a view to use. Whether the legislator is establishing a new state or restoring an old and decayed one, in respect of Gods and temples,--the temples which are to be built in each city, and the Gods or demi-gods after whom they are to be called,--if he be a man of sense, he will make no change in anything which the oracle of Delphi, or Dodona, or the God Ammon, or any ancient tradition has sanctioned in whatever manner, whether by apparitions or reputed inspiration of Heaven, in obedience to which mankind have established sacrifices in connexion with mystic rites, either originating on the spot, or derived from Tyrrhenia or Cyprus or some other place, and on the strength of which traditions they have consecrated oracles and images, and altars and temples, and portioned out a sacred domain for each of them.