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[747a] He must recognize it as a universal rule that the divisions and variations of numbers are applicable to all purposes—both to their own arithmetical variations and to the geometrical variations of surfaces and solids, and also to those of sounds, and of motions, whether in a straight line up and down or circular.1 The lawgiver must keep all these in view and charge all the citizens to hold fast, so far as they can, [747b] to this organized numerical system. For in relation to economics, to politics and to all the arts, no single branch of educational science possesses so great an influence as the study of numbers: its chief advantage is that it wakes up the man who is by nature drowsy and slow of wit, and makes him quick to learn, mindful and sharp-witted, progressing beyond his natural capacity by art divine. All these subjects of education will prove fair and fitting, provided that you can remove illiberality and avarice, by means of other laws and institutions, from the souls of those [747c] who are to acquire them adequately and to profit by them; otherwise you will find that you have unwittingly turned out a “sharper,” as we call him, instead of a sage: examples of this we can see today in the effect produced on the Egyptians and Phoenicians2 and many other nations by the illiberal character of their property, and their other institutions,—whether these results are due to their having had a bad lawgiver, or to some adverse fortune that befell them, or else, possibly, to some natural disadvantage. [747d] For that, too, is a point, O Megillus and Clinias, which we must not fail to notice,—that some districts are naturally superior to others for the breeding of men of a good or bad type; and we must not conflict with this natural difference in our legislation. Some districts are ill-conditioned or well-conditioned owing to a variety of winds or to sunshine, others owing to their waters, others owing simply to the produce of the soil, [747e] which offers produce either good or bad for their bodies, and equally able to effect similar results in their souls as well. Of all these, those districts would be by far the best which have a kind of heavenly breeze, and where the portions of land are under the care of daemons,3 so that they receive those that come from time to time to settle there either graciously or ungraciously. These districts the judicious lawgiver will examine, so far as examination of such matters is possible for mere man; and he will try to frame his laws accordingly. And you too, Clinias, must adopt the same course; when you are proposing to colonize the country, you must attend to these matters first.

Your discourse, Stranger, is most excellent, and I must do as you advise.

1 i.e. the laws of arithmetic apply also to plane and solid geometry, acoustics, and kinetics.

2 Cp. Plat. Rep. 436a.

3 Cp. Plat. Laws 745d ad fin.

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