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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,

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

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