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The greatest objection to the translation is the sense given to

the words (Greek), 'a base of three with a third added to it,

multiplied by 5.' In this somewhat forced manner Plato introduces

once more the numbers of the Pythagorean triangle. But the

coincidences in the numbers which follow are in favour of the

explanation. The first harmony of 400, as has been already

remarked, probably represents the rulers; the second and oblong

harmony of 7600, the people.