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nydus/The Republic of PlatoPublic
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Table of Contents

BOOK VII.

is very true.

Now, suppose a person were to say to them: O my friends, what are these wonderful numbers about which you are reasoning, in which, as you say, there is a unity such as you demand, and each unit is equal, invariable, indivisible,—what would they answer?

They would answer, as I should conceive, that they were speaking of those numbers which can only be realized in thought.

Then you see that this knowledge may be truly called necessary, necessitating as it clearly does the use of the pure intelligence in the attainment of pure truth?

Yes; that is a marked characteristic of it.

The arithmetician is naturally quick, and the study of arithmetic gives him still greater quickness. And have you further observed, that those who have a natural talent for calculation are generally quick at every other

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