That is very true.
[526] 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 [B]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 kind of knowledge; and even the dull, if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would otherwise have been.
Very true, he said.
[C] And indeed, you will not easily find a more difficult study, and not many as difficult.
You will not.
And, for all these reasons, arithmetic is a kind of knowledge in which the best natures should be trained, and which must not be given up.