republic (books 6 - 10)
That is very true.
Now, suppose a person were to say to them: O my friends,
what are these wonderful numbers about which you are rea-
soning, in which, as you say, there is a unity such as you de-
mand, 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
Then you see that this knowledge may be truly called neces-
sary, necessitating as it clearly does the use of the pure intelli-
gence in the attainment of pure truth?
Yes; that is a marked characteristic of it.
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
Very true, he said.
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.
Let this then be made one of our subjects of education. And
next, shall we inquire whether the kindred science also con-
You mean geometry?
Clearly, he said, we are concerned with that part of geometry
which relates to war; for in pitching a camp or taking up a
position or closing or extending the lines of an army, or any
other military manoeuvre, whether in actual battle or on a
march, it will make all the difference whether a general is or is
not a geometrician.
Yes, I said, but for that purpose a very little of either geome-
try or calculation will be enough; the question relates rather
to the greater and more advanced part of geometry--whether
that tends in any degree to make more easy the vision of the
idea of good; and thither, as I was saying, all things tend which
compel the soul to turn her gaze toward that place, where is
the full perfection of being, which she ought, by all means, to
True, he said.