rally 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.

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.

I agree.

Let this then be made one of our subjects of education. And next,
shall we enquire whether the kindred science also concerns us?

You mean geometry?

Exactly so.

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 geometry 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 towards
that place, where is the full perfection of being, which she ought, by
all means, to behold.

True, he said.

Then if geometry compels us to view being, it concerns us; if becoming
only, it does not concern us?

Yes, that is what we assert.

Yet anybody who has the least acquaintance with geometry will not deny
that such a conception of the science is in flat contradiction to the
ordinary language of geometricians.

How so?

They have in view practice only, and are always speaking? in a narrow
and ridiculous manner, of squaring and extending and applying and the
like--they confuse the necessities of geometry with those of daily
life; whereas knowledge is the real object of the whole science.

Certainly, he said.

Then must not a further admission be made?

What admission?

That the knowledge at which geometry aims is knowledge of the eternal,
and not of aught perishing and transient.

That, he replied, may be readily allowed, and is true.

Then, my noble friend, geometry will draw the soul towards truth, and
create the spirit of philosophy, and raise up that which is