y 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 now
unhappily allowed to fall down.

Nothing will be more likely to have such an effect.

Then nothing should be more sternly laid down than that the inhabitants
of your fair city should by all means learn geometry. Moreover the
science has indirect effects, which are not small.

Of what kind? he said.

There are the military advantages of which you spoke, I said; and in all
departments of knowledge, as experience proves, any one who has studied
geometry is infinitely quicker of apprehension than one who has not.

Yes indeed, he said, there is an infinite difference between them.

Then shall we propose this as a second branch of knowledge which our
youth will study?

Let us do so, he replied.

And suppose we make astronomy the third--what do you say?

I am strongly inclined to it, he said; the observation of the seasons
and of months and years is as essential to the general as it is to the
farmer or sailor.

I am amused, I said, at your fear of the world, which makes you guard
against the appearance of insisting upon useless studies; and I quite
admit the difficulty of believing that in every man there is an eye
of the soul which, when by other pursuits lost and dimmed, is by these
purified and re-illumined; and is more precious far than ten thousand
bodily eyes, for by it alone is truth seen. Now there are two classes of
persons: one class of those who will agree with you and will take
your words as a revelation; another class to whom they will be utterly
unmeaning, and who will naturally deem them to be idle tales, for they
see no sort of profit which is to be obtained from them. And therefore
you had better decide at once