The retail use is not required by us; but as our guardian is to be a soldier as well as a philosopher, the military one may be retained.

And to our higher purpose no science can be better adapted; but it must be pursued in the spirit of a philosopher, not of a shopkeeper.

It is concerned, not with visible objects, but with abstract truth; for numbers are pure abstractions--the true arithmetician indignantly denies that his unit is capable of division.

When you divide, he insists that you are only multiplying; his 'one' is not material or resolvable into fractions, but an unvarying and absolute equality; and this proves the purely intellectual character of his study.

Note also the great power which arithmetic has of sharpening the wits; no other discipline is equally severe, or an equal test of general ability, or equally improving to a stupid person.
Let our second branch of education be geometry.