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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. 'I can easily

see,' replied Glaucon, 'that the skill of the general will be

doubled by his knowledge of geometry.' That is a small matter;

the use of geometry, to which I refer, is the assistance given by

it in the contemplation of the idea of good, and the compelling

the mind to look at true being, and not at generation only. Yet

the present mode of pursuing these studies, as any one who is the

least of a mathematician is aware, is mean and ridiculous; they

are made to look downwards to the arts, and not upwards to

eternal existence. The geometer is always talking of squaring,

subtending, apposing, as if he had in view action; whereas

knowledge is the real object of the study. It should elevate the

soul, and create the mind of philosophy; it should raise up what

has fallen down, not to speak of lesser uses in war and military

tactics, and in the improvement of the faculties.