'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.
Shall we propose, as a third branch of our education, astronomy?
'Very good,' replied Glaucon; 'the knowledge of the heavens is necessary at once for husbandry, navigation, military tactics.' I like your way of giving useful reasons for everything in order to make friends of the world.

And there is a difficulty in proving to mankind that education is not only useful information but a purification of the eye of the soul, which is better than the bodily eye, for by this alone is truth seen.
Now, will you appeal to mankind in general or to the philosopher?
or would you prefer to look to yourself only?
'Every man is his own best friend.' Then take a step backward, for we are out of order, and insert the third dimension which is of solids, after the second which is of planes, and then you may proceed to solids in motion.