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?

The readiness acquired by previous training conduces much to the perception of such things as are requisite; but those things which can be perceived...

Consequently, therefore, he applies to the subjects that are a training for knowledge, taking from each branch of study its contribution to the truth....

If, however, it be necessary, dismissing these particulars, to speak what appears to me to be the truth, you do not rightly infer “ that a knowledge...

The same holds also of astronomy. For treating of the description of the celestial objects, about the form of the universe, and the revolution of the...