"For such purposes as these a very slender knowledge of geometry, and a small portion of arithmetic would suffice;—but as for any considerable amount thereof, and great progress in it, we must inquire how far they tend to this,—namely, to make us apprehend more easily the idea of the good:—and we say that all things contribute thereto, which compel the soul to turn itself to that region in which is the happiest portion of true being, which it must by all means perceive. ...this science has an entirely opposite nature to the words employed in it by those who practise it. ...They speak somehow most absurdly, and necessarily so, since all the terms they use seem to be with a view to operation and practice,—such as squaring, producing, adding, and such like sounds; whereas on the other hand, the whole science should be studied for the sake of real knowledge. ...Is this then further to be agreed on? ...That [it be studied] with a view to the knowledge of eternal being, and not of that which is subject to generation and destruction? ...It would have a tendency, therefore... to draw the soul to truth, and to cause a philosophic intelligence to direct upwards [the thoughts] which we now improperly cast downwards. ...We must give special orders, that the inhabitants of that fine state of yours should by no means omit the study of geometry, since even its by-works are not inconsiderable. ...it is not altogether a trifle, but rather difficult to persuade that by these branches of study some organ of the soul in each individual, is purified and rekindled like fire, after having been destroyed and blinded by other kinds of study,—an organ, indeed, better worth saving than ten thousand eyes, since by that alone can truth be seen."