Yes, that is what we assert. Yet anybody who has the least acquaintance with geometry will not deny that such a conception of the science is in flat contradiction to the ordinary language of geometricians. How so? They have in view practice only, and are always speaking, in a narrow and ridiculous manner, of squaring and extending and applying and the like—they confuse the necessities of geometry with those of daily life; whereas knowledge is the real object of the whole science. Certainly, he said. Then must not a further admission be made? What admission? That the knowledge at which geometry aims is knowledge of the eternal, and not of aught perishing and transient. That, he replied, may be readily allowed, and is true. Then, my noble friend, geometry will draw the soul towards truth, and create the spirit of philosophy, and raise up that which is now unhappily allowed to fall down. Nothing will be more likely to have such an effect. Then nothing should be more sternly laid down than that the inhabitants of your fair city should by all means learn geometry. Moreover the science has indirect effects, which are not small. Of what kind? he said. There are the military advantages of which you spoke, I said; and in all departments of knowledge, as experience proves, any one who has studied geometry is infinitely quicker of apprehension than one who has not. Yes indeed, he said, there is an infinite difference between them. Then shall we propose this as a second branch of knowledge which our youth will study? Let us do so, he replied.

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

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...

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