[1806]. At present the science [of geometry] is in flat contradiction to the language which geometricians use, as will hardly be denied by those who have any acquaintance with the study: for they speak of finding the side of a square, and applying and adding, and so on, as if they were engaged in some business, and as if all their propositions had a practical end in view: whereas in reality the science is pursued wholly for the sake of knowledge.
Certainly, he said.
Then must not a further admission be made?
What admission?
The admission that this knowledge at which geometry aims is of the eternal, and not of the perishing and transient.
That may be easily allowed. Geometry, no doubt, is the knowledge of what eternally exists.
Then, my noble friend, geometry will draw the soul towards truth, and create the mind of philosophy, and raise up that which is now unhappily allowed to fall down.—Plato.
Republic [Jowett-Davies], Bk. 7, p. 527.
[1807]. Among them [the Greeks] geometry was held in highest honor: nothing was more glorious than mathematics. But we have limited the usefulness of this art to measuring and calculating.—Cicero.