What was the mistake? he said.
After plane geometry, I said, we proceeded at once to [B]solids in revolution, instead of taking solids in themselves; whereas after the second dimension the third, which is concerned with cubes and dimensions of depth, ought to have followed.
That is true, Socrates; but so little seems to be known as yet about these subjects.
The pitiable condition of solid geometry. Why, yes, I said, and for two reasons:—in the first place, no government patronises them; this leads to a want of energy in the pursuit of them, and they are difficult; in the 231 second place, students cannot learn them unless they have a director. But then a director can hardly be found, and even [C]if he could, as matters now stand, the students, who are very conceited, would not attend to him. That, however, would be otherwise if the whole State became the director of these studies and gave honour to them; then disciples would want to come, and there would be continuous and earnest search, and discoveries would be made; since even now, disregarded as they are by the world, and maimed of their fair proportions, and although none of their votaries can tell the use of them, still these studies force their way by their natural charm, and very likely, if they had the help of the State, they would some day emerge into light.
[D] Yes, he said, there is a remarkable charm in them. But I do not clearly understand the change in the order. First you began with a geometry of plane surfaces?
Yes, I said.
And you placed astronomy next, and then you made a step backward?
The motion of solids. Yes, and I have delayed you by my hurry; the ludicrous state of solid geometry, which, in natural order, should have followed, made me pass over this branch and go on to [E]astronomy, or motion of solids.
True, he said.
Then assuming that the science now omitted would come into existence if encouraged by the State, let us go on to astronomy, which will be fourth.