suppose that you have this distinction of the visible and intelligible fixed in your mind?
I have.
Now take a line which has been cut into two unequal[1] parts, and divide each of them again in the same proportion, and suppose the two main divisions to answer, one to the visible and the other to the intelligible, and then compare the subdivisions in respect of their clearness and want of clearness, and you will find that the first section in the sphere of the visible consists of images. And by images I mean, in the first place, shadows, and in the second place, reflections in water and in solid, smooth and polished bodies and the like: Do you understand?
Yes, I understand.
Imagine, now, the other section, of which this is only the resemblance, to include the animals which we see, and everything that grows or is made.
Very good.
Would you not admit that both the sections of this division have different degrees of truth, and that the copy is to the original as the sphere of opinion is to the sphere of knowledge?
Most undoubtedly.
Next proceed to consider the manner in which the sphere of the intellectual is to be divided.
In what manner?
Thus: There are two subdivisions, in the lower of which the soul uses the figures given by the former division as images; the inquiry can only be hypothetical, and instead of going upward to a principle descends to the other end; in the higher of the two, the soul passes out of hypotheses, and goes up to a principle which is above hypotheses, making no use of images[2] as in the former case, but proceeding only in and through the ideas themselves.
I do not quite understand your meaning, he said.
Then I will try again; you will understand me better when I have made some preliminary remarks. You are aware that students of geometry, arithmetic, and the kindred sciences assume the odd, and the even, and the figures, and three kinds of angles, and the like, in their several branches of science; these are their hypotheses, which they and everybody are supposed
