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?
[B] Most undoubtedly.
Next proceed to consider the manner in which the sphere of the intellectual is to be divided.
In what manner?
Images and hypotheses. Thus:—There are two subdivisions, in the lower of which the soul uses the figures given by the former division as images; the enquiry can only be hypothetical, and instead of going upwards 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[14] as in the former case, but proceeding only in and through the ideas themselves.
[14] Reading ὧνπερ ἐκεῖνο εἰκόνων.
I do not quite understand your meaning, he said. 212
[C] The hypotheses of mathematics. 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 every body are supposed to know, and therefore they do not deign to give any account of them either to themselves or others; [D]but they begin with them, and go on until they arrive at last, and in a consistent manner, at their conclusion?