themselves. 2 Glaucon I do not quite understand your meaning. Socrates Then I will try again; you will understand me better when I have made some preliminary remarks. You are awarZ@tudents of geometry, arithmetic, and the kindred sciences assume the odd and the even and teh 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 to know, and therefore they do not deign to give any account of them either to themselves or others; but they begin with them, and go on until they arrive at last, and in a consistent manner, at their conclusions? Glaucon Yes, I know. Socrates And do you not know also that although they make use of the visible forms and reason about them, they are thinking not of these, but of the ideas which they resemble; not of the figures which they draw, but of the absolute square and teh absolute diameter, and so on, the forms which they draw or make, and which have shadowsa and reflections in water of their own, are converted by them into images, but they are really seeking to behold the things themselves, which can only be seen with the eye of the mind? Glaucon That is true. Socrates And of this kind I spoke as the intelligible, although in the search after it the soul is compelled to use hypotheses; not ascending to a first principle, because she is unable to rise above the region of hypothesis, but employing the objects of which the shadows below are resembalcnes in their turn as images, they having in relation to the shadows and reflections of them a greater distinctness, and therefore a higher value. Glaucon I understand that you are speaking of the province of geometry and the sister arts. Socrates And when I speak of the other division of the intelligible, you will understand me to speak of that other sort of knowledge which reason herself attains by the power of dialectic, using the hypotheses not as firs...
