Another point calls for notice. Geometry works with the sensuous but abstract perception of space; and in space it experiences no difficulty in isolating and defining certain simple analytic modes. To geometry alone therefore belongs in its perfection the synthetical method of finite cognition. In its course, however (and this is the remarkable point), it finally stumbles upon what are termed irrational and incommensurable quantities; and in their case any attempt at further specification drives it beyond the principle of the understanding. This is only one of many instances in terminology, where the title rational is perversely applied to the province of understanding, while we stigmatise as irrational that which shows a beginning and a trace of rationality. Other sciences, removed as they are from the simplicity of space or number, often and necessarily reach a point where understanding permits no further advance: but they get over the difficulty without trouble. They make a break in the strict sequence of their procedure, and assume whatever they require, though it be the reverse of what preceded, from some external quarter,--opinion, perception, conception or any other source. Its inobservancy as to the nature of its methods and their relativity to the subject-matter prevents this finite cognition from seeing that, when it proceeds by definitions and divisions, &c., it is really led on by the necessity of the laws of the notion. For the same reason it cannot see when it has reached its limit; nor, if it have transgressed that limit, does it perceive that it is in a sphere where the categories of understanding, which it still continues rudely to apply, have lost all authority. 232.] The necessity, which finite cognition produces in the Demonstration, is, in the first place, an external necessity, intended for the subjective intelligence alone. But in necessity as such, cognition itself has left behind its presupposition and starting-point, which consisted in accepting its content as given or found. Necessity _quâ_ necessity is implicitly the self-relating notion. The subjective idea has thus implicitly reached an original and objective determinateness,--a something not-given, and for that reason immanent in the subject. It has passed over into the idea of Will. * * * * *