Transcendental Exposition of the Conception of Space SS 3. By a transcendental exposition, I mean the explanation of a conception, as a principle, whence can be discerned the possibility of other synthetical a priori cognitions.
Geometry is a science which determines the properties of space synthetically, and yet a priori.
It must be originally intuition, for from a mere conception, no propositions can be deduced which go out beyond the conception, and yet this happens in geometry. But this intuition must be found in the mind a priori, that is, before any perception of objects, consequently must be pure, not empirical, intuition. But propositions of this kind cannot be empirical judgements, nor conclusions from them. Thus it is only by means of our explanation that the possibility of geometry, as a synthetical science a priori, becomes comprehensible. Every mode of explanation which does not show us this possibility, although in appearance it may be similar to ours, can with the utmost certainty be distinguished from it by these marks.