 In Kant’s Critique of Pure Reason (1781/1787) (see the entry  Kant’s views on space and time)  the situation is more complicated or sophisticated. Kant introduced the notion of a priori knowledge in contrast to a posteriori, and synthetic knowledge in contrast to analytical knowledge to allow for the existence of knowledge that did not rely on experience (and was thus a priori) but was not tautological in character (and therefore synthetic and not analytic). The contentious class of synthetic a priori statements includes the truths of Euclidean geometry; thus he ascribed certainty and necessity to Euclidean geometry. Kant associated geometric knowledge with the pure intution of space; to know that an isosceles triangle (i.e. with two equal sides) has two equal angles at the base, the mathematician must produce a particular construction that makes the truth of the claim demonstrable (see Critique, A 716, B 744).