Note 35 — Chapter III

B. 740 ff., M. 434 ff. Compare especially the following: "Philosophical knowledge is knowledge of reason by means of conceptions; mathematical knowledge is knowledge by means of the construction of conceptions. But the construction of a conception means the a priori presentation of a perception corresponding to it. The construction of a conception therefore demands a non-empirical perception, which, therefore, as a perception, is an individual object, but which none the less, as the construction of a conception (a universal representation), must express in the representation universal validity for all possible perceptions which come under that conception. Thus I construct a triangle by presenting the object corresponding to the conception, either by mere imagination in pure perception, or also, in accordance with pure perception, on paper in empirical perception, but in both cases completely a priori, without having borrowed the pattern of it from any experience. The individual drawn figure is empirical, but nevertheless serves to indicate the conception without prejudice to its universality, because in this empirical perception we always attend only to the act of construction of the conception, to which many determinations, e. g. the magnitude of the sides and of the angles, are wholly indifferent, and accordingly abstract from these differences, which do not change the conception of the triangle."