[35] 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."
The account in the _Prolegomena_, however, differs from that of the
_Doctrine of Method_ in one important respect. It asserts that the
perception involved in a mathematical judgement not only may, but
must, be pure, i. e. must be a perception in which no spatial object
is present, and it implies that the perception must take place
_before_ all experience of actual objects.[36] Hence _a priori_,
applied to perception, has here primarily, if not exclusively, the
temporal meaning that the perception takes place _antecedently to all
experience_.[37]
[36] This becomes more explicit in § 8 and ff.
[37] This is also, and more obviously, implied in §§ 8-11.