ns,
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 Sec. 8 and ff.

[37] This is also, and more obviously, implied in Secs. 8-11.

The thought of the passage quoted from the _Prolegomena_ can be stated
thus: 'A mathematical judgement implies the perception of an
individual figure antecedently to all experience. This may be said to
be the first condition of the possibility of mathematical judgements
which is revealed by reflection. There is, however, a prior or higher
condition. The perception of an individual figure involves as its
basis another pure perception. For we can only construct and therefore
perceive an individual figure in empty space. Space is that _in which_
it must be constructed and perceived. A perception[38] of empty space
is, therefore, necessary. If, then, we can discover how this
perception is possible, we shall be able to explain the possibility of
_a priori_ synthetical judgements of mathematics.'

[38] _Pure_ perception only means that the space perceived is
empty.

Kant continues as follows: "But with this step the difficulty seems to
increase rather than to lessen. For henceforward the question is '_How
is it possible to perceive anything a priori?_' A perception is such a
representation as would immediately depend upon the presence of the
object. Hence it seems impossible _originally_ to perceive _a priori_,
because perception would in that case have to take place without an
object to which it might refer, present either formerly or at the
moment, and accordingly could not be perception.... How can
_perception_ of the object precede the object itself?"[39] Kant here
finds himself face to face with the difficulty created by the
preceding section. Per