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. Perception, as such, involves the actual presence of an object; yet the pure perception of space involved by geometry--which, as pure, is the perception of empty space, and which, as the perception of empty space, is _a priori_ in the sense of temporally prior to the perception of actual objects--presupposes that an object is not actually present. [39] _Prol._ § 8.