The single figure which we draw is empirical, and yet it serves to express the concept, without impairing its universality. Thus philosophical knowledge considers the particular only in the universal, mathematical knowledge the universal in the particular, or even in the single instance, though still always a priori and by means of reason. Accordingly, just as this single object is determined by certain universal conditions of construction, so the object of the concept, to which the single object corresponds merely as its schema, must likewise be thought as universally determined. Those who propose to distinguish philosophy from P 578 mathematics by saying that the former has as its object quality only and the latter quantity only, have mistaken the effect for the cause. The form of mathematical knowledge is the cause why it is limited exclusively to quantities.
Consequently reason can obtain a knowledge of qualities only through con- cepts.
The shape of a cone we can form for ourselves in intuition, unassisted by any experience, according to its concept alone, but the colour of this cone must be previously given in some experience or other. Philosophy, as well as mathe- matics, does indeed treat of quantities, for instance, of totality, infinity, etc. Mathematics also concerns itself with qualities, for instance, the difference between lines and surfaces, as spaces of different quality, and with the continuity of extension as one of its qualities. But although in such cases they have a common object, the mode in which reason handles that object is wholly different in philosophy and in mathematics. He has nothing but the concept of a figure enclosed by three straight lines, and possessing three angles.