PROLEGOMENA TOANYFUTUREMETAPHYSICS 815
these laws are known as necessary) are commonly held by us to be such as have been
placed there by the understanding, in spite of their being similar in all points to the laws
of nature which we ascribe to experience.
§ 38. If we consider the properties of the circle, by which this figure combines in
itself so many arbitrary determinations of space in a universal rule, we cannot avoid
attributing a constitution to this geometrical thing. Two straight lines, for example, which
intersect each other and the circle, howsoever they may be drawn, are always divided so
that the rectangle constructed with the segments of the one is equal to that constructed with
the segments of the other. The question now is: Does this law lie in the circle or in the
understanding? That is, does this figure, independently of the understanding, contain in
itself the ground of the law; or does the understanding, having constructed according to its
concepts (of the equality of the radii) the figure itself, introduce into it this law of the chords
intersecting in geometrical proportion? When we follow the proofs of this law, we soon
perceive that it can only be derived from the condition on which the understanding founds
the construction of this figure, namely, the concept of the equality of the radii. But if we
enlarge this concept to pursue further the unity of various properties of geometrical figures
under common laws and consider the circle as a conic section, which of course is subject to
the same fundamental conditions of construction as other conic sections, we shall find that
all the chords which intersect within the ellipse, parabola, and hyperbola always intersect
so that the rectangles of their segments are not indeed equal but always bear a constant ratio
to one another. If we proceed still farther to the fundamental teachings of physical astron-
omy, we find a physical law of reciprocal attraction applicable to all material nature, the
rule of which is that it decreases inversely as the square of the distance from each attracting
point, that is, as the spherical surfaces increase over which this force spreads, which law
seems to be necessarily inherent in the very nature of things, and hence is usually pro-
pounded as knowable a priori.Simple as the sources of this law are, merely resting upon
the relation of spherical surfaces of different radii, its consequences are so valuable with
regard to the variety and simplicity of their agreement that not only are all possible orbits of
the celestial bodies conic sections, but such a relation of these orbits to one another results
that no other law of attraction than that of the inverse square of the distance can be imag-
ined as fit for a cosmical system.
Here accordingly is nature, which rests upon laws that the understanding knows
a priori,and chiefly from the universal principles of the determination of space. Now
I ask: Do the laws of nature lie in space, and does the understanding learn them by
merely endeavoring to find out the enormous wealth of meaning that lies in space; or do
they inhere in the understanding and in the way in which it determines space according
to the conditions of the synthetical unity in which its concepts are all centered?
Space is something so uniform and as to all particular properties so indeterminate
that we should certainly not seek a store of laws of nature in it. Whereas that which
determines space to assume the form of a circle, or the figures of a cone and a sphere, is
the understanding, so far as it contains the ground of the unity of their constructions.
The mere universal form of intuition, called space, must therefore be the substra-
tum of all intuitions determinable to particular objects; and in it, of course, the condition
of the possibility and of the variety of these intuitions lies. But the unity of the objects
is entirely determined by the understanding and on conditions which lie in its own
nature; and thus the understanding is the origin of the universal order of nature, in that
it comprehends all appearances under its own laws and thereby produces, in an a priori
manner, experience (as to its form), by means of which whatever is to be known only by
experience is necessarily subjected to its laws. For we are not concerned with the nature
322321