146. Geometry is a science of equal value with arithmetic; it is
even as certain, because it has no other propositions; it is equally
eternal, is the same realization of the primary act, the _Deus
geometrizans_ of the Pythagoreans. Everything to be certain must
therefore resemble geometry, must be itself a position of geometry,
only under other relations.
147. Geometry is more real, more finite, therefore also more apparent,
and, as it were, more material than arithmetic. The ideas in it have
become something determinate, have assumed form, while before they
still fluctuated formless in arithmetic; here were they mere ghosts
without veils, but in geometry they have received these veils. _Time_
has received for its form, its body, the line; _space_, the surface;
_life_, the globe, consequently the rotation for its form or body. It
is to be here remarked, that ideas always become more real and more
finite, always approximate nearer to actual manifestation, the lower
they descend or the more they are considered individually. Geometry has
not originated later than arithmetic, but is only a more individual
view of ideas, arithmetic being more universal. Geometry is arithmetic
with stationary numbers, = points. The Divine thus approximates to
manifestation, to materiality, the more individual it becomes; and
this is very natural, for it verily limits itself more and obtains
always more predicates. The more a thing obtains predicates, by so
much the more perfect is its finiteness. By geometry we are actually
transferred into the universe, but only into the formal, in which it
has, like a skeleton, been sketched for us solely upon a general plan;
namely, as infinite extension, in which line and periphery, central and
peripheric action, magnetism, electricity, and rotation, &c., have been
prefigured.
B.--_HYLOGENY._
a. GRAVITY. (_First form of the World. Rest._)
148. In arithmetic the divine acts are only undetermined = numbers. In
geometry the numbers obtain determinate or finite directions, become
figures. All figures have, however, an especial direction to the
centre. Figures are nought but centres manifoldly posited.
149. The direction to a centre is, however, an act, which never ceases
to operate. The primary act strives therefore to posit ad infinitum
nought else than a centre, i. e. points.
150. If there are points without the centre, it so happens only because
the succeeding points have been displaced by the points that were first
posited. The peripheric points are only with reluctance out of the
centre. The globe only exists in an uneasy state, because it has no
place in the centre.
151. Every finite thing strives towards the centre. The finite is only
something, in so far as it is posited in the centre, and it maintains
its value according to its distance from the centre. This exertion
or endeavour, by virtue of which things would be in the centre, is
_Gravity_.
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