philosophy of nature-第6章
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particular forces corresponding to the power of attraction and repulsion； of being conceived more
precisely as the centripetal and the centrifugal forces； which are supposed； like gravity； to act on
bodies； and independently of each other and contingently； to meet together in a third entity； the
body。 In this way whatever profundity was contained in the thought of general gravitation is
destroyed again； and the concept and reason will be unable to penetrate into the theory of
absolute motion； as long as the vaunted discoveries of forces prevail there。
if one closely considers the quantitative determinations which have been identified in the laws of
the centripetal and the centrifugal forces； one very quickly discovers the confusion which emerges
from their separation。 This confusion becomes even greater if the separation is mentioned in
relation to gravitation； gravitation； also called attraction； then seems to be the same as centripetal
force； the law of this individual force is taken as the law of the whole of gravitation； and the
centrifugal force； which at another time is valued as thoroughly essential； is viewed as something
quite superfluous。…In the above proposition； which contains the immediate idea of gravitation；
gravity itself namely； as the concept； which shows itself in the particularity of the body through the
external reality of motion； the rational identity and inseparability of these two moments are
contained。…The relativity of motion also shows itself in this proposition； which only makes sense in
a system of several bodies standing in relation to each other in accordance with a varied
determination； so that a different determination will immediately result。
§ 211。
The particular bodies in which gravity is realised have； as the determinations of their different
natures； the moments of their concept。 One body； therefore； is the general centre of being in itself。
Opposing this extreme stands individuality； existing outside of itself and without a centre。 But the
particular bodies are others； which stand in the determination of being outside of themselves and
are at the same time； as being in themselves； also centres for themselves； and are related to the
first body as to their essential unity。
§ 212。
（1） The motion of bodies of relative centrality； in relation to bodies of abstract； general centrality；
is absolutely free motion； and the conclusion of this system is that the general central body is
brought together through relative centrality with dependent corporeality。
As is well…known； the laws of absolutely free motion were discovered by Kepler； a discovery of
immortal fame。 Kepler proved them； too； in the sense that he found the general expression for the
empirical data （cf § 145）。 Since then it has become a commonplace that Newton first found the
proofs of these laws。 Not often has fame been more unjustly transferred from the first discoverer
to another。 Here I only want to point out what has basically already been admitted by
mathematicians； namely： （1） that the Newtonian formulas can be derived from Keplerian laws； （2）
that the Newtonian proof of the proposition that a body governed by the law of gravitation moves
in an ellipse around the central body proceeds in general in a conic section； whereas the main point
that was to be proven consists precisely in this； that the course of such a body is neither a circle
nor any other conic section； but solely the ellipse。 The conditions which make the course of the
body into a specific conic section are referred back to an empirical condition； namely； a particular
situation of the body at a specific point in time； and to the contingent strength of an impulse which
it is supposed to have received at the beginning。 （3） Newton's 'law〃 of the force of gravity has
likewise only been demonstrated inductively from experience。
On closer inspection it appears that what Kepler； in a simple and sublime manner； articulated in
the form of laws of celestial motion； Newton converted into the nonconceptual； reflective form of
the force of gravity。 The whole manner of this 〃proof〃 presents in general a confused tissue of lines
of merely geometrical construction to which a physical meaning of independent forces is given； of
the empty concepts of the understanding of a force of acceleration； of particles of time； at whose
beginning those forces always play a renewed role； and of a force of inertia； which presumably
continues its previous effect； and so on。 A rational proof of the quantitative determinations of free
motion can only rest on the determinations of the concepts of space and time； the moments whose
relation is motion。
§ 213。
（2） The absolute relation of those dependent bodies； which are merely the extreme of the being
outside of itself of gravity and therefore lack their own centrality to their relative central bodies； is
the residual element of their gravity in them； which because of physical being outside of themselves
is mere striving and； therefore； a pressure directed towards the centre lying outside of them。
§ 214。
The separation of the immediate connection in which such a body rests is a contingent condition；
which the body； if confronted with an external impediment； suspends as motion； … relatively free
motion in which the distancing from the body is not attributed as dependent； but the motion； if the
impediment is removed； is immanent to the body and a manifestation of its own gravity。 This
motion transforms itself for itself into rest。
The attractive force of the sun； for example towards the planets； or of the earth towards those
independent bodies belonging to it； seems to suggest the skewed view that the force would be an
activity inhabiting the central body； and that the bodies found in its sphere would behave only
passively and externally。 Thus absolute motion is also viewed； through the application of terms
from common mechanics； as the dead conflict of an independent； tangential force and of a force
deriving equally independently from the middle point； from which the body would be passively
drawn。
The Galilean law of falling； namely； that traversed spaces behave as the squares of transpired
times； shows； in contrast to the abstract； homogeneous velocity of the lifeless mechanism； where
spaces are proportional to times； the liberation of the conceptual determinations of time and space。
In these terms the former has the determination of the root as the negative moment or principle of
one； whereas the latter has the determination of the square as a being outside of itself more
specifically； without another determinacy like that of the root； a coming outside of itself。 In this law
both moments still remain in the relation； because the freedom of motion in falling； which is also
conditioned； is only formal。 By contrast； in absolute motion there is the relation in its totality； since
this is the realm of free measures in which each determinacy attains its totality。 Because the law is
essentially relational； time and space are retained in their original difference。 Dimensionless time
achieves therefore only a formal identity with itself； space； on the other hand； as positive being
outside of itself achieves the dimension of the concept。 The Keplerian law is thus the relation of the
cubes of the distances to the squares of the times；…a law which is so great because it simply and
directly depicts the reason of the thing。 The Newtonian formula； however； which transforms it into
a law for the force of gravity； exhibits only the perversion and inversion of reflection which has
stopped halfway。
§ 215。
（3） In the extremity of dependent bodies； general gravitation； which bodies have as matter toward
each other； is subordinated to the gravitation which they have towards their shared central bodies。
Towards each other； then； their motion is external and contingent； the cause of the motion is thrust
and pressure。 In this common mechanical motion the size of the mass； which has no
