The Philosophy of Fine Art, volume 1 (of 4): Hegel's Aesthetik
Georg Hegel · en
On the other hand, there is still less uniformity in the _ellipse_ and
the _parabola_, and they are only understood through the law of their
form. In other words the _radii vectores_ of the ellipse are both
unequal and in conformity with rule, and the same qualification applies
to the greater and lesser axis of their lines of differentiation[251];
moreover, their foci are not central as is the case with the circle. We
find in these examples, therefore, a qualitative relation of difference
assert itself in the law applicable to such lines and constructive of
their interconnection. If, however, we divide the ellipse by means of
its greater and lesser axes we obtain four equal sections; regarded as
a whole, therefore, we still find the principle of uniformity paramount
in this figure. Of a higher degree of freedom in its conformity to law
is the _oval._ We know there is such a law, though mathematicians have
been unable to express its formula. This figure is not an ellipse, but
the higher curve differs from that below it. Still we find that even in
this example of freer eccentricity in Nature, if we divide it through
its greater axis, we have still two equal halves. The final expression
of mere uniformity in conformity to law is shown in lines, which, as in
the example of the oval, when divided through the smaller[252] axis,
give us unequal sections, neither section being a mere repetition of
the other. The so-called undulatory line is an example of this, in the
sense Hogarth describes it as the line of beauty. Thus the inclination
of the arms as they fall on either side of the human body is opposed.
Here we have conformity to rule without uniformity pure and simple.
Such a kind of conformity especially characterises with its variety the
conformation of the nobler living organisms.
Conformity to law is, then, an attribute of substantiality, binding
together both its differences and its unity; but it remains still
abstract on the side of its controlling form, unable to supply
individuality with the freedom of motion, or rather by virtue of that
form is entirely without the higher freedom of subjectivity, and quite
incapable of revealing the vitality and ideality proper to it.
_(c) Harmony_