ner. If goodness and beauty always lay in something absolute
and uniform, such as extension, matter, gold, water, and other bodies
assumed to be homogeneous or similar, one must say that the part of the
good and the beautiful would be beautiful and good like the whole, since it
would always have resemblance to the whole: but this is not the case in
things that have mutual relations. An example taken from geometry will be
appropriate to explain my idea.

214. There is a kind of geometry which Herr Jung of Hamburg, one of the
most admirable men of his time, called 'empiric'. It makes use of
conclusive experiments and proves various propositions of Euclid, but
especially those which concern the equality of two figures, by cutting the
one in pieces, and putting the pieces together again to make the other. In
this manner, by cutting carefully in parts the squares on the two sides of
the right-angled triangle, and arranging these parts carefully, one makes
from them the square on the hypotenuse; that is demonstrating empirically
the 47th proposition of the first book of Euclid. Now supposing that some
of these pieces taken from the two smaller squares are lost, something[262]
will be lacking in the large square that is to be formed from them; and
this defective combination, far from pleasing, will be disagreeably ugly.
If then the pieces that remained, composing the faulty combination, were
taken separately without any regard to the large square to whose formation
they ought to contribute, one would group them together quite differently
to make a tolerably good combination. But as soon as the lost pieces are
retrieved and the gap in the faulty combination is filled, there will ensue
a beautiful and regular thing, the complete large square: this perfect
combination will be far more beautiful than the tolerably good combination
which had been made from the pieces one had not mislaid alone. The perfect
combination corresponds to the universe in its entirety, and the faulty
combination that is a part of the perfect one corresponds to some part of
the universe, where we find defects which the Author of things has allowed,
because otherwise, if he had wished to re-shape this faulty part and make
thereof a tolerably good combination, the whole would not then have been so
beautiful. For the parts of the faulty combination, grouped better to make
a tolerably good combination, could not have been used properly to form the
whole and perfe