plished in the development of the world,
and these causes and combinations are ideal forms of this development.
The monad is developed by these laws through all the generative
processes of nature, while at the same time it remains eternal in the
system of the universe; so that things not only have their origin and
essence, their place and time according to numerical causes, but each is
in effect a number as far as its individual properties and the
universal process of cosmic life are concerned. The reason of the number
must depend upon the substance, by the configurations of which it is
defined, divided, added, and multiplied, and to this geometry is added,
which measures all things in relation to themselves and others. This
eternal cause makes it intelligible that if immaterial principles
precede and govern the whole material world, it is also by means of
these that the classification of science is in intrinsic agreement with
that of nature. Numbers have their value in music, in gymnastics, in
medicine, in morals, in politics, in all branches of science. The
Pythagorean arithmetic is the bond and universal logic of the knowable.
But at the same time Pythagoras and his school peopled the world with
demons and genii, which were the causes of disease; they did not abandon
the old mythical ideas of the incarnation of spirits and the
transmigration of souls--theories and beliefs which recur in nearly all
primitive and savage peoples.

In this vast Pythagorean scheme, which contrasts with that of the Ionic
school of physics, thought is more explicitly freed from the ruder
mythical ideas, and rises to a more intelligent and rational conception
of the world, but the ancient popular traditions still persist, and
there is an evident _entification_ of number. The primitive monad,
numbers, their genesis and relations, are not regarded as abstract
conceptions, necessary for understanding the order of nature, and a
merely logical function of the mind; they are the substantial essence
which underlies all mythical representations. Although the essential
life of the world is considered from a more abstract point of view, yet
the mythical analogy of animal life evidently finds a place in the
breath of the void and of time, assumed to be independent entities. The
subsequent train of beliefs in spirits, of their incarnations and
transmigrations, are closely connected with the phantasmagoria of the
past, and display their mythical genesis;