which we find pictured in the most ancient records--a stage in
which men were governed by laws that were perhaps as wisely
adapted to their conditions as our laws are to ours--in which the
phenomena of nature were rudely observed, and striking occurrences
in the earth or in the heavens recorded in the annals of the
nation.

Vast was the progress of knowledge during the interval between
these empires and the century in which modern science began. Yet,
if I am right in making a distinction between the slow and regular
steps of progress, each growing naturally out of that which
preceded it, and the entrance of the mind at some fairly definite
epoch into an entirely new sphere of activity, it would appear
that there was only one such epoch during the entire interval.
This was when abstract geometrical reasoning commenced, and
astronomical observations aiming at precision were recorded,
compared, and discussed. Closely associated with it must have been
the construction of the forms of logic. The radical difference
between the demonstration of a theorem of geometry and the
reasoning of every-day life which the masses of men must have
practised from the beginning, and which few even to-day ever get
beyond, is so evident at a glance that I need not dwell upon it.
The principal feature of this advance is that, by one of those
antinomies of human intellect of which examples are not wanting
even in our own time, the development of abstract ideas preceded
the concrete knowledge of natural phenomena. When we reflect that
in the geometry of Euclid the science of space was brought to such
logical perfection that even to-day its teachers are not agreed as
to the practicability of any great improvement upon it, we cannot
avoid the feeling that a very slight change in the direction of