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
the intellectual activity of the Greeks would have led to the
beginning of natural science. But it would seem that the very
purity and perfection which was aimed at in their system of
geometry stood in the way of any extension or application of its
methods and spirit to the field of nature. One example of this is
worthy of attention.
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