There is, however, one science which admitted of the immediate
application of the theorems of geometry, and which did not require
the application of the experimental method. Astronomy is
necessarily a science of observation pure and simple, in which
experiment can have no place except as an auxiliary. The vague
accounts of striking celestial phenomena handed down by the
priests and astrologers of antiquity were followed in the time of
the Greeks by observations having, in form at least, a rude
approach to precision, though nothing like the degree of precision
that the astronomer of to-day would reach with the naked eye,
aided by such instruments as he could fashion from the tools at
the command of the ancients.

The rude observations commenced by the Babylonians were continued
with gradually improving instruments--first by the Greeks and
afterwards by the Arabs--but the results failed to afford any
insight into the true relation of the earth to the heavens. What
was most remarkable in this failure is that, to take a first step
forward which would have led on to success, no more was necessary
than a course of abstract thinking vastly easier than that
required for working out the problems of geometry. That space is
infinite is an unexpressed axiom, tacitly assumed by Euclid and
his successors. Combining this with the most elementary
consideration of the properties of the triangle, it would be seen
that a body of any given size could be placed at such a distance
in space as to appear to us like a point. Hence a body as large as
our earth, which was known to be a globe from the time that the
ancient Phoenicians navigated the Mediterranean, if placed in the
heavens at a sufficient distance, would look like a star. The