not only the development of applied geometry
but the reduction of other conceptions to a rigorous mathematical form
was indefinitely postponed.

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 obvious conclusion
that the stars might be bodies like our globe, shining either by their
own light or by that of the sun, would have been a first step to the
understanding of the true system of the world.

There is historic evidence that this deduction did not wholly escape
the Greek thinkers. It is true that the critical student will assign
little weight to the current belief that the vague theory of
Pythagoras--that fire was at the centre of all things--implies a
conception of the heliocentric theory of the solar system. But the
testimony of Archimedes, confused