So if the worth of the arts were measured by the matter with which they deal, this art-which some call astronomy, others astrology, and many of the ancients the consummation of mathematics-would be by far the most outstanding. This art which is as it were the head of all the liberal arts and the one most worthy of a free man leans upon nearly all the other branches of mathe matics. Arithmetic, geometry, optics, geodesy, mechanics, and whatever others, all offer themselves in its service.

I can easily conceive, most Holy Father, that as soon as some people learn that in this book which I have written concerning the revolutions of the heavenly bodies, I ascribe certain motions to the Earth, they will cry out at once that I and my theory should be rejected.

The earth together with its surrounding waters must in fact have such a shape as its shadow reveals, for it eclipses the moon with the arc of a perfect circle.

In the midst of all dwells the sun.

So, influenced by these advisors and this hope, I have at length allowed my friends to publish the work, as they had long besought me to do.

Of all things visible, the highest is the heaven of the fixed stars.

First of all, we must note that the universe is spherical.