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

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.

Pouring forth its seas everywhere, then, the ocean envelops the earth and fills its deeper chasms.

We regard it as a certainty that the earth, enclosed between poles, is bounded by a spherical surface.

Therefore I would not have it unknown to Your Holiness, the the only thing which induced me to look for another way of reckoning the movements of the heavenly bodies was that I knew that mathematicians by no means agree in their investigation thereof.

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.

Every light has its shadow, and every shadow hath a succeeding morning.