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.

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

For I am not so enamoured of my own opinions that I disregard what others may think of them.

Mathematics is written for mathematicians.

Those who know that the consensus of many centuries has sanctioned the conception that the earth remains at rest in the middle of the heavens as its center, would, I reflected, regard it as an insane pronouncement if I made the opposite assertion that the earth moves.

In first place we must observe that the universe is spherical. This is either because that figure is the most perfect, as not being articulated, but whole and complete in itself; or because it is the most capacious and therefore best suited for that which is to contain and preserve all things.

Perhaps there will be prattlers who, although completely ignorant of mathematics, nevertheless take it upon themselves to pass judgment on mathematical questions, and on account of some passage in Scripture, badly distorted to their purpose, will dare to censure and assail what I have presented here.