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.

At rest, however, in the middle of everything is the sun.

Those things which I am saying now may be obscure, yet they will be made clearer in their proper place.

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

For it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study.

To know that we know what we know, and to know that we do not know what we do not know, that is true knowledge.

For a traveler going from any place toward the north, that pole of the daily rotation gradually climbs higher, while the opposite pole drops down an equal amount.