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

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

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.

In so many and such important ways, then, do the planets bear witness to the earth's mobility.

I shall now recall to mind that the motion of the heavenly bodies is circular, since the motion appropriate to a sphere is rotation in a circle.

I am aware that a philosopher's ideas are not subject to the judgment of ordinary persons, because it is his endeavour to seek the truth in all things, to the extent permitted to human reason by God.

Mathematics is written for mathematicians.