To know the mighty works of God, to comprehend His wisdom and majesty and power; to appreciate, in degree, the wonderful workings of His laws, surely all this must be a pleasing and acceptable mode of worship to the Most High, to whom ignorance cannot be more grateful than knowledge.

The two revolutions, I mean the annual revolutions of the declination and of the centre of the Earth, are not completely equal; that is the return of the declination to its original value is slightly ahead of the period of the centre. Hence it necessarily follows that the equinoxes and solstices seem to anticipate their timing, not because the sphere of the fixed stars moves to the east, but rather the equatorial circle moves to the west, being at an angle to the plane of the ecliptic in proportion to the declination of the axis of the terrestrial globe.

Mathematics is written for mathematicians.

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.

The strongest affection and utmost zeal should, I think, promote the studies concerned with the most beautiful objects, most deserving to be known.

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.

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.