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.

Although all the good arts serve to draw man's mind away from vices and lead it toward better things, this function can be more fully performed by this art, which also provides extraordinary intellectual pleasure.

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.

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.

So, influenced by these advisors and this hope, I have at length allowed my friends to publish the work, as they had long besought me to do.

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

When, therefore, I had long considered this uncertainty of traditional mathematics, it began to weary me that no more definite explanation of the movement of the world-machine established in our behalf by the best and most systematic builder of all, existed among the philosophers who had studied so exactly in other respects the minutest details in regard to the sphere.