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.
Mathematics is written for mathematicians.
For I am not so enamoured of my own opinions that I disregard what others may think of them.
Of all things visible, the highest is the heaven of the fixed stars.
Those things which I am saying now may be obscure, yet they will be made clearer in their proper place.
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.
Therefore, when I considered this carefully, the contempt which I had to fear because of the novelty and apparent absurdity of my view, nearly induced me to abandon utterly the work I had begun.
For it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study.
I can easily conceive, most Holy Father, that as soon as some people learn that in this book which I have written concerning the revolutions of the heavenly bodies, I ascribe certain motions to the Earth, they will cry out at once that I and my theory should be rejected.
So far as hypotheses are concerned, let no one expect anything certain from astronomy, which cannot furnish it, lest he accept as the truth ideas conceived for another purpose, and depart from this study a greater fool than when he entered it.
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.
First of all, we must note that the universe is spherical.
The earth together with its surrounding waters must in fact have such a shape as its shadow reveals, for it eclipses the moon with the arc of a perfect circle.
Moreover, since the sun remains stationary, whatever appears as a motion of the sun is really due rather to the motion of the earth.
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.
The massive bulk of the earth does indeed shrink to insignificance in comparison with the size of the heavens.
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.
Near the sun is the center of the universe.
Not a few other very eminent and scholarly men made the same request, urging that I should no longer through fear refuse to give out my work for the common benefit of students of Mathematics.
In so many and such important ways, then, do the planets bear witness to the earth's mobility.
