De docta ignorantia

Perhaps those who read these things before unheard will marvel, after learned ignorance shows them to be true. We know now from these that the universe is trine and that nothing of universals is which be not one from potency, act and motion of connection; and that none of these can subsist absolutely without another; so that necessarily they are in all things according to most diverse degrees so differently that no two things in the universe can through all things be simply equal; on account of which that anything have the world machine or this sensible earth or air, or fire or anything else whatever for a fixed and immobile center with the various motions of the orbs considered is impossible; for in motion one does not come to the minimum simply, say a fixed center, since the minimum must coincide with the maximum. The center of the world, therefore, would coincide with the circumference.

The world, therefore, does not have a circumference, for if it had a center and a circumference, then it would have within itself its beginning and end and the world itself would be terminated to something else, outside the world would be another and place, all of which lack truth. Since therefore it is not possible for the world to be enclosed within a corporeal center and circumference, the world is not understood whose center and circumference are God; and since this is not an infinite world, yet it cannot be conceived finite, since it lacks bounds within which it is enclosed. The earth, therefore, which cannot be the center, cannot lack all motion; for it must be moved in such a way that it could be moved less through infinity. As therefore the earth is not the center of the world, so neither is the sphere of the fixed stars its circumference, although even comparing earth to heaven the earth itself seems nearer the center and heaven the circumference. The center, therefore, is neither earth nor the eighth or another sphere, nor does the appearance of six signs above the horizon conclude earth to be in the center of the eighth sphere. For if it were even distant from the center and about the axis passing through the poles, so that on one side it were elevated toward one pole, and on the other depressed toward the other, then to men distant from the poles as much as the horizon extends only half the sphere would appear, as is manifest. Nor even is the center of the world itself more within earth than outside; nor even has this earth, nor any sphere, a center. For since a center is a point equidistant from the circumference, and a most true sphere or circle cannot be, but a truer can be given, it is manifest that a center cannot be given, but a truer can even be given, and the most precise, exact equidistance to diverse things outside God is not to be found, who himself alone is infinite equality. Who therefore is the center of the world, namely blessed God, he is the center of earth and of all spheres and of all things which are in the world, who is at once the infinite circumference of all. Further there are not in heaven immobile and fixed poles, although even the heaven of fixed stars seems through motion to describe gradual circles in magnitude smaller than the colures or than the equinoctial, and so of intermediates, but every part of heaven must be moved, though unequally in comparison of the circles described through motion of the stars.

Whence as certain stars seem to describe the maximal circle, so certain the minimal; but no star is found which describes none. Since therefore there is no fixed pole in the sphere, it is manifest that neither is an equal mean found as it were equidistant from the poles. There is not therefore a star in the eighth sphere which through revolution describes the maximal circle, since it would have to be equidistant from the poles, which are not; and consequently there is none which describes the minimal circle. The poles of the spheres, therefore, coincide with the center, that there be no other center than pole, since blessed God. And since we cannot detect motion except by comparison to the fixed, namely poles or centers, and we presuppose them in measures of motions, hence walking in conjectures we find ourselves to err in all things, and we marvel when according to the rules of the ancients we do not find the stars to agree in situation, since we believe them to have rightly conceived concerning centers and poles and measures. From these indeed it is manifest that earth is moved. And since from motion of comet, air and the elements of fire we have experienced them to be moved, and the moon less from east to west than Mercury or Venus or the sun, and so by degrees, hence the earth itself is still moved less than all, but yet is not as a star describing about center or pole the minimal circle, nor does the eighth sphere or another describe the maximal, as was just proved.

Consider acutely, therefore, since as stars hold themselves about conjectural poles in the eighth sphere, so earth, moon and planets are as stars moved distantly and differently about the pole, conjecturing the pole to be where the center is believed. Whence, although earth as it were a star be nearer the central pole, yet it is moved, and does not describe the minimal circle in motion, as has been shown. Indeed neither sun nor moon, nor earth nor any sphere, although to us otherwise seems, can describe a true circle in motion, since they are not moved upon the fixed. Nor is a true circle givable, but a truer can be given, nor ever in one time as in another equally precisely is it either moved or does it describe a verisimilar equal circle, even if to us this does not appear. It is necessary therefore, if concerning motion of the universe you wish to understand anything else as to what has now been said, that you enfold center with poles, helping yourself as much as you can with imagination: for if one were above earth and under the arctic pole, and another in the arctic pole, as to one existing on earth the pole would appear to be in the zenith, so to one existing in the pole the center would appear to be in the zenith. And as antipodes have heaven above as we, so to those existing in both poles earth would appear to be in the zenith, and wherever one be, he believes himself to be in the center. Enfold therefore these diverse imaginations, that center be zenith, and conversely, and then through intellect, which learned ignorance alone serves, you see the world and its motion and figure cannot be attained, since it will appear as it were wheel in wheel and sphere in sphere, having center or circumference nowhere, as is preferred.