De docta ignorantia

Then it will be seen more clearly that the triangle is a circle. For let it be supposed that there is a triangle abc produced by supposition, through the rotation of the line ab until

FIGURA pg079: curved triangular sector with vertex a below and arc from b to c above

b comes to c, with a remaining fixed, there is no doubt, when the line ab were infinite and b were wholly rotated until it returned to the beginning, that it is the maximal circle; of which bc is a portion, since it is a portion of the infinite arc, then the line bc is straight, and since every part of the infinite is infinite, therefore bc is not less than the whole compass of the infinite circumference; bc will therefore be not only a portion but the most complete circumference. Hence it is necessary that the triangle abc be the maximal circle, since bc the circumference is a straight line, for it is not greater than the infinite ab, since there is nothing greater than the infinite; nor are there two lines, since there cannot be two infinites. Hence the infinite line, which is a triangle, is also a circle, which was proposed. Further, that the infinite line is a sphere is equally manifest: the line ab is the circumference of the maximal circle, indeed also the circle, as has now been proved; and it is in the triangle drawn from b to c, as was said above; but bc is an infinite line, as was also proved at once. Hence ab has returned into c, with the return completed above itself; and when this is so, it follows that a sphere has necessarily arisen from such a revolution of the circle above itself; and since it was proved above that abc is a circle, a triangle, and a line, we have now proved that it is also a sphere. And these are the things which we proposed to investigate.