Every angle acknowledges that it is a likeness of true angularity, for [each angle] is angle not insofar as angle exists in itself but insofar as angle exists in something else, viz., in a surface. And so, true angularity is present in creatable and depictable angles as in a likeness of itself.

A given circle cannot be so true that a truer one cannot be found; and the movement of a sphere at one moment is never precisely equal to its movement at another, nor does it ever describe two circles similar and equal, even if from appearances the opposite may seem true.

There are not many beginnings but there is a single Beginning, prior to multitude. But if you were to say that the beginnings are plural apart from their partaking of the One, that statement would self-destruct. For, surely, these plural beginnings would be both alike, by virtue of their not partaking of the One, and not alike, by virtue of their not partaking of the One.

It has been asserted that there is a separate species on the earth to correspond with each one of the stars. Now if the earth provides in each species a focus for the action of each star, why may not a similar provision be made among other heavenly bodies that are subject to the action of their fellows?

There will be a machina mundi whose centre, so to speak, is everywhere, whose circumference is nowhere, for God is its circumference and centre and He is everywhere and nowhere.

Within itself the soul sees all things more truly than as they exist in different things outside itself. And the more it goes out unto other things in order to know them, the more it enters into itself in order to know itself.

In creating the world, God used arithmetic, geometry, and likewise astronomy.