Hear what profit we derive from the preliminary disciplines, and how excellent the propositions are which we learn through them. Know that there are certain things, which would appear impossible, if tested by man’s imagination, being as inconceivable as the co-existence of two opposite properties in one object; yet the existence of those same things, which cannot be represented by imagination, is nevertheless established by proof, and attested by their reality. E.g., Imagine a large globe, of any magnitude you like, even as large as the all-encompassing sphere; further an axis passing through the centre, and two persons standing on the two extremities of the axis in such a manner that their feet are in the same straight line with the axis, which may be either in the plane of the horizon or not; in the first case both persons would fall, in the second case one, namely the one who stands on the lower extremity would fall, the other would remain standing, as far as our imagination can perceive. It has however, already been proved that the earth has the form of a globe, that it is inhabited on both extremities of a certain diameter, that both the inhabitants have their heads towards the heaven, and their legs towards each other, and yet neither can possibly fall, nor can it be imagined; for it is incorrect to say that the one extremity is above, the other below; but the term “above” and “below” apply to both of them as regards their relative position to each other. Similarly it has been proved in the second chapter of the book on Conic Sections, that two lines, which at first are at a certain distance from each other, may approach each other in the same proportion as they are produced further, and yet would never meet, even if they were produced to infinity, although they are observed to be constantly converging. This is a fact which cannot easily be conceived, and which does not come within the scope of imagination. Of these two lines the one is straight, the other curved, as stated in the aforementioned book. It has consequently been proved that things which cannot be perceived or imagined, and which would be found impossible if tested solely by imagination, are nevertheless in real existence. The non-existence of things which are represented by imagination as possible has likewise been established by proof, e.g., the corporeality of God, and His existence as a force residing in a body. Imagination perceives nothing except bodies, or properties inherent in bodies.