PHYSICS

...with regard to their proportion to the Earth, and the proportion of these to one another during times of conjunction and opposition, and during the times of the eclipses of that which is eclipsed by these, and the measure of that which is eclipsed from their body, and the duration of the eclipse in the past and future, and that which changes regarding it.

However, what I hold to be memorable regarding those suppositions of his and the roots discovered by him is that which is intolerable to me. I cannot support the premise of placing those spheres that are eccentric to the center of the world, revolving around their own eccentric centers, with their centers revolving around other centers, and assuming epicycles revolving around their own centers, with their centers revolving in the breadth of the same sphere against the revolution of those [planets] upon other spheres eccentric to the center of the world. It is as if all these spheres were placed in the same sphere, filling its space and leaving another place empty and void, while the eccentric sphere—that is, the one carrying the center of the epicycle—takes from the breadth of the sphere some part of it from one side, and the opposite part from the other side, and from this, there remains an incomplete circular figure. This would be either motion or change through parts, since those eccentric spheres and epicycles move within it, such that the sphere gathering these spheres—if it existed in air, for example, or in water—would have its parts moved, and an empty space would be given to these spheres while another is filled up as it passes through.

Furthermore, these positions produce falsehoods from the resulting inconsistencies and matters contrary to the truth. He would have acted more correctly had he posited two primary motions for two spheres and placed the planets in eccentrics and epicycles only, and had them move with the motions he imagined—in the air, for example, or similar substances—without positing those eight spheres and each of them carrying a number of spheres of diverse motions as he did.

Therefore, for a time, I was perplexed and amazed. I ceased to proceed further in the rest of the book, remaining as if stunned and deep in thought. Then, God Almighty, by His divine influx—granted by no other—awakened me from my sleep of stupefaction. He illuminated the eyes of my heart from its disturbances regarding that which had never been contemplated by anyone. I did not arrive at this through speculation or the discourse of human ingenuity, but because it pleased God to show His miracles and to lay open the hidden secret in the theory of their spheres, and to make known the truth of their essence and the rectitude of the quality of their motion and change, which I shall bring forward later. I will open up where the diversity that is seen in this originates, and the cause of that which I shall say.

For Ptolemy did not suppose those positions as if they were so in the nature of things, but only that what he posited from those roots might be convenient and consistent with that which appears sensibly in his observation. Rather, he posited them so that the things themselves might correspond to them, and with these posited, those motions might be found to be of a certain rectitude and a certain order, not diverse nor remote. For it did not escape him that that position was impossible and remote from the truth. He well understood what follows from each one and both of the two roots together: that there is either a vacuum when those eccentric spheres move, or that those spheres gathering them are full of another, extraneous body whose parts move according to the motion of the bodies moved within it and leave a place empty and void and fill another place—all of which is ridiculous, remote from rectitude, and different from the truth of celestial reality.

And you also know, my excellent brother, that the excellent judge Abu Bakr ibn Tufail a 12th-century Andalusian polymath and philosopher told us that he had found a theory and roots for those motions, beyond the roots of Ptolemy, without the position of an eccentric or an epicycle at all, and that all those motions are proven by them without anything false following from these. He promised to write about this; his excellence in science is well known. Since I heard this from him, I have not ceased to think about it and to search the words of the ancients concerning it.