On the Revolutions of the Heavenly Spheres

...and its magnitude. Furthermore, in establishing the motions, both of these and of the other five wandering stars i.e., the planets, they do not use the same principles and assumptions and demonstrations of apparent revolutions and motions. For some use only homocentric circles, others eccentric and epicyclic models used in Ptolemaic astronomy, with which, however, they do not fully attain the desired results. For those who trusted in homocentric circles, even though they demonstrated that some diverse motions could be composed from them, could establish nothing certain that would correspond to the phenomena. Those who devised eccentrics, although they seem to have accounted for apparent motions for the most part with matching numbers, have meanwhile admitted many things that seem to contravene the first principles of the uniformity of motion. They also could not find or infer from them the principal thing, that is, the form of the world and the certain symmetry of its parts. It happened to them just as if someone were to take from different places hands, feet, head, and other limbs, drawn very well indeed but not with reference to one body, and not at all corresponding to one another, so that a monster rather than a man would be composed from them. Therefore, in the process of demonstration, which they call a μέθοδον method, they are found to have either passed over something necessary or admitted something alien and not at all pertaining to the matter. This would have happened to them least of all if they had followed certain principles. For if their assumed hypotheses were not fallacious, all that follows from them would undoubtedly be verified. Although these things that I now say are obscure, they will become clearer in their proper place.

When I pondered this uncertainty of mathematical traditions for a long time regarding the calculation of the motions of the spheres of the world, it began to weary me that no more certain theory of the motions of the world's machinery, which was built for us by the best and most orderly Artisan of all, was agreed upon by philosophers, who otherwise scrutinized so exquisitely the smallest details of this world. Therefore, I took it upon myself to reread the books of all the philosophers I could obtain, to investigate whether any one had ever opined that there were other motions of the spheres of the world than those posited by those who taught mathematics in the schools.