PHYSICS

nor a theory by which its possibility might be saved. Their opinion was that the orbit of the fixed stars is that which moves with the diurnal motion, and the orbit of the signs the zodiac, which is the circle of the sun's declination, intersects the equinoctial circle at two points, one of which is called the point of the vernal equinox and the other the autumnal equinox; these are the heads of Aries and Libra, and they always preserve this intersection.

And afterwards, those succeeding them—not long before Alexander the Great, as Hipparchus posited from the observation of Timosthenes and Aristotle, in the year 450 from Bactenzar, and then from the observation of the geometer Milius in the year 845 from Bactenzar, and finally from the observation of Hipparchus himself nearly 400 years after the death of Alexander, and the observation of those who were of that time—said they had found that these stars move according to the order of the signs, and they acted subtly regarding their motions and established that the motion of this orbit is according to the order of the signs alone.

Furthermore, Ptolemy observed nearly 266 years after Hipparchus and found the motion of the fixed stars to always be according to the order of the signs. Hipparchus indeed established the calculation of this motion and said it occurs upon the poles of the circle of the signs according to the motion of their succession, at one degree every one hundred years. And when Ptolemy found that which he had investigated from the places of the stars according to the same path, he established the calculation of that motion, and even more subtly. However, those after Ptolemy, because they observed these stars comparing what they found from their places in observation with the places owed to them from that calculation, and found them to be different, were greatly amazed at those previous observations and did not adhere to that motion.

And someone after Ptolemy—namely Theon of Alexandria—opined that the fixed stars have a motion of access and a motion of recess the theory of trepidation, and each of them consists of eight degrees; and they also have with this a motion according to the order of the signs, one degree every hundred years, which motion the later ones rejected, finding their locations according to observation in places other than the locations in which they were situated in their prior location, for they sometimes add and sometimes diminish according to times determined for them. Further, Al-Battani declared that the fixed stars run from the point of the vernal equinox in equal times with a diverse course, and for this reason, he passed over this motion.

And because Az-Zarqali Arzachel considered these diverse motions, he applied himself to their coupling as it seemed to him, although he did not possess the true and perfect motion of these stars himself. And he composed a theory and calculation of these, that the poles of this orbit move upon two circles equidistant to the equinoctial, so that their motion might follow the motion of these two poles. And that which he said excited us to what we have now encountered, which was never considered by others: namely, to the motion making this in reality. It is truly the motion of this orbit upon its own poles, subjecting and following the motion of the supreme, so that it might perfect the defect by which it is deficient from its motion, and by which it is known and discerned from it. And that motion is now verified as the aforementioned Az-Zarqali posited: that what is seen of the diversity of the motion of the fixed stars is access and recess, because in truth it is in the opposite, for access to them is a motion against the motion of the universe, and recess to them is a motion toward the part of the motion of the universe; yet in reality, it is the contrary of this, as will be more broadly apparent. And with this, the motion which Ptolemy posited against the motion of the universe stands with access and recess, just as the motion of the planets and the appearance of their regression and station stands with this motion of his against the motion of the universe, although its quantity has not been known until now.

AND so that what we have said may be verified, we will return to reciting this motion of this orbit—namely, the orbit of the fixed stars—and we will bring forward an example of it later, so that the imagination of this motion might be more perfect and its truth more open. And we say that this orbit, when it is moved by its own proper motion and is upon its own poles, following the motion of the supreme (which we have called the motion of supplement), and the poles revolve upon two circles of their course, deficient from the supreme toward the part against the motion of the supreme...