PHYSICS

its revolution, and the motion of this orb upon its own poles is called the motion of completion. And when this orb has completed a revolution and arrived at the supreme [orb] in the manner stated above, then the fixed stars have completed their motion in longitude, because they have added [distance] through the motion of their orb, and there remains the deficit by which this orb lacked the poles. For the motion of completion is upon them, and they are as if fixed to it; and the deficit of it is necessarily the opposite, namely, opposite to the motion of the universe.

For since the distance of these poles from the poles of the supreme [orb] is the same and immutable, therefore these two poles of this orb will make, in this deficit of theirs, two circles upon which they move over the length of time, which we shall call the circles of the course of the two poles. And they are indeed in this orb, as we have said, equidistant to the equinoctial circle, and their poles are the poles of the same. The space of this circle is like the space of the declination of the stars existing in the middle of this orb when they are upon the equinoctial [moving] from the equinoctial itself toward the north and south. And that which is between those in the north and those in the south is double the space of this circle, that is, the arc of the great circle preceding upon the poles of the supreme [orb], enclosed by the circle of the course of the pole of this orb, is almost double the declination, and is almost double the declination of the solar circle from the equinoctial. And the declination of the stars that proceed through the middle of this orb will be like the declination of the sun from the equinoctial, and this is indeed as the ancients said, without the precision of that space. And both these circles of the perfect course of both poles are the same two circles which both poles make with the completion of the revolution of the supreme orb.

And since this orb falls short in its entirety from the motion of the universe and completes, for example, by its own motion upon its own poles that deficit, and the pole is fixed to this addition, therefore the stars existing in this orb observe their place in longitude only; in latitude, however, they do not preserve their place, and the pole falls short only as much as the orb has fallen short. The stars, however, that are in it do not fall short, and this is indeed as those who came after this science have done; but it completes for itself by the motion of its orb the motion of completion, that which the orb itself had previously lacked, whence both poles revolve in those two circles of course, for both are at rest in this motion by which the orb is moved upon them.

And since the distance of the stars from each of both poles is not always the same, therefore there appears to the stars a declination of the place toward which the poles move when they revolve defectively, and it is called motion in latitude. For the poles, on account of their deficit, are postponed in the circles of their course, and they will be at different times in different parts of the poles of the supreme [orb], whence the stars decline when they follow the poles, for the distance from them ought to be the same.

The star, however, existing upon the equinoctial circle is not fixed upon it but declines from it according to the places in which the poles of both circles of the course are found, and according to the parts in which they will be with respect to the poles of the supreme [orb]; whence the star will be sometimes in the north from the equinoctial and sometimes in the south, according to the declination of the two poles which revolve from the poles of the supreme [orb]. And thus also the remaining stars are taken from their place and sometimes approach the equinoctial and sometimes withdraw from it.

How, however, are there for the stars both motions of approach and recession which the moderns have recited and have confirmed by observations? It must be said that that motion appears to them necessarily on account of the revolution of both poles upon both circles of the course and the mixture of the deficit of the two poles, namely, its defective motion. Thus, they do not complete a revolution in the time in which the supreme [orb] completes its revolution, as we said before, with the motion of the orb of the stars upon its own poles, from the fact that this motion does not appear to us, and that which follows from it appears from accidents, as will be declared afterward. And we shall set forth that which must be proposed to excite us to imagine this motion. And we say that when there is a sphere whose two poles move upon two small circles, at the motion of which—which is around the pole of another superior sphere—the sphere itself is moved, and a point has been marked...