Epitome Astronomiae Copernicanae: Liber IV, part 6
Chapter V. Of the annual motion of the Earth
This philosophy of Copernicus makes the Earth one of the planets and carries it around among the stars. I ask what is required beyond what has been said for an easier grasp of the doctrine and its arguments. Since the annual motion of the Earth becomes necessary once the centre of the Sun is fixed at rest in the centre of the world, and since the effect is produced in that space by the turning of the solar body, and since it plainly removes the reality of the stationary points and retrogradations of the planets and explains them away as a mere deception of sight, these questions must be carefully distinguished: 1) Does the Sun rest in the centre of the world? 2) Are the orbits of all five planets, and that of the Earth in the midst of them, carried around the Sun, so that the Sun is in the embrace of them all? 3) Does the Sun occupy the very centre of the whole planetary system, or does it merely stand near it? 4) Does this centre of the system, and the Sun in it, travel round in an annual motion, or rather, the Sun remaining motionless, does the Earth have the annual motion through the parts opposite to those in which the Sun is supposed to be at any given time?
You have shown above that the Sun is 1) in the centre of the sphere of the fixed stars; now prove also that it is 2) within the compass of the planetary orbits. That the Sun is in the midst of the planetary revolutions is proved first from an accident of this motion, namely from the appearance of the stationary points and retrogradations, which is a deception of sight, or again from the fact that when the planets are direct they seem swifter than they really are. For, to begin with the inferior planets, for many ages now, among those who followed Ptolemy (to say nothing of the most ancient Aristarchus), it dawned on writers such as Martianus Capella, Campanus and others that it could not be otherwise than that the Sun, Venus and Mercury have the same period of time, namely a year, unless they also have the same orbit, and the Sun holds the centre of the two orbits of Venus and Mercury, and those two run about the Sun. From this it follows that these planets, when they seem retrograde, are not in truth retrograde, but pursue the same course beneath the fixed stars while circling the Sun, which was more in keeping with the nature of the heavenly things.
A few years ago Galileo confirmed this argument by a most brilliant demonstration, having detected by the telescope the illumination of Venus, which, when she is direct and near the Sun, has a round figure, and when retrograde, a horned one (cf. Vol. II, p. 465). From this it is most certainly proved both that her illumination comes from the Sun, and that when she appears round and moves direct she is above the Sun, and when horned and retrograde, below the Sun, and so goes around the Sun. For the sake of clarity let the demonstration of this matter be joined with the demonstration of the illuminations of the Moon (Figure 64). Marius brings forward similar things about Mercury (cf. Vol. II, p. 470): by the help of the same telescope he found that the feebleness of its light diminishes as it descends toward the Earth. The planet is an indication that the appearance of the illumination changes and the light in the horn is attenuated, so that it affects the eye less from near than from afar, which without this attenuation in the horn would be absurd; for things near at hand otherwise appear larger than if they had withdrawn farther. Now as for the three superior planets, Aristarchus, Copernicus and Tycho Brahe show that if we arrange these also around the Sun and set the Sun as, so to say, the common centre of the five planets, so that the motion of the Sun, whether true or apparent, embraces the whole orbits of the five planets, we are freed, as before in Venus and Mercury from two superfluous eccentrics, so now in the superior planets from 1) three epicycles; 2) their real motion in blind and incredible agreement with the motion of the Sun; 3) and so their stationary points and retrogradations, no less than above in Venus and Mercury, with respect to the Sun which they circle, are in truth nonexistent; 4) so also very many intricacies in the motion of latitude are removed from the theoretical doctrine; 5) finally the causes are laid open of the difference by which the five planets become stationary and retrograde, the Sun and Moon never; and why 6) Saturn, the highest of the superior planets, has the smallest arc of retrogradation, Jupiter in the middle a middle one, Mars the nearest the greatest. All these things will be explained below in Book VI. But the causes of these appearances are entirely unknown among the ancient astronomers.
But the secondary planets also give us some testimony of this matter. For Marius found in his Jovian World that the restitutions of the satellites of Jupiter about Jupiter are by no means regular with reference to the lines which we cast from the centre of the Earth to Jupiter, but are regular if they are compared with the lines drawn from the centre of the Sun through Jupiter. This certainly stands as a very great argument that the orbit of Jupiter is ordered about the Sun, and that the distance of the Sun from the centre of Jupiter’s orbit is in a manner certain and fixed, while the Earth varies its distances from this centre through the year.
How many sects of astronomers are there concerning this speculation, from which the second argument is drawn? Three. The first, commonly known under the name of the ancients, has Ptolemy as its leader; the second and third are ascribed to more recent men, although the second, named from Copernicus, is the most ancient; the author of the third is Tycho Brahe.
Ptolemy, then, treats the wandering stars at least one by one, and assigns the apparent causes of all motions, retrogradations and stationary points to each in its own orbit, yet so that in each he posits one definite orbit which completes its period with respect to the motion of the Sun. For what reasons this happens Ptolemy does not explain, except that Latin writers attribute some obscure force to certain rays of the Sun, bewitched by sheer ignorance of the rays.
The other two authors compare the planets with one another, and derive what is found common in their motions from the same common cause. But this common cause (which makes the planets seem stationary and retrograde in some particular configuration of the planet with the Sun) is still attributed by Brahe to the real motion of the whole planetary orbits, while by Copernicus it is wholly removed from the planets’ orbits themselves. For Brahe teaches that all five orbits of the primary planets are joined to some common point, not far from the centre of each orbit (as if all these were drawn together on a common circular tablet B), and that this common knot, as it were, in truth goes round in the annual time together with the Sun, and indeed very near it (in the little circle A, marked with points), and carries the whole orbits about with it and shifts them from their places in the world, as it were, in the manner in which winnowers turn a sieve held at one part of its rim in their hands, tossing it, so that the situation of the whole planetary system is, for example, in the month of June according to circle B, in August according to C, in October according to D, in December according to E, in February according to F, in March according to G, thence again according to B; and meanwhile the planet, nowise disturbed by this dislocation of its orbit, completes its circle within the orbit as around its fixed centre. But Copernicus, as to the annual time, leaves the centres of the orbits wholly fixed, and the centre of the Sun fixed also in the neighbourhood of the said centres, and ascribes the annual motion about the Sun to the Earth and thus to our sight; whence it comes about that, while sight supposes itself at rest and the Sun moved in an annual motion, all five planets appear now to stand, now to go the contrary way, now to proceed swiftest on a direct course.
By what arguments, then, do you prove the third point, that that common knot or centre of all the systems of the primary planets belongs not merely near the body of the Sun, but in the very body and centre of the Sun? The arguments for this are woven in astronomical doctrine as follows. 1. From the motion of altitude and of longitude of the planets. Observations rightly treated testify that the longest line of each primary theory, which exactly bisects the orbit into two semicircles equal both in quantity and in the swiftness of their parts, passes through the centre of the Sun. All five lines of altitudes therefore meet perpetually in the centre of the Sun. Look at the diagrams Nos. 51 and 52.
2. From the motion of latitude of the planets. From the same kind of evidence, namely from observations, we learn that the orbit of each primary planet is cut by the ecliptic at places opposite one another from the centre of the Sun, not from any other neighbouring point.
3. But if these two centres, that of the Sun and that of the region of the movables, were different, then either to the centre of the Sun or to the centre of the region of the movables a very slow motion in a small circle would have to be ascribed, on account of the progress of the Sun’s apogee, as will be taught in Books VI and VII. And thus neither of the two, being moved, could either be or remain in the centre of the world. But it is probable that both are in the centre of the world and rest there: the Sun on account of the arguments both above and to follow, the knot of the movables on account of the reasons and the source of motion, which we have already said wells up from this common centre of the movables; and rest belongs to the source of motion, and on account of rest, a place in the centre of the movables as well as of the whole world.
4. The seat of this same source of motion must be assigned not to some mathematical point near the most noble body, but rather to that most noble body itself, for three reasons: first, that we may escape the absurdity that the source of motion, which is necessarily placed in that common knot of all the spheres, as will be proved below, should be near the heart of the world and yet not in the very heart of the world, the Sun; second, because the moving power cannot reside in a mathematical point but requires a body, namely the heart of the world, the Sun; third, because the moving power altogether demands for itself the centre of the world, in which the Sun itself is, just as rest belongs to the surface of the world, and motion to what lies between.
5. But above all this must be wrested from the opinion of Brahe, and it must be shown that the centre of the region of the movables does not differ from the centre of the Sun. For if Brahe follows this, he will be compelled to assign to the Sun one motion, and to this centre of the movables another, different one, by which it comes about that the Sun now precedes this centre, now follows it, now stands above it, now below, and yet both always have the same period of time.
6. Moreover, something absurd and marvellous would befall Brahe. For the Sun would be moved with the motion of an eccentric, having its apsis today in Cancer, while the centre of the movables would have the apsis of its eccentric motion in the opposite sign, Capricorn. But what would be the cause of this?
7. These last two arguments furnish one argument also against Copernicus, in so far as he too places that knot of all the planets near the Sun, not in the Sun itself. The motions of all the remaining primary planets agree in this, that the points about which their motions appear uniform differ in position from the common centre of the region of the movables; the Earth alone would observe this very point as the norm of its motion, if the Sun were not in the very centre of the region of the movables. But what would be the cause of this difference?
8. Finally, the reason why Copernicus and Brahe made these two centres differ is neither sufficient nor sufficiently astronomical. For they were driven to it only because in the forms of their hypotheses they wished to express complete equivalence with the Ptolemaic form. Yet it was not necessary to tread so closely in Ptolemy’s footsteps. For Ptolemy did not build all the parts of his hypothesis from observations, but founded many on this preconceived false opinion, that the motions of the planets must be presupposed uniform around the whole circle, which is demonstrated from observations to be false. Whoever desires to understand these astronomical arguments solidly, gathered here under a single view, let him turn to my Commentaries on the motions of the star Mars.
By what arguments, finally, do you prove the fourth point, that the centre of the Sun, which is in the midst of the planetary orbits and bears their whole system, does not go round in any annual motion, as Brahe wishes, but, according to Copernicus, stays in one place motionless, while the centre of the Earth goes round in an annual motion? Although when one is demonstrated the other necessarily follows, yet some arguments bear more closely on the Sun itself, some on the Earth, some equally on both.
Here first the same argument avails by which we have just now vindicated for the Sun the middle of the orbits: namely, the removal of a superfluous multitude of orbits and motions. For as it is much more probable that there is some one system of orbits of the Sun, common both to the centre of the Sun and to that knot of the five orbits according to Tycho Brahe, than that we should believe Ptolemy, that in each of the five planets, besides the orbits belonging to their own motions, there is in addition one whole system of orbits, exactly like the sixth system, that of the Sun; so also, further, it is now much more probable that the centre of the Earth alone goes round in an annual motion, the Sun being at rest according to Copernicus, than that this same annual motion (besides the other motions proper to each) belongs to that knot of five systems with their orbits and the planets themselves and the sixth, the Sun, according to Brahe. For he, although he removed those superfluous five theories of Ptolemy, similar to the solar, from the genuine systems of the planets, and brought them down to that common knot of the systems, hid them and fused them into one, yet left in the world the very thing that was effected by those theories: so that any planet, besides that motion which must in truth be granted to it, is still moved in addition by the very motion of the Sun, mingling both into one; and from this mixture, since there are no solid orbits, most intricate spirals are produced in the space of the world. See the diagram of this intricacy in the Commentaries on Mars, fol. 3 (III. 173). Copernicus, on the contrary, strips the five planets entirely of this foreign motion of the Sun by the single simple motion of the Earth’s centre, and brings it about that the centres of the six primary planets, namely of the Earth and the other five, each describe in the space of the world a single simple orbit, always like itself, or a line very near a circle.
The second argument is from the motion of latitude. If, the Earth standing, the epicycles go around, whether according to Ptolemy or according to Brahe, those epicycles, especially of the inferior planets, will have to be shaken in various ways, both at the sides and at head and feet, that is, balanced in two ways; but with the Earth moving, all the orbits are most constantly inclined to the ecliptic. See Book VI, Part III, the latitudes of the inferior planets, which furnish a most evident argument for the motion of the Earth.
Third, as above in the spherical doctrine, the diurnal revolution of the Earth being granted, the immense sphere of the fixed stars was freed from a diurnal motion of unreckonable swiftness, so now, the annual motion being granted to the same Earth after the example of the other planets, we account for that very slow motion of the fixed stars which is called by Copernicus the precession of the equinoxes. See on these things Book VII. For it is much more credible that these things be ascribed to the axis of one small earthly body than to so great a mass.
Fourth, the consideration of the proportion of the orbits avails here. For it is by no means likely that the centre of a great orbit goes around in a small orbit. Now the proper orbits of the three superior planets are much greater than the orbit of the Sun: that of Saturn almost tenfold, of Jupiter fivefold, of Mars one and a half times. These five orbits, therefore, are not carried round or shifted in their position, but their centres remain almost fixed, and consequently the Earth goes round in place of this common motion of theirs and of the Sun.
Let the fifth argument, akin to the former, be the same by which Brahe also tried to cast down the solid orbs. For if Brahe’s reasoning holds, so that the orbit of Mars is one and a half times the orbit of the Sun, the body of Mars will at certain times arrive at that point of the world’s space in which at other times the Sun was; which is very incredible of the primary planets, that their regions, through which they pass, should thus be confused, whereas in Copernicus they are not only distinct but separated by very wide empty intervals.
I weave a sixth, like the fourth, from the magnitude of the movable bodies. For it is more credible that the body is great around which smaller ones circle: thus Saturn, Jupiter, Mars, Venus and Mercury are all smaller bodies than the body of the Sun, around which they go; thus the Moon is smaller than the Earth, around which the Moon goes; thus the four Jovian satellites are smaller than the body of Jupiter, around which they revolve. Now if the Sun moves, the Sun, the greatest, and the three superior planets, all larger than the Earth, will go around the smaller Earth: it is therefore more credible that the Earth, a small body, goes around the great body of the Sun.
The seventh reason is taken from the causes of the intervals, explained above in the first part of this book, which are disturbed and mutilated unless we also grant the Earth its own orbit, which Copernicus gives it between the orbits of Mars and Venus. For although the interval of Saturn and Jupiter might be derived from the cube, that of Jupiter and Mars from the tetrahedron, that of Venus and Mercury from the octahedron, even in Brahe’s ordering, yet there would still remain between Mars and Venus a single interval, while of the figures of the world two remain over. Nor would that interval of Mars and Venus, which is in a ratio greater than double, fit either of these figures, the dodecahedron namely or the icosahedron, nor could it be derived from two figures with no orbit intervening between them.
Eighth, the same must be said also of the harmony of the heavenly motions, which consists in numbers and proportions plainly the same as those of our musical scale, and which, whether you consider the excellence of the work, or the delight of contemplation, or finally the unavoidable force of persuasion, can truly be called the soul and life of the whole of astronomy. And that harmony succeeds at last only if the Earth, in its own place and order among the planets, strikes its own string and, as it were, sings its own tone by the variation of a semitone, for which semitone, which again is the soul of the song, there would otherwise be no representation. Nay, if the Earth’s semitone is taken away, the representation among the heavenly motions of the kinds of song, hard and soft, perishes, a thing most delightful, most subtle and most admirable in this whole treatise. But of this in the Harmonics.
Ninth, if we consider the force of Brahe’s ordering, and imagine for ourselves some material of the five shiftable orbits, which is shifted with the region of the movables itself in an annual motion, then in this material, in this heavenly orb, I say, poured through all the regions of the planets, the Earth also, though at rest, will trace about the Sun just such an orbit as Copernicus assigned to it, with both the Sun and the centre of the region of the movables at rest, between the orbits of Mars and Venus. Thus by an absurd and improper way the same beauty would be hinted at from afar, the Earth, that is, traversing one orbit by remaining at rest. It is more credible that the sixth orbit of the Earth is described by the real motion of the Earth itself, just as the other five orbits are described by as many motions.
Let the tenth argument, taken from the periodic time, be this: that the apparent motion of the Sun has 365 days, a measure which is the mean between the period of Venus of 225 days and that of Mars of 687 days. Does not the nature of things, then, cry out with a loud voice that the circuit in which those 365 days are spent is also in place midway between the circuits of Mars and Venus about the Sun, and so that this circuit is not the Sun’s about the Earth (since about the Earth none of the primary planets has its orbit ordered, as Brahe concedes), but the Earth’s about the resting Sun, just as the other primary planets, for example these very ones, Mars and Venus, complete their periods by running about the Sun.
The eleventh is taken from the moving causes (from the opinion of Brahe, indeed, as supposed, though not conceded by all). For since there are no solid orbs, the moving faculties can be placed nowhere but in the movable bodies themselves. But thus the condition of the moving souls becomes very hard, and harder that of the intelligences, when the former are bidden to carry the body in which they dwell from place to place by a twofold motion without the resistance of anything, and the latter to look to very many things, that they may carry the planet along in its order with two motions wholly distinct and mixed together; for at the least they will be compelled to look at the same moment to the principles, centres, periods and figures of both motions. But if the Sun is at rest and the Earth moved, the motion of each planet is single and can be effected by corporeal magnetic powers, with an animal faculty scarcely beyond a single rotation of the body of the Sun, and the aid of a mind is plainly nowhere needed. See the Commentaries on Mars throughout.
The twelfth is from the source of motion. For it has just been demonstrated, and will be confirmed more fully below, that all the motion of the five primary planets, and in part also of the secondary ones, arises from the Sun. But it is right to believe the first cause of motion to be immovable. The Sun therefore stays in its place immovable, and consequently the Earth is moved with the annual motion, in the Sun’s stead.
The thirteenth is from the instruments of motion. For if we allow the Sun and the Earth to be turned about their own axes, then the forms of these bodies become the subject of the moving powers by which the six planets are moved by the Sun and the Moon by the Earth. But if the Sun goes round in an annual motion while the Earth is at rest, then for moving the Sun there is at hand no form of body to convey motion; nor, if the Earth is not turned about its axis in the diurnal time, has it anything by which to move the Moon. But this argument presses more upon the diurnal motion.
The fourteenth, from the motion of longitude, is of this sort. If the Sun is moved, carrying about the system of all the orbits, something new happens about it: for a certain body will move itself, or at least by an extrinsic and peculiar mover, whereas the other primary bodies are moved by one common Sun and so by something other than themselves. But if the Earth is moved in a circle, being moved by the Sun like the other primary planets, nothing new happens. Therefore it is probable that the Earth is moved, since the cause of its motion is apparent and probable, and that the Sun stands fixed.
The fifteenth argument is from the motion of altitude. It has partly been said already, and will be demonstrated more fully below, that all the planets are librated on a straight line which tends toward the Sun, and from this libration take the laws of their swiftness and slowness at any place of the eccentric, so that it is certain that the Sun is the cause of this variation for all five. It is likewise demonstrated in the Commentaries on Mars and below in Book VI that the same holds good in the Earth, if it is moved, that it also is librated on a diameter extended toward the Sun; whereas if the Sun is set down as moved, then on the contrary the Earth becomes for the Sun the cause of slowness and swiftness and thus also of its circuit. But let the bodies themselves of the Sun and the Earth be considered, and judgment made whether it is more probable that the Sun, the source of motion of the five planets, many times greater than the Earth, together with that knot of the five planetary systems is moved by the Earth, or on the contrary that the Earth, one among the primary planets, is moved by the common source of motion of the rest. See the Commentaries on Mars.
Let the sixteenth probability be this: that since in the first book the diurnal rotation of the Earth about its axis has been asserted by many arguments and solutions of objections, among which these were not the weakest, that, the diurnal motion of the Earth being posited, both the final and the instrumental cause of the obliquity of the ecliptic can be taken from the Earth itself, neither of which, the Earth being at rest, can be explained or sought from the sphere of the fixed stars itself, in which the zodiac is, without regard to this small body which is called the Earth: now therefore the translation of the Earth’s centre can no longer be so absurd. But probability suffices, if the remaining arguments require the thing itself. For this is not to be put forward as a necessary argument, because the Sun also is turned about its own axis, yet is immovable in place as a whole.
The seventeenth reason: if the Earth goes round in an annual motion, we find not only a more probable cause of the translation of the ecliptic itself from the fixed stars to others than if we ascribe this variation to the Sun, the first body, but with the same labour we also give the reason of the unequal progression of the planetary nodes, and, the axis of the Earth’s diurnal motion being taken to help, we explain the causes of the changed obliquity of the ecliptic, as also of some inequality in the precession of the equinoxes (the whole of which we have already cast down by the third argument). But the causes of so many phenomena must be wholly unknown if the Earth does not go round in an annual motion.
Let the eighteenth argument be from the end of the motion, from which it is proved that motion belongs to the Earth as the dwelling of a contemplating creature. For it was not fitting that man, the future inhabitant and observer of this world, should reside in one place of it as in a closed chamber, in which way he would never have attained to the measurement and contemplation of stars so remote, unless he had been endowed with other gifts beyond the human: rather, equipped with these eyes which he now has and these faculties of mind, he ought in this most spacious building, by the annual translation of the Earth, his dwelling, to walk about, to take different stations as surveyors are wont, that is, to range abroad, that he might behold and measure the several parts of the house so much the better. You understand, doubtless, that for the first part of this fourth book to be composed, its writer needed the ship Earth and its annual voyage around the Sun. But the Earth going, the Sun must be at rest.
Chapter VI. Of the diurnal revolution of the body of the Earth about its axis and its effect in moving the Moon, and of the proportions among themselves of the year, the month and the day.
Since to the Earth, which is one of the primary planets, there is ascribed, besides the annual circuit around the Sun, also a diurnal rotation, I ask whether you suppose that all the primary planets are thus turned about their axes? That is indeed probable, first of Venus, which seems to unfold now one spot after another, as is indicated by that scintillation, of a different form from the scintillation of the fixed stars; again of Jupiter, which carries four satellites, and of Saturn, which carries two, as the Earth carries one, called the Moon: of which below.
By what principles is this gyration of the bodies about their axes accomplished? It was said in the first book of the Earth and in this fourth book of the Sun that these bodies are turned by an inborn animal principle or the like. That in the gyration of the Earth this principle is not alone, but is helped by the Sun, is gathered from two proofs. First, because the number of the diurnal revolutions of the Earth in the year, which is 365 and a quarter, exceeds the neighbouring archetypal number 360. For it is fitting that, unless the moving force of the Earth within were quickened by the perpetual presence of the Sun, the Earth would have moved somewhat more slowly about its axis, so that in the same annual space it would have made fewer revolutions, say only 360. This being posited, it follows that the remaining and, as it were, supernumerary five revolutions and a quarter are added to those 360 by reason of the help from the Sun. The other proof demands this condition, that there be room for that part of the equation of time of which it was said in the preceding books I and III, which Tycho Brahe seems to have brought to light by manifest experiments of eclipses, and which I have reduced to a physical form. For since this equation of time makes the summer revolution of the Earth a little slower than the winter, this surely cannot arise from the principle inborn in the Earth, since such things are wont to be perpetually uniform, but must arise from the intervals of the Sun and the Earth, which are longer in summer of our hemisphere than in winter.
Perhaps the whole power producing this turning is in the Sun alone, and none in any principle of motion inborn separately in the Earth. Both of the causes stated oppose this. For 1) if the number 365 were not composed of two effects of two distinct causes, there would be no reason why it should not be one of the archetypal numbers, that is, rather a round number, than one of the unjointed, ignoble and broken. 2) The physical equation of time being posited, then if the Sun did everything, the whole diurnal revolutions of the Earth would be proportional to the intervals of the Sun and Earth; but the quantity of this temporal equation demands that not whole revolutions, but at least some minute parts of revolutions, be proportioned to those variable intervals.
You reckon the inner power of the Earth at 360 revolutions in one year: what cause of this number do you show from the archetype? Because the Sun had to cover the 720th part of the circle or course of its apparent motion in its greatest distance from the Earth, I judge so great a strength to be assigned to this power of turning that the Sun, in mean motion, in each revolution of the Earth, could appear more advanced by two such little parts of its circle, to the number of two parts of the revolution, one of which is called day, the other night, as seen from some one place on the surface of the Earth; so that, of two spaces of the zodiac circle marked by the positions of the Sun on two successive noons, a space equal to either of them would be intercepted empty or unmarked, and as day is to night, so would be the space filled by the Sun to the empty space, namely the diurnal space of the Sun’s centre to the nocturnal.
For in all these things the nature of man, the observing creature, the future inhabitant of the Earth, was received among the archetypal causes, as one who was to estimate the quantity of the solar body and to contemplate the differences of day and night.
But if this had been sought, it seems it would also have been obtained; yet now you yourself confess that those reasons are disturbed, since, with those additional incitements from the Sun, 365 days have come to be in place of 360, etc., and so the daily journeys are shorter. 1) It cannot be said that this was sought simply, but at least in the adaptation of the principle of inner motion in the Earth; in which way it was also obtained. 2) And although in this secondary motion the concurrence of causes disturbs the number established, yet the disturbance was not so great that even so, in the months of November and January, this very quantity should not be obtained, because then the quantity of the Sun’s diurnal motion is one degree or twice 30 minutes. And even before, if there were no such disturbance, that quantity would have occurred only twice in the year, as the diurnal motion of the Sun, because of the necessary inequality of the Sun’s apparent motion.