Epitome Astronomiae Copernicanae: Liber VI, part 1
Book VI. First Part. Of the theory of the Sun
solitary, as was said in book II, folio 193, and the motion of longitude consists of one inequality only, whereas in the other planets two, and in the Moon several apparent inequalities are mingled together; and so for demonstrating the Sun’s motions we are content with a single circle. Third, the motions of the other planets cannot be explained without the apparent motion of the Sun most exactly known. For that second inequality, which mingles itself with the first in the other planets, not only has its beginning from that point of time when the Earth and the planet appear joined in their true motions, but in the five primary planets also has its whole origin and causes from that circle of the Earth by which the Sun’s motions are demonstrated. Nay, even the digressions of the planets in latitude, which occur by reason of the first inequality itself, are referred to that circle which the Sun seems to complete under the fixed stars.
What kind of appearances of the Sun’s motion do diligent astronomers observe, and how? 1. When they explore the meridian altitudes of the Sun with quadrants through all the days of the year (of which also in book I, folio 125, and book III, folio 262), they find that the Sun from the day of the winter solstice gradually becomes higher at the following noons up to the day of the summer solstice; and this at the beginning about the winter day, and at the end about the solstitial day, quite insensibly, in the middle, especially about the equinoxes, quite evidently. In the same way also from the day of the summer solstice to the winter solstice it becomes lower at noon.
2. Meanwhile, however, while the Sun comes from the lowest to the highest solstice, half the stars also emerge from the Sun’s rays, and conversely, while the Sun at noon from the highest becomes again lowest, the remaining semicircle of the stars is also born. From this, therefore, astronomers gathered that that diversity of the Sun’s meridian altitudes is spread through the whole circuit of the fixed stars, that is, that the Sun advances under the fixed stars in a perfect circle oblique to the equator, which is called the ecliptic: that it is not, namely, moved as in some one circle of declination fixed immovably to the sphere of the fixed stars, straight up and down by its own motion, as in a balance, but at once both upward and to the left, for us who dwell in the northern hemisphere.
But I thought that the fixed stars emerge from the Sun’s rays and set under them by their own motion, not by the Sun’s or the Earth’s motion. This is one of the deceptive appearances about which astronomers speak with the common people, but convict the sight of deception, the causes being detected. For the stars do not emerge by motion from the Sun’s rays (or from the place which the brightness diffused about the Sun occupies), but the Sun departing, as Ptolemy holds, or seeming to depart, as Copernicus, uncovers them, themselves motionless: nor do the stars hide themselves under the Sun’s rays, but the Sun approaching, or seeming to approach, covers them. As this is so concerning the heliacal risings and settings of the stars, all astronomers granting it, it is strange why they should be disturbed if we dispute in the same manner also about the first motion (which is much swifter and is attributed with much greater incredibility to the stars themselves), saying that the stars do not emerge from the mountains or horizon, but that the mountains, by their turning aside or departure, uncover the stars.
Prove from optics that by the motion of the Earth it can be brought about that the fixed stars seem to go out from the Sun’s rays. Euclid demonstrates in the Optics, propositions 57 and 58: when the eye is carried along, among things at rest, those which are seen farther off seem to go on ahead, those nearer to be left behind, to be deserted. For so this proposition is to be completed in Campanus’s edition. Now Copernicus adds: but the Earth being carried round the Sun with annual motion, our eye is transferred with the same motion; and the fixed stars, which are looked at, are farther from the Earth, the Sun nearer, all of which, both the stars and the Sun, Copernicus makes to be at rest. Therefore, these things being posited, it is necessary that the fixed stars seem to come forth from the Sun, and the Sun to be left by the fixed stars, as if behind them.
Let the Earth be in P, the Sun in O, the fixed star M will be hidden behind the Sun; let the Earth pass from P to G, now not M but A will be hidden behind the Sun, and the fixed star M seems to have advanced as if from the place A by the space AM, while the Sun O, which is judged to be in A, whereas before it was judged to be in M, seems to have been left behind by M, which has advanced from the Sun.
How do we detect these digressions of the Sun from some fixed star exactly, in the smallest parts, since the Sun and the fixed stars do not come into view at the same time? This was explained above in book III, folio 273 ff., when we treated of the length of the sidereal year, or of the emergence of the fixed stars from the Sun’s rays. For astronomers try various ways. If, however, a clock were at hand, indicating hours, minutes and seconds and having a most uniform motion, then the easiest way would be this: that by night we should note that hour, minute and second of the index on the clock when some fixed star (whose right ascension, declination and, through it, longitude are known) is exactly on the meridian, and on the following day we should again attend to the position of the index when the very centre of the Sun comes to the same meridian; the same would be done a third time on the following night, when the fixed star returns to the same. For what is the proportion of time between two arrivals of the fixed star to the time between the first arrival of the fixed star and the arrival of the Sun, the same is the proportion of the 360 degrees of the equator to the arc between the two circles of declination of the fixed star and of the Sun. Thus, the right ascension of the Sun being established and its declination explored from the meridian altitude, the longitude of the Sun in the ecliptic, and its distance from the fixed star according to this longitude, are easily computed by the doctrine of the primum mobile.
What, then, makes the Sun seem, its course completed, to return to its beginning, when it is posited that the Sun stands immovable in the centre of the world? The same thing as just now, the motion of the Earth, and in it of our eyes, about the Sun under the ecliptic. See book II, folio 193. For if the Earth is between the Sun O and the constellation of Capricorn, say in G, the Sun will be reckoned diametrically opposite, as if under the fixed stars themselves and the constellation of Cancer in A. For the eye (which popular reasoning follows) does not notice the distance between the most remote fixed stars A and the Sun O, nearer and placed in the centre, though they are situated in the same straight line GOA with the eye G, but supposes that the Sun O touches the fixed stars A.
Give a popular and easy example of this fancy. Imagine a temple or some spacious basilica, round, not encumbered with seats, and in its middle a baptistery with a cover rising on high; let a spectator walk around the baptistery at a distance, his eyes turned to it: the baptistery with its cover will seem to him to creep along all the walls of the basilica in order, until the spectator returns to his first place and the baptistery to that part of the wall which it seemed at the beginning to cover. Here, by the walls are represented the fixed stars B, M, A in the zodiac, by the baptistery the Sun O, by the spectator the Earth, our dwelling, carried about the Sun from F to P and G, and so on.
How could astronomers know that the circle of the apparent motion of the Sun through the fixed stars is perfect and not tortuous? Because they found that the meridian altitudes of the Sun correspond to its digressions from some fixed star, according to the law of a perfect circle oblique to the equator.
The Sun, then, is found to complete this circle under the fixed stars, a perfect one, with an unequally swift motion. Altogether unequal; for equal arcs of this circle do not correspond to equal times.
By what arguments is this made manifest? 1. For since this circle is bisected by the equator, as was said in book II, yet the Sun tarries in that semicircle which is the upper for us 186¾ days, in the lower 178½; which we hold as certain from the days and hours in which we observe each equinox, attending to the interval of time that elapses from the vernal to the autumnal and conversely.
2) So, though the solstitial points divide the semicircles into two equal segments, the Sun nevertheless tarries longer in one than in the other. The same is made manifest also by any other digressions of the Sun from any fixed star, so that it advances more in its journey in one part of the year than in an equal other.
What cause makes the Sun seem to run through a perfect circle, the ecliptic, with unequal speed? Because the Earth, since it advances not under the fixed stars themselves but far below them and very near about the Sun, runs through its true circle FPG eccentric to the Sun O, so that the line through the centre of the Sun, perpendicular to the line FG, the line of apsides of the Earth (let it now be ED), divides the Earth’s orbit into unequal parts, while it divides the ecliptic into equal parts. Therefore, according to the doctrine of the fifth book, the Earth, for two reasons, dwells longer under one semicircle of the ecliptic: one, because EGD is a part of its orbit greater than a semicircle; the other, because it is more remote from the Sun O, the source of motion, and therefore the Earth is truly slower in advancing through it. Wherefore also the Sun seems to tarry longer under the opposite semicircle of the ecliptic, namely as long as the Earth tarries in the greater part of its orbit EGD.
What is the great orb in the astronomy of Copernicus? So Copernicus calls this very true orbit of the Earth about the Sun, placed midway between the orbits of Mars, the outer, and Venus, the inner; and he calls it great, not on account of quantity, since the orbits of the superior planets are circular and much wider, but on account of the singular use which it has in saving the apparent motions not of the Sun only but of all the primary planets.
What is the proportion of this orb to the sphere of the fixed stars? Copernicus sets it as wholly insensible on account of the other planets. And so the proportion introduced above, in book IV, folio 331, as probable, because it is itself insensible and unobservable, agrees well with the position of Copernicus.
Have you any evident argument that the hypothesis of the eccentric, or variable distance of the Earth from the Sun, is most true? This can be shown altogether to the eye: that the diameter of the Sun appears smaller in summer than in winter, if at both times we use the same instrument. For from this it is certain that the distance of the Earth from the Sun, OG, about the summer solstice is greater than OF about the winter solstice. For so runs proposition 56 in Euclid’s Optics: when the eye approaches the thing seen near, it will be thought to increase.
Why do you not set the motion of the Earth in its orbit as truly uniform, and ascribe the cause of the apparent inequality to eccentricity alone, considered simply and in the first manner, as the ancients did in the theory of the Sun? 1. Because the quantity of the eccentricity OC, which is elicited from the apparent increase and decrease of the Sun’s diameter, does not suffice to express the quantity of the apparent inequality in motion, except at least by half. 2. Because the other planets also, or rather their second inequalities, do not bear so great an eccentricity of the Earth as (namely OQ) would be required to save the inequality of the Sun after the manner of the ancients, but bear only half of it, OC, unless we are willing to multiply orbs in vain and to set up in each planet new little circles to compensate this excess, which springs up of itself from the one excessive eccentricity of the Earth that has been used. 3. Because it is contrary to the physical causes explained in book IV to set the eccentric course of the Earth from the Sun equal in its very orbit, when the parts of the orbit are unequally distant from the Sun, the source of motion. But now, the eccentricity of the Sun or Earth, OQ, of Brahe being bisected according to Copernicus, the Earth is moved exactly by the same laws by the Sun by which the other primary planets are moved by the same, and so all things agree with all. See the Commentaries on Mars, part III. 4. Because the eclipses of the Moon also require that the shadow of the Earth vary less than with the ancients, of which below in part 4.
But why do you ascribe the annual motion rather to the Earth, when the ancients themselves, transferring this motion to the Sun, effected the same concerning the appearances of the Sun? 1. Because Copernicus, in saving the apparent motions of the Sun, looks not only to the Sun but also to the other planets, to which the same motion of the Earth becomes useful for demonstrating their second inequalities. Unless, therefore, we said that the Earth is moved in the Sun’s place, it would be necessary that single planets, besides their own proper motions, be moved in truth also by this very motion of the Sun or one like it, as is done in the old astronomy, which superfluity of orbs Copernicus strives to cut away. 2. Because it is repugnant to the physical causes of the motions, explained in book IV, that the Sun should be moved (especially with a motion in truth unequal) in proportion to its distance from the Earth. For why should the speed of the solar motion be bound to the distance of the Sun from the Earth, when the Earth cannot be a cause of motion to the Sun? But if we ascribe this annual motion to the Earth, so that it is carried by that motion about the Sun, then the same befalls the Earth as the other primary planets, that the Sun exists as mover of all of them and so also of the Earth, and impels each, and so the Earth also, faster or slower in proportion to their distance from the centre of his body, which is at any place.
In what direction does the centre of the Earth move about the Sun? In the same direction as the other planets, among which the Earth marks out its orbit in the middle place; “placed in the middle of the course,” says Aristarchus in Archimedes; in the same direction under one part of the zodiac as that in which the Sun seems to move under the opposite part of the zodiac: finally, the centre of the Earth moves in the same direction in which also the surface of the Earth turns in the diurnal motion on the part turned away from the Sun, namely in the direction which in respect of the diurnal motion is called the direction of the east.
How great is the period of the centre of the Earth under the fixed stars, how great its advance in one day, or the mean diurnal motion? One period has 365 days 6 hours 9′ 26″ 43½‴ under the fixed stars, according to Tycho; hence the diurnal motion of the centre becomes 0° 59′ 8″ 11‴ 27ⁱᵛ 14ᵛ. But under the ecliptic, whose beginning, or section with the equator, meets the Earth (for causes to be told in book VII), the mean period See book III, folio 246 and 274.
Beware of ambiguity here; one thing is the diurnal motion or advance of the centre of the Earth in the circle about the Sun, another the motion or entire diurnal revolution of the body about its own axis, as if that axis were immovable, of which was treated in the spherical doctrine. The diurnal motion of the centre we seek here for the sake of measuring; that of the body about its own axis was an entire revolution, itself the measure of itself.
See in book VII more on the year, both tropical and sidereal, and on the inequality of its beginning from a positive starting-point.
How are the apsides called in this planet and where are they? If we treat of the true motion of the Earth, they are called aphelion and perihelion, as in the other primary planets, and then the aphelion of the Earth is today in 6°; but if, as of the apparent motion of the Sun we speak, they keep the same names as in the old astronomy, and are called apogee and perigee, and then the apogee of the Sun is In the diagram G is the aphelion of the Earth, its place under the fixed stars B, and A is the place of the apogee of the Sun.
How are the lines of motion drawn here? If we treat of the true motion of the Earth, the lines are drawn as in the other primary planets from the centre of the Sun through the centre of the Earth to the fixed stars; but if of the apparent motion of the Sun, which has prevailed in the usage of speech even with Copernicus, they are drawn on the contrary from the Earth through the centre of the Sun straight on to the fixed stars, namely to the points of the fixed stars opposite to the places of the Earth under the fixed stars.
Here in the diagram OPI is the line of the true motion of the Earth when placed in P, POM the line of the corresponding apparent motion of the Sun. And since C is the centre of the Earth’s eccentric, O, Q the two foci of the ellipse FG, OH, parallel to QP drawn through the planet, is very nearly the line of the Earth’s mean motion; but OK, in the same straight line with OH, is the line of the Sun’s mean motion, nearly, I say, and in the form of the old astronomy. But in this reformation of astronomy, according to physical causes, we do not need the line of mean motion HOK, but in place of the angle POH, less accurate, we seek both the area OQP and the angle OPC, which two together are equivalent to the angle POH.
How great is the eccentricity of the Earth? Tycho Brahe, imitating the ancients alone, fixed it (namely OQ) at 3586, of which CF, the semidiameter of the orbit, is 100000; according to the doctrine of book V, therefore, the true eccentricity OC will be half of that, namely 1793, in place of which in the appendix of Brahe’s Progymnasmata the round number 1800 is set down.
But the harmonic ratios, which claim the semitone for the motions of the Earth and the diesis for those of Venus, yet neither pure, bid us take from the proportion 5:8 the proportion 243:250, and the remainder from the proportion 3:5, so that there remains the proportion 2916:3125 of the extreme motions, whose roots 54 and 56 will nearly become the extreme intervals, the mean 55, the eccentricity 1, which is worth a little more than How is this eccentricity found? 1. Brahe, who had not yet recognised that the progress of the planets through their orbits is physically unequal, following the method of Ptolemy and Regiomontanus, used only observations of the Sun and the lengths of the quadrants of the year. For if today the summer has 186¾ days, so that the Earth tarries so many days in EGD, but in DFE (when it is winter) 178½, the eccentricity OQ comes out very nearly 3600; but if the summer is 186¼ days, the winter 179, the eccentricity will come out 3200. Therefore the true eccentricity OC will be half of this, namely 1800 or 1600.
2. A more subtle method, though in the smallest quantities not sufficiently trustworthy, is by the Sun’s diameter, which in winter is 31′, in summer 30′, and so at the intermediate time 30½′; as 30½′ is to 31′, or as 61 to 62, so is the semidiameter 100000 to the apogee distance 101640: so that the eccentricity is 1640, from these data at least.
3. From three observations of the planet Mars (or also of Venus or Mercury), the planet being at the same place of its eccentric on all three occasions, there are first computed three distances of the Earth from the Sun at three distinct places of its circle: from these, for example FO, EO, PO, and from the angles FOE, EOP at the Sun intercepted (which we know from the interval of time and the computed places of the Sun), the eccentricity is elicited. See the Commentaries on Mars, part III, chapter 25 ff. For geometers teach that three points F, E, P not in the same straight line determine a circle which passes through all three points. And the Earth’s orbit, on account of the small eccentricity OC, is very nearly a circle.
Is so great an eccentricity always constant? That it is constant is very probable: 1. because the causes of the eccentricity are internal, placed in the body of the planetary globe, as was argued in book IV. 2. Because the Moon retains the same eccentricity today that it had of old. The same can be said of the other planets also. Why then should the Earth alone change its own? 3. Because although Hipparchus, and Ptolemy imitating him, report it greater in their age, namely 4200, which would be, according to physical hypotheses, 2100, not 1800, yet they themselves warn that their observations of the equinoxes are not certain within 6 hours. But if observations are uncertain within 6 hours, the eccentricity also will come out uncertain between 1800 and 2100. The observations of the ancients, therefore, have nothing to oppose to the constancy of the quantity of the eccentricity.
How does the aphelion of the Earth, G, or the apogee of the Sun, A, move, and with it the centre of the Sun’s eccentric? The causes of the translation were stated in book IV. The direction of the translation is under the fixed stars in the order of the signs; in quality their motion is set as most uniform, in quantity it is very slow, so that from Hipparchus it has not advanced beyond one sign, and so the annual motion of the apogee of the Sun from the equinox is about 1′ 3″ and is completed under the ecliptic in about twenty thousand five hundred and seventy-two years: since the beginning of the ecliptic meets it. But under the fixed stars the apogee of the Sun scarcely returns after 108 thousand years, as far as it is given to reason about the whole period from the short age of observations. In this longest space of time, therefore, the centre of the Earth’s orbit describes a small circle about the body of the Sun, with a semidiameter a little more than four times the semidiameter of the solar body; such a little circle as we shall say in its place is described also by the Moon about the Earth in 8½ years. But unless we had corrected the hypothesis of Copernicus, who places the centre of the great orb in the centre of the world, it would be necessary that the Sun itself be twisted in such a little circle about the centre of the world in so prolix a return. And this is that from which in book IV, folio 355, we took one argument for the motion of the Earth.
Is not the motion of the apogee of the Sun unequal, as Copernicus holds? If the observations of the Arabs, who lived between our times and those of Hipparchus, were altogether exact, it would be necessary to set this motion as unequal. But the least little error of theirs, which could easily be admitted, accounts for all this inequality. And the likeness of the apogee of the Moon pleads for the constancy of the motion.
How great is the greatest equation of the Sun, how great the diurnal? The eccentricity CO 1800 gives the greatest equation (compounded of the angle OPQ and the value of the area OQP, that is, the angle POH or OPQ, nearly 2° 3′ 45″), the diurnal in the apogee 57′ 3″, in the perigee 1° 1′ 20″, since 57′ 3″ to 1° 1′ 20″ contains the interval of a semitone, namely the proportion 15 to 16.
How great does the summer become hence, how great the winter? Since the upper semicircle is completed in 187 days less 4 hours 38 minutes, the longest summer of all can be 187 days less 4 hours 38 minutes, the shortest winter 178 days 10 hours 27 minutes. This happened at the time when the apogee of the Sun was at 0° of Cancer, about the year 1260 after Christ. But at the beginning of the world the apogee was with the equinoctial point: then, therefore, summer and winter were equal. In book VII will be explained what inequality of years arises hence.
How do we learn the equation of the Sun? From the annual anomaly of the Sun, by the method delivered above in book V.
What is the annual anomaly? The same in the Sun as is in all the planets the mean anomaly, of the eccentric, or the equated, nearly. Therefore, according to the doctrine of book five, the mean anomaly of the Earth is to be defined by the area GOP, the anomaly of the eccentric by the arc of the orbit GP, the equated anomaly by the angle GOP at the Sun O, comprehended between the lines OG, OP, drawn from the Sun’s centre O through the aphelion G of the Earth and through the centre of the body of the Earth P; but after the prescript of the ancients the annual anomaly of the Sun, mean and equated, is defined as the arc of the ecliptic between the place of the apogee of the Sun and the lines of the mean and true motion of the Sun. As, the Earth being in P, the mean anomaly of the Sun is AOK, because OK, parallel to PQ, is the line of the mean motion of the Sun. But AOM is the equated anomaly; both in the Sun are called annual.
What is the reason of the name annual? Copernicus named it annual to distinguish it from the secular anomaly, by which, with him, the eccentricity and the motion of the apogee were varied. We have no need of that variation, yet we say annual for the solar, because the return of the Sun completes the year; and indeed the period of the anomaly of the Sun is not more than 5 minutes of an hour longer than the sidereal year.
What belongs to this place? First, to be referred here is the diurnal motion of the body of the Earth about its own axis, as if immovable, of which was treated in the spherical doctrine in books I, II, III, chiefly folio 248. Next, the inclination of the axis of this diurnal rotation to the ecliptic, of which folio 229, 269, 272, and below in book VII. Third: how the succession of the declinations of the parts of the ecliptic through the year depends on this has been explained in books II and III, especially folio 229, 231. Fourth: how from the inclination and revolution of this axis the precession of the equinoxes follows has been said in book III, folio 273, and will be explained at greater length below in book VII. Finally, there pertain here also the two parts out of three of the equation of time, or of days, of which one depends on the equation of the Sun, the other on the distance of the Earth from the Sun. See book III from folio 250 to 251.
Explain the former of these, which is proper to theoretical doctrine. The equal day then begins when the mean place of the Sun stands on the meridian, the apparent day when the true place of the Sun. But if the equation of the Sun is subtractive, the true place of the Sun, as preceding, comes to the meridian before the mean, and noon will be observed sooner than it will be in the uniform manner. Wherefore something is to be added to the equal time, that it may become apparent. In an additive equation something is to be subtracted from the equal time, that it may become apparent. If, however, conversely, apparent times are to be equated, the contrary is to be done in each case. The quantity of the addition or subtraction will be shown by the quantity of the equation itself, of which one degree is worth a little less than 4 minutes of an hour, on account of the addition. The greatest will therefore be 8′ 15″ of an hour from the greatest equation Explain also the reasons and the quantity of the latter cause of equating time. It was said in book IV that the motive power, which is implanted in the bowels of the Earth and which turns the Earth about its axis, is so intense and tempered that, if it alone moved the Earth, in the time while its centre is carried once about the Sun it would revolve exactly three hundred and sixty times about its own axis, the same part of the Earth returning to the same line which connects the centres of the Sun and Earth; and that this power implanted in the Earth, in respect of itself as solitary, always acts uniformly. But now this power is strengthened by the presence of the Sun, at one time in one way, at another in another, and the whole and consummated effect of this strengthening in one period of the Earth about the Sun, or in one year, is 5¼ supernumerary days. These days, or revolutions of the Earth about its own axis, are brought about by all the distances of all the parts of the Earth’s orbit from the Sun taken together, so that the longer distances strengthen less, the shorter more; or, what is quite the same, those diurnal revolutions of the Earth which happen about the aphelion, reckoned as of equal time, make longer delays, those about the perihelion shorter.
Since, however, the plane of the eccentric segment of the Earth, for example PGO, is worth all the distances of its equal arcs, as was demonstrated in book V, and the plane of the equatorial triangle PCO (which in the Earth’s eccentric is 180000000 where greatest) represents the excess of the plane of the eccentric segment (PGO, made by the line PO from the Sun) over PGC, the plane of the sector: the same plane will therefore represent also the equation of time of which we now treat. For if the area of the whole eccentric, 31415926536, is worth 365¼ revolutions of the Earth, a part of it, namely this equatorial triangle, will be worth 21′ 40″ of an hour at most. And so the summer revolutions from the apogee of the Sun to the mean longitude, or the apparent days, are worth, beyond the mean, as many minutes more in equal number. And so long as the equation of the Sun is subtractive, this equation is always added to the apparent time, to make it mean; where, however, the equation is additive, it is subtracted; from the mean time the apparent is made in the contrary way in both cases. Thus the reasons of this equation are contrary to those of the former.
By what experiment is it known that this part of the equation is to be applied? 1. Tycho Brahe could not reconcile his observations of the Moon otherwise than by throwing away that part of the equation of time which is on account of the equations of the Sun. Since, then, this present equation is diametrically contrary to that and destroys it, the observations of Brahe therefore stand for the parts of this. 2. But not even so does Brahe maintain all his observations; rather he would have wished that what he throws away were much greater: and behold, this our present equation exceeds that by more than double. Yet I would not contend more stubbornly with anyone over this third cause of the equation. For if anyone shall reconcile Brahe’s observations of the Moon more closely by the customary equation of time, I will gladly yield the palm to him, the part of the equation of time here overturned.
Is the Earth also moved in latitude? If the latitude of the heavens, as in book three, is reckoned from the ecliptic toward the north or south, the Earth cannot wander in latitude, since, wherever it wanders, it carries the ecliptic with it, as being described under the fixed stars by a line drawn from the centre of the Sun through the centre of the Earth, and to it are referred the motions of the planets and the places of the fixed stars. But if this ecliptic (that is, the orbit of the Earth under the fixed stars) is compared with itself, according to different ages, Brahe indeed discovers from the changed latitudes of the fixed stars that the present ecliptic has departed to the sides of the former ecliptic: so that in this matter also of the inclination and translation of the nodes there is a complete analogy of the Earth’s motions to the motions of the other planets. This consideration, however, is not necessary in this place, either for collecting the motions of the Sun or for explaining the appearances of the other planets, and so let it be deferred to book VII.
Does no inequality appear to be in the motions of the Sun on account of the distance of the centre of the Earth from its surface? Some very slight variation does arise hence, called diurnal parallax; but since it is of no moment at all in respect of the motions of the Sun himself, and is sought for scarcely any other reason than on account of the eclipses of the luminaries, it is to be deferred below to the theory of the Moon and the doctrine of eclipses.
What of things putting themselves forward beyond the bounds of astronomy belongs to the doctrine of the motion of the Sun? The doctrine of political solar years and months.
What is political time? That which is constituted by a number of whole days, the minutes of an hour being neglected or compensated by art.
How many are the principal political or civil solar years? Three. 1) The Egyptian, of 365 days always, such as the year of the Flood is also gathered to have been. 2) The Julian, computed in one period of four years, of which the first three each consist of 365 days, the fourth of 366 days; for in the month of February the same name and the same letter of the 24th day is repeated, and the sixth day before the Kalends of March is pronounced twice, whence this fourth year has the name bissextile, in German Schaltjahr, as if you should say dislocated: hence also that day is called bissextile, intercalary, in Greek embolimos, inserted, Schaltag. Of these Julian years 1460 equal 1461 Egyptian. For both they and the ancient Persians observed an intercalary day every fourth year, by one day, the rising of the Dog-star descending; whence among the Persians arose a period of 120 years, within which this beginning of the sidereal year descends through all the names of the thirty-one months which they had imposed on the days from their heroes. And so then one month was intercalated. 3) The Gregorian, computed in one period of four hundred years, in which the other fourth years have 366 days, and only the century years, the first three, are simple, of 365 days. See book III, folio 247, and below on the civil lunar years, and also book VII.
Was an inequality of the Sun’s motion observed also in the political months? In the Egyptian and in the diluvian it is not observed; for 30 days were reckoned to the month through the whole year, and the last five, supernumerary, were called epagomenae, an appendix, and were held for nothing; for they were spent in feasting. In the Julian a dim observation of the solar inequality is seen in this, that to six months, the beginning being made from March (as in the middle of which the Sun would advance most slowly), 184 days were given, to the rest only 181. In the year of Dionysius the mathematician the months are named from the signs of the heavens; as to the number of days of each, however, it is not wholly certain.