Epitome Astronomiae Copernicanae: Liber VI, part 4
Third Part. Of the two inferior of the primary planets, Venus and Mercury.
What is the cause why these two planets are separated from the three superior, though they agree with them in the number and form of the inequalities? 1. Because their situations separate these from those, as indicated by the very name; for those three go round the orbit of the Earth on the outside with their courses, these two exercise their courses within the orbit of the Earth. 2. The annual circuit of the Earth procures for these two appearances not so evident, and opposed in certain respects to the appearances of the superior. 3. The Copernican astronomy differs from the ancient in one way concerning the superior, in another concerning the inferior. 4. There is added the mechanical cause and the convenience of theories. For although a common theory could be made for all five and for the Sun or the Earth as sixth, which would at last be the genuine and intrinsic image of the moving world: yet because the orb, called great from its use, has to be adjusted to Saturn as very small, it, remaining of the same quantity, requires the eccentrics of Venus and Mercury much smaller than itself and less manageable. It is better, therefore, that a peculiar great orb be made for the inferior planets, and a sufficiently ample one, that the eccentrics of the inferior may also be able to obtain some due quantity.
Review what appearances of motions the two inferior planets, Venus and Mercury, make. 1. The anomaly or inequality first, arising from the eccentric, does not become known in the inferior planets by occasions so ready as in the three superior, but must at length be investigated by long reasoning. The true anomaly of these, especially of Mercury, is disentangled with greatest difficulty from the appearance which the great orb causes, because they never appear except involved in this second inequality: for as often as they fall on the line from the Earth through the Sun, lacking the second inequality, they are always hidden under the Sun’s rays. And so the old astronomy did not even suspect their first and genuine inequality, although it betrayed itself somewhat, but under the appearance of one very different.
But the deceptions of the eyes, which draw their cause from the annual circuit of the Earth’s orb, being removed, we find that these planets also go round the Sun by the rule of the others with motions eccentric from the Sun, and are swift when near the Sun, slow when remote from him, in double proportion of the angles at the centre of the Sun which their diurnal eccentric motions subtend.
2. By the motion compounded of both inequalities, which compound motion first falls under the eyes, they appear swiftest when in the morning hours they begin to hide under the Sun’s rays, or when in the evening hours they come out from them; phases which the three superior lack. But when they are hidden in the evening or emerge in the morning (in which case the three superior were swiftest), the inferior on the contrary become stationary, namely after the greatest evening elongations and before the morning; in the intermediate time they become retrograde, again in conjunction with the Sun, which is for these inferior in place of opposition with the Sun, which they lack; for they always run near the Sun, which at certain spaces they now precede, now follow, returning again and again to him. Venus indeed goes farthest from the Sun and makes fewer stations, and so is joined to the Sun as often; Mercury has short excursions and often becomes stationary, often is joined to the Sun and therefore appears rarely.
3. As regards motion in height, although it is not difficult to notice that they descend toward the Earth or flee into the height, Venus indeed by the increase of her body in certain places, Mercury by the swiftness or slowness of the appearances and concealments, which must be according to the apparent increase of the body, as happens in the superior planets: yet this observation too is much more perplexed than in the superior, for the apparent magnitude of the body of Venus, when she advances nearest the Earth, long tormented astronomers, because this magnitude seemed not to correspond to the least interval of approach, which was clear from other arguments, until the telescope being invented the cause appeared.
4. As to the cause of latitude, this was noted: that northern latitudes in Venus, other things being equal, are greater, in Mercury southern, and in both those always greater in which, the line from the Sun through the planet falling on the same place of the zodiac, after completed periods the Earth has been nearer to the planet.
How are the greatest elongations of these planets determined? By the lines of sight which, drawn from the Earth, touch their eccentrics. For the planets, falling on the points of contact, are nearly at their greatest elongations.
How do these two planets move in truth in their eccentrics? The mean diurnal motion of Venus about the Sun, in the order of the signs, is 1° 36′ 7″ 39‴ (under the fixed stars); she returns about the Sun under the ecliptic in 17 hours 44′ 55″.
By what method can these planets be stripped of the second inequality, which comes from the great orb, if they are not in opposition to the Sun? The greatest elongations themselves come to our aid, in which the planets, being placed, can be seen and observed, how far in all they are distant from the Sun. For then the line drawn from the centre of the eccentric, as here from B to the planet or point of contact M, cuts the line of sight TM at right angles and falls on the place of the zodiac in quadrature to the place of the visible planet, marked by TM produced, because BMT is a right angle; but AM itself, drawn from the Sun A through the planet M, which we chiefly seek, falls nowhere farther from BM in the zodiac than the optical part of the equation is at any place, or the angle AMB. How great this optical part is, is easy to foresee from the measure of the lines from the Sun A to the planet, placed in the apsides P, R, namely from AP, AR, the comparison of which lines with each other yields the eccentricity AB, and so also the angle AMB at any place.
What do you call the eccentric in the inferior planets, and how was it called in the old astronomy? In the three superior planets, which the old astronomy called eccentrics, the same were eccentrics also to us; in the inferior, which were called epicycles by the ancients and by Tycho Brahe, we must set up eccentrics. But the eccentrics which were ascribed by the ancients to Venus and Mercury we must now wholly forget. For the same great orb in the old astronomy took away three epicycles from the three superior planets, and from the Sun and the two inferior three eccentrics entrusted to antiquity; all of which six Copernicus fuses into one great orb or orbit of the Earth.
Have you any evident argument by which to prove that the inferior planets do not remain through the whole circuit below the Sun, but go in a circle about the Sun, now superior to the Sun in respect of us, now inferior? That brought forward above, in book IV, folio 352, is properly of this place. For Venus is illuminated like the Moon, for she undergoes all the phases of the Moon; but this could not happen unless Venus, who never departs farther from the Sun, now went above the Sun, now below him. The demonstration will follow below. Of Mercury, so far as the same can be said, see the place cited.
But if you take the body of the Sun out of the centre of these two eccentrics, like the heart out of the body, which he does who makes their motions regular about another point than the centre of the Sun, following the incorrect hypotheses either of Copernicus or of Tycho: then no causes appear why these two planets should move in a circle about an empty centre, unless we return to the Aristotelian gods, diffused through the whole breadth of the hollow orbs. See book IV, folio 354, 355.
How great are the greatest elongations of these stars from the Sun? The elongations of the three superior could commonly grow to a semicircle, but not so those of the inferior. For the elongations of Venus from the apparent place of the Sun under the zodiac seem to run out at most to 47¼°; the elongations of Mercury are restrained within 29° at the apogee, within 18° at the perigee.
By what arguments are their greatest elongations detected? 1) If their diurnal motions equal the diurnal motion of the Sun. 2) In the greatest elongations, the line of sight touching the orbit, Venus appears half-lit, like the Moon; which would hold also in Mercury, if it were not hindered by the brightness of twilight and the smallness of the body. The demonstration will follow below in part V.
In what places of the zodiac do the aphelia of these eccentrics stand, and what is their motion? Today the aphelion of Venus is at 2° of Aquarius, of Mercury at 15°. In ancient times where the aphelion of Venus was can be shown only roughly, namely between Libra and Pisces, the perihelion between Gemini and Leo. But the aphelion of Mercury was about 4°. Since, then, the aphelion of Mercury, like that of all the rest, advances in the order of the signs and of the fixed stars, the same is probable also of that of Venus; it must therefore in those ancient times have been in Capricorn.
What is the cause of the greater uncertainty in Venus than in Mercury? 1) Because Venus has a very small eccentricity, insensible through the crude observations of the ancients, Mercury the greatest of all and most evident. 2) Because the ancients did not record Venus observed about the place of the aphelion (or when the line from the Sun through the star falls in Aquarius), while for Mercury more and more convenient observations were left. 3) Because the theory of the Sun in the old astronomy is not free from suspicion of error concerning the place of the apogee and the quantity of the eccentricity; but the ancient greatest elongations of Venus and Mercury cannot be measured exactly without knowledge of the true place of the Sun at those times, and the fault arising hence harms the small eccentricity of Venus, not so the great eccentricity of Mercury.
Did the ancients, however, scent out the places of the aphelia of these planets, and by what means? Since the ancients ordered those which we here call eccentrics, called epicycles, equally about points corresponding to the mean place of the Sun, which nevertheless were to be ordered, both about those points and about the true place of the Sun itself, at unequal intervals, and from the single great orb, which is also eccentric from the Sun, made two eccentrics of the inferior planets: it came about that both eccentricities, both of the great orb and of the eccentric of the planet (so called by us), were confounded in the old astronomy into one, in respect of which Ptolemy gave out the apogee of Venus at 25° and of Mercury at 10°; in these places, therefore, lie hid the traces of our aphelia. For because the eccentricity of the great orb is much greater than the eccentricity of Venus, the ancients found the apogee of Venus much nearer to the apogee of the Sun, then at 10° of Gemini, than to the aphelion of Venus, yet between the two, because, as I said, the two eccentricities had been confounded into one. Conversely, because the eccentricity of Mercury is much greater than the eccentricity of the great orb, the apogee of Mercury, established by the intention of the old astronomy, was found much nearer to the aphelion of Mercury at 4° of Scorpio than to the apogee of the Sun at 10° of Gemini, yet again between the two on account of the confounded eccentricities. For another argument by which Ptolemy is convicted of having observed his epicycles as eccentric from the assumed point of mediocrity, see below under latitude.
How great is the eccentricity of the inferior planets, and what the dimension of the orbs, in common with the great orb? This too the old astronomy does not know, so that when it makes the orbs and epicycles of the three superior as large as the mechanical reason demands, building contiguous theories (since above nothing hinders them, the ether lying open free as far as one pleases), now below the Sun the place between him and the Moon does not suffice for receiving the orbs which the old astronomy feigns for these inferior planets; the dimension of the orbs of the Sun, which they delivered, standing. But the Copernican astronomy yields these proportions:
Of the great orb, as above, aphelion 101800 Of Venus, aphelion 72900 Of Mercury, aphelion 46955 Eccentricity, of which the semidiameter is 100000.
Copernicus himself, however, set up also more orbs in the inferior planets, an eccentric of the eccentric being added. This befell him on account of ignorance of the true eccentricity of the great orb, which is at least half of that which he himself believed with the ancients, the equant making up the rest. By as much, therefore, beyond what was due as he by his hypothesis varied the distances of the Earth from the Sun and so also from the orbits of Venus and Mercury, by so much in turn had he to compensate through the eccentrics of the eccentrics.
By what arguments do you prove that this was the cause of his superfluous circles, and that this excessive eccentricity of the Earth was thus known to him? 1. Because he gave the eccentric of the eccentric this office, that it should make the centre of the eccentric of Venus librate through a space as great as this superfluous half in the great orb; the centre of the eccentric of Mercury through a somewhat smaller space, because the line of apsides of Venus nearly coincided with the line of apsides of the Sun, that of Mercury departed farther from it. 2. Because the librating motion of the centre of the orbit of Venus is set contrary to the motion of the centre of Mercury, and each analogous to the thing which we argue: that, Venus being in the apsides, the centre of the orbit would be low, Mercury being in the apsides, the centre of the orbit would be high. For the apogee of Venus was very near the apogee of the Sun and was raised too much by the excessive eccentricity of the great orb; the apogee of Mercury on the contrary was toward the perigee of the Sun and was depressed too much on account of the same cause. 3. Tycho Brahe had noticed the same also in Mars and was about to introduce an epicycle or eccentric of the eccentric, such as Copernicus in the theory of Venus, had not the bisection of the eccentricity of the great orb come to his aid. For he too had found the apogee of Mars near the apogee of the Sun.
What is chiefly to be observed in the inferior planets compared with each other concerning their eccentric orbits? 1. The causes of eccentricity stand to each other in contrary ways: Venus has the smallest eccentricity, for that is less than the eccentricity of the Earth, less than the differences of all the eccentricities; Mercury on the contrary has the greatest eccentricity, so that those of the two inferior taken together equal the eccentricity of the four superior, namely in the proportion of those to their radii. 2. Hence it follows that the diurnal eccentric motions of Venus are in the least variety, of Mercury in the greatest, so that the diurnal motion of Mercury in perihelion is more than double that in aphelion. See in book IV the causes from folio 373. Wherefore the old astronomy, setting this motion uniform, could err very little in predicting or computing the place of Venus, in Mercury it must needs have erred very much. 3. Hence it follows also that the lunes of the eccentric of Mercury (of which in book V) are in Mercury of very notable breadth, and the diameter of the apsides, or straight line, sensibly much longer than the transverse diameter of the ellipse.
Did the ancients learn anything also of this elliptical figure of the orbit of Mercury? Indeed this is why Ptolemy was compelled to set two perigees in Mercury; for in Libra his epicycle (which to us is the eccentric) appeared least, in Aries not greatest, but greater in Aquarius and likewise in Gemini and nearly equal on both sides. Because, namely, when the Sun was in Libra and the Earth in Aries, as in fig. 87 at T, there was turned toward it the very shortest part of the line of apsides, namely the perihelion R of Mercury, lying in Scorpio, and so it looked at the eccentric (which to them was the epicycle) from the sides M, N, by which it is corrected by the cutting off of the lunes; it was therefore reckoned very small and therefore higher, on account of two concurrent causes of diminution, namely the shortness of BM, BN themselves and the length of TB. For the ancients placed the Earth in the inner circle T, on account of the double of the true eccentricity used, whereas in truth it was in the outer T. But on passing to Aries, the Sun being seen, and the Earth having passed to Libra, as in D, the epicycle seemed in turn to have become great, on account of the approach, or shortness of the line BD, but because it was looked at again from the meagre sides C, K, the aphelion P of Mercury tending toward the Earth in D, placed in Taurus (whose nearest place is in Scorpio), the one cause of the apparent smallness of the epicycle when in apogee remained here also in perigee, namely the shortness of the transverse diameter of the ellipse and of BC, BK themselves; on the contrary, the Sun appearing in Gemini or Leo, when the Earth was in Sagittarius or Aquarius, the straight diameter, or that of the apsides PR, which is much longer than the transverse diameter, was presented to the sight in Sagittarius or Leo more directly, as if the epicycle had been made greater. Although the numbers do not agree exactly on both sides, it readily appears that the observations of Mercury, gathered by Ptolemy and as it were begged from the ancients, being crudely noted, were so taken that what happened in one third from the apogee could also be represented by the hypothesis in the other third.
What is the cause why the two inferior planets become stationary and finally retrograde? Nearly the same which the old astronomy brings, with the necessary changes. For since their eccentrics are hidden within the orbit of the Earth and the planets run through their orbits more swiftly than the Earth through its own, it happens first in the part of the eccentric more remote from the Earth that they seem to go in the order of the signs; they would seem to do so even if they rested like the Sun, because the Earth from the opposite side goes in the order of the signs, whose motion by a deception of sight would be thought to inhere in them. Now they also exceed the motion of the Earth in swiftness, so much the more therefore do they seem there to go in the order of the signs. Here, then, the same cause operates in the inferior planets as formerly in the superior. But in the part of the eccentric nearer the Earth they seem retrograde because the opposite parts of circles, looked at from outside, seem to have opposite motions. For although then also the Earth is carried together with them in the same direction, yet they, being inferior planets, are swifter than the Earth, so that they make greater diurnal arcs in their orbits than the Earth in its own; wherefore the lines of sight, which join the corresponding ends of the diurnal arcs, are bent back against the order of the signs and cut one another behind the Earth in the region turned away from the Sun. But since here now the Earth is in that situation in which one of the superior planets was above, and the inferior planet in that in which the Earth was above, the appearance of retrograde motion is produced by the same principles. It follows, therefore, that there are some places of the eccentrics of Venus and Mercury in which, when they are placed, they cease to be seen direct and begin to appear retrograde, that is, become stationary, although in truth they always move direct and in the order of the signs; and this happens by parallel lines of sight, as in the superior planets.
In the above diagram (86) of the stations let the orbit of the Earth now be OP, and the motion in it of the Earth from O to P, Q, T, K in the same time in which the inferior planet is moved from A to B, C, D, G, and let the diurnal arcs of the planet in the eccentric AB be longer than the diurnal arcs of the Earth in its orbit OP. Therefore the Earth being in O, the planet in A, the more remote part of the circle, it appears direct and swift, and swifter than the Sun, because the lines of sight OA, PB cut each other about F, on this side of the centre of the great orb.
On the contrary, the Earth being in K, the planet in G, the nearer part of the circle, making greater degrees than the Earth, makes the lines of sight TD, KG, which I understand continued toward the parts D, G to the fixed stars, to incline to the right, against the order from the apparent place of the Sun E. But the planet, being earlier in H, the Earth in I, about the tangent IH, the planet moved from H to D descends straight toward the Earth I and is made equal to one standing, while the Earth meanwhile goes on in I; wherefore the intersection of the lines of sight falling above H, the planet will still be seen direct. But about T, D the lines of sight TD go parallel, therefore the planet appears stationary.
Where are the points of the stations in the eccentrics? Two straight lines SB, SC being drawn from S the Earth, touching the eccentrics of the inferior planets in B, C, the points or arcs of the stations are always within BC, in Venus more remote from the points of contact B, C than in Mercury. The same causes hold here as in the superior planets.
Whence is this that you said, that the stations are nearer the Sun than the greatest elongations? From this very fact, that they are indeed most elongated when they fall on the tangents SB, SC, but become stationary only at the inner points. (Let the line SB be so drawn that it touches the circle ABC.)
How are the stations distinguished by names? The first station after direct motion is called the evening station, the second after retrogradation the morning; as also the greatest elongations, which occur at the points of contact.
Mars, the swiftest of the superior planets, made fewer stations than the rest; why now has Venus, the slowest of the inferior, fewer? The old astronomy conjectures the cause in the slowness of the epicycle, but does not indicate the cause of that slowness; the true cause Copernicus gives thus: because as above the Earth overtook the very swift Mars more slowly and surpassed him, so also here Venus, slower than Mercury, overtakes and surpasses the Earth more rarely and more slowly.
What cause do you assign that the apparent magnitude of Venus is not proportioned throughout to her approach to the Earth? Because Venus, having advanced in the evening from the Sun’s rays, shining with a full disc and long retaining that appearance and seen to increase in her descent, at last, the evening station being completed, gradually, like the Moon, diminishes to a slender horn, so that she by no means appears as great as she would have appeared, had she shone with full face, in this nearness.
Where are the nodes and limits of the inferior planets, and what is their motion? Ptolemy placed the nodes of Venus in the apsides called by him, namely the ascending at 25°, the descending at 25°, so that the northern limit (the line drawn from the Sun through it) was at 25°; the nodes of Mercury likewise in the apsides, the ascending at 10°, the descending at 10°, so that the northern limit was at 10°. For this is the force of that double inclination which he says the epicycle makes, which to us here is the eccentric. But how he deduced these things from observations, and from which, he does not indicate. Today the ascending node of Venus is at 12½°, of Mercury at 13½°, the opposite ones in places precisely opposite from the Sun; the northern limit, therefore, for the former in Virgo, for the latter at 13½°, from the Sun, the lines being drawn.
As far as concerns Venus, then, she agrees with the rest in this also, that she has a node going retrograde under the fixed stars with a very slow motion, but under the ecliptic going in the order of the signs. But the nodes of Mercury would in this way go also under the fixed stars in the order of the signs. Therefore the tradition of Ptolemy, as to the very place of the node in the apsides, is justly suspected, and he seems to have done violence to observations, themselves crude, by contemplating the apsides and the example of Venus and by zeal for a neat opposition, so that the nodes of Mercury were not in the first but in the last half of Libra in Ptolemy’s time. Unless, however, book VII helps us here.
How great and of what kind is the inclination of these eccentrics, and how great the latitudes? In Venus the inclination is 3° 22′, in Mercury 6° 54′, and that always constant and fixed, unless the late ages change something on account of the transposition of the ecliptic. And so, from the approach and recession of the Earth, the apparent northern latitude of Venus, retrograde in Pisces, runs out to almost 9 degrees in Virgo, though in other ages it will not be much less also toward the south.
But of retrograde Mercury the greatest southern latitude reaches to 5°, still less than the inclination, the northern stands at nearly half of that. So these two have the ratios of inclinations interchanged with the ratios of latitudes; Venus has a great latitude and a small inclination, Mercury has a great inclination and a smaller latitude.
Whence, then, is it that Ptolemy made this epicycle, so called by him, librating in a double manner, if the inclination is fixed? The cause is in the unknown annual motion of the Earth. For he himself looked at the same orbit of the planet which we also look at, whose limits, since they extend toward certain parts of the fixed stars, constantly declining from the plane of the ecliptic, it comes about, the Earth going round it on every side, that it extends now its northern limit to the Earth, now the nodes, now the southern. But Ptolemy had transferred this our circuit of the Earth to the centre of this epicycle called by him, saying that the Earth rests, but the epicycle, with its centre, measures out the whole zodiac annually; and in this epicycle he called that point the perigee which at any time was extended toward the Earth, as if it were one, whereas in truth all the parts in order of this epicycle called by him, to us the eccentric, successively and by accident become perigees. So it happened that to Ptolemy this perigee of the epicycle named by him was now in the north, now in the ecliptic, now in the south.
In diagram No. 87 suppose the northern limit of the true eccentric of Mercury PMR to be constantly in R, the node in K, the southern limit in P; let the Earth go round the way TXD. If, therefore, the Earth is in T, the parts near R will be reckoned perigees, since they are northern. If the Earth passes to X, the parts of K about the node will be reckoned perigees; finally if the Earth comes to D, the parts near P, since they are southern, will be held perigees. He, therefore, who is persuaded that the perigee is always really the same, who, namely, does not know the annual motion of the Earth in TXD, will be persuaded that the perigee of his epicycle PMR is librated from north to south and back.
And behold the most evident argument for the annual motion of the Earth about the Sun, promised above in book V, folio 356. For since the eccentrics of the superior planets have fixed inclinations to the ecliptic, why should only the eccentrics of the inferior be set as librating with a double libration, when in itself every libration of orbits is absurd, because it generates a tortuous course of the planet instead of a circular one. As much probability, therefore, as the fixed inclination has, so much does the motion of the Earth gain from it; as much absurdity as the double libration has, so much also does the immobility of the Earth totter.
Did the ancients also observe that the northern latitude of Venus is greatest, the southern of Mercury? Ptolemy noted this altogether, and therefore introduced into these planets a third element of latitude, which he called the inclination of the eccentric so called by him, and that too librating, against the example of the three superior and also of the Moon; the effect of which in Mercury was only and solely this, to increase the southern latitudes of Mercury. But if he had set his epicycles as unequally surrounding a point corresponding to the mean place of the Sun, as we do today, teaching that those which he calls epicycles are eccentric from the Sun, he would not have needed that third apparatus of libration. For the southern limit of Mercury is nearer to his aphelion P, which, the farther it goes out from the Sun than the northern about R, the nearer it comes to the Earth in D, when the planet is retrograde, than the northern limit about R comes to the Earth in T, the planet similarly retrograde: therefore on this account also the southern latitude appears greater than the northern.
Why, then, are the northern latitudes of Venus also greater, since her northern limit is in Virgo, near the perihelion? The cause of this in Venus is very different from the above; namely if latitude depended on inclination alone, the northern would have been less, because Venus at the northern limit, that is in Virgo, goes out less from the Sun toward the Earth than at the southern and in Pisces, near the aphelion itself.
But the eccentric orbit of the Earth now comes in: for the Earth in Virgo, when the Sun and the northern limit of Venus appear in Pisces, is less distant from the Sun than if the Earth in Pisces looked at the Sun and the southern limit of Venus in Virgo (truly existing also under Pisces). So the unequal distance of the limits of Venus from the Sun is not only compensated, but even surpassed, since the eccentricity of the Earth is much greater than that of Venus.
Let A be the Sun and let AE of the Earth and AG of the southern limit of Venus, long distances, tend to 13° of Pisces, on the contrary AC of the Earth and AF of the northern limit of Venus, shorter, tend to 13° of Virgo, so that the proportion EG to DF is the same as AG to AF, and F is seen from C in Pisces, but G from B in Virgo. The rest will therefore be thus.
Was there also another use in Venus of that librating eccentric of Ptolemy? Indeed the excess of the northern latitude of Venus over the southern is very slight. Ptolemy seems, therefore, to have attached some slight inclination, a perpetual one, to the eccentric of Venus, that by this he might guard against Venus ever running under the Sun. For the ancients placed these two above the Sun, using this argument, that they never run under the Sun, as the Moon does. Ptolemy answered that the cause why they do not run under the Sun could be the motion of latitude. Since, then, he himself placed them below the circle of the Sun, he had to guard also against their being interposed between the Sun and the Earth, which he obtained through the said librating inclination.
Compare the latitudes of the inferior planets with the inclinations. Venus, no less than the superior, has now a latitude less than the inclination, now greater, by laws also similar, yet not wholly the same; less indeed from the superior conjunction with the Sun until the arc of the anomaly of commutation from the Sun, numbered forward or backward, with the arc of elongation from the Sun which is on that day, makes a semicircle; greater, however, below. And in the greatest elongation the latitude already exceeds the inclination, and this up to the inferior conjunction of Venus with the Sun, where this excess is greatest.
But in Mercury, otherwise than in the rest, the latitude never equals the inclination, but is always less. For Mercury, even when he is most remote from the Sun, is always nearer to him than to the Earth.