ASTRONOMICAL

THE FOURTH STATEMENT.

To investigate the longitudes of the fixed stars in the Zodiac and their latitudes—that is, their deviations from the ecliptic—from the creation of the world; furthermore, to determine the certain degrees, minutes, and auges From the Arabic "awj," meaning the apogee or the point in a planet's orbit furthest from the Earth. of the planets before and after the time of Christ. Additionally, to discover which fixed stars any of the planets approach daily, or which they may hide by their proximity.

Decorative woodcut initial 'L' depicting a man in 16th-century scholarly dress standing in a landscape with a building and hills in the background, holding a long instrument, possibly a cross-staff or measuring rod. The letter 'L' is formed by the vertical figure and a horizontal base. the previous statement has abundantly taught the motions of the Eighth, Ninth, and Tenth spheres. Therefore, regarding the theory, I shall add nothing further at present. Instead, I will briefly and without ambiguity reveal how you may, quicker than a word is spoken, grasp the courses of all the fixed stars and the planetary apogees through the following instrument. ¶ Since the tenth sphere is moved from east to west, as has been said, and the ecliptic or Zodiac is established for us in that same heaven, we shall treat no further of its motion (which is understood through that immobile or fixed Zodiac); rather, we shall henceforth always position the Zodiac as firm through all instruments, like the tenth heaven, the outermost. You now see such a thing, after which follows a certain rotating disk original: "rotula" upon which the images of the heavens are placed. In the middle, each constellation embraces its own stars. Some of the stars are white in the middle, bearing six points at their edges; such is the one that occupies the Eye of the Bull The star Aldebaran. and the mouth of the Greater Dog The star Sirius., the figure of which is this: ✳. These are of the first magnitude, of which astronomers have described no more than 15. After these, 45 of the second magnitude shine, a little smaller and lower than the first; there are seven such stars constituting a larger one, specifically three representing the tail, which, to distinguish them from the others, are depicted in black with six distinct points, as you see here: ✶. Although stars have been described by astronomers down to the sixth degree of difference, I have indicated at least the first and second magnitudes, as well as nebulous stars with a mark like this: ☉. Because of the narrowness of the instrument, I could not signify the distinctions of the rest, but expressed them simply with a certain mark: o. In the middle of this wheel, a certain black circle is seen which represents the ecliptic, in which the twelve signs are described in order. Near Scorpio, a certain transverse line appears, divided into 16 degrees, containing 8 on each side of the ecliptic, which demonstrate the latitude of the zodiac. Near the end of Eridanus, there is a star named Achernar, next to which a pointer is held containing ♈ Aries, marking the common apogee, through which it is known how many degrees the eighth and ninth spheres travel together at any proposed time, and likewise for the fixed stars and the apogees of the wandering stars The planets.. Near the star of the Greater Dog is another pointer, signifying the apogee of the Sun and Venus. Again, at the Ship The constellation Argo Navis. there are two pointers, bearing the apogees of Saturn and Jupiter. The apogees of the planets always remain at the same and equal distance from each other. At the Centaur you see the apogee of Mercury, and at the Altar that of Mars. These pointers remain perpetually at the same and equal distance from one another. Finally, a certain circle divided everywhere into parts is seen near Cetus with a pointer marked X, which represents that small circle I spoke of before—the one that encircles the beginning of Aries in the ninth sphere. Since the beginning of Aries in the eighth sphere circles the circumference of this circle once in 7,000 years, I made this circle also into as many parts, so that each section notes 100 years. I inserted the numbers of years after Christ in the inner circle, proceeding by 500s, starting from the pointer. The years elapsed before the Incarnation of Christ are written on the outer part of the circle, through which the trepidation An astronomical theory that the equinoxes move back and forth in a slow oscillation. of the eighth sphere is investigated. Having declared the parts of the instrument, I shall add its use. ¶ If you wish to verify the fixed stars together with the apogees of the planets for any time proposed to you, lift the wheel near the Aries of the tenth sphere, where you will find certain degrees, each containing 100 years. The method of operation. If the proposed time is before Christ, you will count downwards starting from Aries toward the beginning of ✶. If, however, it is after Christ, you will count starting from Aries upwards, according to the order of the signs. The end of the number found shows in the zodiac how far the ninth sphere has moved under the tenth in that many years; move the pointer marked X to that place. After this, count the same number of years in the small circle of trepidation, starting from the pointer (either inside, if the time is after Christ's birth, or outside, if the time is before Christ), and apply the thread that hangs from the center of the wheel to the end of the required years. With the thread well extended, observe how many degrees there are in the zodiac between the thread and the pointer; for those indicate the equation of the eighth sphere with the ninth. Keeping the thread unmoved, move pointer Y, which is the common apogee, under the same spot, and thus leave the wheel unchanged, for it is now verified for your time. With it lying thus, extend the thread from its center over any star you please, which demonstrates the degree in the zodiac in which it was, or will be, at the predefined time. Furthermore, the pointers of the planets show the degrees and minutes of the apogees in which they are or were at that time. Let there be an example of this.

CAESAREAN

The example of Emperor CHARLES.

¶ CHARLES the Fifth, Emperor of the Romans, forever August, was born on the 24th of February The Latin says 23rd, but the historical date is the 24th; Apian's calculations often use specific astronomical start-times. at 15 hours and 44 minutes in the afternoon, in the 1500th year after Christ. When I directed the present figure with its pointers to this time (although we do not consider days, hours, and minutes so much in these slower motions), I wished to know what place in the heavens the Heart of the Lion Regulus held at that time. I therefore extend the thread through the star, and I find it to occupy the longitude of 22 degrees and 8 minutes of Leo. You may do the same for the rest, and the true motion will always be shown in the zodiac.
The apogees of the wandering stars in the time of King FERDINAND.

¶ Another Example: FERDINAND, King of the Romans, Bohemia, and Hungary, came into this world in the year of Christ 1503, on the 10th of March, at 8 hours and 47 minutes before noon. With the figure positioned for that number, the star of the Northern Crown is found to hold 4 degrees and 15 minutes. The apogee of the Sun is at 1 degree and 12 minutes of Cancer; Saturn at 13 degrees and 10 minutes of Sagittarius; Jupiter at 23 degrees and 24 minutes of Virgo; Mars at 14 degrees and 59 minutes of Aquarius; and Venus at 10 degrees and 26 minutes of Taurus.
¶ If you require the latitudes—that is, the distances of a star from the ecliptic—draw the thread through the star itself, and at the place where the ecliptic is cut, fix one foot of a compass there, with the other extended to the body of the star. Then examine that same extension of the compass on the scale of latitude drawn near the tail of Sagittarius, in which you will clearly recognize how great the latitude is. If the star is drawn from the ecliptic toward the center, it is said to be in northern latitude; if toward the edge, in southern latitude. Truly, it is no less pleasant to know which of the fixed stars a planet stands near or covers. Take this proof of that matter: At the birth of King FERDINAND, the Moon held 1 degree and 21 minutes of Taurus; its latitude from the ecliptic was 3 degrees and 24 minutes North. Now if you count 3 degrees and 24 minutes from the ecliptic toward the Altar on the scale near the tail of Scorpio, and draw the thread through them, and place the bead original: "margarita" (a bead on a string used as a cursor) over the degree and minute, and finally direct the thread together with the immobile bead over 1 degree and 21 minutes of Taurus (where the Moon was according to longitude), then the bead demonstrates the place between the 17th and 18th stars of Leo, which are in the belly of Leo, where it was seen at the time of the royal birth. Indeed, because of its parallax original: "diversitatem aspectus", the Moon obscured or covered those two stars positioned in the belly of Leo, namely the 17th and 18th.
It will be worth your while here to take account of the years before Christ to which you wish to trace the fixed stars and planetary apogees; to understand this more clearly, I will propose an example.
The apogees of the planets at the time of the Flood.

¶ If someone were to investigate the apogees and fixed stars for the time of the Flood. First, one will learn from the table of times that Noah's Flood occurred 3103 years and 319 days before Christ. Then, starting from the Cross ☊ The descending node against the succession of the signs, let him seek 3103 years and the days by a likely conjecture, which in a way make up a year. Having found them, let him place pointer X over them, which will show 11 degrees and 6 minutes of Aquarius. Next, let him seek the same number of years in the small circle (which is called the circle of the trepidation motion of the eighth sphere) at the outermost number, and the said thread will indicate 11 degrees and 3 minutes of Aquarius in the zodiac, which is the common apogee. If you then place pointer Y over the thread, you will have positioned the wheel most truly. If you would rather prepare the disk in another way (I say this so that you may see that in all the instruments of the theorists, we can use not only this one way but also a second), it is like this: Write down the age of the Flood from the table, which is 3103 years and 319 days. The nearest hundredth is now to be taken, which is 3200; count that many years from the cross ☊, and once found, pointer X must be fitted, which immediately shows 11 signs, 6 degrees, and 29 minutes in the Zodiac. Then in the circle of trepidation, at the outer number (namely before Christ), let 3200 be sought, and let a point be marked, which shall be named B. From here, let 3103 years and 319 days be subtracted from 3200 years; there remain 98 years and 47 days, which reach the light of the 16th of February. Now again, from 3200 years, count backwards and against the order of signs the remaining 98 years (neglecting the days due to the smallness of the instrument), to which join pointer X again, which will indicate 11 signs, 7 degrees, and 32 minutes on the rim of the Zodiac. Next, let point B be seen again in the circle of trepidation, previously marked near 3200, from which again 98 years are taken backwards (for days cannot be had); through the 98th year let a thread be drawn from the center, which refers to the common apogee in the zodiac at 11 signs, 4 degrees, and 8 minutes. To this, pointer Y will again be applied; once done, the wheel will be entirely verified for the day of the Flood, which was the 16th of February and a Thursday, at which time the Dominical letter A letter used to determine the day of the week for any date in the year. must have been A. The apogee of the Sun was at 15 degrees and 34 minutes of Taurus; the apogee of Saturn at 27 degrees and 32 minutes of Sagittarius; the apogee of Jupiter at 7 degrees and 45 minutes of Leo; the apogee of Mars at 29 degrees and 20 minutes of Pisces; the apogee of Mercury at 14 degrees and 48 minutes of Virgo. All these apogees are revealed with their pointers as soon as the first, namely the common apogee, has truly held its place. You will see the true locations of the fixed stars in the Zodiac if you extend the thread through their centers or midpoints. This seemed altogether necessary for me to advise.