ASTRONOMICAL ENUMERATION

OF THE PARTS OF THE FOLLOWING INSTRUMENTS.

How many and of what kind the parts of the instruments are.

¶ We shall now examine the parts of the instruments that teach the movements of the three superior planets The "superior planets" are those further from the Sun than Earth: Saturn, Jupiter, and Mars. in a general and unified way—as the saying goes, "one faithful account"—since they agree with each other in all respects. However, only the motion of Saturn will be detailed here; through it, you will also understand the courses of the others. First, therefore, in the figure that follows immediately, a certain fixed or firm Zodiac is shown, representing the imaginary divisions of the tenth sphere. After this, a revolving small wheel (or rotula) with a pointer, inscribed with the letter M, turns at the "center of the world" In this geocentric model, the Earth is the stationary center of the universe.. On its rim are numbers, assigned to certain lines in a complex order, proceeding from 1 up to 100. Each of these lines denotes one year. Next to the pointer, the twelve months of the year are expressed, each of which is divided into 6 degrees; each degree contains 5 days, except in January, March, May, July, August, October, and December. In these, the last degree is 6 days long, while in February it is at most three. This applies to a common year.

A general rule for finding the motion of all planets in a leap year must be diligently noted; its use is not only for finding the mean motion, but also for the Argument.

In a leap year original: "anno bissextili", the calculation is different. When you wish to find the motion of any star on a specific day, you must observe the 24th day of February. If the proposed day follows February 24th, you must add one more day before seeking the motion. For example: if in a leap year you desire the motion of Saturn for February 25th, you will investigate it not for the 25th, but for the 26th. Or another way: if you want the motion of Saturn for March 12th, you will take the thirteenth day instead of the twelfth, and you will proceed in this manner through the entire remaining course of the year. This wheel contributes nothing more to the theory except that through it, the mean motion Mean motion: the theoretical average speed of a planet, assuming it moves in a perfect circle at a constant speed. can be sought without calculation. This is followed by another wheel, having the same center of the world, with a pointer or indicator marked with the letter P. Additionally, it has two circles marked by G H I K L M near the opposite of the apogee original: "augis"; the apogee is the point in an orbit farthest from the Earth.. Each of these is divided in the astronomical fashion into 360 degrees, that is, 12 Signs. Although the circle K L M is drawn from the center of the deferent Deferent: the large circular path along which the center of a planet's smaller orbital circle (the epicycle) moves., its division is nevertheless taken from the center of the equant Equant: a mathematical point used to account for the observed speed variations of planets.. The degrees of both circles are connected by certain thin lines. Their numbers or ciphers are written below the circle K L M, starting from the indicator P and moving to the left. Through these degrees, the center is sought, with which the latitude is then investigated. On the same small wheel, there are also two "lily" marks hidden by the deferent, which indicate the intersections of the deferent and the Ecliptic; these are called the head and tail of the dragon The "Dragon" refers to the nodes where a planet's path crosses the Sun's path (the ecliptic).. Furthermore, you should know that as long as Saturn moves with its epicycle on the deferent from the middle (called the "southern belly") between the head and tail, near the opposite of the apogee, toward the head, it is called "southern ascending." Conversely, when the epicycle moves with the deferent from the head of the dragon to the middle or "northern belly" near the apogee, the planet is said to be "northern ascending," which is signified by the letters MA and SA Original Latin abbreviations for Meridionalis Ascendens and Septentrionalis Ascendens. expressed there. In the same way, the other mark of the half-circle toward the tail of the dragon will be called "northern descending," and the other toward the middle, near the opposite of the apogee, "southern descending," represented by the letters SD and MD. Beyond these, a third wheel remains, inscribed DEFERENS SATVRNI, which carries the epicycle. On this, two epicycles are presented, the lower of which encompasses 360 degrees, or 12 Signs. Its beginning is marked with a Cross +, and it denotes the mean apogee of the epicycle. There is another epicycle whose pointer is marked with Y; the edge of this one has years separated by small minute lines, with numbers from 1 up to 100 added around them in order. Then, toward the center, the days of the months (so to speak) are written out. Last of all, a small circumference near the center, marked with a certain star, is seen, showing the true circulation of the Saturnian epicycle. Furthermore, three threads—one from the center of the world A, another from the center of the Equant E, and a third from the center of the epicycle F—protrude, belonging to the completion of this theory. And now I believe I have declared the parts of the instrument enough and more than enough, advising meanwhile that similar things are to be understood for Jupiter and Mars as have been put forth for Saturn. One difference remains: the true circulation of Mars is depicted at the edge of the epicycle, marked with a star just like Saturn's.

THE USE OF THE INSTRUMENT FOLLOWS.

The use of the lower wheel.

¶ He who intends to investigate the motion of Saturn with this instrument should first propose to know the year he desires. One should consider whether that year is before or after Christ. If it is after the birth of our Lord, the "root" The "root" (radix) is a reference value for a specific point in time used as a starting point for calculations. must be sought for as many hundreds as the proposed number contains in itself, for the roots are always placed in the present table for hundred-year intervals. If, however, the year is before the birth of Christ, then the root

IMPERIAL

must be sought at the next hundred-year mark following that year, as you will learn from what follows. Therefore, once the root has been taken from the attached tables, the same number of signs, degrees, and minutes must be sought in the Zodiac. At the end of these found values, the pointer of the lowest disc, marked with the letter M, should be placed. From there, on the rim, count the proposed year—think of it as the complete year elapsed beyond the hundredth—and through this year, draw the thread hanging from the center A. Without moving this, substitute the pointer M together with its alignment line alignment line: or "fiducial line," the straight edge used for taking readings. under the thread. With the wheel remaining firm in this manner, also draw the thread from center A through the day of the month (since hours cannot be observed in motions so slow and within the constraints of instruments of this kind). Again, replace the indicator M beneath that same thread. Thus, the first or larger of the discs will be truly ordered, whose pointer shows in the Zodiac the mean motion of Saturn, which must be taken from the beginning of Aries according to the order of the signs. And although that mean motion does not help the use of this instrument at all by itself, nevertheless, that disc had to be prepared or adjusted in this way for the use that follows.

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USE OF THE SECOND SMALL WHEEL.

Use of the second wheel.

¶ Now, therefore, proceed to the second disc, and place its indicator, where you find "Saturn's Apogee" original: "Saturni aux" written, over the apogee of Saturn in the Zodiac (which was sought previously through the Announcement). You shall keep it thus unmoved until you have the true motion. There, consider which degree of the circle G H I the pointer M touches; see that same degree in circle K L M as well, where the mean center of Saturn ends. For example, if the pointer touches the letter G, then pass from line G to K, and so on. After this, extend the thread of center E through that point or degree of the center; beneath that thread, set the deferent again, together with the center of the epicycle, and thus hold the deferent firm. Next, arrange the epicycle, which is done by taking the sums from the second table under the title of "Argument" The "Argument" is a value representing the planet's position within its epicycle., across from the century included in the proposed years. Count those signs, degrees, and minutes on the lower or smaller epicycle starting from the cross + according to the succession of the signs, and move the indicator Y of the lower epicycle to the end of that number. Consequently, seek the proposed time on the rim of the upper epicycle; once found, place the thread from center F upon it, and move the indicator with its alignment line beneath it. When this is done, examine the specific day along with the hour in the Calendar of the upper epicycle according to the calculation; having examined it, apply the thread again, and bring the pointer Y back within it. Keeping both epicycles firm in this way, draw the thread of the equant from E through the center of the epicycle, and place the lower epicycle with the cross beneath it. Thus you have the entire theoretical completion for the present purpose finished with the wheels. Now, therefore, you can contemplate how high the planet stands in the epicycle, how much the epicycle varies from the center of the world on the deferent, what place in the epicycle the planet occupies, and things of this sort.

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TO FIND THE TRUE PLACE OF SATURN.

Inquiry into the true place.

¶ Furthermore, if you desire to know the true motion of Saturn (the primary reason this present instrument was made), extend the thread from the center of the world through the middle of the small star located in the "true circulation" of the epicycle. That thread indicates the true place of Saturn in the Zodiac for the appointed day.

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HOW THE TRUE CENTER OF SATURN IS TO BE FOUND.

Calculation of the Equated Center.

¶ The thread drawn from center A through the center of the epicycle shows the true and equated center in circle G H I. This is necessary for finding the latitude of Saturn. The signs, degrees, and minutes should be counted starting from the indicator P according to the succession of the signs.