Goodness, this really is a manual for ancient astronomical calculations! Let's break it down sentence by sentence and take it slow.
First paragraph: First, calculate the accumulation of gains and losses in the calendar for one year, then multiply this gain and loss figure by the number of days in a year to get an actual value. Then, multiply the daily gain and loss rate by a constant (likely referring to a fixed coefficient) and use this result to adjust the actual value; this is the method for calculating the fluctuations in gains and losses throughout the year. Next, multiply the monthly reduction in degrees by half the number of days in a year to get a difference value, and use this difference to divide the previous gain and loss value to obtain a remainder of gains and losses. The size of this remainder determines the exact timing of the new moon (the first day of the lunar calendar), whether it is advanced or delayed. The gain and loss remainders for the full moon (the fifteenth and twenty-third of the lunar month) are used to determine more precise values.
Second paragraph: Multiply the total gain and loss for the year by the previously calculated additional gain and loss number, then divide by the difference to get a full cycle count (likely referring to a complete cycle), which represents the magnitude of the gains and losses. Then adjust the daily positions of the sun and moon based on this gain and loss number; if there is a surplus, it is advanced, and if there is a deficiency, it is delayed, ultimately determining the precise position of the sun and moon each day.
Third paragraph: Multiply half the number of days in a year by the small remainder from the new moon, then divide by the constant, and subtract this result from the remainder of the days calculated from the calendar. If the result is a negative number, add the number of days in a year and then subtract one day; this way, you get the specific time at which it enters the calendar at midnight.
Fourth paragraph: To determine the second day, start from the remainder of the previous day and continue calculating up to the twenty-seventh day. If the remainder exceeds the number of days in a year, subtract the number of days in a year; if not, keep the remainder, and this remainder represents the day number that will enter the calendar for the second day.
Paragraph Five: Multiply the remainder of the number of days entered into the calendar at midnight by the profit and loss rate. If the result equals the number of days in a week, take the whole number; if not, take the remainder and use it to adjust the accumulated profit and loss. If the remainder cannot be evenly divided, divide it by the number of days in a week. This way, the profit and loss value at midnight is obtained. For a full year, take the whole number; for less than a year, take the remainder. Then multiply by the number of cycles; if the remainder can be divided evenly by the number of days in a week, take the whole number; if the remainder can be divided evenly by a cycle, take the whole number, then use this result to adjust the degree and remainder at midnight to finally determine the precise degree.
Paragraph Six: Multiply the remainder of the number of days entered into the calendar by a value called "column decay" (possibly referring to some kind of decay coefficient). If the result equals the number of days in a week, take the whole number; otherwise, take the remainder. This way, you can understand how the daily changes decay.
Paragraph Seven: Multiply the virtual number of days in a week by column decay to obtain a constant. After the calendar calculation is completed, add this constant to the changing decay value. If it exceeds the value of column decay, subtract the value of column decay, then move on to the calculation of the changing decay value of the next calendar.
Paragraph Eight: Adjust the degrees for the year in the calendar with the changing decay value. If there is an excess or deficiency in degrees, adjust the degrees for the year. Then multiply by the number of cycles, add the degree determined at midnight, to obtain the degree of the second day. If the calendar calculation result is not equal to the number of days in a week, subtract 1338, then multiply by the number of cycles; if it equals the number of days in a week, add 837, then divide 899 by a smaller number, then add the changing decay value of the next calendar, and perform the same calculation.
Paragraph Nine: Subtract or add the profit and loss rate with the changing decay value to obtain a new profit and loss rate, then use this new profit and loss rate to calculate the profit and loss value at midnight. If there is an excess or deficiency in the calendar calculation result, move to the next calendar, then adjust according to the above method.
Section Ten: Multiply the number of degrees traveled each month by the timekeeping marks during the recent night of the nearest solar term (ancient timing tool), then divide by 200 to get a value called "mingfen." Subtract this mingfen from the number of degrees traveled each month to get a value called "hunfen." If the value can be divided evenly by the number of years elapsed, take the integer part, then multiply by the number of passages, and add the degree measured at midnight to get the exact degree of twilight. If the remainder is less than half, discard it.
In conclusion, this passage describes an extremely complex ancient calendar calculation method involving a large number of coefficients and operational steps, the intricacy of which is truly astounding! Modern people may find it difficult to understand directly and need to combine the knowledge of ancient calendars and astronomical observation data to fully grasp it.
For ancient people, calculating the calendar was truly a science! First, they divided the year into many small segments, using methods like "the moon has four phases and three paths of entry and exit, and the sky is divided by the moon's rate to determine the day." In simple terms, they established calendars based on the moon's movement patterns. They also used methods like "multiplying the week by the conjunction of the sun and moon, which occurs when the moon is new" to calculate the length of the synodic month, and through a series of complex calculations, such as "multiplying the passage by the conjunction, the remainder is similar to the new moon, indicating the retreat," they eventually calculated the specific time of each day. Among these, "meeting once indicates the difference rate" refers to a key ratio.
Next, they will adjust the calculation results according to the "Yin and Yang calendar, rate of loss and gain, and multiple numbers." This part is quite complicated. Specifically, on the first day, they need to "subtract one and initially gain seventeen," on the second day "subtract one and gain sixteen and seventeen," and so on. The increase or decrease values are different each day, and there is also a "remaining limit," for example, "second day (remaining limit of one thousand two hundred and ninety, differential four hundred and fifty-seven.) This represents the previous limit." These numbers represent various complex correction parameters, until the thirteenth day, "remaining limit of three thousand nine hundred and twelve, differential one thousand seven hundred and fifty-two." This calculation is truly mind-boggling! And there are special algorithms like "smaller method, four hundred and seventy-three." In the end, they calculated a series of key values such as "lunar cycle, one hundred and seventy-five thousand six hundred and five. Rate of difference, eleven thousand nine hundred and eighty-six. Lunar conjunction, eighteen thousand three hundred and twenty-eight. Differential, nine hundred and fourteen. Differential method, two thousand two hundred and nine."
Finally, they will determine the specific date based on these values. "Using the month of the meeting to accumulate the month, the remainder is multiplied by the lunar conjunction and the differential, the differential is full of its method from the conjunction, the conjunction is full of the week to go, the rest that does not meet the lunar cycle is the solar calendar; if it meets, it is the lunar calendar." This part feels like reading a cryptic text! It means that using various complex calculation methods to determine whether a day belongs to the solar calendar or the lunar calendar. If there is still a remainder in the calculation, "the remainder counts as a day, similar to a lunar week," then add another day. In addition, they will also consider "adding two days, with a remainder of two thousand five hundred and eighty, differential nine hundred and fourteen, applying the method to finalize the day, reaching thirteen, subtracting the remainder as the fractional day." This calculation is aimed at more accurately determining the date. Finally, "the lunar and solar calendars ultimately converge, entering the calendar before the remaining limit, and after the remaining limit, the moon travels along the midpoint," summarizes the entire calculation process and the relationship between the lunar and solar calendars.
Finally, they also need to consider "the various arrangements of late and early dates, calculating small fractions as differentials, the adjustments of yin and yang according to the remaining days, when the remaining days are insufficient, and the determination of advances and retreats by the sun." This indicates that they will also make slight adjustments to the calculation results based on actual conditions. In the end, they will use "to determine the remaining days multiplied by the profit and loss rate, as in the monthly and weekly calculations, to establish a constant for additional time" to finalize the date. In short, the calculations of ancient calendars are incredibly intricate, almost beyond comprehension!
First, by multiplying the difference rate by the decimal part of the remaining days of the new moon, a numerical value is obtained similar to calculus. This value is then subtracted from the remaining days in the calendar; if it is not enough, a month's weeks are added before subtracting again, and then we subtract one day. The resulting days plus their fractional part are simplified using the summation method, thus obtaining the date when the new moon enters the calendar at midnight.
Next, to find the next day, add one day, and the remaining days are 31, with the decimal part also being 31. If the decimal part is subtracted from the remaining part like the summation method, when the remaining part is filled with complete weeks, it is subtracted, and then one day is added. The calendar calculation continues until the remaining days are full of fractional days, at which point it is subtracted, marking the starting date of entry into the calendar. If it does not reach a fractional day, it is retained, and 2772 is added, with the decimal part being 31, thus obtaining the date for entering the next calendar.
Using the universal number multiplied by the late and early entries of the calendar at midnight and the remaining part, when the remaining part is filled with half a week, it is treated as the decimal part. The increase and decrease of yin and yang based on the remaining days are adjusted using the weeks of the month. The determined remaining days are then multiplied by the profit and loss rate, similar to obtaining one from the monthly and weekly numbers, and using the comprehensive value of profit and loss, a determined value for midnight is obtained.
The profit and loss rate is multiplied by the number of night watches during the recent solar periods; every 200 watches represent one day's bright time. This value is then subtracted from the profit and loss rate to calculate dusk time, and the profit and loss figure for midnight is used as the reference for dusk and dawn.
Establish overtime; if the values for dimness and brightness are the same, divide by 12 to obtain degrees. One-third of the remainder is classified as "less"; any remainder under one is termed "strong," while two "less" values indicate "weak." The resulting value indicates the angle by which the moon deviates from the ecliptic. For the solar calendar, subtract the extreme degree from the ecliptic corresponding to the added day; for the lunar calendar, add the extreme degree to the ecliptic corresponding to the added day, thus obtaining the degrees the moon is away from the extreme. "Strong" is positive, "weak" is negative; add strengths and weaknesses together, same names add, different names subtract. When subtracting, same names subtract, different names add, with no mutual cancellation. Two "strong" plus one "less" minus one "weak."
Starting from the year of Jichou in the Shangyuan period to the year of Bingxu in the eleventh year of Jian'an, a total of 7,378 years.
Jichou, Wuyin, Dingmao, Bingchen, Yisi, Jiayin, Guiwei, Renshen, Xinyou, Gengxu, Jihai, Wuzi, Dingchou, Bingyin.
Five elements: Wood, Year Star; Fire, Wandering Star; Earth, Filling Star; Metal, Bright Star; Water, Chen Star. Use their end days and sky degrees to derive the weekly rate and daily rate. Multiply the annual figure by the weekly rate to get the lunar calculation method. Multiply the monthly chapter by the daily rate to get the monthly fraction. The monthly fraction, like the lunar calculation method, gives the lunar number. Multiply the common number by the lunar calculation method to get the daily degree method. Multiply the Dou fraction by the weekly rate to obtain the Dou fraction. (The daily degree method uses the calendar method multiplied by the weekly rate, so here it also uses fractions.)
The five stars' new moon day, large remainder, small remainder. (Using the common method, multiply by the lunar number; using the daily method, divide by the lunar number to get the large remainder, with the indivisible part being the small remainder. Subtract the large remainder from 60.)
The five stars enter the lunar day, daily remainder. (Using the common method to multiply by the lunar remainder, using the combined lunar method to multiply by the new moon small remainder, add them together, simplify using the combined total, and divide the resulting value by the daily degree method to obtain the results.)
What is written above is a series of numbers that look like the results of some astronomical calculations. "Five-star degree, degree remainder. (Subtract excess for degree remainder, multiply by the weekly sky, simplify using the daily degree method; the result is the degree, the remainder is the degree remainder; if it exceeds the weekly sky, subtract the weekly sky and add Dou fraction.)" This passage roughly means to calculate the degrees and remainders of planetary movements; the method is to first subtract the excess part, then multiply the weekly number by the remainder, and finally simplify using the daily degree method to get the degrees, with the remainder being the degree remainder. If it exceeds the weekly sky, subtract the weekly number and then calculate the Dou fraction. Ultimately, the calculations are quite complex, and I find them difficult to comprehend.
Next is a bunch of numbers, recording various astronomical parameters. "Month Count, 7285. Intercalary Months, 7. Extra Days, 235. Years, 12. Total Cycle, 43026. Daily Cycle, 1457. Meeting Count, 47. Orbital Days, 215130. Divisions of the Dipper, 145." I have no idea what these numbers represent; it feels like ancient astronomers were making records.
Then there are calculations about Jupiter. "Jupiter: Orbital Period, 6722. Daily Orbit, 7341. Total Lunar Count, 13. Lunar Remainder Days, 64801. Total Lunar Cycle, 12718. Daily Degree Count, 3959258. Major New Moon Remainder Days, 23. Minor New Moon Remainder Days, 1307. Lunar Entry Day, 15. Daily Remainder Days, 3484646. New Moon Fraction, 150. Divisions of the Dipper, 974690. Degree Count, 33. Degree Remainder Count, 2509956." A bunch of numbers, but I can't understand any of them; they are probably various parameters of Jupiter's orbit.
Next are the calculations for Fire, Earth, and Venus, which are a bunch of numbers. "Fire: Pi value, 3407. Solar days, 7271. Total lunar months, 26. Remaining lunar days, 25627. Total lunar days, 64733. Solar days, 206723. Remaining large lunar cycles, 47. Remaining small lunar cycles, 1157. Days to enter the lunar month, 12. Remaining solar days, 973113. Remaining empty lunar cycles, 300. Constellation divisions, 494015. Degrees: 48. Remaining degrees: 199176. Earth: Pi value, 3529. Solar days, 3653. Total lunar months, 12. Remaining lunar days, 53843. Total lunar days, 6751. Solar days, 278581. Remaining large lunar cycles, 54. Remaining small lunar cycles, 534. Days to enter the lunar month, 24. Remaining solar days, 166272. Remaining empty lunar cycles, 923. Constellation divisions, 51175. Degrees: 12. Remaining degrees: 173148. Venus: Pi value, 9022. Solar days, 7213. Total lunar months, 9." These numbers, I can only say, I am completely amazed; this must be the incredible astronomical calculation! Anyway, I completely don't understand. One month later, the number is 152293. According to the total lunar days calculation, the result is 171418. Using solar days calculation, the result is 531958. Remaining large lunar cycles are 25. Remaining small lunar cycles are 1129. Days to enter the lunar month are 27. Remaining solar days are 56954. Remaining empty lunar cycles are 328. Constellation divisions are 1308190. Degrees: 292. Remaining degrees: 56954. The Pi value for Water is 11561. The Pi value for solar days is 1834. Total lunar months are 1. One month later, the number is 211331. According to the total lunar days calculation, the result is 219659.
Using the daily calculation method, the result is six million eight hundred and nine thousand four hundred and twenty-nine. The new moon remainder is twenty-nine. The small new moon remainder is seven hundred and seventy-three. The entry date of the month is twenty-eight. The day remainder is six million four hundred and one thousand nine hundred and sixty-seven. The virtual fraction of the new moon is six hundred and eighty-four. The division is one hundred sixty-seven thousand six hundred thirty-five. The degrees are fifty-seven. The degree remainder is six million four hundred and one thousand nine hundred and sixty-seven. First, multiply the first year's value by π. If it can be evenly divided by the daily rate to yield one, it is called the product, and the undivided part is called the remainder. Use π to divide the product; if it can be evenly divided to yield one, it indicates the star conjunction in previous years; if it can be evenly divided to yield two, it indicates the star conjunction in the two years prior; if it cannot be evenly divided, then it is the conjunction in this year. Subtract the remainder from π to get the degree division. The product of gold and water indicates that odd numbers represent morning and even numbers represent evening.
Then, multiply the month number and month remainder by the product respectively. If the result can be evenly divided by the monthly conjunction method to yield a complete month, then the remainder is the new month remainder. Subtract the accumulated month from the record month; the remainder is the entry record month. Then multiply the chapter leap by the entry record month; if it can be evenly divided by the chapter month to yield a leap month, subtract this leap month, and the remaining part is used within the year. This part is calculated outside the solar calculation and is called the conjunction month. If it is at the boundary of the leap month, then adjust using the new moon.
Use the common method to multiply by the month remainder, and the conjunction month method to multiply by the small new moon remainder, then simplify using the meeting number. If the result can be evenly divided by the daily method to yield one, then that is the entry date of the star conjunction; if it cannot be evenly divided, the remainder is the day remainder, which is calculated outside the new moon calculation.
Use the weekly heavenly cycles to multiply by the degree division; if the result can be evenly divided by the daily method to yield one degree, the undivided part is the remainder, and use the five oxen method to determine the degree.
The above is the method for determining star conjunctions. Add the month numbers and month remainders; if the result can be evenly divided by the conjunction month method to yield a month, then it indicates this year; if it cannot be evenly divided, check if the result is enough for a year; if it is, subtract one year, accounting for any leap months, and the remaining part is for the following year; if it is enough for another year, then it indicates the following two years. Adding gold and water in the morning yields evening, and adding evening yields morning.
First, let's calculate the new moon's waxing and waning (the first day of the lunar calendar). Add the new moon's waxing and waning to the total waxing and waning of the moon; if it exceeds one month, add twenty-nine days; if it is not enough, add seven hundred seventy-three minutes. If it is less than a day, calculate it as a whole number, using the same method as before.
Next, calculate the degrees of the moon's entry into the twenty-eight mansions and the remaining days. Add the entry degrees and the remaining days; if it exceeds one day's worth of degrees, record it as one day. If the new moon's waxing and waning calculated earlier is exactly enough for one day, subtract one day; if the waxing and waning of the new moon exceeds seven hundred seventy-three minutes, subtract twenty-nine days; if it does not exceed seven hundred seventy-three minutes, subtract thirty days. The remainder will be the date of the moon's entry into the mansions.
Then, add the degrees together and also add the remaining degrees; if it exceeds one day's worth of degrees, record it as one degree.
Below is the running situation of Jupiter:
Jupiter is in hiding (speed decreases) for 32 days, with a running distance of 3,484,646 minutes; it is visible (speed increases) for 366 days. When Jupiter is in hiding, it runs five degrees and 2,509,956 minutes; when it is visible, it runs forty degrees (subtracting twelve degrees for retrograde motion, the actual distance traveled is twenty-eight degrees).
Mars's running situation:
Mars is in hiding for 143 days, with a running distance of 973,113 minutes; it is visible for 636 days. When Mars is in hiding, it runs one hundred ten degrees and 478,998 minutes; when it is visible, it runs three hundred twenty degrees (subtracting seventeen degrees for retrograde motion, the actual distance traveled is three hundred three degrees).
Saturn's running situation:
Saturn is in hiding for 33 days, with a running distance of 166,272 minutes; it is visible for 345 days. When Saturn is in hiding, it runs three degrees and 1,733,148 minutes; when it is visible, it runs fifteen degrees (subtracting six degrees for retrograde motion, the actual distance traveled is nine degrees).
Venus's running situation:
Venus is in morning concealment in the east for 82 days, with a running distance of 113,908 minutes; it is visible in the west for 246 days (subtracting six degrees for retrograde motion, the actual distance traveled is two hundred forty-six degrees). When Venus is in morning concealment in the east, it runs one hundred degrees, with a running distance of 113,908 minutes; when it is visible in the east (the daily degrees are the same as in the west, hiding for ten days and retrograding eight degrees).
Mercury's running situation:
Mercury is in conjunction in the west for 33 days, with an orbital distance of 612,505 minutes; it appears in the west for 32 days (subtracting one degree for retrograde, the actual angle is thirty-two degrees). When Mercury is hidden, it moves sixty-five degrees in its orbital path, with an orbital distance of 612,505 minutes; it then appears in the east (the solar daily motion is the same as in the west, hidden for eighteen days, retrograde for fourteen degrees).
First, let's talk about how to calculate the movement of this planet. Start by subtracting the degrees of the planet's movement from the solar daily motion. The remaining degrees, if divisible by the solar daily motion, results in an integer. This is similar to previous calculations, allowing us to know when the planet will be visible. Then, multiply the planet's running minutes by the visible degrees of the planet. The remaining degrees, if divisible by the solar daily motion, results in an integer; if not, if it exceeds half, it is also counted as an integer. Next, add the degrees of the planet's movement to the solar daily motion; if the degrees fill the numerator of the planet's running cycle, increase by one degree. The methods for calculating direct and retrograde motion differ and must be calculated based on the current running cycle's numerator, which provides the current movement degrees of the planet. The remaining degrees carry over the result from the previous step; if it is retrograde, subtract it. If the degrees are insufficient, use the degrees of a full cycle for division, using the planet's running cycle's numerator as a ratio, which will cause the degrees to increase or decrease, working together. In summary, anything said as "like fullness" is the result of precise division; "to remove and divide," and "to take the complete division" are divisions yielding integer results.
Next, let's talk about Jupiter. Jupiter appears in the morning alongside the sun and then becomes invisible; this indicates direct motion. After sixteen days, Jupiter will have moved 1,742,323 minutes, while the planet has moved 2,323,467 minutes, at which point Jupiter can be seen in the east, behind the sun. During direct motion, its speed is fast, moving 11 degrees in 58 days, or 58 minutes per day. Continuing direct motion, the speed slows, moving 9 degrees in 58 days, or 9 minutes per day. It stops moving, and after 25 days, it begins to move again. During retrograde motion, it moves one-seventh of a degree per day, retreating 12 degrees after 84 days. Then it stops again, and after 25 days, it begins direct motion, moving 9 degrees in 58 days, or 58 minutes per day. During direct motion, its speed increases again, moving 11 degrees in 58 days, or 11 minutes per day; at this point, it is in front of the sun and becomes invisible in the west at night. After sixteen days, Jupiter will have moved 1,742,323 minutes, while the planet has moved 2,323,467 minutes, and at this time, it appears again alongside the sun. One complete cycle concludes, totaling 398 days and 3,484,646 minutes, with the planet having moved 43 degrees and 2,509,956 minutes.
The Sun: In the morning, the Sun encounters Mars, and Mars hides. Then Mars begins to move forward for 71 days, traveling 1,489,868 minutes, which is 55 degrees and 242,860.5 minutes. After that, Mars appears in the morning sky to the east, behind the Sun. While moving forward, Mars covers 14 minutes for every 23 minutes of time each day, covering 112 degrees in 184 days. Then its forward speed slows down, and Mars covers 12 minutes for every 23 minutes of time each day, covering 48 degrees in 92 days. Next, Mars halts for 11 days. Then it begins to retrograde, covering 17 minutes for every 62 minutes of time each day, retreating 17 degrees in 62 days. After another 11 days, it starts moving forward again, traveling 12 minutes each day, covering 48 degrees in 92 days. Once again moving forward, the speed increases, with Mars traveling 14 minutes each day, covering 112 degrees in 184 days, at which point it is in front of the Sun and sets in the west in the evening. After 71 days, it has traveled 1,489,868 minutes, or 55 degrees and 242,860.5 minutes, and finally encounters the Sun again. One cycle ends, totaling 779 days and 973,113 minutes, with a distance of 414 degrees and 478,998 minutes.
Saturn: In the morning, the Sun encounters Saturn, and Saturn hides. Then Saturn begins to move forward for 16 days, traveling 1,122,426.5 minutes, or 1 degree and 1,995,864.5 minutes. After that, Saturn can be seen in the east in the morning, positioned behind the Sun. While moving forward, Saturn covers 3 minutes for every 35 minutes of time each day, covering 7.5 degrees in 87.5 days. Then Saturn stops moving for 34 days. Next, it begins to retrograde, covering 1 minute for every 17 minutes of time each day, retreating 6 degrees in 102 days. After another 34 days, Saturn starts moving forward again, traveling 3 minutes each day, covering 7.5 degrees in 87 days, at which point it is in front of the Sun and sets in the west in the evening. After 16 days, it has traveled 1,122,426.5 minutes, or 1 degree and 1,995,864.5 minutes, and finally encounters the Sun again. One cycle ends, totaling 378 days and 166,272 minutes, with a distance of 12 degrees and 1,733,148 minutes.
Wow, this ancient text is quite overwhelming! Let’s take it step by step and translate it into plain English.
The first paragraph describes the conjunction of Venus with the Sun in the morning. First, Venus "is hidden," meaning it is concealed behind the Sun, then it retrogrades, moving four degrees over five days, which allows it to be seen in the east in the morning, even though it is still behind the Sun. Next, it continues to retrograde, moving three thirty-sixths of a degree each day, resulting in a total of six degrees over ten days. Then it comes to a stop, remaining stationary for eight days, a phase known as "stationary." After that, it begins to move direct at a slow pace, traversing three thirty-sixths of a degree each day, covering a total of thirty-three degrees in forty-six days. Then it accelerates, moving one degree and fifteen ninety-firsts each day, covering one hundred sixty degrees in ninety-one days. The speed increases further, moving one degree and twenty-two ninety-firsts each day, covering one hundred thirteen degrees in ninety-one days, at which point it moves behind the Sun again, becoming visible in the east in the morning. Finally, it moves direct, traversing one-fiftieth of a circle over forty-one days, totaling fifty degrees and one-fiftieth of a circle, before it conjuncts with the Sun again. The entire conjunction cycle lasts two hundred ninety-two days and one-fiftieth of a circle, and Venus travels this distance too.
The following is about Venus's conjunction with the Sun in the evening. When Venus and the Sun come together at night, Venus first "hides," then moves forward. It takes forty-one days to travel one fifty-six thousand nine hundred fifty-fourth of a complete orbit, covering fifty degrees of arc. At night, it can be seen in the western sky, positioned in front of the Sun. It then continues moving forward, accelerating, covering one degree and fifteen minutes each day for ninety-one days, resulting in a total of one hundred thirteen degrees. It then slows down, covering one degree and fifteen minutes each day for ninety-one days, totaling one hundred sixty degrees. It slows down again, covering forty-six minutes and thirty-three seconds each day for forty-six days, totaling thirty-three degrees. Then it remains stationary for eight days. It then moves backward, covering three-fifths each day for ten days, resulting in a total retreat of six degrees. At this point, it can be seen in the western sky at night in front of the Sun. It then continues moving backward, accelerating, covering four degrees in five days, finally coming into conjunction with the Sun. One complete cycle of conjunction lasts five hundred eighty-four days and one hundred thirty-nine thousand eight hundred ninety-first of a complete orbit, which Venus also travels.
The last paragraph describes Mercury's conjunction with the Sun in the morning. When Mercury and the Sun come together in the morning, Mercury first "hides," then moves backward, retreating a total of seven degrees over nine days. It can be seen in the eastern sky in the morning, positioned behind the Sun. It then continues moving backward, accelerating, retreating one degree each day. It remains stationary for two days. It then moves forward, slowly, covering eight ninths each day for nine days, totaling eight degrees. It accelerates, covering one degree and one quarter each day for twenty days, totaling twenty-five degrees. At this point, it can be seen in the eastern sky in the morning behind the Sun. Finally, it moves forward, covering a total of thirty-two degrees and six hundred forty-one thousand nine hundred sixty-sevenths of a complete orbit over sixteen days, and then comes into conjunction with the Sun again. One complete cycle of conjunction lasts fifty-seven days and six hundred forty-one thousand nine hundred sixty-sevenths of a complete orbit, which Mercury also travels.
In summary, this text details the various movements of Venus and Mercury in conjunction with the Sun, including retrograde, direct motion, and stationary periods, as well as their respective cycles and speeds. The calculations are quite precise! Speaking of Mercury, it sets with the Sun and then becomes hidden, moving in a direct trajectory. Specifically, it can travel thirty-two degrees, six hundred forty-one thousand, nine hundred sixty-seven minutes in sixteen days (that number is indeed quite precise!). At this time, it can be seen in the west in the evening, and it is positioned in front of the Sun. When moving directly, it travels quite fast, covering one and a quarter degrees in a day, and can cover twenty-five degrees in twenty days. If it moves slowly, it covers about seven-eighths of a degree in a day, taking nine days to cover eight degrees. If it is stationary, it remains still for two days. When in retrograde, it moves backward at a rate of one degree per day, during which it is positioned in front of the Sun and becomes hidden in the west by evening. During retrograde, it also moves slowly, taking nine days to retreat seven degrees, and eventually comes back into conjunction with the Sun. From its conjunction with the Sun to the next conjunction, the entire cycle lasts one hundred fifteen days and six hundred twelve thousand five hundred fifty-one minutes, and this is the nature of Mercury's movement.
