Wow, this is truly an astronomical calendar calculation manual! Let's break it down sentence by sentence and explain it in plain language.
First, subtract the new moon day (the first day of the month) from the length of the year, then subtract the days that have already passed. If the result isn't enough, add the length of the year and subtract again, then take away one more day. After subtracting, add the length of the year and its fraction to find the date and time at midnight when entering the calendar.
Next, calculate the second day. Add one day to the date and continue until reaching twenty-seven days. If the leftover days are exactly a fraction of the length of the year, drop the fraction. If it’s not a complete length of the year, add the remaining part of the year, and the remaining days are the days left to enter the calendar for the second day.
Then, multiply the remaining days to enter the calendar by the profit and loss rate. If the result is exactly a multiple of the length of the year, there is no remainder. If there is a remainder, calculate based on the profit and loss balance. If there is no remainder, subtract the length of the year. This is the calculation of the profit and loss at midnight. After calculating for a year, the leftover part that is not a complete year is the fraction. Multiply the total number of days by the fraction and the leftover part. If the leftover part is equal to the length of the year, subtract it from the fraction. If the fraction is full, subtract it from the degree. Subtract the profit from the loss and subtract the degree and leftover part at midnight to get the specific degree.
Multiply the remaining days to enter the calendar by the decline coefficient. If the result is exactly a multiple of the length of the year, there is no remainder. If there is a remainder, you can know the daily decline in change.
Multiply the leftover part of the length of the year by the decline coefficient to get a constant. After the calendar calculation, add it to the change in decline. If it exceeds the decline, subtract it, then move on to the calculation of the change in decline for the next calendar.
Use the change in decline to increase or decrease the conversion of days to minutes. If there's not enough surplus, that’s the degree of the year. Multiply the total number of days by the fraction and the leftover part, then add the determined degree at midnight to get the date of the second day. If the calendar calculation result isn't a multiple of the length of the year, subtract 1338 and then multiply it by the total number of days. If it is a multiple of the length of the year, add the remaining 837, then divide by the smaller fraction 899, add the change in decline for the next calendar, and keep calculating like before.
Subtract or add the profit and loss rate to the decay rate to obtain the change in profit and loss rate, and then use it to calculate the profit and loss at midnight. If the profit and loss is not sufficient after the calendar calculation is completed, subtract in reverse, enter the next calendar, and the remaining addition and subtraction are the same as before. Multiply the score of each month's operation by the nighttime duration of the most recent solar term, then divide by 200 to obtain the Ming minutes (daytime duration). Subtract the Ming minutes from the monthly operation score to obtain the Huan minutes (evening minutes). If the score equals one year, it is considered a degree. Multiply the total number of days by the score, add the degree determined at midnight, and you can obtain the degree determined by Huanming. If the remaining score exceeds half, keep it; if it is not enough, discard it. The calendar system consists of four tables, three entrances and exits, and days are divided alternately. Divide the monthly rate by it to obtain the calendar date. Multiply the week by the conjunction of the new moon, just like the number of months in conjunction, to obtain the conjunction minutes. Multiply the total number of days by the conjunction number, and the remaining portion corresponds to the conjunction months, obtaining the retreat minutes. Based on the monthly and weekly cycles, obtain the daily progress minutes. Divide the number of months in conjunction by one to obtain the difference rate. Finally, the table section: Yin-Yang calendar, decay, profit and loss rates, and joint numbers; On the first day, subtract three, add four, resulting in sixty-eight. On the second day, subtract three (if there isn't enough to subtract, then add instead; it should reduce by three, if not enough to reduce, add one), add one, and get seventy-two. On the third day, add four, subtract two, and get seventy-three. (If the limit is exceeded, subtract, meaning the moon has run to half a week, already exceeding the limit, must subtract.) On the fourth day, add four, subtract six, and get seventy-one. On the fifth day, add three, subtract ten, and get sixty-five. On the sixth day, add two, subtract thirteen, and get fifty-five. On the seventh day, add one, subtract fifteen, and get forty-two. On the eighth day, (remaining three thousand nine hundred and twelve, differential one thousand seven hundred and fifty-two.) This is the upper limit. Add one (start of the calendar, divide by day), subtract sixteen, and get twenty-seven. For the daily calculation (five thousand two hundred and three), subtract sixteen to get eleven. Subtracting Dafa results in four hundred and seventy-three.
The calendar cycle is 107565. The rate difference is 11986. The conjunction fraction is 8328. The micro-differential is 914. The micro-differential method is 2209.
Subtract the accumulated month from the conjunction month of the previous year, then multiply the remaining result by the conjunction fraction and micro-differential respectively. Subtract the micro-differential from the conjunction until it reaches its limit; when the conjunction reaches a week, what remains is the solar calendar; when it is full, the remainder corresponds to the lunar calendar. The remaining days are treated as a day, similar to how we treat months. Calculate the desired month conjunction into the calendar; if it is less than a day, it is the remaining days.
Add two days; the remaining days are 2580, and the micro-differential is 914. Calculate the days according to the method; subtract when it reaches thirteen, and treat the remaining days like fractional days. The lunar and solar calendars eventually enter each other; the calendar entry occurs first, followed by the remaining days, as the moon reaches its midpoint.
Set the entry into the delayed and fast calendar separately; the number of meetings multiplied by the small division gives the micro-differential. Add or subtract the lunar and solar remaining days; if the remaining days are insufficient, postpone or advance by a day to determine. Multiply the determined remaining days by the profit-loss ratio; treat it as a day like a month, using the profit and loss as a dual number, as a fixed number for overtime.
Multiply the rate difference by the remaining days of the conjunction day; like the micro-differential method, this gives one, which is used to subtract from the remaining days of the calendar entry. If it is not enough, add a month and then subtract, resulting in one day less. Then add the fractional days to its fraction; simplify the number of meetings into a small division, which indicates the conjunction night entering the calendar.
To find the second day, add one day; the remaining days are 31, and the small division is 31. Subtract the small division from the remainder like the number of meetings; subtract when the remainder reaches a month, add one day, and the calendar ends. Subtract when the remaining days reach the fractional days, which is the beginning of the calendar entry. If it is less than the fractional days, subtract directly. Then, add the remainder of 2702. The small division is 31, which indicates the next calendar entry.
Paragraph 1: Multiply a number called "universal number" by a certain value to calculate the changes in the length of day and night, as well as the remaining time. When the remaining time reaches half a cycle, it is considered as a small unit. Use surplus and deficit values to calculate the remaining days of the lunar calendar. If there is a surplus or deficit in the remaining days, adjust the days using the monthly cycle. Finally, multiply the adjusted remaining days by a number called "gain-loss ratio" to calculate the fixed value of midnight using the gain-loss ratio and other values if the monthly cycle is 1.
Paragraph 2: Multiply the gain-loss ratio by the nighttime hourglass time of the most recent solar term. Every 200 hourglasses count as one day of daylight. Subtract the value from the gain-loss ratio to calculate dusk duration, then use the gain-loss ratio and the midnight value to determine the values of dusk duration and daylight time.
Paragraph 3: Add the values of dusk duration and daylight time, divide by 12, and get a value. One-third of the remainder is considered "weak", less than one is considered "strong", and two "weak" are considered "weak". This result is the angle of the moon's deviation from the ecliptic. For the solar calendar, add this value to the moon's position on the ecliptic and subtract the extreme; for the lunar calendar, subtract this value to get the degree to which the moon leaves the extreme. "Strong" is positive, "weak" is negative. Combine the strong and weak values, add the same names, and subtract the different names. When subtracting, the same names cancel each other out, different names add up, and those without corresponding ones cancel each other out; two "strong" cancel out one "weak" and one "weak".
Paragraph 4: From the Ji-Chou year of the Shangyuan era to the Bing-Xu year of the Jian'an era, a total of 7378 years have accumulated.
Paragraph 5: Five elements: Wood corresponds to the year star; Fire corresponds to the Mars star; Earth corresponds to the Earth star; Metal corresponds to the Venus star; Water corresponds to the Dragon star. Combine the end day and celestial degree of each star to obtain the weekly rate and daily rate. Multiply the annual chapter by the weekly rate to get the monthly method, and multiply the monthly chapter by the daily rate to get the monthly share. Divide the monthly share by the monthly method to get the month number. Multiply the universal number by the monthly method to get the daily method. Multiply the Dipper share by the weekly rate to get the Dipper share. (The daily method is multiplied by the record method by the weekly rate, so here it is also multiplied by the share.)
Paragraph 6: The larger and smaller remainders of the five stars. (Multiply the common method by the month number respectively, divide the daily method by the month number to get the larger remainder; the portion that cannot be evenly divided is the smaller remainder. Subtract the larger remainder from 60.)
Paragraph Seven: The number of days until the five planets enter the new month. (Multiply the remainder of the month by the common method, multiply the remainder of the new moon by the synodic month method, add them together, simplify, and divide by the daily calculation method to obtain the result.)
Paragraph Eight: The degrees and the remainder of the degrees of the five planets. (Subtract the excess values to get the degree remainder, multiply by the synodic month to get the degrees, simplify by the daily calculation method; the remainder is the degree remainder, and if it exceeds the synodic month, subtract the synodic month and the lunar mansion.)
Paragraph Nine: Month Record: 7285; Leap months: 7; Chapter months: 235; Months in a year: 12; Common method: 43026; Daily method: 1457; Number of meetings: 47; Synodic months: 215130; Lunar mansions: 145; Wood: Synodic rate: 6722.
This text describes an intricate astronomical calendar calculation method, involving many professional terms. Understanding it still requires a certain level of expertise.
Wow, what are all these numbers! It seems like ancient astronomical calculation records. Let's break it down sentence by sentence and put it into modern language.
Paragraph Three: This is the calculation result for the Earth (possibly referring to a celestial body or astronomical phenomenon). The circumference (周率) is 3,529, the daily rate is 3,653, totaling twelve months, which is approximately 53,843 for each month. According to the calculation method, the total number is 67,051, with a daily degree measurement of 278,581. The major lunar surplus is 54, the minor lunar surplus is 534, with 24 days in each month. The following numbers are also various calculation results, with specific meanings unclear.
Paragraph Four: Finally, this is the calculation result for Metal (possibly referring to a celestial body or astronomical phenomenon). The circumference (周率) is 9,022, the daily rate is 7,213, totaling nine months, with approximately 152,293 for each month. According to the calculation method, the total number is 171,418, with a daily degree measurement of 531,958. The major lunar surplus is 25, the minor lunar surplus is 1,129, with 27 days in each month. The subsequent numbers are still various calculation results, which I find difficult to understand. It must have been ancient astronomers who were so powerful to calculate these numbers!
In summary, this text records a series of astronomical calculation results, including circumference, daily rate, total months, lunar surplus, and various other terms and numerical values. The specific meanings need to be interpreted in conjunction with the background and astronomical knowledge at that time. Unfortunately, I cannot fully understand the meanings of these numbers at the moment. The circumference is 11,561, the daily rate is 1,834, with a total of one month. The lunar surplus is 211,331, the combined lunar method is 219,659, the daily degree is 680,942. The major lunar surplus is 29, the minor lunar surplus is 773, the entry month day is 28, the daily surplus is 641,967, the lunar virtual division is 684, the division is 1,676,345, the degree is 57, and the degree surplus is 641,967.
The method of calculating the conjunction of stars is as follows: first, multiply the year you want to calculate by the annual rate (周率). If the result can be divided by the daily rate, it means the conjunction amounts to one year; if it cannot be divided, the remainder is the conjunction's remainder. Then divide the conjunction remainder by the annual rate. If the result is 1, it means go back one year; if it is 2, go back two years; if the result is 0, then it is the current year. Subtracting the annual rate from the conjunction remainder yields the degree and minute. For the conjunction of Venus and Mercury, odd results indicate morning occurrences, while even results indicate evening occurrences.
Multiply the month and the month remainder by the conjunction. If the result can be divided by the monthly conjunction method, it means it is a full moon, and the remainder is the new monthly remainder. Subtract the accumulated months from the conjunction months, and the remaining is the entered month. Then multiply the intercalary month by the entered month. If the result can be divided by the intercalary month, it means there is an intercalary month. Subtract it from the entered month, then subtract the remaining part from the year; this represents the conjunction beyond the Tianzheng calculations. If it coincides with the intercalary month, use the new moon to guide the calculations.
Multiply the common method by the monthly remainder, then multiply the conjunction method by the new moon remainder, and then divide by the meeting number. If the result is divisible by the daily degree method, the result indicates the conjunction of stars within the month and day; if it cannot be divided, the remainder is the day remainder, recorded outside of the new moon. Multiply the week by the degree; if the result is divisible by the daily degree method, it equals one degree, and the remainder is recorded using the method of the previous five days. This is the method of calculating the conjunction of stars.
Next is the method of calculating the year: add the month and the month, add the month remainder and the month remainder. If the result can be divided by the monthly conjunction method, it means one year. If it cannot be divided, check the result. If it exceeds one year, subtract one year; if there is an intercalary month, add it; the remaining is the next year; if it exceeds another year, it corresponds to the year after that. Venus and Mercury, morning plus morning results in evening, while evening plus evening results in morning.
Add the new moon and conjunction remainder; if it exceeds a month, add either twenty-nine (for a large remainder) or seven hundred and seventy-three (for a small remainder). If the small remainder exceeds the daily rate, subtract it from the large remainder, using the same method as before.
Add the day and degree; add the day remainder and degree remainder. If the result is divisible by the daily degree method, it equals one degree.
Jupiter: It remains hidden for thirty-two days, totaling three million four hundred eighty-four thousand six hundred forty-six minutes; it appears for three hundred sixty-six days. The movements of these five planets are quite complex. Look at Jupiter, which moves retrograde for five degrees, totaling two million five hundred nine thousand nine hundred fifty-six minutes. It moves forward for forty degrees, but we must subtract the twelve degrees of retrograde motion, so it actually moves twenty-eight degrees.
Mars, on the other hand, has a period of retrograde motion lasting one hundred forty-three days, totaling nine hundred seventy-three thousand one hundred thirteen minutes. Its appearance lasts for six hundred thirty-six days. It moves retrograde for one hundred ten degrees, totaling four hundred seventy-eight thousand nine hundred ninety-eight minutes; it moves forward for three hundred twenty degrees, subtracting the seventeen degrees of retrograde motion, so it actually moves three hundred three degrees.
Saturn has a short period of retrograde motion of only thirty-three days, totaling sixteen thousand six hundred seventy-two minutes. However, its appearance lasts for three hundred forty-five days. It moves retrograde for three degrees, totaling one hundred seventy-three thousand three hundred forty-eight minutes; it moves forward for fifteen degrees, subtracting the six degrees of retrograde motion, so it actually moves nine degrees.
Venus is quite special; it remains hidden in the east each morning for eighty-two days, totaling eleven thousand three hundred ninety-eight minutes; then it appears in the west for a total of two hundred forty-six days, and these two hundred forty-six days do not require subtracting retrograde degrees. In the morning, it is hidden in the east, moving retrograde for one hundred degrees, also totaling eleven thousand three hundred ninety-eight minutes; then it appears in the east, its daily motion is the same as when it appears in the west, remaining hidden for ten days, with eight degrees of retrograde motion.
Finally, Mercury is hidden in the east each morning for thirty-three days, totaling six million twelve thousand five hundred five minutes; then it appears in the west for only thirty-two days, subtracting one degree of retrograde motion, so it actually moves thirty-one degrees. It moves retrograde for sixty-five degrees, totaling six million twelve thousand five hundred five minutes; then it appears in the east, its daily motion is the same as when it appears in the west, remaining invisible for eighteen days, with fourteen degrees of retrograde motion.
This calculation method is really confusing! To calculate the time and degree of appearance of a star, you need to first add the solar day degree to the remainder, then add it to the remainder of the star's conjunction degree. If the remainder reaches a full solar cycle, you will get a complete cycle, just like the previous calculation, and then you can calculate the time and degree of the star's appearance. Then multiply the denominator of the star's motion by the apparent degree. If there is still a remainder, continue according to the solar day method until the remainder is less than half, then consider it as one degree. Add the solar day to the fraction traveled, and if the fraction equals the denominator, add one degree. For retrograde and direct motion, the denominators are different, so use the denominator of the current motion to multiply the obtained fraction until the result equals the original denominator, thus obtaining the fraction of the current motion. The remaining values should be carried over from previous calculations, subtracting for retrograde motion. If the retrograde motion does not complete a degree, divide the fraction by its denominator, using the denominator as a proportion, with the fraction adjusting up or down, influencing each other. Any mention of "如盈约满" indicates precise division, while "去及除之" and "取尽之除" refer to exhaustive division.
In the morning, when the Sun and Jupiter rise together, Jupiter hides. Jupiter's orbit is in direct motion, with a period of 16 days. During this time, it travels for 1,742,323.2 minutes, while the planet travels 232,467 minutes. It then rises in the east after the Sun. Its speed varies, sometimes moving quickly, covering 58 minutes daily, and covering 11 degrees in 58 days, and sometimes slower at 9 minutes daily, covering 9 degrees in 58 days. Sometimes it stops for 25 days before moving again, or retrogrades at 1/7 minutes per day, moving 12 degrees in 84 days before stopping for another 25 days. Then it resumes direct motion, traveling 9 minutes daily, covering 9 degrees in 58 days. It then accelerates, moving at 11 minutes daily, covering 11 degrees in 58 days, appearing ahead of the Sun and setting in the west at dusk. After 16 days, it appears simultaneously with the Sun again, completing a cycle of 398 days total, traveling 3,484,646 minutes and covering 43 degrees and 2,509,956 minutes.
Next is Mars. In the morning, the sun and Mars appear at the same time, and Mars disappears. Mars is in direct motion, with a cycle of 71 days, during which it travels for a total of 1,489,868 minutes, covering 55 degrees in planetary movement over 1,242,860.5 minutes, and then rises in the east after the sun. Its speed varies, moving at a rate of 23 minutes and 14 seconds each day on fast days, covering a total of 112 degrees over 184 days; and moving at a rate of 23 minutes and 12 seconds each day on slow days, covering a total of 48 degrees over 92 days, sometimes stopping for 11 days. Then it retrogrades, moving back at a rate of 62 minutes and 17 seconds per day, covering 17 degrees in 62 days, then stops for 11 days, and moves forward again, moving 12 minutes each day, covering a total of 48 degrees over 92 days. Finally, it accelerates forward again, moving 14 minutes each day and covering a total of 112 degrees over 184 days, setting in the west in the evening. After 71 days, it aligns with the sun again, completing a cycle totaling 779 days, during which it travels 97,313 minutes, and the planet covers 414 degrees, totaling 478,998 minutes.
In the morning, Saturn and the sun appear at the same time. Saturn's trajectory is to move forward first, covering 112,2426.5 minutes in sixteen days, with the planet moving 1,995,864.5 minutes. At this time, Saturn can be seen in the east in the morning, behind the sun. When moving forward, Saturn moves at a rate of 35/3 minutes each day, covering a total of 7.5 degrees in 87.5 days, then stops for 34 days. It then retrogrades, moving 1/17 degrees each day, covering 6 degrees in 102 days. After another 34 days, it starts moving forward again, covering 1/3 degrees each day and 7.5 degrees in 87 days, appearing in the west in the evening when in front of the sun. In sixteen days, it covers 112,2426.5 minutes, with the planet moving 1,990,5864.5 minutes, then aligns with the sun again. One complete cycle is 378 days, which totals 166,272 minutes, with the planet covering 12 degrees, totaling 1,733,148 minutes.
In the morning, Venus and the sun appear at the same time. Venus initially goes into retrograde, and it retreats four degrees after five days; then it can be seen in the east in the morning, behind the sun. During its retrograde phase, it moves 3/5 degrees per day and retreats six degrees after ten days. It then stops for eight days. It then moves forward slowly, covering 33/46 degrees per day, totaling 33 degrees over 46 days. Its speed then increases, covering 15/91 degrees per day, totaling 160 degrees over 91 days. The speed continues to increase, moving 22/91 degrees per day, totaling 113 degrees over 91 days; at this point, it is behind the sun and is visible in the east in the morning. The total duration of forward movement is 41 days, during which it covers 56,954 minutes, with the planet also traveling 50 degrees over 56,954 minutes, then it appears simultaneously with the sun again. One conjunction lasts a total of 292 days, covering 56,954 minutes, with the planet also traversing the same distance.
In the evening, Venus and the sun appear at the same time. Venus initially moves forward, covering 56,954 minutes over 41 days; the planet travels 50 degrees over 56,954 minutes, visible in the west in the evening, positioned in front of the sun. The forward motion is quite rapid, moving 22/91 degrees per day, totaling 113 degrees over 91 days. Then the speed slows down, moving 1/15 degrees per day, totaling 160 degrees over 91 days, continuing to move forward. The speed slows down further, moving 33/46 degrees per day, totaling 33 degrees over 46 days. It then stops for eight days. It then goes into retrograde, moving 3/5 degrees each day, retreating six degrees after ten days; at this point, it is in front of the sun and is visible in the west during the evening. The retrograde speed is very fast, retreating four degrees after five days, then it appears simultaneously with the sun again. After two conjunction cycles, spanning a total of 584 days and covering 113,908 minutes, the planet also traverses the same distance.
In the morning, Mercury and the Sun conjunct. Then it seems to retreat, starting retrograde, retrograding seven degrees over nine days. At sunrise, it appears behind the Sun in the east. Then it continues retrograde, moving quickly, retreating at a rate of one degree per day. Pausing briefly, it stays still for two days. Then it begins to turn, going direct, moving slowly, covering eight-ninths of the Sun's distance per day, going forward eight degrees in nine days. The motion is direct. As it speeds up, it moves one and a quarter degrees each day, covering twenty-five degrees in twenty days, still positioned behind the Sun. In the morning, Mercury appears in the east, starting direct; after sixteen days, equivalent to six hundred forty-one million nine hundred sixty-seven minutes, it has moved thirty-two degrees six hundred forty-one million nine hundred sixty-seven minutes (original text, not translated), and ultimately conjuncts with the Sun again. The entire conjunction took fifty-seven days and six hundred forty-one million nine hundred sixty-seven minutes (original text, not translated), and the degree of Mercury's movement remains the same.
At night, Mercury conjuncts with the Sun. Then it appears to retreat, starting its direct motion for sixteen days, equivalent to six hundred forty-one million nine hundred sixty-seven minutes (original text, not translated); it has moved thirty-two degrees six hundred forty-one million nine hundred sixty-seven minutes (original text, not translated), and then at sunset, it appears in front of the Sun in the west. Then it continues direct, moving quickly, covering one degree plus a quarter each day, twenty-five degrees in twenty days, in the direct direction. The speed slows down, covering eight-ninths of the Sun's distance per day, moving forward eight degrees in nine days. Pausing briefly, it stays still for two days. Then it begins to turn, going retrograde, retrograding at a rate of one degree per day, still in front of the Sun; at night, it "retreats" in the west. Continuing retrograde, moving slowly, retreating seven degrees in nine days, and ultimately conjuncts with the Sun again. From one conjunction to the next, a total of one hundred fifteen days and six hundred one million two thousand five hundred five minutes elapses (original text, not translated), and the degree of Mercury's movement remains the same.
