First, write down the year, then multiply the remainder by the number of days you want to calculate. If the result is a multiple of the year, mark it as "lost product." If there is a remainder, add the remainder to the result of the "product" to get a new number "one." Then multiply it by the number of days you want to calculate. If the result is a multiple of "no result," you get a "large remainder"; if not, the remaining is a "small remainder." Use the "large remainder" to determine the date, counting the "no day" following the winter solstice.
Next, calculate the next "no day." Add 69 to the large remainder and 64 to the small remainder. If the result exceeds the specified limit, use the large remainder to calculate; if there is no remainder, this indicates the end of the calculation.
Multiply the number of years by the number of days you want to calculate, then subtract multiples of the week days. Divide the remaining number by the multiples of the year; the result is the degree. Start counting from the fifth degree of the constellation of the Ox, dividing the degree by the constellation degree. If it is insufficient for a full constellation, that indicates the position where the sun is at midnight.
To calculate the next day, add one degree to the degree, then divide the degree by the constellation; if the degree is not enough, subtract one degree, then add it to the multiples of the year.
Multiply the number of weeks in a month by the number of days you want to calculate, then subtract multiples of the week days. If it is a multiple of the year, you get the degree; if not, the remaining is the remainder. By following the above method, you can calculate the position of the moon at midnight on the first day of the month.
To calculate the next month, add 22 degrees and 258 minutes for a shorter month, and add 1 day, 13 degrees, and 217 minutes for a longer month. If it exceeds the specified limit, add an additional degree. In the last ten days of December, the moon is located between the Zhang and Xin constellations.
Multiply the number of years by the remainder of the new moon day; if the result is a multiple of the constellation, you get the large fraction; if not, the remaining is the small fraction. Subtract the degree of the new moon day at midnight from the large fraction; if the result is a multiple of the year, you can calculate the time and position of the conjunction of the sun and moon using the method described above.
To calculate the next month, add 29 degrees, 312 large fractions, and 25 small fractions. If the small fraction exceeds the constellation, add it to the large fraction; if the large fraction exceeds the multiple of the year, add it to the degree, then divide the large fraction by the constellation.
To calculate the position of the waxing crescent moon, add 7 degrees and 225 minutes to the degree of the conjunction, as well as 17.5 small fractions. By following the same method, you can calculate the full moon, third quarter moon, and the position of the conjunction of the next month.
To calculate the position of the waxing crescent moon, add 98 degrees, 480 minutes, and 41 seconds to the conjunction's degree, and follow the same method to calculate the position of the first quarter moon. By continuing this process, you can calculate the position of the full moon, last quarter moon, and the conjunction of the next month.
To calculate the position of solar and lunar eclipses, multiply the multiple of the year by the number of hours in the night of the nearest solar term, then divide by 200 to get the bright minutes. Subtract the multiple of the year by the number of days, subtract the number of months by the number of weeks, and the remainder is the dark minutes. Add the bright minutes and dark minutes to midnight, and calculate the degrees according to the method above.
First, set a date in the Shangyuan year, then subtract the number of years you want to calculate. Multiply the remaining number of years by the rate; if the result is a multiple of the total years, record it as a total eclipse. If there is a remainder, add it to the result of the total eclipse to get a new number. Then multiply it by the number of months; if the result is a multiple of the rate, you get the cumulative months; if not a multiple, the remainder is the month remainder. Multiply the remaining number of years by the number of leap months; if the result is a multiple of the number of leap years, you get the cumulative leap months. Subtract the cumulative months from the cumulative leap months to find the result, and subtract the number of years; the remaining is the number of days from the beginning of Tianzheng.
To calculate the next solar eclipse, add 5 months; the month remainder is 1635. If it exceeds the rate, add a month; this month is the full moon.
On the day of the winter solstice, double the small remainder to get the large remainder; this is the day when the Kan hexagram is in charge. Then add 175 to the small remainder and subtract from the large remainder according to the algorithm of the Qian hexagram; this is the day governed by the Zhongfu hexagram.
Next, calculate the next hexagram by adding 6 to the large remainder and 103 to the small remainder. The four positive hexagrams double the small remainder according to the day they are in charge.
List out the large and small remainders of the winter solstice; add 27 to the large remainder, add 927 to the small remainder, and subtract 2356 from the large remainder to get the day governed by the Earth hexagram. Add 18 to the large remainder, add 618 to the small remainder, and get the day when the Wood hexagram of Lichun is in charge. Add 73 to the large remainder, add 116 to the small remainder, and get the Earth hexagram again. If you continue adding after the Earth hexagram, you can get the Fire hexagram, and set aside the Metal and Water hexagrams.
Multiply the small remainder by 12 to get a Chen (Earthly Branch), and count from Zi (midnight); this calculation is performed externally, with the new moon, first quarter, and full moon used to determine the small remainder.
Using 100 multiplied by the small fraction, you get a quarter of an hour. If it is less than one-tenth of the total, then seek the fraction, referencing the recent solar terms, starting from midnight until the water level at night is insufficient, using the most recent values.
The calculations have both gains and losses; gain means addition, loss means subtraction of the results. There are differences in gain and loss, starting from two degrees, increasing or decreasing every four degrees, with each reduction halved. After three reductions, stop when the difference reaches three, and after five degrees, return to the initial state.
The moon's speed varies, repeating in cycles with a consistent pattern. Numbers can be obtained from various figures between heaven and earth, multiplied by the remainder rate and then squared. If it equals the calculated number, divide by one to get the lunar phase. Subtract it from the total of the week, then divide by the lunar week to get the number of days. The speed of the moon experiences decay, and changes are a trend. Adding the decay value to the lunar motion rate gives the daily rotation degree. The decay values added together yield the profit and loss rate. Profit means increase, loss means decrease, and surplus refers to accumulation. Multiply half of a small week by the common method; if it equals the common number, divide by one, then subtract it from the historical week to get the new moon phase.
The following table shows daily rotation degrees, decay, profit and loss rate, surplus accumulation, and lunar motion:
| Daily Rotation Degrees | Decay | Profit and Loss Rate | Surplus Accumulation | Lunar Motion |
|---|---|---|---|---|
| One day fourteen degrees ten minutes | One reduction | Profit twenty-two | Initial surplus | Two hundred seventy-six |
| Two days fourteen degrees nine minutes | Two reductions | Profit twenty-one | Surplus twenty-two | Two hundred seventy-five |
| Three days fourteen degrees seven minutes | Three reductions | Profit nineteen | Surplus forty-three | Two hundred seventy-three |
| Four days fourteen degrees four minutes | Four reductions | Profit sixteen | Surplus sixty-two | Two hundred seventy |
| Five days fourteen degrees | Four reductions | Profit twelve | Surplus seventy-eight | Two hundred sixty-six |
| Six days thirteen degrees fifteen minutes | Four reductions | Profit eight | Surplus ninety | Two hundred sixty-two |
| Seven days thirteen degrees eleven minutes | Four reductions | Profit four | Surplus ninety-eight | Two hundred fifty-eight |
| Eight days thirteen degrees seven minutes | Four reductions | Loss | Surplus one hundred two | Two hundred fifty-four |
On September 9th, it is thirteen degrees three minutes, subtract four, then add four, resulting in a surplus of one hundred two and a total of two hundred fifty.
On October 10th, it is 12 degrees 18 minutes, after subtracting 3 and then adding 8, the result is 98, which brings the total to 246.
On October 11th, it is 12 degrees 15 minutes, after subtracting 4 and then adding 11, the result is 90, which brings the total to 243.
On October 12th, it is 12 degrees 11 minutes, after subtracting 3 and then adding 15, the result is 79, which brings the total to 239.
On October 13th, it is 12 degrees 8 minutes, after subtracting 2 and then adding 18, the result is 64, which brings the total to 236.
On October 14th, it is 12 degrees 6 minutes, after subtracting 1 and then adding 20, the result is 46, which brings the total to 234.
On October 15th, it is 12 degrees 5 minutes, adding 1 and subtracting 21, the result is 26, which brings the total to 233.
On October 16th, it is 12 degrees 6 minutes, adding 2 and subtracting 20 (Note: If there isn't enough to subtract, add 5 to the surplus instead. Since the initial subtraction was 20 and there wasn't enough, we adjust accordingly). The surplus is 5 after adjusting for the initial subtraction of 20, which brings the total to 234.
On October 17th, it is 12 degrees 8 minutes, adding 3, the result is 18, subtracting 15, which brings the total to 236.
On October 18th, it is 12 degrees 11 minutes, adding 4, the result is 15, subtracting 23, which brings the total to 239.
On October 19th, it is 12 degrees 15 minutes, adding 3, the result is 11, subtracting 48, which brings the total to 243.
On October 20th, it is 12 degrees 18 minutes, adding 4, the result is 8, subtracting 59, which brings the total to 246.
On October 21st, it is 13 degrees 3 minutes, adding 4, the result is 4, subtracting 67, which brings the total to 250.
On October 22nd, it is 13 degrees 7 minutes, adding 4 and subtracting a certain amount, which brings the total to 254 after reducing 71.
On October 23rd, it is 13 degrees 11 minutes, adding 4 and subtracting 4, which brings the total to 258 after reducing 71.
On October 24th, it is 13 degrees 15 minutes, adding 4 and subtracting 8, which brings the total to 262 after reducing 67.
On October 25th, it is 14 degrees, adding 4 and subtracting 12, which brings the total to 266 after reducing 59.
On October 26th, it is 14 degrees 4 minutes, adding 3 and subtracting 16, which results in reducing the total by 47, bringing the total to 270.
On the twenty-seventh of October, it is 14 degrees and 7 minutes. This is the third initial addition, adding three major Sundays, subtracting nineteen, reducing by thirty-one, for a total of 273.
Sunday division is 14 degrees (9 minutes), with less addition, subtracting twenty-one, reducing by twelve, for a total of 275.
Sunday division, 3,303.
Zhou Xu, 2,666.
Sunday method, 5,969.
Total for the week, 185,039.
Historical calculation, 164,466.
Less big method, 1,101.
Shuo Xing Da Fen, 10,801.
Small remainder, 25.
Week and a half, 127. This part consists of numbers and does not require translation.
The next part describes the calculation method; in contemporary terms, it is calculating the next month's New Moon (lunar calendar first day) based on the previous month's New Moon, as well as the dates of Full Moon (lunar calendar fifteenth and sixteenth), and some related correction values. The specific steps are cumbersome, involving many professional terms in astronomical calendars, such as "big and small divisions," "total number," "week method," "profit and loss accumulation," and so on, which are difficult to completely express in colloquial language. This passage describes a complex calculation process, aiming to accurately calculate the lunar date.
Next is the calculation for the next month, adding one day, leaving 5,832, small remainder 25. This part is the calculation result; in simple terms, it calculates that the first day of next month is one day later than this month’s first day, with some remainder.
Next, calculate Full Moon (fifteenth or sixteenth), adding seven days respectively, with a remainder of 2,283, small remainder twenty-nine and a half. According to the rules, the remainder is converted into days, and if it exceeds 27 days, we subtract it, and the remaining is distributed proportionally.
This section describes a more complex correction process, using professional terms such as "Zhang Sui," "profit and loss accumulation," and "profit and loss ratio," aiming to refine the calculations for greater accuracy. It involves multiple calculations and adjustments to the results, with the ultimate goal of obtaining more accurate New Moon, Full Moon dates, and related values. The core idea is to address calculation errors through a series of adjustments to achieve more accurate lunar dates.
Next is a further refining of the new moon time based on previous calculations, precise to midnight. This part of the calculation is very complex, involving specialized terms such as "common multiple," "week method," "profit and loss rate," and "decline rate," with the aim of determining the exact time of the new moon (the first day of the month).
The following section continues to describe the calculation methods for subsequent dates and how to infer future date values based on previous calculations. This part still involves complex calculations and adjustments, to ensure the accuracy of calendar calculations. The entire calculation process is interlinked, requiring a deep understanding of astronomical calendars to comprehend.
This text describes the ancient methods of calendar calculation, which are quite complex. Let's go through it sentence by sentence and express it in modern terms.
First paragraph: The length of each day varies, so adjustments must be made based on different days. The time for each day is totaled, and if it exceeds one day, the excess is subtracted; if it falls short of one day, the deficiency is added. This is similar to the changing lengths of days throughout the four seasons. After calculating for one day, if the time does not exactly equal one day, the total time is multiplied by a coefficient for further adjustment until it exactly equals one day.
Second paragraph: Adjust the daily addition and subtraction values according to the pattern of daily time variation. If the final calculated time is insufficient or exceeds one day, adjustments must be reversed, as previously mentioned, by adding or subtracting.
Third paragraph: Calculate the lengths of day and night. Multiply the moon's travel distance by the nighttime length of a specific solar term, then divide by 200 to obtain the daytime duration. Subtract the daytime duration from the moon's travel distance to get the nighttime duration. The calculation method is similar to the previous one, also using the total time multiplied by a coefficient for further adjustment.
Fourth paragraph: The moon's travel cycle and the pattern of its phases is used to calculate the days in the calendar. The moon's travel cycle is multiplied by the synodic month (the time from one new moon to the next), with further adjustments to determine the daily time.
From the fifth paragraph to the end: Next is a table that records the values that need to be added or subtracted each day, as well as some important parameters. The words "Yin Yang Calendar, Decline, Profit and Loss Rate, and Combined Values" are the titles, indicating the decline, profit and loss rate, and some auxiliary numbers of the Yin Yang Calendar. The numbers following indicate the values that need to be added or subtracted each day, as well as some limits and differential values. "Method of Shao Da, 473" refers to a specific calculation method, with the value being 473. Finally, important parameters such as calendar cycles, differences, conjunctions, and differentials are listed. These numbers are very professional and require a deep understanding of ancient calendars to grasp their specific meanings. In short, these numbers describe the precise calculation process in ancient calendars to ensure accuracy.
Let's first talk about how to calculate the days from the beginning of the year to the accumulation of months. I first multiply the new moon day (lunar first day) and the conjunction of new moons (the time between two new moons) by the differential (a very small value), and when the differential is full, I use the conjunction of new moons to offset it. When the count is complete, I subtract one week (which is one month), and the remaining days that are less than a month correspond to the solar calendar days; when the count is complete, I subtract it, and the remaining days are the days in the lunar calendar. The remaining days are calculated based on the number of days in a month, and any days beyond that need to calculate the remaining days after entering the calendar, expressing any that are less than a day as decimals.
Then add two days, with a remainder of 2580 days and a differential of 914. According to the method of calculating days, subtract 13 when it reaches 13, and calculate the decimal part of the days proportionally for the remaining days. This is how the Yin Yang Calendar converts back and forth, with the entry limits of the calendar listed first, the remaining days at the front, and the limits and remaining days at the back, indicating that the moon has reached the middle position.
Next, calculate the speed, gain and loss, magnitude, and other values of entering the calendar separately, multiplying the constant by the small fraction to get the differential, then adjust the remaining days in the Yin Yang Calendar according to the gain and loss values. If the remaining days are insufficient or excessive, adjust them accordingly to reach the correct count. Multiply the determined remaining days by the profit and loss rate (a ratio), and if one month is considered as 1, then using the profit and loss rate along with this number will determine the additional time constant (a correction value).
By multiplying the difference rate (a ratio) by the decimal remainder of the new moon day, calculating the value of 1 using differential methods, then subtracting the remaining days of the lunar calendar. If that isn't enough, add the number of days in a month, then subtract one day. By adding the decimal portion of the days and simplifying the differential with the total, this gives the time of the new moon at midnight when entering the calendar.
For the calculation of the second day, add one day; the remaining days and the total both equal 31. Subtract the total from the remaining days based on the total; when the remaining days are full, subtract one month, add one day, and the calendar calculation ends here. Subtract the decimal portion of the days when the remaining days are full of the decimal portion; this marks the beginning of the calendar. For those whose decimal portion of days is not full, just use it directly, then add 2720; the total will be 31; this is the calculation for entering the next calendar.
By multiplying a constant by the surplus and remaining values of the lunar calendar, if the remaining value equals half a week, this is considered the total, adding and subtracting the remaining days of the lunar calendar according to the surplus of yin and yang. If the remaining days are not enough or too many, adjust the days to determine. Multiply the determined remaining days by the profit and loss rate; if one month is considered as 1, then using the profit and loss rate together with this number, the midnight constant (a correction value) can be calculated.
Multiply the profit and loss rate by the nighttime measurement of the recent solar terms (an ancient timing tool); 1/200 is regarded as daytime, subtract this number from the profit and loss rate to calculate the night, then calculate the dusk and dawn constant (correction value of day and night) using the profit and loss midnight number.
Divide the overtime or dusk/dawn constant by 12 to get degrees; one-third of the remaining number is regarded as weak, and less than 1 is considered strong; two weak are considered weak. The resulting calculation indicates the degree to which the moon has moved away from the ecliptic. The solar calendar uses the ecliptic calendar where the sun is located, and the lunar calendar uses subtraction to calculate the degree of the moon leaving the ecliptic pole. Assign positive values for strong and negative values for weak; combine the strong and weak values together, adding the same names and subtracting different names. When subtracting, subtract the same names, add different names; if there are no opposites, add two strong and subtract one weak.
From the year Ji Chou during the Upper Yuan period to the year Bing Xu in the Jian'an period, a total of 7378 years have been accumulated.
Ji Chou, Wu Yin, Ding Mao, Bing Chen, Yi Si, Jia Wu, Gui Wei.
Ren Shen, Xin You, Geng Xu, Ji Hai, Wu Zi, Ding Chou, Bing Yin—these are all years; I won’t go into detail. Next are the five elements: wood corresponds to Jupiter, fire corresponds to the Fire Star, earth corresponds to the Earth Star, metal corresponds to Venus, and water corresponds to Mercury. Each star has a cycle of movement and daily speed of movement; these data all need to be calculated. How to calculate? First, calculate how many degrees each star moves in a year, then calculate how many degrees each star moves in a month, and finally calculate how many degrees each star moves in a day. You also need to calculate the Dipper division, which is related to the cycle of the stars.
Then you need to calculate the surplus and deficit residues of the five stars, that is, how many degrees they have left when they reach the end of each month. This calculation method is quite complex and requires various data calculated earlier, including the excess and the deficit. The remainder is what exceeds the whole number, and the deficit is the part that falls short of the integer value; subtracting the excess from sixty gives the deficit. Next, calculate the number of days and remaining days that the five stars move in each month; this requires complex calculations using the various data calculated earlier, and finally calculate the degrees and remaining degrees of movement of each star. If it exceeds the zodiac (360 degrees), it must be subtracted from the zodiac, and also consider the Dipper division.
Next is a list of some key data: the record for months is 7285, the leap month is 7, the chapter month is 235, the year center is 12, the common method is 43026, the daily method is 1457, the meeting number is 47, the zodiac is 215130, and the Dipper division is 145. These numbers are constants used in the calculation process.
Below are the specific data about Jupiter: the weekly rate is 6722, the daily rate is 7341, the synodic month is 13, the lunar surplus is 64810, the synodic month method is 127718, the daily degree method is 3959258, the lunar excess is 23, the lunar deficit is 1370, the entry day of the month is 15, the daily remainder is 3484646, the virtual division of the lunar cycle is 150, the Dipper division is 974690, the degree is 33, and the degree remainder is 2509956.
Then the data for Mars: the weekly rate is 3447, the daily rate is 7271, the synodic month is 26, the lunar surplus is 25627, the synodic month method is 64733, the daily degree method is 2067223, the lunar excess is 47, the lunar deficit is 1157, the entry day of the month is 12, the daily remainder is 973113, the virtual division of the lunar cycle is 300, the Dipper division is 494115, and the degree is 48. This data helps astronomers calculate the paths of the planets.
These numbers may look complex, but in reality, they are methods used by ancient astronomers to predict the positions of the planets. Through these complex calculations, they determined the positions of the planets in the sky, which were essential for creating calendars and guiding agricultural practices.
Goodness, these densely packed numbers are making my head spin! Let me translate it for you in plain language, sentence by sentence.
First paragraph:
"Degree remainder, 1,999,706." This means that the remaining degrees of something are 1,999,706. What exactly this refers to will be explained later.
"Earth: circumference value, 3,529." This refers to the Earth (possibly referring to the Earth element in the Five Elements theory, or a specific celestial body), with a circumference value of 3,529. Circumference can be understood as a value within a cycle.
"Daily rate, 3,653." The value for Earth's daily rate is 3,653.
"In total, there are 12 months." Altogether, there are 12 months.
"Month remainder, 53,843." The value remaining after 12 months is 53,843.
"Total month calculation method, 67,051." The calculated value using the method for months is 67,051.
"Daily degree method, 2,078,581." The value obtained using the method for daily degrees is 2,078,581.
"New moon remainder, 54." The larger remainder for a new moon day is 54.
"New moon small remainder, 534." The smaller remaining value for a new moon day is 534.
Second paragraph:
"Entering month day, 24." The number of days before entering a new month is 24.
"Daily remainder, 166,272." The remaining number of days is 166,272.
"New moon virtual division value, 923." The virtual division value for a new moon is 923.
"Dou division value, 511,705." The Dou division value is 511,705.
"Degree value, 12." The degree value is 12.
"Degree remainder, 1,073,148." The remaining degrees value is 1,073,148.
"Venus: circumference value, 9,022." The circumference value of Venus is 9,022. The calculation method is similar to that of Earth.
Third paragraph:
"Daily rate, 7,213." The daily rate for Venus is 7,213.
"Total months: nine." The remaining value after nine months is one hundred fifty-two thousand two hundred ninety-three.
"Value from the combined month method: one hundred seventy-one thousand four hundred eighteen." The value obtained by the daily method is five million three hundred thirteen thousand nine hundred fifty-eight.
"Larger remainder on the new moon: twenty-five." The smaller remainder on the new moon is one thousand one hundred twenty-nine.
Fourth paragraph:
"Number of days in the month: twenty-seven." The remaining days value is fifty-six thousand nine hundred fifty-four.
"Virtual division on the new moon: three hundred twenty-eight." Value from the Big Dipper division: one hundred thirty thousand eight hundred ninety.
"Degrees: two hundred ninety-two." The remaining degrees value is fifty-six thousand nine hundred fifty-four.
"Orbital rate of Mercury: eleven thousand five hundred sixty-one."
Fifth paragraph:
"Daily value of Mercury: one thousand eight hundred thirty-four." Total months: one. The remaining value after one month is two hundred eleven thousand three hundred thirty-one.
"Value from the combined month method: two hundred nineteen thousand six hundred fifty-nine." The value obtained by the daily method is six million eight hundred thousand four hundred twenty-nine.
"Larger remainder on the new moon: twenty-nine." The smaller remainder on the new moon is seven hundred seventy-three.
Sixth paragraph:
"Number of days in the month: twenty-eight."
"Remaining days value: six million four hundred nineteen thousand six hundred seventy." The remaining number of days is six million four hundred nineteen thousand six hundred seventy.
"New moon fraction: six hundred eighty-four." The new moon fraction is six hundred eighty-four.
"Dou fraction value: one hundred sixty-seven thousand six hundred forty-five." The Dou fraction value is one hundred sixty-seven thousand six hundred forty-five.
"Degree: fifty-seven." The degree is fifty-seven.
"Remaining degree: six million four hundred nineteen thousand six hundred seventy." The remaining degree is six million four hundred nineteen thousand six hundred seventy.
"Set the year sought for the upper element and multiply by the circumference ratio; the full day ratio yields one, called accumulation, which is not exhausted for the accumulated remainder. Divide by the circumference ratio to get one, the star accumulation of previous years. Two, the accumulation of previous years. If nothing is obtained, accumulate for that year. The accumulated remainder minus the circumference ratio is the degree fraction. Gold and water accumulate; odd numbers indicate morning, even numbers indicate evening." This section summarizes a complex calculation method that requires specific algorithms for understanding. Simply put, it involves a series of calculations based on the upper element (an era in ancient calendars) and the year, using the circumference ratio to obtain the final result. The results for Venus and Mercury indicate odd numbers for morning and even numbers for evening.
Now, let's break down these astronomical calculation steps into plain language step by step.
First paragraph: First, multiply the number of months by the remaining months to get a total. If this total can be divided by the accumulated month method, it indicates a full moon, and the remainder is the remaining month. Then subtract the accumulated month number from the recorded month number; the remainder is the recorded month. Next, multiply the leap month number by this result; if an integer multiple of the leap month number is obtained, it indicates a leap month, which should be subtracted from the recorded month. The remaining part is adjusted within the year, called the accumulated month outside of the standard day calculation. In cases of leap month transitions, adjustments are made using the new moon day.
Second paragraph: Multiply the remaining month by the common method, then multiply the new moon day fraction by the accumulated month method; add these two results together and simplify using the meeting number. If the result yields an integer multiple of the daily degree method, it indicates that the date of the celestial body entering the month and day has arrived. If the result falls short of the daily degree method, the remainder is the remaining days, referred to as the new moon calculation outside.
Third paragraph: Multiply the weeks by the degree fraction; if an integer multiple of the daily degree method is obtained, one degree is achieved, and the remainder is noted. Record this degree in the fifth position relative to the ox.
Paragraph Four: The above is the calculation method for seeking the conjunction calculation method of celestial bodies. Next is another calculation method: add up the number of months and the remainders of the months. If the sum is a multiple of the conjunction calculation method, it signifies a complete month. If it does not reach a year, it is combined within that year. If it completes a year, it is subtracted. If there is a leap month, it should be considered, and the remaining part is placed in the following year. If it completes again, it is placed in the next two years. For Venus and Mercury, adding morning gives evening, and adding evening gives morning. (This refers to the conversion of Venus and Mercury from morning stars to evening stars).
Paragraph Five: Add the remainders of the new moon and conjunction days. If it exceeds a month, add 29 to the larger remainder and 773 to the smaller remainder. If the smaller remainder can be divided by the daily method, subtract it from the larger remainder, using the previously described method.
Paragraph Six: Add the new moon day and its remainder, then add the conjunction day and the remainder. If the remainder can be divided by the daily method, one day is obtained. If the previous conjunction's smaller remainder completes a virtual part, subtract one day. If the subsequent smaller remainder exceeds 773, subtract 29 days. If it does not complete, subtract 30 days, and the remaining is the new moon day for the next conjunction.
Paragraph Seven: Add up the degree values and their remainders. If it can be divided by the daily method, one degree is obtained.
Paragraph Eight: The following are specific data for Jupiter, Mars, Saturn, and Venus: Jupiter retrogrades for 32 days, 3,484,646 minutes; it directs for 366 days; it retrogrades for 5 degrees, 2,509,956 minutes; it directs for 40 degrees. (Retrograde 12 degrees, actual movement 28 degrees). Mars retrogrades for 143 days, 973,013 minutes; it directs for 636 days; it retrogrades for 110 degrees, 478,998 minutes; it directs for 320 degrees. (Retrograde 17 degrees, actual movement 303 degrees). Saturn retrogrades for 33 days, 166,272 minutes; it directs for 345 days; it retrogrades for 3 degrees, 173,148 minutes; it directs for 15 degrees. (Retrograde 6 degrees, actual movement 9 degrees).
Venus: Venus is in conjunction in the east for 82 days, 113,908 minutes; then it appears in the west for 246 days. (Retrograde for 6 degrees, actually moves forward 246 degrees.) In the morning, it moves 100 degrees, 113,908 minutes; then appears in the east. (The Sun's movement is westward, so it is in conjunction for 10 days, retreats 8 degrees.)
Mercury appears in the morning for 33 days, covering a total of 6,012,505 minutes (I don't know what unit this is, but it's a very precise number). Then it appears in the west for 32 days. (Subtracting 1 degree here results in a final movement of 32 degrees.) Then it moves forward 65 degrees, still 6,012,505 minutes. Then it appears in the east. Its speed in the west is the same as in the east; it stays in the east for 18 days, then retreats 14 degrees.
The calculation method for Mercury's movement is as follows: add the daily movement degree of Mercury to the remaining degrees, then add the degree difference between Mercury and the Sun. If this sum meets the standard for daily movement, it counts as one day. Continue this calculation to determine when Mercury appears and how far it has moved. Multiply Mercury's movement denominator by its appearance degree, and if the remaining part can be divided by the standard daily movement degree to get a whole number, then it's considered a day. Add up the daily movement degrees; if it reaches one degree, then add one more degree. The methods for direct and retrograde motion differ: multiply its current denominator by the previous degrees, then divide by the previous denominator to get its current movement degree. If Mercury remains stationary, use the previous data; if it is retrograde, subtract accordingly. If Mercury's movement degrees are insufficient, use the Big Dipper to adjust the degrees, applying its movement denominator as a proportion; this will influence the degrees accordingly. In summary, terms like "full moon" are used for precise calculations, while "remove and divide, take the remainder" refers to complete division.
Jupiter, in the morning, is alongside the sun, then it disappears, moving forward at a fast speed, covering a total of 16 days and traversing 174,233 minutes. The planet moves 2 degrees, totaling 323,467 minutes, then in the morning it appears in the east, behind the sun. Moving forward, it traverses 11/58 degrees each day; it takes 58 days to travel 11 degrees. Then it moves forward again, but at a slower speed, moving 9 minutes each day; it takes 58 days to travel 9 degrees. It then remains stationary for 25 days before it starts moving again. Moving backward, it moves 1/7 of a degree each day; after 84 days, it retreats by 12 degrees. It then stops again and resumes moving forward after another 25 days, traversing 9/58 degrees each day; it takes 58 days to travel 9 degrees. Moving forward at a fast speed, it traverses 11 minutes each day; it takes 58 days to travel 11 degrees, appearing in front of the sun and disappearing in the west at night. In total, over 16 days, it covers 174,233 minutes, and the planet moves 2 degrees, totaling 323,467 minutes, and then it aligns with the sun again. The entire cycle lasts 398 days, during which it covers 348,464 minutes, and the planet traverses 43 degrees, totaling 250,956 minutes.
In the morning, the sun met Mars, and Mars went dark. Then it began to move forward, traveling for 71 days, and traveled a distance of 1,489,868 minutes, equivalent to 55 degrees and 242,860.5 minutes along its orbital path. After that, people could see it in the east at sunrise, positioned behind the sun. During its forward motion, Mars traveled 14 minutes and 23 seconds each day, covering 112 degrees in 184 days. Then it slowed down, moving 12 minutes each day, covering 48 degrees in 92 days. Next, Mars stopped for 11 days. After that, it began to move in retrograde, traveling 17/62 of a minute each day, moving backward 17 degrees in 62 days. Then it stopped again for 11 days, after which it resumed forward motion, traveling 12 minutes each day, covering 48 degrees in 92 days. Once again moving forward, it accelerated, traveling 14 minutes each day, covering 112 degrees in 184 days. At this point, it had moved in front of the sun and set in the west in the evening. After another 71 days, traveling a distance of 1,489,868 minutes, equivalent to 55 degrees and 242,860.5 minutes along its orbital path, it encountered the sun again. In total, this cycle lasted 779 days and 97,313 minutes, moving 414 degrees and 478,998 minutes along its orbital path.
In the morning, the sun met Saturn, and Saturn went dark. Then it began to move forward, traveling for 16 days, and traveled a distance of 1,122,426.5 minutes, equivalent to 1 degree and 1,995,864.5 minutes along its orbital path. After that, people could see it in the east at sunrise, positioned behind the sun. During its forward motion, Saturn traveled 3 minutes and 35 seconds each day, covering 7.5 degrees in 87.5 days. Then it stopped for 34 days. After that, it began to move in retrograde, traveling 1/17 of a minute each day, moving backward 6 degrees in 102 days. After another 34 days, it resumed forward motion, traveling 3 minutes each day, covering 7.5 degrees in 87 days. At this point, it had moved in front of the sun and set in the west in the evening. After another 16 days, traveling a distance of 1,122,426.5 minutes, equivalent to 1 degree and 1,995,864.5 minutes along its orbital path, it encountered the sun again. In total, this cycle lasted 378 days and 166,272 minutes, moving 12 degrees and 1,733,148 minutes along its orbital path.
Venus, when it meets the sun in the morning, first dips below the horizon, then goes retrograde, receding four degrees over five days, and then you can see it in the east, just behind the sun in the morning. During its retrograde phase, it moves three-fifths of a degree each day, retreating six degrees in ten days. Then it stops for eight days. Then it resumes direct motion, moving thirty-three degrees over forty-six days. When it speeds up, it travels one degree and fifteen-ninths each day, covering one hundred sixty degrees in ninety-one days. Then it continues to move forward, faster, covering one hundred thirteen degrees in ninety-one days; at this time, it is positioned behind the sun, visible in the east during the morning. In its forward motion, it travels one fifty-six thousand nine hundred and fifty-fourth of a complete orbit in forty-one days; the planet also moves fifty degrees in one fifty-six thousand nine hundred and fifty-fourth of a circle, then it aligns with the sun again. One alignment takes a total of two hundred ninety-two days and one fifty-six thousand nine hundred and fifty-fourth of a complete orbit; the planet is the same.
When Venus meets the sun in the evening, it first dips low, then moves forward, traveling one fifty-six thousand nine hundred and fifty-fourth of a complete orbit in forty-one days; the planet also moves fifty degrees in one fifty-six thousand nine hundred and fifty-fourth of a circle, then in the evening you can see it in the west, in front of the sun. Moving forward quickly, it covers one hundred thirteen degrees in ninety-one days. Then it continues to move forward, but the speed slows down, moving one degree and fifteenth of a degree each day, covering one hundred sixty degrees in ninety-one days to move forward. When moving slowly, it moves forty-six-thirds of thirty-three degrees each day, moving thirty-three degrees in forty-six days. Then it stops again for eight days. Then it goes retrograde, moving five-thirds of a degree each day, receding six degrees in ten days; at this time, it is in front of the sun, appearing in the west in the evening, moving retrograde quickly, receding four degrees in five days, then it aligns with the sun again. After two alignments, a total of five hundred eighty-four days and eleven thousand three hundred ninety-eighths of a complete orbit; the planet is the same.
Mercury, when it meets the sun in the morning, first hides, then retrogrades, retreating seven degrees in the sky over nine days. In the morning, it can be seen in the east, behind the sun. It continues to retrograde, moving quickly, retreating one degree per day. Then it stops moving for two days. After that, it goes direct, moving slowly at a rate of eight-ninths of a degree per day; after nine days, it moves eight degrees and goes direct. When it moves quickly, it covers one and a quarter degrees per day, totaling twenty-five degrees in twenty days; at this point, it is behind the sun and appears in the east in the morning. During its direct motion, it covers six hundred forty-one million nine hundred sixty-seven fractions of a circle in sixteen days, while the planet also covers thirty-two degrees and six hundred forty-one million nine hundred sixty-seven fractions of a circle, then it meets the sun again. In one meeting, it covers fifty-seven days and six hundred forty-one million nine hundred sixty-seven fractions of a circle, and the planet follows the same pattern.
Mercury, when it sets with the sun, then goes into hiding. Its movement pattern is as follows: in sixteen days, it covers thirty-two degrees and six hundred forty-one million nine hundred sixty-seven fractions of a degree. In the evening, it can be seen in the west, always positioned ahead of the sun. When it moves quickly, it covers one and a quarter degrees per day, totaling twenty-five degrees in twenty days. When moving slowly, it covers eight-sevenths of a degree per day, taking nine days to cover eight degrees. Sometimes it stops and doesn't move for two days.
Then it retrogrades, moving backwards, retreating one degree per day, still in front of the sun, and in the evening, it can be seen hiding in the west. During retrograde motion, it also moves slowly, taking nine days to retreat seven degrees, ultimately meeting the sun again. From one meeting to the next, it takes a total of one hundred fifteen days and six hundred one million two thousand five hundred five fractions of a day; the cycle of Mercury's movement follows this pattern.
