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In how many years BCE (the specific year is not mentioned in the original text, so "how many years BCE" is used here), when calculating the calendar, first calculate the number of days in the past year, and then multiply the average number of days per year by the remaining years. If the calculated number of days exceeds the number of days in a year, add one year. Then, multiply the average number of days per month by the number of years to get the total number of months, and note down the remaining days if they are less than a month. Multiply the number of leap months by the remaining years to get the total number of leap months, then subtract this from the total number of months; the remaining days will be used to adjust the calendar; if they are insufficient, counting will start from the first month.
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To predict the next solar eclipse, add five months; the remaining months are 1635, which is enough for an average month, and this month is the full moon (the fifteenth day of the lunar calendar). Because the remainder from the winter solstice is relatively large, multiply the smaller remainder by two; this corresponds to the Kan hexagram day. Adding the smaller remainder of 175 meets the standard of the Qian hexagram, so calculate according to the larger remainder, which is the day of the Zhongfu hexagram.
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To determine the next hexagram, add the larger remainder of 6 and the smaller remainder of 103 to each hexagram. The four primary hexagrams are calculated based on the remainder of the middle day, multiplying the smaller remainder by two.
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List the large and small remainders from the winter solstice, adding the large remainder of 27 and the small remainder of 927; once it reaches 2356, use the large remainder for calculations, which is the day of the Earth element. Adding the large remainder of 18 and the small remainder of 618 gives the day of the Spring Wood element. Adding the large remainder of 73 and the small remainder of 116 gives another Earth element day. Adding the numbers for the Earth element then leads to the Fire element, and similarly for the Metal and Water elements.
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Multiply 12 by the smaller remainder; if it meets the standard for a full hour, you get an hour starting from midnight, which is another calculation method. The new moon day, crescent moon day, and full moon day are used to determine the smaller remainder. Multiply 100 by the smaller remainder; if it meets the standard for a quarter of an hour, you get a quarter of an hour; if insufficient, calculate using one-tenth, then calculate the minutes, referencing the nearest solar term, starting from midnight until dawn; if the water level has not dropped before dawn, use the most recent time to indicate.
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During the calculations, there are both increments and decrements; advancements are added, and retreats are subtracted. The difference between increments and decrements starts from two degrees, decreasing by four degrees each time, halving the difference with each reduction; after three reductions, multiply by three, and stop when the difference reaches three, returning to the original value after five degrees.
The speed of the moon's movement varies, moving quickly at times and slowly at others, in a repeating cycle. The average lunar months are derived from various numerical calculations related to the cosmos, multiplying the remaining proportion by itself. If it matches the average number of months, a fractional representation of the cycle is obtained. Dividing this fraction by 360 degrees (the total degrees in a circle) gives the number of days in a month. The speed of the moon's movement gradually diminishes, showing varying trends. By adding the decay value to the moon's movement ratio, we can determine the degrees and fractions moved each day. Adding the values of decay on the left and right sides gives the net gain or loss rate. Adding profits and subtracting losses accumulates gains and losses. Multiplying half of a minor cycle by a standard method, if it matches the common value, subtract it from the number of degrees in a week to get the fractional movement of the new moon.
Table content is in the original text, no translation needed:
Day Rotation Degrees Decay Profit and Loss Rate Profit and Loss Accumulation Movement Fraction
First day, the water level decreased by fourteen degrees, then subtracted by four degrees, increased by twelve degrees, resulting in a total of seventy-eight degrees, with a water level of two hundred sixty-six.
Second day, the water level decreased by thirteen degrees and fifteen minutes, then subtracted by four degrees, increased by eight degrees, resulting in a total of ninety degrees, with a water level of two hundred sixty-two.
Third day, the water level decreased by thirteen degrees and eleven minutes, then subtracted by four degrees, increased by four degrees, resulting in a total of ninety-eight degrees, with a water level of two hundred fifty-eight.
Fourth day, the water level decreased by thirteen degrees and seven minutes, then subtracted by four degrees, decreased, resulting in a total of one hundred two degrees, with a water level of two hundred fifty-four.
Fifth day, the water level decreased by thirteen degrees and three minutes, increased by four degrees, decreased by four degrees, resulting in a total of one hundred two degrees, with a water level of two hundred fifty.
Sixth day, the water level decreased by twelve degrees and eighteen minutes, increased by three degrees, decreased by eight degrees, resulting in a total of ninety-eight degrees, with a water level of two hundred forty-six.
Seventh day, the water level decreased by twelve degrees and fifteen minutes, increased by four degrees, decreased by eleven degrees, resulting in a total of ninety degrees, with a water level of two hundred forty-three.
On the eighth day, the water level dropped by twelve degrees and eleven units, rose by three degrees, decreased by fifteen degrees, totaling seventy-nine degrees, resulting in a water level of two hundred thirty-nine.
On the ninth day, the water level dropped by twelve degrees and eight units, rose by two degrees, decreased by eighteen degrees, totaling sixty-four degrees, resulting in a water level of two hundred thirty-six.
On the tenth day, the water level dropped by twelve degrees and six units, rose by one degree, decreased by twenty degrees, totaling forty-six degrees, resulting in a water level of two hundred thirty-four.
On the eleventh day, the water level dropped by twelve degrees and five units, decreased by a total of twenty-two degrees, totaling twenty-six degrees, resulting in a water level of two hundred thirty-three.
On the twelfth day, the water level dropped by twelve degrees and six units, rose by two degrees, decreased by twenty degrees (because the decrease was insufficient, it was adjusted to reflect an increase of five degrees; thus, the total was five degrees), resulting in a water level of two hundred thirty-four.
On the thirteenth day, the water level dropped by twelve degrees and eight units, rose by three degrees and then by eighteen degrees, decreased by fifteen degrees, resulting in a water level of two hundred thirty-six.
On the fourteenth day, the water level dropped by twelve degrees and eleven units, rose by four degrees and then by fifteen degrees, decreased by twenty-three degrees, resulting in a water level of two hundred thirty-nine.
On the fifteenth day, the water level dropped by twelve degrees and fifteen units, rose by three degrees and then by eleven degrees, decreased by forty-eight degrees, resulting in a water level of two hundred forty-three.
On the sixteenth day, the water level dropped by twelve degrees and eighteen units, rose by four degrees and then by eight degrees, decreased by fifty-nine degrees, resulting in a water level of two hundred forty-six.
On the seventeenth day, the water level dropped by thirteen degrees and three units, rose by four degrees and then by four degrees, decreased by sixty-seven degrees, resulting in a water level of two hundred fifty.
On the eighteenth day, the water level dropped by thirteen degrees and seven units, rose by four degrees, decreased by seventy-one degrees, resulting in a water level of two hundred fifty-four.
On the nineteenth day, the water level dropped by thirteen degrees and eleven units, rose by four degrees, decreased by four degrees, decreased by seventy-one degrees, resulting in a water level of two hundred fifty-eight.
On the twentieth day, the water level dropped by thirteen degrees and fifteen units, rose by four degrees, decreased by eight degrees, decreased by sixty-seven degrees, resulting in a water level of two hundred sixty-two.
On the twenty-first day, the water level decreased by fourteen degrees, then increased by four degrees, decreased by twelve degrees again, and finally decreased by fifty-nine degrees, resulting in a water level height of two hundred and sixty-six.
On the twenty-second day, the water level decreased by fourteen degrees and four minutes, increased by three degrees, decreased by sixteen degrees, decreased by forty-seven degrees, and the water level height was two hundred and seventy.
On the twenty-third day, the water level decreased by fourteen degrees and seven minutes, after an initial increase, increased by three Sundays, decreased by nineteen degrees, decreased by thirty-one degrees, and the water level height was two hundred and seventy-three.
On Sunday, the temperature was fourteen degrees (nine minutes). After adding and then subtracting, subtract twenty-one, then subtract twelve, resulting in two hundred and seventy-five.
The virtual number for Sunday is two thousand six hundred and sixty-six.
The large legal figure for Sunday is five thousand nine hundred and sixty-nine.
The total number of weeks is one hundred and eighty-five thousand thirty-nine.
The historical week is one hundred and sixty-four thousand four hundred and sixty-six.
The large legal figure is one thousand one hundred and one.
The new moon great division is eleven thousand eight hundred and one.
The small division is twenty-five.
The half week is one hundred and twenty-seven.
The following are the methods for calculating the monthly product using the large and small divisions of the new moon. When the small division is full, subtract thirty-one from the large division; when the large division is full, subtract from the historical week. If there is still a remainder, it counts as a day; if not enough, it remains as is. Put the remainder aside; we are calculating how the conjunction fits into the historical week.
To calculate the next month, add one day; the remainder amounts to five thousand eight hundred and thirty-two, and the small division is twenty-five.
To calculate the crescent moon, add seven days each; the remainder is two thousand two hundred and eighty-three, and the small division is twenty-nine point five. Convert the division into days according to the method; subtract when it reaches twenty-seven days, and the remaining value is similar to the virtual number for Sunday. If it doesn't divide evenly, subtract one day and add the virtual number for Sunday.
Multiply the calculated profit and loss by the total number of weeks as a real figure. Then multiply the total by the remainder division, and then multiply by the profit and loss rate; use it to decrease or increase the real figure; this is the addition of time profit and loss. Subtract the monthly division from the year's movement, multiply by half a week to get the difference, use it to divide, and get the profit and loss addition and subtraction. If the total is insufficient according to the daily profit law, the new moon will be added before or after a few days. The crescent moon's position shifts based on the large remainder, which is used to determine the small remainder.
Multiply the total number of chapters by the variations in time, divide it by the difference method, and the resulting figure represents the extent of the increase and decrease. Adjust the current day and month by adding the calculated increase and decrease. If the increase is insufficient, use the calendar method to adjust the values of degrees and minutes to determine the exact degree and minute of the current day and month.
Multiply the number of days in half a week by the remaining days of the month, divide by the total number, and subtract this value from the remaining days in the calendar. If the result of the subtraction is insufficient, add the weekly method and then subtract, followed by subtracting one day. After subtracting, add the number of Sundays and their minutes to get the time of midnight in the calendar.
To calculate the second day, add one day. If the remaining days reach twenty-seven days, subtract the number of Sundays. If it is exactly the number of Sundays, no adjustment is needed. If not, add the virtual number of Sundays, and the remaining days represent the second day's remaining days in the calendar.
Multiply the remaining days of midnight in the calendar by the gain and loss ratio, divide by the weekly method. If there is a remainder, use it to adjust the increase and decrease. If the remainder is not enough to adjust, adjust proportionally. This represents the midnight variations. The full number of chapters is the degree, and if not enough, it is the minute. Multiply the total number by the minute and remainder, convert the remainder to minutes according to the weekly method, convert the minutes to degrees according to the calendar method, subtract the degree and remainder from the increase and decrease of midnight to determine the final degree.
Multiply the remaining days in the calendar by the rate of decline, divide by the weekly method to know the daily change in decline.
Let's first discuss this calendar calculation, which uses something called "weekly virtual multiplied by the rate of decline" to calculate the days as if using a fixed number. After completing a cycle, adjust the value of "decline" based on the situation, and then continue to calculate the next cycle.
Then, based on the adjusted value of "decline," add or subtract some days, hours, and degrees to adjust the number of days in a year. Add all the numbers together, and calculate the exact time for the next day based on the duration of day and night. If the calculated time does not match the actual length of the week, apply a fixed value of 1338 for adjustments. If it is more, subtract it; if it is less, add it, then fine-tune with another value of 899, and continue calculating according to the previous steps.
Next, based on this "decline" value, calculate the gain and loss ratio for each day to adjust the length of each night. If the gain and loss are still not enough after one cycle, reverse the adjustment direction, using the same method as above.
Then, we calculate the monthly operations. Multiply the degrees of movement for each month by the length of nights during each solar term, and then divide by 200 to obtain the length of daytime. Subtract this length of daytime from the total degrees of movement for the month to get the length of nighttime. These time lengths help adjust the day and night durations, similar to how days are counted in a year. If there's any excess, it is kept if it exceeds half; otherwise, it is discarded.
Calculating a month requires considering four aspects and three directions of movement, and intricately distributing them to each day. By dividing these data by the monthly movement rate, we can determine the number of days in each month. By integrating the weeks with the new and full moons, according to the lunar operation pattern, we calculate the new moon time for each month and the difference in the number of days for each month. Using these differences, we can calculate the daily rate of movement. When the moon completes a cycle, the resulting difference represents the final rate of difference.
Below are the specific daily calculation data, the "decline" and profit and loss rates of the lunar and solar calendars, as well as the specific values:
On the first day, subtract one, add seventeen; on the second day, subtract one, add sixteen or seventeen (remaining 1290, differential 457), this indicates the upper limit; on the third day, subtract three, add fifteen, totaling thirty-three; on the fourth day, subtract four, add twelve, totaling forty-eight; on the fifth day, subtract four, add eight, totaling sixty; on the sixth day, subtract three, add four, totaling sixty-eight; on the seventh day, subtract three (not sufficient to subtract, so we add instead, which means adding one; it should have been three subtracted, so it is insufficient), add one, totaling seventy-two; on the eighth day, add four, subtract two, totaling seventy-three (exceeds the limit, so it must be reduced because when the moon is halfway through its cycle, the degrees have already exceeded the limit, so it must be reduced); on the ninth day, add four, subtract six, totaling seventy-one; on the tenth day, add three, subtract ten, totaling sixty-five; on the eleventh day, add two, subtract thirteen, totaling fifty-five; on the twelfth day, add one, subtract fifteen, totaling forty-two; on the thirteenth day (remaining 3912, differential 1752), this is the lower limit; on the thirteenth day, add one (beginning of the calendar, dividing the day), subtract sixteen, totaling twenty-seven; for the division of the day (5203), the lesser amounts are subtracted, totaling eleven; according to the larger rules, four hundred seventy-three.
The calendar cycle is 107,565, and the difference value is 11,986. Let's calculate first; the combined lunar phase is 18,328, the micro-difference is 914, and the micro-difference method is 2,290. Next, subtract the monthly meeting from the lunar month, and then multiply this difference by the combined lunar phase and micro-difference respectively. If the micro-difference exceeds the micro-difference method, subtract it from the combined lunar phase; if the combined lunar phase exceeds a week (which is 360 degrees), subtract a week. The remainder that is less than a week is the value for the solar calendar; if it exceeds a week, the remaining value after subtracting a week is the value for the lunar calendar. The remaining value is counted as one day for every full week, calculated separately. The result is the number of days in this month's lunar phase; any fraction less than a day is noted as a remainder.
Adding two days, the solar remainder is 2,580, and the micro-difference is 914. According to the above method, calculate the number of days; if it reaches thirteen, subtract thirteen, and the remainder is calculated as full days based on the fraction. This is how the lunar and solar calendars alternate, with the remainders within the previous limits corresponding to the front, and the remainders within the later limits corresponding to the back, indicating that the moon has reached the middle path.
Next, consider the magnitude of excess and shortage in the late and early calendars, using the monthly meeting number multiplied by the small fraction to obtain the micro-difference, and then adding the excess and shortage to the solar and lunar remainders. If the solar remainder has excess or shortage, adjust the days based on the surplus or deficit. Then multiply the determined solar remainder by the profit and loss rate; if the result is sufficient for a month's worth of weeks, count it as one day, using the combined value of profit and loss to determine the fixed time.
Multiply the difference value by the lunar small remainder; if the result meets the criteria for the micro-difference method, subtract it from the lunar calendar's solar remainder. If not enough, add a full month's worth of weeks and then subtract. Then subtract one day and add the fraction to the fraction. Use the monthly meeting number to simplify the micro-difference to obtain the small fraction, thus determining the time for the lunar day at midnight to enter the calendar.
For the second day, add one day; the solar remainder is 31, and the small fraction is also 31. If the small fraction meets the monthly meeting number, subtract it from the remainder; if the remainder is enough for a full month's worth of weeks, subtract a full month's worth of weeks. Add another day, and the calendar calculation is complete; if the solar remainder is enough for the fractional day, subtract the fractional day, which represents the initial value for entering the calendar. If it is insufficient for the fractional day, add 2,720 directly; the small fraction is 31, which is the value for entering the secondary calendar.
Multiply the total number by the excess and deficit of the late and early hours of the night, and the remainder. If the remainder is enough for half a week, it is recorded as a small fraction. Use the excess and deficit of the sun's daily surplus to adjust the days if there are surpluses or shortages. Then, multiply the determined day surplus by the profit and loss rate; if the result is enough for a month, it is recorded as one day, using the comprehensive value of profit and loss to determine the midnight constant.
Multiply the profit and loss rate by the recent seasonal nightly fluctuations; one two-hundredth is bright, and subtracting the profit and loss rate gives dusk. Then, use the profit and loss midnight value to determine the constants for dusk and dawn.
Combine the extra hours with the dusk and dawn constants, then divide the sum by twelve; one-third of the remainder is considered 'less'; if it’s less than a full point, it’s classified as 'strong,' and if there are two 'less,' it’s categorized as 'weak.' The result calculated this way is the degree of the moon's distance from the ecliptic. In the solar calendar, use the solar calendar's ecliptic based on the added day to calculate the extreme, while in the lunar calendar, subtracting the extreme gives the degree of the moon's distance from the extreme. Strong is positive, weak is negative; same names are added, different names are subtracted. When subtracting, same names cancel out, different names are added, and if there is no corresponding one, they are swapped, with two strong becoming one less and weak.
From the year 132 AD to 223 AD, a total of 7378 years have passed. (This sentence is clearly incorrect; it should be 7378 days, or 7378 years is an exaggeration, this part is kept as is without modification.)
Jichou, Wuyin, Dingmao, Bingchen, Yisi, Jiawu, Guiwei, Renshen, Xinyou, Gengxu, Jihai, Wuzi, Dingchou, Bingyin, these are all years.
Next are the five elements: Jupiter, Mars, Saturn, Venus, Mercury. Their daily speeds in the sky are different, with a weekly rate (the degree of movement in one week) and a daily rate (the degree of movement in one day). Multiply the annual rate (one year) by the weekly rate to get the monthly method (the degree of movement in one month). Then multiply the monthly rate (one month) by the daily rate to get the monthly fraction (the degree of movement in one month). Dividing the monthly fraction by the monthly method gives the number of months. Multiply the total days by the monthly method to get the daily degree method. The degree of the Dipper constellation multiplied by the weekly rate gives the Dipper fraction. (The daily degree method is obtained by multiplying the calendar method by the weekly rate, so here it is also multiplied by the fraction.)
Next is the method for calculating the major and minor remainders of the five celestial bodies. (Use the total method to multiply by the number of months, and the daily method to divide by the number of months to get the major remainder; the portion that cannot be evenly divided is the minor remainder. Subtract the major remainder from 60.)
Next, we have the calculation methods for the five planets' entry into the month and the remaining days. (Multiply the month remainder by the common method, then multiply the new moon remainder by the synodic month method, add the results together, simplify, and finally divide by the simplified result using the daily method.) Finally, there is the calculation method for the degree and degree remainder of the five planets. (Subtracting the excess gives the degree remainder, multiply by the synodic month, then divide by the daily method, get the degree; the remaining part is the degree remainder, subtract the excess part exceeding the synodic month, also consider the constellation division.) The month recorded is 7285, the leap month is 7, the lunar month is 235, the year is 12, the common method is 43026, the daily method is 1457, the count is 47, the synodic month is 215130, the constellation division is 145. Below are the specific data for Jupiter: synodic period 6722, daily rate 7341, synodic month number 13, month remainder 64810, synodic month method 127718, daily method 3959258, new moon remainder 23, synodic month remainder 1370, entry into the month 15, remaining days 3484646, synodic month division 150, constellation division 974690, degree 33, degree remainder 2509956. Below are the specific data for Mars: synodic period 3447, daily rate 7271, synodic month number 26, month remainder 25627, synodic month method 64733, daily method 2006723, new moon remainder 47... This passage describes a complex calendar calculation method, involving a large number of numbers and astronomical terms. The specific calculation process is quite cumbersome. Here, it is only translated into modern spoken Chinese without elaborating on the specific calculation steps. The main focus of this passage is to explain how to calculate the positions and related parameters of the planets. In a certain year before Christ, I conducted an astronomical observation record. First, the new moon remainder is 1,157. The entry into the month is the twelfth day. The remaining days are 973,113. The synodic month division is 300. The constellation division is 494,105. The degree is 48. The degree remainder is 1,991,706. Regarding Saturn: the synodic period is 3,529. The daily rate is 3,653. The synodic month number is 12. The month remainder is 53,843. The synodic month method is 67,051. The daily method is 278,581. The new moon remainder is 54. Next, the new moon remainder is 534. The entry into the month is the twenty-fourth day. The remaining days are 166,272. The synodic month division is 923. The constellation division is 51,175. The degree is 12. The degree remainder is 1,731,148.
Venus: The week rate is nine thousand twenty-two. The day rate is seven thousand two hundred thirteen. The total month count is nine. The remaining month is one hundred fifty-two thousand two hundred ninety-three. The total month method is one hundred seventy-one thousand four hundred eighteen. The day degree method is five million three hundred eleven thousand nine hundred fifty-eight. The new moon remainder is twenty-five. Then, the small new moon remainder is one thousand one hundred twenty-nine. The day of entry for the month is the twenty-seventh. The day remainder is fifty-six thousand nine hundred fifty-four. The new moon virtual fraction is three hundred twenty-eight. The 斗分 is one hundred thirty thousand eight hundred ninety. The degree value is two hundred ninety-two. The degree remainder is fifty-six thousand nine hundred fifty-four.
Mercury: The week rate is eleven thousand five hundred sixty-one. The day rate is one thousand eight hundred thirty-four. The total month count is one. The remaining month is two hundred eleven thousand three hundred thirty-one. The total month method is two hundred nineteen thousand six hundred fifty-nine. The day degree method is six million eight hundred thousand four hundred twenty-nine. The new moon remainder is twenty-nine. Finally, the small new moon remainder is seven hundred seventy-three. The day of entry for the month is the twenty-eighth. The day remainder is six hundred forty-one million nine hundred sixty-seven. The new moon virtual fraction is six hundred eighty-four. The 斗分 is one hundred sixty-seven million six thousand three hundred forty-five. The degree value is fifty-seven. The degree remainder is six hundred forty-one million nine hundred sixty-seven. This record lists numerous figures related to astronomical observations.
First, calculate how many days are in a year by multiplying the week days by it. If the result is an integer, it's referred to as a "total sum"; if not, it results in a "sum remainder." Then divide it by the week days; if the result is 1, it means the celestial body combined in previous years; if the result is 2, it means the celestial body combined in the two years prior. If it cannot be divided evenly, it indicates that the celestial body combined in this year. Subtract the "sum remainder" from the total days to obtain a degree fraction value. For Venus and Mercury, the "total sum": odd numbers indicate morning, while even numbers indicate evening.
Next, calculate the months. Multiply the number of months and the leftover months by "Ji He" (accumulated total). If the result is an integer, count it as full months; if not, it remains as "leftover months." Subtract the number of months from the total months to get the "entry month." Then multiply the number of leap months by it; if the result is an integer, it indicates there is a leap month, which should be deducted from the "entry month." The remaining part is then deducted from the year, and this part is called "Tian Zheng Suan Wai (天正算外，合月)." If it occurs during the transition of a leap month, use the new moon day to adjust.
Use the general method to multiply by the leftover months, and use the conjunction method to multiply by the small leftover of the new moon day, then simplify the result. If the result is an integer, it indicates the conjunction of celestial bodies on a certain day of a certain month; if not, it remains as "day leftover," which is called "Shuo Suan Wai."
Multiply the number of weeks by the degree minute value; if the result is an integer, you get one degree; if not, it leaves a remainder, which should be noted in the five positions in front of the ox.
The above outlines the steps for calculating the conjunction of celestial bodies.
Next, calculate the year of the conjunction of celestial bodies. Add the number of months together, and also add the leftover months; if the result is an integer, it indicates a certain month; if not, in this year, if it is an integer, subtract it, and if there is a leap month, consider that; the remainder will be the situation for the following year; if it exceeds, then look at the next two years. Venus and Mercury, when they are in conjunction in the morning, add up to the evening, and when they are in conjunction in the evening, they add up to the morning.
Add the size of the new moon day leftover and the size of the conjunction month leftover; if it exceeds one month, add a large remainder of twenty-nine and a small remainder of seven hundred seventy-three. If the small remainder exceeds the day degree calculation, subtract it from the large remainder, using the same method as before.
Add the entry month day and the day leftover together; if it exceeds the day degree calculation, it results in one day. If the previous new moon day small leftover exceeds the fractional part, subtract one day; if the later small leftover exceeds seven hundred seventy-three, subtract twenty-nine days; if it is less, subtract thirty days; the remainder will indicate the entry month day of the later conjunction.
Add the degrees together, and also add the degree remainders; if it exceeds the day degree calculation, it results in one degree.
Jupiter:
Retrograde for thirty-two days and three million four hundred eighty-four thousand six hundred forty-six minutes.
Direct motion for three hundred sixty-six days.
Retrograde for five degrees and two million nine thousand nine hundred fifty-six minutes.
Direct for forty degrees. (Except for retrograde twelve degrees, fixed for twenty-eight degrees.)
Mars: Retrograde for one hundred forty-three days and nine hundred seventy-three thousand thirteen minutes.
Direct for six hundred thirty-six days.
Venus: It rises in the east in the morning, stays for a total of 82 days, and travels 113,980 minutes of travel. Then, it shifts to the west and stays for 246 days. (Here, accounting for the retrograde motion of 6 degrees, the final calculation is that it travels 246 degrees.) When it rises in the morning, it travels 100 degrees, which is 113,980 minutes of travel. Then it transitions back to the east. (When Venus is in the west, the degree of movement is the same as in the east. It will stay for 10 days and then move back 8 degrees.)
Mercury: It rises in the morning, stays for a total of 33 days, and travels 61,255 minutes of travel. Then it shifts to the west and stays for 32 days. (Here, accounting for the retrograde motion of 1 degree, the final calculation is that it travels 32 degrees.) It travels 65 degrees through its orbit, which is 61,255 minutes of travel. Then it transitions back to the east. (When Mercury is in the west, the degree of movement is the same as in the east. It will stay for 18 days and then it will move back 14 degrees.)
Next is the calculation method: first calculate the number of days the planet stays and the remaining degrees, then add the remaining degrees of the celestial body to the Sun's conjunction. If the remaining degrees reach a full cycle, a complete cycle is achieved. As mentioned earlier, this allows us to calculate the degrees of its visibility and movement. Multiply the denominator of the celestial body's movement by the degrees of its visibility; if the remaining degrees reach a full cycle, a complete cycle is achieved; if the denominator does not divide evenly and exceeds half, it is considered a complete cycle; then add the fractional part of its movement. If the fractional part reaches the denominator, it equals one degree. The denominators for retrograde and direct motion are different; multiply the current movement's denominator by the original fractional value. If the result equals the original denominator, the current movement's fractional part is obtained. The remaining part inherits the previous result; for retrograde, subtract it. If the number of days of stay is insufficient to complete a degree, divide the degrees by the fractional part, using the moving denominator as a ratio; the fractional part will increase or decrease, affecting each other. Whenever terms like surplus or approximately full are mentioned, they refer to division seeking precise results; to go, to reach, and to divide all refer to division seeking complete results.
As for Jupiter, in the morning it is together with the Sun, then it stays, moving in a direct path for 16 days, covering 1,742,323 minutes of movement, and the planet moves 2 degrees and 323,467 minutes. Then it appears in the east in the morning, behind the Sun. Moving direct, its speed is fast, covering 11 minutes per day, moving 11 degrees in 58 days. Then it continues moving direct but at a slower speed, covering 9 minutes per day, moving 9 degrees in 58 days. It remains stationary for 25 days, then turns. In retrograde, it moves 1/7 of a degree per day, retreating 12 degrees in 84 days. It stays again for 25 days, then moves direct, covering 9 minutes per day, moving 9 degrees in 58 days. Moving direct, its speed is fast again, covering 11 minutes per day, moving 11 degrees in 58 days, appearing in the western sky, ahead of the Sun, and staying in the west in the evening. For 16 days, it covered 1,742,323 minutes of movement, and the planet moved 2 degrees and 323,467 minutes, then it conjoins with the Sun. A complete cycle lasts 398 days and 3,484,646 minutes, during which the planet moves a total of 43 degrees and 2,509,956 minutes.
When the sun rises in the morning, Mars and the sun align, and then Mars becomes less visible. Next, it starts moving forward for a total of 71 days, covering 1,489,868 minutes, equivalent to 55 degrees and 242,860.5 minutes. Then, in the morning, it can be seen in the east, behind the sun. While moving forward, it covers 14/23 of a degree each day, covering 112 degrees over the course of 184 days. Then its forward speed slows down, covering 12/23 of a degree each day, covering 48 degrees over 92 days. Then it stops, remaining stationary for eleven days. Then it starts moving backward, covering 17/62 of a degree each day, retracting 17 degrees over the course of 62 days. It stops again for eleven days, then starts moving forward again, covering 1/12 of a degree each day, covering 48 degrees over 92 days. After that, its forward speed increases, covering 1/14 of a degree each day, covering 112 degrees over the course of 184 days. At this point, it runs ahead of the sun, and in the evening, it can be seen setting in the west. After 71 days, it aligns with the sun again, covering a total of 1,489,868 minutes, equivalent to 55 degrees and 242,860.5 minutes. Based on these calculations, one complete cycle lasts 779 days and 973,113 minutes, covering 414 degrees and 478,998 minutes.
Turning to Saturn, it also aligns with the sun in the morning and then disappears from view. Next, it starts moving forward for 16 days, covering 1,122,426.5 minutes, which is 1 degree and 199,864.5 minutes. Then, in the morning, it can be seen in the east, behind the sun. While moving forward, it covers 3/35 of a degree each day, covering 7.5 degrees over the course of 87.5 days. Then it stops, remaining stationary for 34 days. Then it starts moving backward, covering 1/17 of a degree each day, retracting 6 degrees over the course of 102 days. After another 34 days, it starts moving forward again, covering 1/3 of a degree each day, covering 7.5 degrees over 87 days. At this point, it runs ahead of the sun, and in the evening, it can be seen setting in the west. After 16 days, it aligns with the sun again, covering a total of 1,122,426.5 minutes, which is 1 degree and 199,864.5 minutes. Based on these calculations, one complete cycle lasts 378 days and 166,272 minutes, covering 12 degrees and 173,148 minutes.
Venus, when it meets the sun in the morning, 'retreats', meaning it is in retrograde. It moves back four degrees over five days, and then in the morning you can see it in the east, positioned behind the sun. During retrograde, it shifts by three-fifths of a degree each day, retreating six degrees over ten days. Next, it 'pauses' for eight days without moving. Then it 'rotates', indicating it starts moving forward at a slower speed, moving three-forty-sixths of a degree each day, covering thirty-three degrees over forty-six days. Then its speed increases, moving ninety-one twenty-fifths of a degree each day, covering one hundred and six degrees over ninety-one days. It then increases speed, moving ninety-one twenty-second of a degree each day, covering one hundred and thirteen degrees over ninety-one days; at this point, it is positioned behind the sun, appearing in the east in the morning. It moves forward for forty-one days, covering one fifty-thousand six hundred fifty-fourth of a full circle, which equals fifty degrees plus one fifty-thousand six hundred fifty-fourth of a degree, and then meets the sun again. One complete conjunction cycle is two hundred and ninety-two days and one fifty-thousand six hundred fifty-fourth of a day; Venus travels this far.
When Venus meets the sun in the evening, it also 'retreats', but this time it is in direct motion. It moves fifty degrees plus one fifty-thousand six hundred fifty-fourth of a full circle over forty-one days, which equals fifty degrees plus one fifty-thousand six hundred fifty-fourth of a degree, and then in the evening you can see it in the west, positioned in front of the sun. It moves quickly, covering one hundred and thirteen degrees over ninety-one days. Then its speed decreases slightly, moving one-sixth of a degree each day, covering one hundred and six degrees over ninety-one days while continuing forward. Then its speed slows down, moving three-thirty-thirds of a degree each day, covering thirty-three degrees over forty-six days. It then 'pauses' for eight days without moving. It then 'rotates', starting retrograde, moving five-thirds of a degree each day, retreating six degrees over ten days; at this point, it is positioned in front of the sun, appearing in the west in the evening. It 'retreats' retrograde at a high speed, retreating four degrees over five days, and then meets the sun again. Two conjunctions complete one cycle, totaling five hundred eighty-four days and one eleven-thousand three-hundred ninety-eighth of a day; Venus travels this far.
When Mercury meets the Sun in the morning, it "retreats" and moves backward, retreating seven degrees over nine days, and then it can be seen in the east behind the Sun in the morning. It continues to move backward quickly, retreating one degree in a day. Then it "pauses" for two days. After that, it "rotates" and begins to move forward, but at a slower speed, moving nine-eighths of a degree each day and covering eight degrees in nine days. Then its speed increases to one and a quarter degrees each day, covering twenty-five degrees in twenty days; at this point, it appears behind the Sun in the east in the morning. It moves forward for sixteen days, covering six hundred forty-one million nine hundred sixty-seven parts of a degree, which is thirty-two degrees six hundred forty-one million nine hundred sixty-seven parts of a degree, and then meets the Sun again. The complete meeting cycle lasts fifty-seven days and six hundred forty-one million nine hundred sixty-seven parts of a day, and Mercury travels this far in total.
So, what on earth is this all about? Let me explain it to you sentence by sentence.
First, "When Mercury meets the Sun in the morning, it 'retreats', moves forward, sixteen days cover thirty-two degrees (with such precise measurements of six hundred forty-one million nine hundred sixty-seven parts of a degree), and it appears in the west in front of the Sun." This means that when Mercury meets the Sun, it starts moving backward, and then it starts moving forward. After approximately sixteen days, it covers about thirty-two degrees, and at this time, it can be seen in the west in the evening, in front of the Sun.
Next, "Moving forward quickly, covering one and a quarter degrees per day, and in twenty days it covers twenty-five degrees." This means that when Mercury moves forward, its speed is fast, covering one and a quarter degrees in a day, and in twenty days it covers twenty-five degrees.
"Moving slowly, covering seven-eighths of a degree per day, taking nine days to cover eight degrees." This means that sometimes, when Mercury moves forward, its speed slows down, covering approximately seven-eighths of a degree in a day, taking nine days to cover eight degrees.
"Pausing, not moving for two days." This means that Mercury sometimes "pauses" or remains stationary for about two days.
"Retrograde, backward, one day retreats one degree; the previous day, it hides in the west." Then it starts to "retrograde," which refers to moving backward! It retreats one degree each day, still positioned in front of the sun, and can be seen in the west in the evening, but at that point, it appears to be moving backward. "Retrograde, slow; it takes nine days to retreat seven degrees and conjuncts with the sun." When moving backward, its speed is slow. It takes nine days to retreat seven degrees and eventually conjuncts with the sun again. Finally, "Each time it conjuncts, it takes one hundred fifteen days and six hundred one million two thousand five hundred five minutes; the planets are the same." In short, from one conjunction of Mercury with the sun to the next, it takes a total of one hundred fifteen days (specifically to six hundred one million two thousand five hundred five minutes; this level of precision is remarkable!), and other planets follow a similar pattern. In conclusion, this passage describes the observations of ancient astronomers on the movement patterns of Mercury, using extremely precise numbers to describe phenomena such as direct motion, retrograde motion, and stationary points, as well as the time of one cycle. This level of precision is impressive even by today's standards!
