First, let's discuss how to calculate the new moon (the first day of the lunar calendar) for each month. First, add the number of large divisions to the number of minor divisions to obtain a total. If this total is less than a full month's total, then use minor divisions to make up the difference. Then, subtract the time of the new moon (which is midnight on the first day of the lunar calendar) from this total; the remainder indicates the time difference between the new moon and sunrise, indicating the time when the sun and moon appear in the sky simultaneously.
Next, to calculate the new moon for the next month, add 29 degrees to the degree of the new moon from the previous month. There are 312 large divisions and 25 minor divisions. If the minor divisions exceed the specified amount, use them to increase the number of large divisions; if the number of large divisions exceeds the specified amount, use that to recalculate the degrees, then divide by the number of large divisions using the Dou unit (an ancient astronomical unit).
Then, we calculate the degrees for the first quarter moon, full moon, and last quarter moon. To find the first quarter moon, add 7 degrees to the new moon's degree from the previous month. The number of large divisions is 225, and the number of minor divisions is 17.5. Use the same method to calculate the full moon, last quarter moon, and the new moon for the next month.
Calculating the degrees of the moon's movement is similar. Add 98 degrees to the degree of the new moon from the previous month. The number of large divisions is 480, and the number of minor divisions is 41. Use the same method to calculate the full moon, last quarter moon, and the new moon for the next month.
To calculate the times of day and night for the sun and moon, you need to use the calculation method for their cycles, then multiply by the nighttime measurement of the nearest solar term (an ancient timekeeping unit), and then divide 200 by this result to get the daytime minutes. Subtract this result from the cycles of the sun and moon to get the nighttime minutes. Finally, add the midnight time to determine the specific angles.
Now, let's start calculating the accumulated years and months. First, set a starting time for the Yuan year, then subtract this from the Hui year (a calendar cycle), and multiply the remaining years by the Hui rate (a calendar coefficient). If the result is a Hui year, add the accumulated eclipses (an astronomical phenomenon); if it is less than a Hui year, add the month accumulation (a calendar cycle). Then multiply the intercalary month by the remaining years to get the accumulated leap months, and subtract the accumulated months from the accumulated leap months; the remainder is the remaining days in the year, and if there are not enough, start calculating from the celestial time (new moon).
To calculate the next solar eclipse, you need to add 5 months and the remaining months; if the remaining months exceed 1635, it corresponds to one month, which corresponds to the full moon.
If the value of Dayu on the Winter Solstice (an astronomical measurement) is large, double the value of Xiaoyu (another astronomical measurement), indicating that the Kan hexagram (one of the eight trigrams) is in effect. Then add 175 to Xiaoyu; if it exceeds the value of the Qian hexagram, calculate using Xiaoyu, indicating that the Zhong Fu hexagram is in effect.
To calculate the next hexagram, add 6 to Dayu and 103 to Xiaoyu. The four principal hexagrams (the four principal hexagrams of the eight trigrams) need to double Xiaoyu based on their respective middle days.
Set the values of Dayu and Xiaoyu for the Winter Solstice, add 27 to Dayu and 927 to Xiaoyu; if it exceeds 2356, calculate using Dayu, indicating that the Earth element is in effect. Continuing in this way, add 18 and 618 to determine the date when the Wood element is in effect at the beginning of spring; add 73 and 116 to once again determine the date when the Earth element is in effect; if you continue to add the value of the Earth element, you can determine the dates when the Fire, Metal, and Water elements are in effect.
Multiply Xiaoyu by 12; if the result reaches a certain value, you obtain a 'chen' (an ancient time unit), starting from Zi (one of the earthly branches). The dates of the new moon, waxing moon, and full moon are all determined by Xiaoyu.
Finally, multiply Xiaoyu by 100; if the result reaches a certain threshold, you obtain a 'ke' (an ancient time unit); if insufficient, calculate using one-tenth, then calculate the nighttime based on the nearest solar term. If the water level at night has not decreased, use the most recent value to represent it.
First, let's discuss the calculation of advancement and retreat. To calculate advancement and retreat, add for advancement and subtract for retreat, and the result is your final outcome. The difference in advancement and retreat begins at two degrees, decreases by four degrees with each turn, and is halved with each decrease. After three halvings, when the difference reaches three, it stops; after five degrees, the difference resets to its original state.
The following is the calculation of the Moon's orbital speed. The Moon's orbital speed varies, but overall, the time it takes to complete one orbit is constant. The calculation method involves multiplying the number of conjunctions (the instances when the Moon is in alignment with the Sun) by a constant called the Earth-Moon ratio, then squaring the remainder repeatedly until it equals the number of conjunctions, resulting in the excess period (the portion exceeding one cycle). This excess period is added to one synodic month (the time it takes for the Sun to return to the same position relative to the Moon), and then divided by the number of days it takes the Moon to complete one orbit, resulting in the actual elapsed days. The variations in the Moon's orbital speed are regular, and these changes can be represented by "tendency." Based on the pattern of speed changes, adding the speed variation to the Moon's orbital rate gives us the daily degrees of orbit. The cumulative effect of speed variations results in the profit/loss rate. If it is a gain, it continues to add; if it is a loss, it continues to subtract, leading to the accumulation of either surplus or deficit. Multiplying half a small cycle by the common method, then dividing by the common number, and finally subtracting the result from the historical cycle gives the new moon's orbital degrees.
Here are the specific daily data:
Day 1: The daily rotation is 14 degrees and 10 minutes, with a retreat of 1 minute, and a profit/loss rate of +22, and the surplus initial value is 276.
Day 2: The daily rotation is 14 degrees and 9 minutes, with a decrease of 2 minutes, and a profit/loss rate of +21, and the surplus is 275.
Day 3: The daily rotation is 14 degrees and 7 minutes, with a decrease of 3 minutes, and a profit/loss rate of +19, and the surplus is 273.
Day 4: The daily rotation is 14 degrees and 4 minutes, with a decrease of 4 minutes, and a profit/loss rate of +16, and the surplus is 270.
Day 5: The daily rotation is 14 degrees, with a decrease of 4 minutes, and a profit/loss rate of +12, and the surplus is 266.
Day 6: The daily rotation is 13 degrees and 15 minutes, with a decrease of 4 minutes, and a profit/loss rate of +8, and the surplus is 262.
Day 7: The daily rotation is 13 degrees and 11 minutes, with a decrease of 4 minutes, and a profit/loss rate of +4, and the surplus is 258.
Day 8: The daily rotation is 13 degrees and 7 minutes, with a decrease of 4 minutes, and a profit/loss rate of -1, and the surplus is 254.
Day 9: The daily rotation is 13 degrees and 3 minutes, with a decrease of 4 minutes, and a profit/loss rate of -4, and the surplus is 250.
Day 10: The daily rotation is 12 degrees and 18 minutes, with a decrease of 3 minutes, and a profit/loss rate of -8, and the surplus is now at 246.
Day 11: The daily rotation is twelve degrees and fifteen minutes, decreasing by four minutes, the profit and loss rate is minus eleven, and the surplus is two hundred and forty-three.
Day 12: The angle is twelve degrees and eleven minutes, decreasing by three minutes, the profit and loss rate is minus fifteen, and the surplus is two hundred and thirty-nine.
Day 13: The angle is twelve degrees and eight minutes, decreasing by two minutes, the profit and loss rate is minus eighteen, and the surplus is two hundred and thirty-six.
Day 14: The angle is twelve degrees and six minutes, decreasing by one minute, the profit and loss rate is minus twenty, and the surplus is two hundred and thirty-four.
Day 15: The angle is twelve degrees and five minutes, increasing by one minute, the profit and loss rate is minus twenty-one, and the surplus is two hundred and thirty-three.
Day 16: The angle is twelve degrees and six minutes, increasing by two minutes, the profit and loss rate is minus twenty (due to insufficient loss, the adjustment changes from minus five to plus five). The surplus is five, and the initial loss is two hundred and thirty-four.
Day 17: The angle is twelve degrees and eight minutes, with a three minutes decrease, increased by eighteen, decreased by fifteen, the total is two hundred and thirty-six.
Day 18: The angle is twelve degrees and eleven minutes, with a four minutes decrease, increased by fifteen, decreased by twenty-three, the total is two hundred and thirty-nine.
Day 19: The angle is twelve degrees and fifteen minutes, with a three minutes decrease, increased by eleven, decreased by forty-eight, the total is two hundred and forty-three.
Day 20: The angle is twelve degrees and eighteen minutes, with a four minutes decrease, increased by eight, decreased by fifty-nine, the total is two hundred and forty-six.
Day 21: The angle is thirteen degrees and three minutes, with a four minutes decrease, increased by four, decreased by sixty-seven, the total is two hundred and fifty.
Day 22: The angle is thirteen degrees and seven minutes, with a four minutes increase, a loss of seven-one, the total is two hundred and fifty-four.
Day 23: The angle is thirteen degrees and eleven minutes, with a four minutes increase, a loss of four, the total is two hundred and fifty-eight.
Day 24: The angle is thirteen degrees and fifteen minutes, with a four minutes increase, a loss of eight, the total is two hundred and sixty-two.
Day 25: The angle is fourteen degrees, with no minutes added, a loss of twelve, the total is two hundred and sixty-six.
Day 26: The angle is fourteen degrees and four minutes, with a three minutes increase, a loss of sixteen, the total is two hundred and seventy.
On the 27th, at fourteen degrees seven minutes, three days into the third major week, a loss of nineteen, a reduction of thirty-one, totaling two hundred and seventy-three. On Sunday, at fourteen degrees (nine minutes), with a minor increment, a loss of twenty-one, a reduction of twelve, totaling two hundred and seventy-five. Next are some numbers: Sunday points: three thousand three hundred and three; fictitious week, two thousand six hundred and sixty-six; Sunday method, five thousand nine hundred and sixty-nine; through the week, one hundred and eighty-five thousand thirty-nine; historical week, one hundred and sixty-four thousand four hundred and sixty-six; slightly larger method, one thousand one hundred and one; new moon large points, eleven thousand eight hundred and one; small points, twenty-five; half a week, one hundred and twenty-seven.
What are these numbers used for? The original text says: "Multiply the accumulated month by the large points of the new moon, the small points are complete, the total number is thirty-one from the large points, subtract the historical week from the full large points, the remainder corresponds to the full week calculation, which results in one day, not a complete day. The remaining days are calculated separately, and the total is added to the historical lunar month." In simple terms, these numbers are used for a series of multiplication, addition, and subtraction operations to ultimately determine the time for the new moon to enter the historical calendar.
To calculate the next month, add one day; the current remaining days total five thousand eight hundred thirty-two, with twenty-five small points. To calculate the crescent moon, add seven days to each; the current remaining days are two thousand two hundred and eighty-three, with twenty-nine point five small points. These points are converted into days based on the previous rules; if it exceeds twenty-seven days, subtract twenty-seven, and the remaining part is handled according to the week points. If there aren't enough to divide, subtract one day, then add the fictitious week.
Wow, this is a lot to take in! Let's break it down sentence by sentence and explain it in plain language. First, it explains how to calculate the calendar, specifically adjusting the dates based on the accumulated gains and losses to make the calendar more accurate. "Set the accumulated gains and losses into the calendar, and multiply by the weekly factor to obtain the actual value." This means we take the previously accumulated gains and losses in the calendar, multiply them by a constant (the weekly factor), to get the actual value.
Next, it discusses how to calculate date adjustments resulting from daily gains and losses. "Multiply the constant by the daily remainder, then multiply by the profit and loss rate and the actual gains and losses, to adjust for time gains and losses." In simple terms, this means using a constant to multiply the daily profit and loss values, then multiplying by an adjustment coefficient, and finally adjusting to the actual date, a process referred to as "time gains and losses." "Subtract the lunar months from the solar years, multiply by half a week for the difference, and divide it; the resulting gains and losses will dictate the size of the remainder. If the daily gains are insufficient, add time to the days before and after the new moon. The waxing and waning will determine the small remainder." This section explains how to subtract the lunar values from the solar year, multiply by a constant (half a week) to get a difference, divide it by the previous profit and loss value to obtain the final profit and loss adjustment value, and adjust the date of the new moon (the first day) and the waxing and waning dates (the fifteenth and twenty-fifth) based on the profit and loss situation.
This part discusses how to calculate the "full meeting number," which is the total amount of gains and losses within a cycle, and adjust the positions of the sun and moon based on this value. "Multiply the solar year by the time gains and losses, divide by the difference, and the resulting full meeting number represents the magnitude of the gains and losses. Based on the gains and losses, adjust the positions of the sun and moon; if the gains are insufficient, apply the calendar method to adjust the positions accordingly." This means using one year (solar year) multiplied by the previously calculated date adjustment value, then dividing by a difference to obtain the total amount of gains and losses within a cycle, and then adjusting the positions of the sun and moon based on this total.
This section explains how to calculate the date of midnight. "Multiply half a week by the small remainder of the new moon; if it equals the total and one, subtract the remaining calendar days. If the remainder is insufficient, add a constant and then subtract it, and the result will give the date of midnight in the calendar." This means using a constant to multiply the remainder value of the new moon, then subtracting the remainder value of the calendar days; if the result is not enough, add a constant and then subtract it, ultimately obtaining the date of midnight.
Next, it talks about how to calculate the profit and loss value at midnight. "Take the remainder of the day from the calendar at midnight, multiply by the profit and loss ratio; if the weekly calculation results in one, not everything remains. Use the accumulated profit and loss to shrink; if there is no loss left, break all losses as the law. This is the profit and loss at midnight. A full chapter year corresponds to a degree, not everything is a minute. Multiply the common number by the minute and the remainder; the remainder follows the minute from the weekly method, and the minute follows the degree from the record method. Add or subtract the degree and remainder of this midnight to determine the degree." This passage talks about multiplying the remaining value of the midnight date by an adjustment factor to obtain the profit and loss value at midnight, and then adjusting the midnight date based on this profit and loss value.
This describes how to calculate the daily depreciation value. "Take the remainder of the day from the calendar, multiply by the column of depreciation values; if the weekly method yields one, not everything remains. Then each knows its daily depreciation." This means calculating the daily depreciation value based on the remaining value of the calendar day.
This talks about how to update the depreciation value. "Multiply the column of depreciation values by the weekly void; if the weekly method is a constant, at the end of the historical period, add the variable depreciation, remove the full column depreciation, and turn it into the next historical period's variable depreciation." This means updating the depreciation value based on a constant, and if the depreciation value exceeds the upper limit, subtract the limit value and update it to the next period's depreciation value.
This discusses how to adjust the date based on the depreciation value. "By adjusting the historical day forward or backward by subtracting minutes, if the minutes are insufficient, the chapter year corresponds to the degree. Multiply by the minute and the remainder, and add the midnight fixed degree to turn it into the next day. The historical period does not align perfectly with Sunday; subtract one thousand and thirty-eight, then multiply by the common number. For those who reach Sunday, add the remaining eight hundred and thirty-seven, subtract the small fraction of eight hundred and ninety-nine, add the next historical period's variable depreciation, and seek as before." This means adjusting the daily date based on the depreciation value, and if the final date is not equal to a period, make the corresponding adjustments.
Lastly, this section discusses how to calculate the twilight moments. "Multiply the monthly travel minutes by the nearest solar term at night; two hundred units for one bright minute. Subtract the monthly travel minutes to find the twilight minute. If the minute is a degree, multiply by the minute, and add the midnight fixed degree for the twilight moment. Any remaining minutes above half are disregarded." This passage explains how to calculate the twilight (evening) and bright (morning) moments based on the lunar travel values.
In summary, this text describes a fairly complex calendar calculation method, involving a large number of constants and intricate computation steps, aimed at improving the accuracy of the calendar. This can't be summed up in just a few words; it requires in-depth study to understand its essence.
First, let us explain this ancient astronomical calendar calculation method. This text mainly discusses how to calculate dates in the calendar, involving many technical terms, and we will understand it step by step.
The first section states that a month has four tables (possibly referring to four different points or stages in time) and three entries and exits (possibly referring to three key operational processes), with these points and processes interwoven throughout the month. The method calculates the days in the calendar based on the lunar movement patterns. By multiplying the lunar year by the number of lunar phases (the cycle from new moon to full moon or from full moon to new moon), a value is obtained, which is then divided by a certain number (the original text does not specify what this number is) to determine the days in the calendar.
It then describes another calculation method, multiplying the total by a specific composite number, and dividing the remainder by a certain count, to derive another value for adjusting the calculation result. Finally, based on the lunar cycle, it calculates the daily fractional parts, as well as a value called "differential rate."
Next, this text lists a table showing the daily fluctuations in the lunar and solar calendars along with specific values. This part is relatively complex, involving daily decrement values and some critical values (such as "upper limit" and "lower limit"). Understanding these values and their calculation methods requires specialized knowledge. For example, it mentions "insufficient reduction, reverse loss as addition," indicating that there are special cases to consider during the calculation process. It also states "excessive loss at extremes," indicating that when the moon reaches certain extremes, the calculation method changes.
The text continues to explain other parameters, such as "calendar week," "differential rate," "lunar phase fraction," "micro fraction," etc., as well as the relationships and calculation methods between these parameters. It also mentions a "minor major method," with a value of 473, but the specific meaning requires further research. Finally, it provides a final calculation formula to determine specific dates and whether they fall under the solar or lunar calendar.
The last section summarizes the entire calculation process. It explains how to use the parameters obtained from previous calculations to determine the final date. It also mentions parameters such as "entry delay, speed, calendar fullness, reduction, size, and division," and how to use these parameters to adjust the final date. Finally, it explains how to calculate the final date based on the "profit and loss rate." In summary, this text describes a very complex calendrical calculation method that requires profound expertise to fully understand. The text is filled with specialized terms from ancient astronomical calendars, which can indeed be quite difficult for modern readers to comprehend.
Let's first discuss how to calculate the new moon day. Multiply the difference rate by the small remainder of the new moon day, similar to how one would calculate in calculus to arrive at a result, and then subtract the day remainder from the calendar. If the result is insufficient, add the number of days in a month, subtract again, and then subtract one more day. After this, add the obtained number of days to its fractional part. Then simplify the fraction to get the calendrical date for midnight of the new moon day.
Next, calculate the following day by adding one day. The remaining days are 31, and the small fraction is also 31. If the small fraction exceeds the whole number, subtract the number of days in a month. Then add one more day, and when the calendar reaches the end, if the remaining days exceed the fractional day number, subtract the fractional day number, which gives the starting date for the calendar cycle. If the remaining days do not exceed the fractional day number, simply use it and add 2720, with the small fraction being 31, which gives the date for the next calendar entry.
Then, calculate the changes in the length of day and night. Multiply the base number by the fullness and reduction of the calendar at midnight, along with the remainder; if the remainder exceeds half a week, it is treated as a small fraction. Add the fullness to the reduction and subtract the yin-yang remainder. If there is a surplus or deficiency in the day remainder, adjust the date using the month week number. Multiply the determined day remainder by the profit and loss rate; if the result equals the month week number, use the comprehensive number of profit and loss as the constant for midnight.
Next, calculate the dawn and dusk moments. Multiply the profit and loss rate by the nocturnal duration of the most recent solar term, then divide by 200 to get the number of moments for daylight; subtract the profit and loss rate from the calculated value to get the number of moments for dusk; use the midnight profit and loss value as the constant for dawn and dusk calculations.
Set the overtime; if it matches the constant defined at dawn, divide by 12 to obtain the degree. Multiply the remainder by one third; if it's less than one, it's considered strong; if it exceeds one, it's regarded as weak, and two weak values combine to count as one strong. The result is the degree to which the moon deviates from the ecliptic. For the solar calendar, subtract the extreme from the solar calendar based on the ecliptic; for the lunar calendar, add the extreme to obtain the degree of the moon's deviation from the extreme. Strong values are positive, while weak values are negative; same names are added, and different names are subtracted. When subtracting, same names cancel out, and different names add up; there is no complementary situation, so two strong minus one weak. From the Ji Chou year in the Shangyuan period to the Bing Xu year in the Jian'an period, a total of 7378 years have passed. 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. The five elements: Wood (Jupiter), Fire (Mars), Earth (Saturn), Metal (Venus), and Water (Mercury). Use their final day counts to approximate the celestial degrees, to obtain the weekly rate and daily rate. Multiply the chapter year by the weekly rate to derive the lunar method; multiply the chapter month by the daily rate to get the month part; divide the month part by the lunar method to get the month number. Multiply the common number by the lunar method to get the daily degree method. Multiply the Dipper by the weekly rate to get the Dipper part. (The daily degree method is multiplied by the record method by the weekly rate, so we also use parts to multiply here.) Finally, there are the large and small remainders of the new moon of the five stars. (Multiply the common method by the month number respectively; divide the daily method by the month number respectively, to get the large remainder; the remainder is the small remainder. Subtract the large remainder from 60.) The five stars enter the moon day and the daily remainder. (Multiply the common method by the month remainder respectively; use the conjunction method with the small remainder of the new moon, add them together, simplify with the meeting number, then divide by the daily degree method to get the final result.) This passage documents data from ancient astronomical calculations, which appears to be a record of a specific calendar or astrological calculation. Let's break it down sentence by sentence to discuss what these numbers represent in contemporary terms.
First, "the degree of the five stars and the remainder. (Subtract the excess amount to obtain the remainder, multiply by the number of weeks, and use the solar degree method to simplify; the result is the degree, and the remainder is referred to as the degree remainder. If the degree exceeds the number of weeks, subtract the number of weeks and add the Doufen.)" This sentence means to calculate the degrees and remainders of the five stars. The calculation method is: first subtract the excess amount to get the remainder; then multiply the remainder by the number of weeks, and use the solar degree method to divide it, with the quotient being the degree and the remainder being the degree remainder. If the degree exceeds the number of weeks, subtract the number of weeks and add the Doufen. In simple terms, it is a complex method for calculating the positions of celestial bodies, involving astronomical units such as weeks, solar degrees, and Doufen.
Next, the month count is 7,285; there are 7 leap months; the total number of months is 235; there are twelve in a year; the general method is 43,026; the solar method is 1,457; the meeting count is 47; the number of weeks is 215,130; Doufen is 145. These are some astronomical constants, such as the number of days in a year (month count), how many leap months there are (leap months), how many months are in a year (month count), and so on. The specific meanings of these numbers must be interpreted in the context of the calendrical system of the time. "Weeks" refers to a complete circumference, and "Doufen" may refer to a finer unit of measurement.
"Jupiter: orbital period, 6,722; solar period, 7,341; conjunction month count, 13; month remainder, 64,801; conjunction month method, 127,718; solar degree method, 395,925,858; new moon large remainder, 23; new moon small remainder, 1,307; entry month day, 15; day remainder, 348,466; new moon empty division, 150; Doufen, 974,690; degree count, 33; degree remainder, 250,995,956." This part is about the calculation data related to Jupiter. "Orbital period" and "solar period" may refer to some kind of orbital speed of Jupiter; "conjunction month count" may refer to the number of times Jupiter aligns with the moon within a cycle; these subsequent numbers may represent some intermediate or final results in the calculation process, and their specific meanings must be referenced against the calculation methods used at that time.
"Fire: Orbital circumference, three thousand four hundred seventy; solar period, seven thousand two hundred seventy-one; total lunar cycles, twenty-six; remaining days, twenty-five thousand six hundred twenty-seven; combined lunar method, sixty-four thousand seven hundred thirty-three; solar day method, two million six thousand seven hundred twenty-three; major new moon surplus, forty-seven; minor new moon surplus, one thousand one hundred fifty-seven; day of the new moon, twelve; remaining days, nine hundred seventy-three thousand one hundred thirteen; new moon virtual division, three hundred; Dipper division, four hundred ninety-four thousand one hundred fifteen; degrees total two hundred ninety-two; remaining degrees, one hundred ninety-nine thousand one hundred seventy-six." This section is about the calculation data for Mars, similar to the calculation method for Jupiter.
"Earth: Orbital circumference, three thousand five hundred twenty-nine; solar period, three thousand six hundred fifty-three; total lunar cycles, twelve; remaining days, fifty-three thousand eight hundred forty-three; combined lunar method, sixty-seven thousand fifty-one; solar day method, two hundred seventy-eight thousand five hundred eighty-one; major new moon surplus, fifty-four; minor new moon surplus, five hundred thirty-four; day of the new moon, twenty-four; remaining days, one hundred sixty-six thousand two hundred seventy-two; new moon virtual division, nine hundred twenty-three; Dipper division, five hundred eleven thousand seven hundred five; degrees total twelve; remaining degrees, one hundred seventy-three thousand three hundred forty-eight." This is about the calculation data for Saturn, with a similar calculation method.
"Metal: Orbital circumference, nine thousand twenty-two; solar period, seven thousand two hundred thirteen; total lunar cycles, nine." This is about the calculation data for Venus, with only partial data provided.
In summary, this text records the precise calculations of ancient astronomers regarding the movements of planets, involving a large number of values and complex calculation methods. This data can be quite challenging for modern readers to comprehend and requires in-depth study of the historical calendar and astronomical knowledge to fully grasp its meaning.
One month has passed; the data now stands at one hundred fifty-two thousand two hundred ninety-three.
According to the combined lunar method, the result is one hundred seventy-one thousand four hundred eighteen.
Using the solar day method, the result is five hundred thirty-one thousand three hundred ninety-eight.
Major new moon surplus is twenty-five.
Minor new moon surplus is one thousand one hundred twenty-nine.
Day of the new moon is twenty-seven.
Remaining days are fifty-six thousand nine hundred fifty-four.
New moon virtual division is three hundred twenty-eight.
Dipper division is one hundred thirty thousand eight hundred ninety.
Degrees total two hundred ninety-two.
Remaining degrees are fifty-six thousand nine hundred fifty-four.
Water: The Zhou constant is eleven thousand five hundred sixty-one.
The Sun rate is one thousand eight hundred thirty-four.
The combined lunar count is one.
In the next month, the remaining days of the month are two hundred thirteen thousand three hundred thirty-one.
The result of the combined lunar method is two hundred nineteen thousand six hundred fifty-nine.
The result of the daily method is six hundred eighty-nine thousand four hundred twenty-nine.
The major remainder is twenty-nine.
The minor remainder is seven hundred seventy-three.
The entry day of the month is twenty-eight.
The remaining days are six hundred forty-one thousand nine hundred sixty-seven.
The empty lunar month is six hundred eighty-four.
The constellation count is one hundred sixty-seven thousand six hundred forty-five.
The number of degrees is fifty-seven.
The remaining degrees are six hundred forty-one thousand nine hundred sixty-seven.
First, put the data of the previous year into it, multiply it by the Zhou constant; if it can be divided by the Sun rate to get one, it is called the accumulated total, and the part that cannot be divided is called the combined remaining. Divide it by the Zhou constant; if it can be divided to get one, it is the accumulated total of the previous year; if it gets two, it is the previous year of the combined total; if it cannot be divided, it is the combined year. Subtracting the Zhou constant from the combined remaining yields the degree. The accumulation of gold and water values: odd numbers signify morning, while even numbers signify evening.
Multiply the number of months and the remaining months respectively by the accumulated total; if the result can be divided by the combined lunar method, the month is obtained, and the part that cannot be divided is the remaining month. Subtract the accumulated month from the month, and the remaining is the entry month. Then multiply it by the leap month; if it can be divided by the chapter month to get a leap month, subtract the entry month, and the remaining part is subtracted in the middle of the year, which is outside the astronomical calculation, belonging to the combined month. If it coincides with the transition of the leap month, adjust it using the new moon.
Multiply the common method by the remaining months, and multiply the combined lunar method by the minor remaining, and then divide it by the number of meetings. If the result can be divided by the daily method to get one, it is the accumulated total of the month; the part that cannot be divided is the remaining days, which is outside the calculation of the new moon.
Multiply the Zhou constant by the number of degrees; if it can be divided by the daily method to get one degree, the remaining part is the remainder, and use the method of the first five cows to determine the number of degrees.
The above is the method of seeking the accumulated total.
Add up the number of months, add up the remaining months; if it can be divided by the combined lunar method to get a month, then it is the combined year; if it cannot be divided, in the middle of the year, consider the leap month, the remaining part is the following year; if it can be divided again, it is the next two years. The accumulation of gold and water: odd numbers signify morning, while even numbers signify evening.
First, let's calculate the moon's size. Add up the sizes of the new moon days; if the total exceeds a month, add another 29 (if it's a large remainder) or 773 (if it's a small remainder). When the small remainder is full, apply the same method used for the large remainder.
Next, calculate the entry days of the moon and the remaining days. Add up the entry days and the remaining days; if the remaining days are sufficient for a full day, add one more day. If the small remainder from the new moon perfectly fills the gap, subtract one day; if the small remainder exceeds 773, subtract 29 days; if it doesn't exceed, subtract 30 days, then calculate the entry day using the method for the next new moon.
Then, add up the degrees and the remaining parts of the degrees; if it's enough for a day's degree, add one degree.
Here are the movement data for Jupiter, Mars, Saturn, Venus, and Mercury:
Jupiter: Remains hidden for 32 days, 3,484,646 minutes; appears for 366 days; remains hidden to move for 5 degrees, 2,509,956 minutes; appears to move for 40 degrees (subtracting retrograde 12 degrees, actual movement 28 degrees).
Mars: Remains hidden for 143 days, 973,113 minutes; appears for 636 days; remains hidden to move for 110 degrees, 478,998 minutes; appears to move for 320 degrees (subtracting retrograde 17 degrees, actual movement 303 degrees).
Saturn: Remains hidden for 33 days, 166,272 minutes; appears for 345 days; remains hidden to move for 3 degrees, 1,733,148 minutes; appears to move for 15 degrees (subtracting retrograde 6 degrees, actual movement 9 degrees).
Venus: Remains hidden in the east in the morning for 82 days, 113,908 minutes; appears in the west for 246 days (subtracting retrograde 6 degrees, actual movement 240 degrees); remains hidden to move in the morning for 100 degrees, 113,908 minutes; appears in the east (daily degrees are the same as in the west, remains hidden for 10 days, retrograde 8 degrees).
Mercury: Remains hidden in the east in the morning for 33 days, 612,505 minutes; appears in the west for 32 days (subtracting retrograde 1 degree, actual movement 31 degrees); remains hidden to move for 65 degrees, 612,505 minutes; appears in the east (daily degrees are the same as in the west, remains hidden for 18 days, retrograde 14 degrees).
Wow, this text is pretty complicated; let's break it down line by line and put it in simpler terms.
First, use a fixed value referred to as "Law" to subtract the daily degree of the sun's movement and note the remainder. Then, add the daily degree of the star's movement to this remainder; if this new remainder reaches the value of "Law," it indicates that the stars and the sun have encountered each other, and the degree of their encounter has been calculated.
Next, use the denominator of the star's daily movement to multiply by the previously calculated encounter degree. The remainder, when the daily degree is subtracted from "Law," equals one; if it does not divide evenly and the remainder exceeds half of "Law," it is treated as if it were completely divided, counted as 1. Then, add the degrees of the sun's daily movement to the star's daily movement, and if it reaches a certain point, it counts as one degree. The calculation methods for direct and reverse movements differ and must be adjusted according to the current movement conditions to ultimately calculate the actual degrees of the stars' movement.
Those who stay inherit the previous calculations; if the stars are moving in reverse, subtract the appropriate degree. If the degree is insufficient after subtraction, a method of adjustment based on the star's speed ratio must be employed, during which there will be increases and decreases, and the results of calculations before and after will influence each other.
Any terms like "almost full" aim for precise calculations to obtain whole numbers; while "subtracting" and "completely dividing" require precise calculations to their final result.
Next is a description of the movement of Jupiter. "Jupiter: In the morning, it joins with the sun, disappears, follows, on the sixteenth day, at 2,742,323 minutes, the planet moves 2 degrees and 323,467 minutes, and is seen in the east in the morning after the sun. Then, it moves quickly; the sun travels 11 minutes out of a total of 58 minutes, and on the fifty-eighth day, it moves 11 degrees. Further on, it slows down, and the sun moves 9 minutes, and on the fifty-eighth day, it moves 9 degrees, remaining stationary for 25 days. In retrograde motion, the sun moves one-seventh of a degree and retreats twelve degrees on the eighty-fourth day. After another 25 days of no movement, it progresses again; the sun travels 9 minutes out of 58 minutes, and on the fifty-eighth day, it moves 9 degrees. Then, it moves quickly; the sun travels 11 minutes out of 58 minutes, and on the fifty-eighth day, it moves 11 degrees, appearing in the western sky in the evening before sunset. On the sixteenth day, at 2,742,323 minutes, the planet moves 2 degrees and 323,467 minutes, and joins with the sun. In total, after 398 days, or 348,446,646 minutes, the planet moves 43 degrees and 259,956 minutes." This passage describes the cycle of conjunction between Jupiter and the sun, the different speeds of Jupiter at various stages, and its position during conjunction with the sun. It details various scenarios of Jupiter's movement, including direct motion, retrograde motion, and stationary periods, along with corresponding speeds and times. The final sentence provides complete cycle data. This text is highly specialized, making it challenging to fully capture its essence in everyday language. It can only be summarized in general terms. In conclusion, this passage outlines how ancient astronomers calculated the trajectories of planets, which involved complex calculations and specialized terminology. Even when explained in modern Chinese, it remains somewhat obscure and difficult to understand.
Speaking of Mars, it appears in the morning with the sun, then it vanishes. Next, it proceeds direct for a total of 71 days, covering 1489868 minutes, which is 55 degrees and 242860.5 minutes. Then, in the morning, it can be seen in the east, behind the sun. While proceeding direct, it traverses 14 minutes and 23 seconds each day, covering 112 degrees over 184 days. Then, it slows down, covering 48 degrees in 92 days, moving 12 minutes each day. After that, it halts for another eleven days without moving. Then it starts moving in the opposite direction, retrograde, covering 17 degrees in 62 days, moving 17 minutes and 62 seconds each day. It stops again for eleven days, then starts proceeding direct again, covering 48 degrees in 92 days, moving 12 minutes each day. Moving in the same direction again, it speeds up, covering 112 degrees over 184 days, moving 14 minutes each day. At this point, it is in front of the sun and hides in the west at night. After 71 days, covering 1489868 minutes, which is 55 degrees and 242860.5 minutes, it aligns with the sun again. Overall, this cycle spans 779 days and 97313 minutes, covering 414 degrees and 478998 minutes.
Now, regarding Saturn, it also appears in the morning with the sun, then vanishes. It then proceeds direct for a total of 16 days, covering 1122426.5 minutes, which is 1 degree and 1995864.5 minutes. Then, in the morning, it can be seen in the east, behind the sun. While proceeding direct, it travels 3 minutes and 35 seconds daily, covering 7.5 degrees in 87.5 days. Then it halts for 34 days without moving. Then it starts moving in the opposite direction, covering 6 degrees in 102 days, moving 1 minute and 17 seconds daily. After 34 days, it starts proceeding direct again, covering 7.5 degrees in 87 days, moving 3 minutes each day. At this point, it is in front of the sun and hides in the west at night. After 16 days, covering 1122426.5 minutes, which is 1 degree and 1995864.5 minutes, it aligns with the sun once more. Overall, this cycle spans 378 days and 166272 minutes, covering 12 degrees and 1733148 minutes.
Venus, when it meets the sun in the morning, first "retrogrades," moving backwards five days and four degrees. Then in the morning, it can be seen in the east, behind the sun. Continuing to retrograde, it moves three-fifths of a degree each day, retreating a total of six degrees over the course of ten days. Then it "pauses," staying still for eight days. Next it "rotates," or begins to move forward, slowly at a speed of forty-six and a third degrees each day, covering a total of thirty-three degrees over the course of forty-six days. Then the speed increases, moving one degree and fifteen ninety-firsts each day, covering one hundred and six degrees over ninety-one days. It accelerates further, moving one degree and twenty-two ninety-firsts each day, covering one hundred and thirteen degrees over ninety-one days, at which point it is behind the sun and appears in the east in the morning. Finally, it moves forward for forty-one days, covering one five-thousand six-hundred ninety-fourth of a circle, with the planet also moving fifty degrees in this time, before meeting the sun again. In total, one complete cycle of meeting the sun takes two hundred and ninety-two days and one five-thousand six-hundred ninety-fourth of a circle, with the planet following this pattern.
When Venus meets the sun in the evening, it first "retrogrades" or moves forward for forty-one days, covering one five-thousand six-hundred ninety-fourth of a circle, with the planet moving fifty degrees in this time, before it becomes visible in the western sky in the evening, positioned ahead of the sun. It then continues moving forward at a faster speed, covering one hundred and thirteen degrees over ninety-one days. The speed then slows down, moving one degree and fifteen sixty-fourths each day, covering one hundred and six degrees over ninety-one days, before moving forward again. The speed slows down further, moving forty-six and a third degrees each day over forty-six days. It then "pauses," staying still for eight days. It then "rotates," or begins to retrograde, moving three-fifths of a degree each day, retreating six degrees over ten days, at which point it is in front of the sun and appears in the west in the evening. It then retrogrades, retreating four degrees in five days, before meeting the sun again. Two meetings with the sun make up one cycle, totaling five hundred eighty-four days and one one hundred thirty-nine thousand eight hundred ninety-first of a circle, with the planet following this pattern.
Mercury, when it meets the sun in the morning, first "伏," moves backward, retreats seven degrees in nine days, and then can be seen in the east in the morning, behind the sun. It continues to move backward quickly, retreating one degree each day. It then "pauses," remaining stationary for two days. It then starts to move forward slowly, covering eight-ninths of a degree per day, eight degrees in nine days. Then it speeds up, moving one and a quarter degrees per day, twenty-five degrees in twenty days, appearing in the east in the morning behind the sun. It then moves forward, covering six hundred forty-one million nine hundred sixty-seven millionths of a circle in sixteen days, the planet also covering thirty-two degrees and six hundred forty-one million nine hundred sixty-seven millionths of a circle, before meeting the sun again. The total duration of one conjunction is fifty-seven days and six hundred forty-one million nine hundred sixty-seven millionths of a circle, and the planet repeats this process.
Mercury, when it meets the sun, seems to conceal itself and obediently follow the sun. Specifically, every sixteen days, it moves thirty-two degrees and six hundred forty-one million nine thousand six hundred sixty-seven parts (this number is really precise!), and then can be seen in the evening to the west, positioned ahead of the sun. When it moves fast, it can cover one and a quarter degrees in a day, twenty-five degrees in twenty days. When it moves slowly, it only covers seven-eighths of a degree per day, eight degrees in nine days. If it "pauses," it will remain stationary for two days.
If it retrogrades, moving backwards, it retreats one degree per day, appearing in front of the sun, hiding in the west in the evening. When retrograding, it also travels slowly, retreating seven degrees in nine days, before finally meeting the sun again. From one conjunction to the next, it takes a total of one hundred fifteen days and six hundred one million two thousand five hundred five parts, and Mercury continues this repetitive cycle of motion.
