Paragraph 1:
Multiply the number of days it takes for the moon to orbit the Earth by the number of days that have elapsed, then subtract the number of whole weeks; the remainder is expressed in degrees, and any remainder less than one degree is considered a fraction. By using this method, you can calculate the position of the moon at midnight on the first day of the lunar month.
Paragraph 2:
To calculate the position of the moon in the next month, add 22 degrees, 258 minutes for a small month (29 days), and add 1 day, 13 degrees, and 217 minutes for a large month (30 days); one full degree is counted as one degree. By the end of the last ten days of winter, the moon is roughly near the Zhang and Xin constellations.
Paragraph 3:
Multiply the number of days in a year by the remaining degrees on the first day of the lunar month; the integer part you get is the major fraction, while the remaining part that is less than one is the minor fraction. Subtract the degrees at midnight on the first day from the major fraction, then calculate the degrees using the method mentioned above; this gives the position where the sun and moon are in conjunction.
Paragraph 4:
To calculate the situation for the next month, you need to add 29 degrees, 312 major fractions, and 25 minor fractions. Subtract the minor fractions from the major fractions when they reach their maximum, subtract the degrees when the major fractions are full, then divide by the major fractions. (This involves specific methods of ancient astronomical calculations, which are difficult to express accurately in modern language, retaining the original professional terminology.)
Paragraph 5:
To calculate the position of the first quarter moon, which occurs on the 7th, 15th, and 23rd days of the lunar month, add 7 degrees, 225 minutes, and 17.5 minor fractions to the conjunction degrees; by following the method mentioned above, you can find the position of the first quarter moon. By continuing this process, you can calculate the full moon (15th day of the lunar month), last quarter moon, and the position of the next month's conjunction.
Paragraph 6:
To calculate the position of the waxing gibbous moon, add 98 degrees, 480 major fractions, and 41 minor fractions to the conjunction degrees; by following the method mentioned above, you can determine the position of the waxing gibbous moon. By continuing this process, you can calculate the full moon, last quarter moon, and the position of the next month's conjunction.
Paragraph 7:
To calculate the degrees of solar and lunar eclipses (sunrise and sunset), multiply the degrees for a day by the number of days it takes the moon to orbit the Earth, multiply by the number of moments passed since the last solar term nightfall (an ancient timekeeping tool), then divide by 200 to get the daylight duration. Subtract the degrees for the day from this result, subtract the degrees for the month from this result; the remainder is the nighttime duration. Then, separately add the time at midnight, and calculate the degrees using the method mentioned above.
Paragraph 8:
Set the starting year (a specific reference year), subtract the cycle year of the specified year, multiply the remaining years by the cycle rate; if this equals the cycle year, it indicates the number of eclipses. If there is a remainder, add one. Multiply the remaining years by the meeting month (meeting cycle month) to get the accumulated months; any remainder less than a month counts as a month remainder. Multiply the intercalary month by the remaining years to get the accumulated intercalary months, then subtract it from the accumulated months. Subtract the remaining from a year, and the result is the number of days from the first day of the first month.
Ninth paragraph:
To calculate the next solar or lunar eclipse, add 5 months; this results in a full moon, with a month remainder of 1635.
Tenth paragraph:
Using the remainders from the winter solstice, multiply the remainder by two to get the day of the Kan hexagram (corresponding day of the Kan hexagram). Add 175 to the remainder, and subtract it from the remaining days of the Qian method (calculation method corresponding to the Qian hexagram) to determine the corresponding day of the Zhong Fu hexagram (corresponding day of the Zhong Fu hexagram).
Eleventh paragraph:
To calculate the next hexagram, add 6 to the remaining days and 103 to the remainder. For the four primary hexagrams (Qian, Kun, Zhen, Xun), multiply the remainder by two based on the middle day.
Twelfth paragraph:
Set the remaining days of the winter solstice, add 27 to the remaining days and 927 to the remainder, then subtract it from 2356 from the remaining days to determine the corresponding day of the Earth hexagram (corresponding day of the Earth hexagram). Add 18 to the remaining days and 618 to the remainder to obtain the corresponding day of the Wood hexagram (corresponding day of the Wood hexagram). Add 73 to the remaining days and 116 to the remainder to obtain the Earth again. According to the algorithm of Earth, you can then obtain the days corresponding to Fire, Metal, and Water.
First, multiply the remainder by twelve, then divide by a certain number (method) to get a Chen (a unit of time). Begin calculations from Zi Shi, using the remainder to determine the other lunar phases of Shuo, Xian, and Wang (lunar calendar lunar phases).
Next, multiply the remainder by one hundred, divide by a certain number (method) to get a quarter of an hour; if the result isn't a whole number, determine the decimal portion, then calculate from midnight based on the closest solar term until dawn. If the water level has not reached before dawn, use the closest value to represent it.
During the calculation process, there is advancement and retreat; advancement refers to addition, while retreat refers to subtraction. The difference between advancement and retreat starts from two degrees; for every increase of four degrees, the difference decreases by half. Repeat this three times until the difference reaches three; then, after five degrees, the difference returns to the initial state.
The speed of the moon's movement varies, sometimes fast and sometimes slow, cycling repeatedly, with the laws governing these changes remaining consistent. During calculations, various values between heaven and earth are combined by multiplying the remainder by itself, until the result matches a specific value, which gives the portion that exceeds a cycle. Then, the total number of weeks is subtracted from the number of lunar weeks to obtain the number of calendar days. The variations in the moon's speed reflect its movement patterns. By adding the decay value to the lunar movement rate, the daily movement in degrees and minutes is calculated. The decay values are summed, resulting in the net gain and loss rate. Profits are summed, and losses are deducted, leading to an accumulation of net gains and losses. Half a small week is multiplied by the standard method, then divided by the common number, and this result is then subtracted from the total number of weeks to obtain the minutes of the new moon's movement.
Here are the specific daily data:
Day | Rotation (Degrees:Minutes) | Retreats | Profit | Gain | Lunar Movement Minutes
Day 1: 14 degrees 10 minutes, one retreat, profit of 22, initial gain of 276
Day 2: 14 degrees 9 minutes, two retreats, profit of 21, gain of 22, 275
Day 3: 14 degrees 7 minutes, three retreats, profit of 19, gain of 43, 273
Day 4: 14 degrees 4 minutes, four retreats, profit of 16, gain of 62, 270
Day 5: 14 degrees, four retreats, profit of 12, gain of 78, 266
Day 6: 13 degrees 15 minutes, four retreats, profit of 8, gain of 90, 262
Day 7: 13 degrees 11 minutes, four retreats, profit of 4, gain of 98, 258
Day 8: 13 degrees 7 minutes, four retreats, loss of 102, 254
Day 9: 13 degrees 3 minutes, four retreats, loss of 4, profit of 102, 250
Day 10: 12 degrees 18 minutes, three retreats, loss of 8, gain of 98, 246
Day 11: 12 degrees 15 minutes, four retreats, loss of 11, gain of 90, 243
Day 12: 12 degrees 11 minutes, three retreats, loss of 15, gain of 79, 239
Day 13: 12 degrees 8 minutes, two retreats, loss of 18, gain of 64, 236
Day 14: 12 degrees 6 minutes, one retreat, loss of 20, gain of 46, 234
This text describes a complex lunar calculation method, involving many astronomical terms and calculation steps. Simply put, it explains how to calculate the daily movements of the moon using various astronomical data and provides specific data for fourteen days.
On the 15th, the moon is positioned at 12 degrees and 5 minutes. In the first calculation, reduce by 21 degrees and increase by 26 degrees, resulting in 233 degrees.
On the 16th, the moon is positioned at 12 degrees and 6 minutes. In the second calculation, reduce by 20 degrees (because it's insufficient, we need to adjust by changing the 20-degree reduction into a 5-degree increase; the increased 5 degrees must be deducted from the initial 20 degrees, resulting in insufficiency). Increase by 5 degrees, deducting from the initial 20 degrees, resulting in 234 degrees.
On the 17th, the moon is positioned at 12 degrees and 8 minutes. In the third calculation, increase by 18 degrees and reduce by 15 degrees, resulting in 236 degrees.
On the 18th, the moon is positioned at 12 degrees and 11 minutes. In the fourth calculation, increase by 15 degrees and reduce by 23 degrees, resulting in 239 degrees.
On the 19th, the moon is positioned at 12 degrees and 15 minutes. In the fifth calculation, increase by 11 degrees and reduce by 48 degrees, resulting in 243 degrees.
On the 20th, the moon is positioned at 12 degrees and 18 minutes. In the fourth calculation, increase by 8 degrees and reduce by 59 degrees, resulting in 246 degrees.
On the 21st, the moon is positioned at 13 degrees and 3 minutes. In the fifth calculation, increase by 4 degrees and reduce by 67 degrees, resulting in 250 degrees.
On the 22nd, the moon is positioned at 13 degrees and 7 minutes. In the fifth calculation, reduce degrees by 71 degrees, resulting in 254 degrees.
On the 23rd, the moon is positioned at 13 degrees and 11 minutes. In the fifth calculation, reduce 4 degrees and reduce by 71 degrees, resulting in 258 degrees.
On the 24th, the moon is positioned at 13 degrees and 15 minutes. In the fifth calculation, reduce 8 degrees and reduce by 67 degrees, resulting in 262 degrees.
On the 25th, the moon is positioned at 14 degrees. In the fifth calculation, reduce 12 degrees and reduce by 59 degrees, resulting in 266 degrees.
On the 26th, the moon moved to a position of fourteen degrees and four minutes. In the third calculation, add sixteen degrees (should be decreased), subtract forty-seven degrees, for a total of two hundred and seventy degrees.
On the 27th, the moon moved to a position of fourteen degrees and seven minutes. In the third calculation, add the value of three major Sundays, subtract nineteen degrees, subtract thirty-one degrees, for a total of two hundred and seventy-three degrees.
On Sunday, it was fourteen degrees and nine minutes. Subtract twenty-one degrees, subtract twelve degrees, for a total of two hundred and seventy-five degrees.
Sunday points, three thousand three hundred and three.
Zhou Void, two thousand six hundred and sixty-six.
Sunday method, five thousand nine hundred and sixty-nine.
Total Zhou, one hundred and eighty-five thousand thirty-nine.
Li Zhou, one hundred and sixty-four thousand four hundred and sixty-six.
Less big method, one thousand one hundred and one.
Shuo Xing Da Fen, eleven thousand eight hundred and one.
Small points, twenty-five.
Zhou half, one hundred and twenty-seven.
The above are various parameters for calculating the movement of the moon. Using these parameters and multiplying by the accumulated months of the month, subtract the small points from the large points when the small points reach thirty-one, subtract when it reaches one hundred and sixty-four thousand four hundred and sixty-six, and then divide by the Sunday method (five thousand nine hundred and sixty-nine) to get the number of days. If it is not a full day, it is treated as a remainder. This remainder must be calculated separately, with the ultimate goal of calculating the conjunction date into the calendar.
To calculate the next month, add one day, with a remainder of five thousand eight hundred and thirty-two and twenty-five small points. To calculate the crescent moon, add seven days to each, with a remainder of two thousand two hundred and eighty-three and twenty-nine point five small points. Break these down into days, subtract when it exceeds twenty-seven days, and treat the remainder like Sunday points. If it is not enough, subtract one day and add Zhou Void.
Wow, this is some serious astronomical calendar math! Let's break it down step by step, and I'll do my best to explain it simply.
First, it talks about how to calculate the gains and losses in the calendar. Multiply the accumulated gains and losses value (historical gains and losses accumulation) by the number of days in a week (weekly multiplication), then multiply by the daily gain and loss rate (profit and loss rate), add or subtract this result to obtain the gains and losses in overtime (overtime gains and losses). Then, subtract the degree of the moon's movement from a year (subtract the moon's movement from the year), multiply by half of the number of days in a week (half a week), to get a difference (known as the difference method), which is used to divide the gains and losses value to obtain the final size of the gains and losses. If the result is consistent with the daily gains and losses situation (daily gains are insufficient), adjust the time of the new moon (new moon overtime on the previous and following days). The adjustment of gains and losses during the waxing and waning phases of the moon (the 7th, 8th, 22nd, and 23rd of the lunar calendar) uses a larger remainder to determine (the waxing and waning moons have a large remainder, to determine the small remainder).
Next, it talks about how to determine the positions of the sun and moon. Multiply a year (year) by the overtime gains and losses, then divide by that difference (difference method) to obtain a full number, which is the size of the gains and losses. Then, adjust the positions of the sun and moon daily according to the gains and losses (increase or decrease the position of the sun and moon today; if there is a surplus, use the method to advance or retreat the degree to determine the position of the sun and moon).
Next is the calculation of the midnight entry into the calendar (calendar data at midnight). Multiply half of the number of days in a week (half a week) by the small remainder of the new moon day (new moon small remainder), then divide by the total number of days, and then subtract the remainder of the historical day (historical day remainder). If the result is insufficient, add a week’s worth of days and then subtract one day (subtract one day). Finally, add the number of days in a week to the remainder, which indicates the time of midnight entry into the calendar (subtract the number of days in a week and add its minute, thus obtaining the entry into the calendar at midnight).
To calculate the situation for the second day, begin with the previous day’s remainder and calculate through to twenty-seven days. If the remainder exceeds a week, subtract a week; if it’s less than a week, add the imaginary value of a week. The remainder is the remainder of the entry into the calendar on the second day (if it’s not a complete week, add the imaginary value to the remainder, all remaining as the remainder of the next day's entry into the calendar).
Then, it explains how to calculate the profit and loss of midnight. Multiply the remainder of the midnight calendar entry by the profit and loss ratio. If the result can be divided by the number of days in a week, the remainder represents the profit or loss value. If it cannot be divided, adjust the profit and loss value with the remainder (using the remainder of the midnight calendar entry multiplied by the profit and loss ratio; if the result is one based on the weekly method, then the remainder indicates the profit and loss value; if it is not, use the profit and loss to adjust the value of profit and loss (if the remainder is not lost, break it all as a loss, for the profit and loss of midnight)). One year is a unit, less is a fraction. Multiply the total by the fraction and the remainder; if the remainder can be divided by the number of days in a week, add it to the fraction; if the fraction reaches its limit, add it to the unit. Finally, adjust the midnight degree and remainder according to the profit and loss (by adding or subtracting the degree and remainder of midnight for profit and loss, to determine the degree).
Next, it describes how to calculate the daily decay change. Multiply the remainder of the calendar day by the column decay (a decay coefficient); if the result cannot be divided by the number of days in a week, the remainder is the daily decay change (multiply the remainder of the calendar day by the column decay; if the result is one based on the weekly method, then the remainder indicates the daily decay change).
Then, it explains how to update the decay coefficient. Multiply the virtual count of days in a week by the column decay to obtain a constant; add this constant after completing the calendar calculation. If it exceeds the column decay, subtract the column decay to get the decay coefficient of the next calendar (multiply the virtual count of days in a week by the column decay; if the weekly method is a constant, at the end of the calendar, add the change in decay, subtract the full column decay, and convert to the next calendar change in decay).
Finally, it describes how to adjust the degree of the calendar day using the decay coefficient. Adjust the degree and fraction of the calendar day with the decay coefficient; if the fraction exceeds or falls short, adjust the annual cycle (by adding or subtracting the decay to advance or retreat the calendar day to the fraction; if the fraction is insufficient, the annual cycle enters and exits the degree). Multiply the total by the fraction and the remainder, and add the midnight degree to get the degree of the next day. If the result of the calendar calculation does not align with Sunday, subtract 1338, then multiply by the total; if it aligns with Sunday, add 837, then subtract 899, finally add the decay coefficient of the next calendar and continue the calculation (if the calendar does not align with Sunday, subtract 1338, then multiply by the total; if it aligns with Sunday, add 837, then subtract 899, add the next calendar decay coefficient, and continue as before).
Finally, it explains how to calculate the profit and loss rate and use it to adjust the profit and loss at midnight. If the calculation result is insufficient, reverse the adjustment and add the remainder (to increase the profit and loss rate for the variable profit and loss rate, and to shrink the profit and loss at midnight. If the historical loss is insufficient, subtract it to the next historical loss, and adjust by adding and subtracting the remainder as mentioned above).
Finally, it explains how to calculate the twilight time. Multiply the monthly distance by the nighttime duration of the nearest solar term, then divide by 200 to get the bright minutes; subtract the bright minutes from the monthly distance to get the dark minutes. If the minutes exceed one year, multiply by the total count and add the nighttime distance to get the twilight moment distance. If the remainder is more than half, keep it; if less than half, discard it (multiply the historical monthly minutes by the nearest solar term nighttime duration, divide by 200 to get the bright minutes. Subtract the monthly distance to get the dark minutes. If the minutes exceed a year, multiply by the total count, add the nighttime distance to get the twilight moment distance. If the remainder is half or more, retain it; if less than half, discard it).
In conclusion, this passage outlines a complex method for calculating ancient calendars, involving many astronomical parameters and calculation steps. After reading it, I find my awe for ancient astronomical calendars has deepened even further!
This passage describes the calculation method of ancient calendars; in modern terms, it is to formulate calendars based on the lunar cycle. First, it explains how to calculate the length of a month and how to combine the lunar cycle with the solar cycle.
"The moon has four tables, three paths in and out, intersecting in the sky, dividing by the moon's rate to get the day of the calendar." This means that based on the four stages of the moon's orbit (tables) and the three changes in the moon's trajectory (three paths in and out), one can calculate the number of days in each month.
"Multiplying the weekly days by the conjunction of the new moon and full moon, like a month in one, the conjunction is also divided. Multiply the total by the conjunction number, subtract the remainder like the conjunction number, and retreat. To advance the minutes from the month, for the daily progress. The conjunction number is one, for the rate of difference." This passage describes a more complex calculation method, involving the weekly days (one year), the new moon to full moon cycle, and some coefficient multiplication and division operations, ultimately obtaining a rate of difference used to adjust the calendar.
Next, the table lists the "profit and loss rate" for each day, which is the number of days requiring adjustment each day, as well as the cumulative adjustment value. "On the first day, reduce by seventeen," "On the second day (upper limit of one thousand two hundred and ninety, differential four hundred and fifty-seven). This is the upper limit," and so on. These are specific calculation steps that look very complicated but are actually adjusted based on the subtle changes in the moon's movement to ensure that the calendar matches the actual celestial phenomena. "When excessive loss occurs, it means the moon has traveled half a week; once it has passed the extreme, it should be reduced." This indicates that corresponding adjustments must be made after the moon has traveled a certain distance.
"On the thirteenth day (limit of three thousand nine hundred and twelve, differential one thousand seven hundred and fifty-two). This is the rear limit... slightly larger value, four hundred and seventy-three." These numbers represent some intermediate results and parameters in the calculation process.
"Calendar cycle: one hundred seventy-five thousand six hundred sixty-five. Rate difference: one hundred ninety-eight thousand eighty-six. New moon conjunction: eighteen thousand three hundred twenty-eight. Differential: nine hundred fourteen. Differential method: two thousand two hundred nine." These numbers represent the cycle of the calendar, rate differences, and some important parameters.
"To calculate the month's departure from the upper element, multiply the remaining new moon conjunction and differential, and take the full differential from the conjunction. The remainder that does not complete the calendar week corresponds to the solar calendar; the full goes, the rest is the lunar calendar. All calculations assume the moon completes a week; the month's conjunction is calculated with the calendar, not solely based on the remaining days."
"Add two days, with two thousand five hundred and eighty days remaining, differential nine hundred fourteen. As required, complete the day in thirteen, except for the remaining fractional days. The Yin and Yang calendars ultimately enter the end, with the calendar before the front limit, and after the rear limit, the moon travels the middle way." This paragraph explains how to handle the remaining days, as well as the mutual conversion of the Yin and Yang calendars.
Finally, "each set of late and fast calendar surplus and reduction size distribution, multiply the number of meetings by the small distribution for the differential, surplus and reduction, add Yin and Yang days remaining. If the remaining surplus is insufficient, adjust the day accordingly to determine. Multiply the remaining days by the profit and loss rate; if the moon completes a week, use the profit and loss together as the determined time." This paragraph summarizes the final steps of the entire calendar calculation, determining the date of each day through adjustments of various parameters. In summary, this text outlines a highly intricate calendar calculation method that necessitates a strong grasp of mathematics and astronomy.
First, multiply the deviation rate by the decimal part of the new moon's remaining days to calculate a value, in a manner similar to calculus, and then subtract this value from the remaining days calculated in the calendar. If the result is insufficient, add the number of days in a month and subtract again, then subtract one more day. Next, add the remaining days to its fractional part, using the common denominator to simplify this fraction, thus determining the moment of the new moon's entry into the calendar at midnight.
Next, calculate the second day by adding one day to the first; the remaining days are 31, and the fraction is also 31. If this fraction exceeds the common denominator, subtract the number of days in a month. Then add one day; if the calendar calculation is complete and the remaining days exceed the fractional days, subtract the fractional days, which indicates the initial moment of entry into the calendar. If the remaining days do not reach the fractional days, simply add 2720, and the fraction adds 31, which gives the moment of entering the next calendar.
Multiply the common denominator by the late or early night half of the calendar and the remaining part; if the remaining part exceeds half a week, treat it as a small fraction. Add the surplus number to the reduced number and subtract the yin-yang remaining days. If the remaining days are surplus or insufficient, adjust the days using the monthly week. Multiply the determined remaining days by the profit-loss rate; if it equals the monthly week, use the combined profit-loss number to determine the value at midnight.
Multiply the profit-loss rate by the number of time segments at night of the nearest solar term and divide by 200 to get the brightness number. Subtract this brightness number from the profit-loss rate to get the dimness number, then use the profit-loss midnight number as the dim-bright constant.
If adding time equals the dim-bright constant, divide 12 by it to get the degree; multiply the remainder by one-third; if less than one, it is weak; if not reaching one, it is strong, and two weak values make it weaker. The result gives the degree to which the moon has departed from the ecliptic. The solar calendar uses the calendar of the ecliptic where the day is added and subtracts the extreme, while the lunar calendar uses the calendar of the ecliptic where the day is added and adds the extreme, thus determining the degree of the moon's departure from the extreme. Strong values are positive, weak values are negative; strong values and weak values are added together, same names are added, different names are subtracted. When subtracting, same names cancel out, and different names are added; there is no complementary situation, and two strong values add one weak value.
From the year of the first month of the Ji Chou to the year of the eleventh year of Jian'an in the year of Bing Xu, a total of 7,378 years have elapsed.
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
Five Planets: Wood corresponds to Jupiter; Fire to Mars; Earth to Saturn; Metal to Venus; and Water to Mercury. Each corresponds to specific days and celestial measurements, obtaining the weekly and daily rates. Multiply the annual rate by the weekly rate to calculate the lunar method; multiply the lunar method by the daily rate to obtain the lunar division; divide the lunar division by the lunar method to determine the number of months. Multiply the total by the lunar method to obtain the daily method. Multiply the constellation by the weekly rate to obtain the constellation division. (The daily method is multiplied by the calendar calculations to obtain the weekly rate, so multiplication is also used here.)
The five planets yield both large and small remainders. (Multiply the total calculation method by the number of months separately, divide the daily method by the number of months separately, to obtain the large remainder, and then subtract the large remainder from 60 to get the small remainder.)
The five planets enter the lunar day and the daily remainder. (Multiply the total calculation method by the lunar remainder separately, multiply the total lunar method by the remaining small remainder of the new moon day, add them up, simplify the results, then divide by the daily method to obtain the results.)
This passage documents calculations from ancient astronomical calendar systems, which appears to be the calculation parameters of a certain calendar system. Each sentence is translated into modern vernacular while trying to maintain the original meaning.
First, this passage describes the calculation method of the movement of celestial bodies (possibly Jupiter, Mars, Saturn, Venus). "Calculate the degree and remaining degree of the five planets. If the result exceeds a week (a full rotation), subtract the week; the remaining is the remaining degree, and consider the constellation division (a more subtle unit of measurement). This part involves professional terms in astronomical calculations, and we only need to understand that it is a method for calculating the positions of celestial bodies.
Next is a list of various parameters: "Recorded months: 7,285; Intercalary months: 7; Recorded months: 235; Months in a year: 12; Total method: 43,026; Daily method: 1,457; Simplification: 47; Week: 215,130; Constellation division: 145." These numbers represent different astronomical calendar parameters, such as the recorded months referring to the total number of months in a certain period, intercalary months indicating the number of intercalary months, recorded months possibly being the number of months in a special cycle, and months in a year referring to the months in a year. The meanings of these numbers should be interpreted within the context of the calendar system of that era.
Continuing to look further down, it is about the calculation parameters for Jupiter: "Jupiter: circumference, six thousand seven hundred twenty-two; daily angular motion, seven thousand three hundred forty-one; synodic month count, thirteen; remaining lunar months, sixty-four thousand eight hundred one; synodic month method, one hundred twenty-seven thousand seven hundred eighteen; daily degree method, three million nine hundred fifty-nine thousand two hundred fifty-eight; new moon remainder, twenty-three; small new moon remainder, one thousand three hundred seven; new moon entry day, fifteen; day remainder, three million four hundred forty-six thousand four hundred sixty-six; new moon virtual division, one hundred fifty; Big Dipper division, ninety-seven thousand four hundred sixty-nine; total degree count, thirty-three; degree remainder, two hundred fifty million nine hundred ninety-five thousand six." These numbers represent various rates, cycles, and remainders of Jupiter's orbit; for example, the circumference may indicate the speed at which Jupiter completes one orbit around the heavens, and the daily angular motion may reflect the degrees Jupiter travels in one day, etc. This data is highly specialized, but all we need to know is that it's used to calculate Jupiter's position.
Next are similar parameters for Mars, Saturn, and Venus, which list their respective circumferences, daily angular motions, synodic month counts, remaining lunar months, and other data in the same manner. "Mars: circumference, three thousand four hundred seven... degree remainder, one hundred ninety-nine thousand one hundred seventy-six; Saturn: circumference, three thousand five hundred twenty-nine... degree remainder, one hundred seventy-three thousand three hundred forty-eight; Venus: circumference, nine thousand twenty-two; daily angular motion, seven thousand two hundred thirteen; synodic month count, nine." These figures are similar to Jupiter's and are parameters used to calculate the positions of each planet. The specific meanings and calculation methods behind these figures require a deep understanding of ancient astronomical calendars to comprehend. In summary, this passage records a set of very complex ancient astronomical calculation data, rich in ancient astronomical knowledge.
A month has passed, and the calculated value is one hundred fifty-two thousand two hundred ninety-three. Using the synodic month method, the result is one hundred seventy-one thousand four hundred eighteen. Using the daily degree method, the result is five million three hundred eleven thousand nine hundred fifty-eight. The new moon remainder is twenty-five. The small new moon remainder is one thousand one hundred twenty-nine. The new moon entry day is twenty-seven. The day remainder is fifty-six thousand nine hundred fifty-four. The new moon virtual division is three hundred twenty-eight. The Big Dipper division is one hundred thirty thousand eight hundred ninety. The total degree count is two hundred ninety-two. The degree remainder is fifty-six thousand nine hundred fifty-four.
Water: The weekly rate is eleven thousand five hundred sixty-one.
The day rate is one thousand eight hundred thirty-four.
The total number of months is one.
For the next month, the remainder for the month is two hundred eleven thousand three hundred thirty-one.
The result from the combined month method is two hundred nineteen thousand six hundred fifty-nine.
The result calculated by the day degree method is six million eight hundred ninety-four thousand two hundred twenty-nine.
The large remainder of the new moon is twenty-nine.
The small remainder of the new moon is seven hundred seventy-three.
The entry month day is twenty-eight.
The day remainder is six million four hundred one thousand nine hundred sixty-seven.
The new moon's virtual division is six hundred eighty-four.
The Doufen is one million six hundred seventy-six thousand three hundred forty-five.
The degree number is fifty-seven.
The degree remainder is six million four hundred one thousand nine hundred sixty-seven.
First, calculate the value for the Yuan year and multiply it by the weekly rate. If the result is evenly divisible by the day rate, record it as the combined total; any remainder is the combined remainder. Using the weekly rate to divide the combined remainder, if it can be evenly divided, it represents how many years ago the star conjunction was; if it cannot be divided, check which year it is. Subtracting the weekly rate from the combined remainder gives the degree division. The combined total of gold and water, odd numbers are for morning, even numbers are for evening.
Using the month number and month remainder to multiply by the combined total, if the result can be evenly divided by the combined month method, we get the month, and the part that cannot be divided is the new month remainder. Subtract the combined month from the recorded month, and the remainder is the entry recorded month. Then multiply by the chapter leap; if it can be evenly divided by the chapter month, we get a leap month, subtract it from the entry recorded month, and the remaining part is then subtracted from the year, resulting in the total days beyond the correct calculation of the combined month. If it is during the transition of the leap month, use the new moon to adjust.
Using the general method to multiply by the month remainder, the combined month method to multiply by the small new moon remainder, and then simplify the combined number, if the result can be evenly divided by the day degree method, we get the entry month day of the star conjunction. The part that cannot be divided is the day remainder, noted outside the correct calculation.
Using the weekly sky to multiply by the degree division, if it can be evenly divided by the day degree method, we get one degree; the part that cannot be divided is the remainder, and this degree number starts counting from five before the ox.
This is the method for determining star conjunctions.
Add the month numbers together and also add the month remainders; if it can be evenly divided by the combined month method, we get one month. If it is within one year, use it to determine the year. If it exceeds one year, subtract one year and account for any leap months. The remaining part is the value for the following year; if it exceeds one year again, it is the value for the following two years. Gold and water added in the morning yield evening, and adding evening yields morning.
Let's first calculate the size of the lunar cycle. Add the sizes of the new moon together; if it exceeds one month, add another twenty-nine days (for the large remainder) or seven hundred seventy-three minutes (for the small remainder value). When the small remainder value is full, calculate it using the method for large remainders, and everything else remains the same as before.
Next, calculate the lunar date and the day remainder. Add the lunar date and the day remainder together; when the remainder is full, it counts as one day. If the small remainder value from the previous new moon just fills the fractional part, subtract one day; if the small remainder value exceeds seven hundred seventy-three, subtract twenty-nine days; if it does not exceed, subtract thirty days, and the remainder will be calculated based on the lunar date of the next new moon.
Finally, add the degree values together, and also add the remainders of the degrees; when the total reaches a full degree, it counts as one degree.
Below are the operational data for Jupiter, Mars, Saturn, Venus, and Mercury:
Jupiter: Latent phase operation 32 days, 3484646 minutes; Visible phase operation 366 days; latent phase operation 5 degrees, 2509956 minutes; visible phase operation 40 degrees. (Retrograde 12 degrees, actual operation 28 degrees.)
Mars: Latent phase operation 143 days, 973113 minutes; Visible phase operation 636 days; latent phase operation 110 degrees, 478998 minutes; visible phase operation 320 degrees. (Retrograde 17 degrees, actual operation 303 degrees.)
Saturn: Latent phase operation 33 days, 166272 minutes; Visible phase operation 345 days; latent phase operation 3 degrees, 1733148 minutes; visible phase operation 15 degrees. (Retrograde 6 degrees, actual operation 9 degrees.)
Venus: Latent phase in the eastern sky for 82 days, 113908 minutes; Visible phase operation in the west, 246 days. (Retrograde 6 degrees, actual operation 240 degrees.) Latent phase operation in the morning for 100 degrees, 113908 minutes; visible phase operation in the east. (The day degree is the same as in the west, latent for 10 days, retrograde 8 degrees.)
Mercury: Latent phase in the morning for 33 days, 612505 minutes; Visible phase operation in the west, 32 days. (Retrograde 1 degree, actual operation 31 degrees.) Latent phase operation 65 degrees, 612505 minutes; visible phase operation in the east. (The day degree is the same as in the west, latent for 18 days, retrograde 14 degrees.)
First, let's calculate the positions of the sun and stars. Calculate the degrees the sun travels each day, and then add the degrees the stars travel each day. If the total is an exact integer multiple of the degrees the sun travels each day, it indicates that the stars and the sun are coinciding, and we will be able to see the stars. The calculation method is: multiply the degrees the stars travel each day by the denominator, then divide by the degrees the sun travels each day. If the division does not yield a whole number, any remainder over half is rounded up to the nearest integer. Then add the resulting integer to the degrees the stars travel each day; if it equals the denominator, it indicates the stars have traveled one degree. The methods for direct and retrograde motion are different and should be calculated based on the current direction of the stars and the denominator. If the stars are stationary, meaning they have stopped moving, then maintain the previous value; if they are in retrograde, subtract. If the calculated degrees are not integers, use the method of Dou division to adjust based on the stars' speed. In short, expressions like "盈约满" are used for precise calculations involving division; "去及除之，取尽之除也" means to eliminate all parts that can be divided completely.
Next, let's talk about Jupiter. Jupiter appears in the morning alongside the sun and then becomes invisible, which is direct motion. According to the calculations, after 16 days, the sun has traveled 1,742,323 minutes, and Jupiter has traveled 2,323,467 minutes. At this point, Jupiter appears behind the sun in the east. While in direct motion, Jupiter moves quickly, covering 11/58 of a degree each day, or 11 degrees in 58 days. Following this, Jupiter remains stationary for 25 days. During retrograde motion, it moves at a rate of 1/7 of a degree each day, or retreats 12 degrees in 84 days. Then it stops again for 25 days, after which it resumes direct motion, traveling 9/58 of a degree per day, or 9 degrees in 58 days. The speed during direct motion increases again, traveling 11 minutes per day, or 11 degrees in 58 days. At this stage, Jupiter is positioned in front of the sun and disappears from view in the west by evening. After 16 days, the sun has traveled 1,742,323 minutes, and Jupiter has traveled 2,323,467 minutes, and they coincide again. Thus, one complete cycle is calculated to last 398 days, during which the sun travels 3,484,646 minutes and Jupiter covers 43 degrees and 2,509,956 minutes.
Sun: In the morning, it appears together with the sun and then hides away. Next is direct motion, lasting 71 days, with a total of 1,489,868 minutes, meaning the planet moved a total of 55 degrees and 242,860.5 minutes. Then it can be seen in the eastern sky in the morning, positioned behind the sun. During direct motion, it moves approximately 14/23 degrees each day, covering a total of 112 degrees over the course of 184 days. The speed of direct motion increases a bit and then slows down, moving approximately 12/23 degrees per day, covering a total of 48 degrees over the course of 92 days. Then it stops moving for 11 days before going retrograde. After that, it goes retrograde, moving approximately 17/62 degrees per day, retreating 17 degrees in 62 days. It stops moving again for 11 days, then it resumes direct motion, moving 1/12 degrees per day, covering a total of 48 degrees over the course of 92 days. It goes direct again, moving quickly at 1/14 degrees per day, covering a total of 112 degrees over the course of 184 days, at which point it is positioned in front of the sun and sets in the western sky in the evening. For 71 days, it is active for a total of 1,489,868 minutes, meaning the planet moved a total of 55 degrees and 242,860.5 minutes, and then it appears again with the sun. This entire cycle lasts a total of 779 days and 973,113 minutes, with the planet moving a total of 414 degrees and 478,998 minutes.
Mars: In the morning, it appears together with the sun and then hides away. Next is direct motion, lasting 16 days, with a total of 1,122,426.5 minutes, meaning the planet moved a total of 1 degree and 1,995,864.5 minutes. Then it can be seen in the eastern sky in the morning, positioned behind the sun. During direct motion, it moves approximately 3/35 degrees each day, covering a total of 7.5 degrees over the course of 87.5 days. Then it stops moving for 34 days. After that, it goes retrograde, moving approximately 1/17 degrees per day, retreating 6 degrees in 102 days. After another 34 days, it resumes direct motion, moving 1/3 degrees per day, covering a total of 7.5 degrees over the course of 87 days, at which point it is in front of the sun and hides in the west in the evening. For 16 days, it is active for a total of 1,122,426.5 minutes, meaning the planet moved a total of 1 degree and 1,995,864.5 minutes, and then it appears again with the sun. This entire cycle lasts a total of 378 days and 166,272 minutes, with the planet moving a total of 12 degrees and 1,733,148 minutes.
Venus, when it meets the sun in the morning, first "hides," meaning it goes into retrograde. In five days, it moves back four degrees; then, in the morning, it can be seen in the east, positioned behind the sun. As it continues to retrograde, it moves three-fifths of a degree each day, totaling six degrees in ten days. Next comes "station," where it remains still for eight days. Then it "turns," starting to move forward at a slower speed, moving forty-six-thirds of a degree each day, covering thirty-three degrees in forty-six days. Speeding up, it moves one degree and fifteen ninety-firsts each day, moving one hundred and sixty degrees in ninety-one days. Further increasing its speed, it moves one degree and twenty-two ninety-firsts each day, moving one hundred and thirteen degrees in ninety-one days; at this point, it has moved ahead of the sun, becoming visible in the east in the morning. Finally, after moving forward for forty-one days and five hundred sixty-nine minutes, covering fifty degrees and five hundred sixty-nine minutes, it meets the sun again. The conjunction cycle lasts two hundred ninety-two days and five hundred sixty-nine minutes, with Venus's movement degrees being identical.
When Venus meets the sun in the evening, it also first "hides," but this time it is in direct motion. It then continues moving forward, accelerating to one degree and twenty-two ninety-firsts each day, moving one hundred and thirteen degrees in ninety-one days. The speed then begins to decrease, moving fifteen minutes daily, and subsequently, the forward movement slows down. The speed slows down, moving forty-six-thirds of a degree each day, covering thirty-three degrees in forty-six days. Next comes "station," where it remains stationary for eight days. This time, it enters retrograde, moving three-fifths of a degree each day, reversing six degrees in ten days; at this point, it has moved behind the sun, becoming visible in the west during the evening. While "hiding" and retrograding at a fast pace, it reverses four degrees in five days, and finally meets the sun again. Two conjunctions constitute one cycle, totaling five hundred eighty-four days and eleven thousand three hundred ninety-eight minutes, with Venus's movement degrees being identical.
When Mercury conjoins with the Sun in the morning, it first "lies in wait," moves in retrograde, moves back seven degrees over nine days, and can then be seen in the east in the morning, positioned behind the Sun. Continuing its retrograde motion at a fast pace, it retreats one degree each day. It then "stays," remaining stationary for two days. Next, it "spins," beginning its direct motion, moving at a slower speed of 0.8 degrees each day, completing eight degrees over a period of nine days to move past the Sun. Its speed increases to 1.25 degrees per day, covering twenty-five degrees in twenty days, at which point it moves ahead of the Sun and appears in the east in the morning. On the sixteenth day, while in direct motion and "lying in wait," it has traveled thirty-two degrees and six hundred forty-one million nine hundred sixty-seven minutes, and it conjoins with the Sun again. The period for one conjunction is fifty-seven days and six hundred forty-one million nine hundred sixty-seven minutes, and the degrees Mercury travels are the same.
When the Sun sets, it conjoins with Mercury, which then becomes hidden. The pattern of Mercury's motion shows it travels thirty-two degrees and six hundred forty-one million nine hundred sixty-seven minutes over a period of sixteen days. Then, in the evening, it can be seen in the west, ahead of the Sun. If Mercury moves quickly, it can travel 1.25 degrees in a day, covering twenty-five degrees in twenty days. If it moves slowly, it travels just seven-eighths of a degree each day, taking nine days to travel eight degrees. Sometimes it will stop, remaining motionless for two days. If Mercury is in retrograde, it retreats one degree each day, positioned ahead of the Sun, and then becomes hidden in the west in the evening. If the retrograde motion is slow, it retreats seven degrees over nine days before conjoining with the Sun again.
From the time of the first conjunction of Mercury with the Sun to the final conjunction, it takes a total of one hundred fifteen days and six hundred one million two thousand five hundred five minutes for Mercury to follow this motion pattern.
