First, determine the year, then multiply the number of days you want to calculate by the year’s remainder. If the result exceeds the calendar system (also known as a cycle), note the excess as the large remainder, and the portion that remains is the small remainder. Divide by 60 to get a number; this number represents the date of the winter solstice.
Next, take the small remainder from the winter solstice and add 15 times the large remainder to it, where the small remainder is 515 and the large remainder is 2356, calculated as previously described.
Subtract the leap remainder from the standard year (one year), and multiply the remaining number by the day of the year (a certain day in the year). If the result exceeds the chapter leap (the leap month in a year), it counts as one month; if not, exceeding half also counts as one month. If it’s a whole month, it’s disregarded; otherwise, it’s not counted.
Then, add 7 to the large remainder, which gives a small remainder of 557. Subtract the small remainder from the large remainder using the daily calculation method, and calculate the remaining part as before to find the date of the first quarter moon. By adding, you can then determine the full moon, last quarter, and new moon for the following month. If the small remainder for the quarter moon is below 410, multiply by 100 for the fraction; if it exceeds the daily calculation, it counts as a quarter; if insufficient, calculate the fraction proportionally, and based on the solar terms and the time not completed at night, determine the specific date.
Next, recalculate the year by multiplying the desired number of days by the year’s remainder; exceeding the calendar system indicates the accumulated loss, and the remainder is added to the accumulated loss, resulting in 1. Then multiply this result by the meeting method; exceeding the loss means it is the large remainder, and not exceeding is the small remainder. The large remainder is the date of the solar eclipse occurring after the winter solstice.
To calculate the next solar eclipse, add 69 to the large remainder and 64 to the small remainder; if the result exceeds, subtract it from the large remainder, and if there is no fraction, it is not considered.
Use the calendar system to multiply by the accumulated days (the number of days the solar eclipse occurs), subtract the weekly cycle (one cycle), and divide the remainder by the calendar system; the resulting value is expressed in degrees. Starting from the five degrees before the constellation of the Cow, subtract the constellation order; if it falls short of one constellation order, that is the position of the sun at midnight on the first day of the first month (the midnight of the New Year).
To calculate the next day, add one degree, and divide by the fraction using the Dipper (constellation); if the fraction is small, subtract one degree as the calendar method and then add it back in.
Multiply the monthly week by the accumulated days, subtract the weekly cycle; if the remainder exceeds the calendar system, it is the degree; if not, it is the fraction. Use the aforementioned method to determine the moon's position at midnight on the first day of the month.
Next month, Xiao Yue will add 22 degrees and 258 minutes; Da Yue adds one day, 13 degrees, and 217 minutes, exceeding the limit counts as one degree. In the latter part of winter, the moon is near Zhang Su and Xin Su.
Multiply the number of years by the remainder of the lunar month on the first day; if it exceeds the total, it counts as a large fraction; if not, it counts as a small fraction. Subtract the midnight fraction from the large fraction; if it exceeds the law, subtract it from the degrees. Calculate the time of the new moon (first day) according to the method above.
For the next month, add 29 degrees, 312 large fractions, and 25 small fractions. If the small fraction exceeds the total, subtract it from the large fraction; if the large fraction exceeds the law, subtract it from the degrees, then divide by the large fraction.
To calculate the position of the first quarter moon, add 7 degrees, 225 minutes, and 17.5 small fractions; using the method outlined above, calculate the position of the first quarter moon.
First, we need to calculate the position of the first quarter moon. Add 98 degrees (the degree of the new moon) to the first day of the month, then add 48 large fractions and 41 small fractions respectively. Add up these degrees and fractions, and if they match the degree of the new moon calculated before, you will get the position of the first quarter moon. Continue to calculate, and you can get the positions of the full moon, last quarter, and the new moon of the next month.
Next, calculate the brightness of the day and night. Multiply the method of recording days using the lunar cycle by the night leak of the nearest solar term, then divide by 200 to get the bright fraction (daytime). Subtract the method of recording days for the day, and subtract the lunar week for the month; the remaining is the dark fraction (nighttime). Add the bright fraction and the dark fraction to midnight to calculate the specific degrees.
Then, we need to consider the calculation for the first year. Subtract the year you want to calculate from the year of the first year, and multiply the remaining years by the fixed rate. If the result is the year of the meeting (the number of years of the first year), then add 1; if the result is the month of the meeting, then record the remainder. Multiply the remaining years by the leap (leap month situation); if it completes a full cycle of years, record the accumulated leap (number of leap years), subtract from the accumulated month, and subtract from the year. If there is still a remainder, start calculating from the first day of the first month.
To calculate the next solar eclipse, add 5 months; if the remainder is 1635, you will get a month, and this month corresponds to the full moon.
Calculate the days based on the major and minor remainders of the Winter Solstice. The major remainder of the Winter Solstice multiplied by two is the day for the Kan trigram. If the minor remainder plus 175 follows the pattern of the Qian trigram, then use the major remainder for the Zhong Fu trigram day.
Calculate the hexagram figure by adding 6 to the major remainder and 103 to the minor remainder. Each of the four trigrams uses one of these days, then double the minor remainder.
Calculate the major and minor remainders of the Winter Solstice; add 27 to the major remainder and 927 to the minor remainder. If it follows the pattern of 2356, then use the major remainder to determine the day associated with the Earth trigram. Add 18 to the major remainder and 618 to the minor remainder to obtain the day for the Wood trigram of the Beginning of Spring. Add 73 to the major remainder and 116 to the minor remainder to obtain Earth again. Continue calculating in the order of Earth, Fire, Metal, Water.
Multiply the minor remainder by 12; if it completes a full cycle, you will obtain a Chen (Earthly Branch), counting from Zi. Apart from this calculation, use the new moon, first quarter, and full moon phases to calculate the minor remainder.
Multiply the minor remainder by 100; if it completes a full cycle, you will obtain a moment; otherwise, express it in fractions. Then calculate the minutes, starting from midnight of the nearest solar term; if the water level is not full at midnight, use the nearest value to describe.
During the calculation, there will be progress or regression: add for progress and subtract for regression. Differences in progress and regression begin at two degrees, decreasing by four degrees, halving, then multiplying by three, decreasing three times and stopping. After five degrees, it returns to the initial value.
The moon's speed varies, repeating in cycles. Use the numbers between heaven and earth for a cycle, multiply by the square of the remainder rate, then divide by the cycle to get the excess part of the cycle. Divide 360 degrees by the lunar cycle to get the number of days in a cycle. The speed varies with attenuation; the change is a trend. Add the attenuation and the lunar rate to get the daily rotation degree. Add the left and right attenuation to get the profit and loss rate. Add for profit, subtract for loss; this represents the accumulation of both gains and losses. Multiply half of the small cycle by the general method, then divide by the general number, subtract from the historical cycle, to get the degree of the new moon (the degree of movement of the new moon).
Ancient people's calculation of the daily movement is truly complex! Take a look at the first sentence: "daily rotation degree, attenuation, profit and loss rate, accumulation of gains and losses, lunar movement degree." It discusses the sun's daily movement, which fluctuates over time and ultimately influences the moon's trajectory.
Next, let's start the specific calculations. Fourteen degrees and ten minutes for the day, then subtract a little and add a little, recording the surplus and the total clearly. For example, on the second day, it is fourteen degrees and nine minutes; it decreased again but increased by a larger amount, so the surplus increases to twenty-two, and the total is two hundred and seventy-five. On the third day, it is fourteen degrees and seven minutes, decreased more, increased less, making the total become two hundred and seventy-three.
Continuing on to the fifth day, fourteen degrees, the degrees of decrease and increase are fluctuating, the surplus is also changing, and the total is also changing, making it quite confusing to look at. This ancient calculation method is different from what we use now; it is truly admirable for their patience and meticulousness.
From the sixth day to the tenth day, the degrees and surplus are changing every day, sometimes increasing, sometimes decreasing, and the total is constantly changing. This calculation process is so complex that it gives you a headache; no wonder the ancients spent a lot of time studying astronomy and calendars.
From the eleventh day to the fifteenth day, the pattern of degree changes remains complex; the decrease and increase in degrees are changing, the surplus also fluctuates, and the total changes accordingly. This is just a numbers game that gives you a headache!
By the sixteenth day, the calculation method changes again, with the emergence of a phrase: "if the decrease is insufficient, add five instead; if there is a surplus of five, add five, and the initial decrease of twenty degrees, hence the insufficiency." This ancient method of calculation is truly baffling!
From the seventeenth day to the twenty-third, the changes in degrees, surplus, and total continue, still complex and ever-changing. This calculation method is truly amazing; the wisdom of the ancients is truly impressive! The following lines succinctly summarize the essence of the entire calculation process: "day turns into degrees, listed as decline, loss and gain ratio, surplus and contraction accumulation, month divided into minutes." This complex calculation also allows us to appreciate the hardships of ancient astronomical calendar research.
On the twenty-fourth day, thirteen degrees and fifteen minutes, add eight, subtract eight, reduce by sixty-seven, a total of two hundred and sixty-two. On the twenty-fifth day, fourteen degrees, add twelve, subtract twelve, reduce by fifty-nine, a total of two hundred and sixty-six.
For twenty-six, fourteen degrees and four minutes, add sixteen and subtract sixteen, reduce by forty-seven, a total of two hundred and seventy.
For twenty-seven, fourteen degrees and seven minutes, three times initial advance, add three big Sundays, subtract nineteen, reduce by thirty-one, a total of two hundred and seventy-three.
For big Sunday, fourteen degrees and nine minutes, make a slight advance, add or subtract twenty-one, reduce by twelve, a total of two hundred and seventy-five.
Next, here are some astronomical terms: Sunday division, three thousand three hundred and three; Sunday void, two thousand six hundred and sixty-six; Sunday law, five thousand nine hundred and sixty-nine; through Sunday, one hundred and eighty-five thousand thirty-nine; historical Sunday, one hundred and sixty-four thousand four hundred and sixty-six; less big law, one thousand one hundred and one; first walk big points, eleven thousand eight hundred and one; sub-points, twenty-five; half of the week, one hundred and twenty-seven.
This paragraph explains how to calculate some parameters of the moon's movement, including Sunday division, Sunday void, Sunday law, etc., which will be used in subsequent calculations. These numbers represent different astronomical cycles and parameters, used to more accurately calculate the lunar orbit.
To calculate the conditions for the next month, add one day; the remaining days total five thousand eight hundred thirty-two, and the sub-points are twenty-five. To calculate the crescent moon (the fifteenth and first day of the lunar month), add seven days respectively; the remaining days total two thousand two hundred and eighty-three, and the sub-points are twenty-nine point five. These points must be converted into days according to established rules; subtract twenty-seven days when it reaches twenty-seven days, and the remaining days are the weekly division. If it is not enough to divide, subtract one day, and then add the Sunday void.
Multiply the accumulated gains and losses by the total number of Sundays to get a result. Then multiply the total number by the remaining days, and then multiply by the profit and loss rate; use this result to adjust the previous gains and losses; this represents the adjustments for gains and losses. Subtract the month's travel points from the lunar age, multiply by half of the week to get a difference value, use it to divide the previous result, and get the addition and subtraction value of gains and losses. Then adjust the date of the new moon (first day) according to the profit and loss situation; the advance and retreat of the crescent moon is also determined by the big remaining.
Multiply the lunar age by the additional gain and shrinkage, divide by the difference method; the result is the size of the gain and shrinkage. Adjust the position of the sun and moon of the day according to the gains and losses; if there are insufficient gains, adjust the degrees and minutes according to the calendar method, ultimately determine the positions and angles of the sun and moon.
Using the remainder of the week multiplied by the day of the new moon, divided by the total number of days in the calendar cycle, then subtracted from the remaining days in the calendar cycle. If the subtraction is not sufficient, apply the week method and then subtract, followed by subtracting one day. After subtracting, add the Sunday and its minutes to obtain the time of midnight in the calendar.
For the second day's calculations, add one day; if the remaining days exceed the Sunday minutes, subtract the Sunday minutes. If it does not exceed, add the week void; the remainder represents the second day's remaining days in the calendar.
In summary, this passage outlines a complex method for calculating the calendar, involving many astronomical parameters and intricate calculation steps, with the aim of accurately determining the position of the moon and the lunar date.
This calendar calculation is indeed a science. First, we need to calculate the waxing and waning of midnight. Multiply the remaining days of midnight by the profit and loss rate, similar to dividing the total days in a week by a certain number, and the remainder is left. Then continue to accumulate profit and loss using the profit and loss method until the remainder cannot be reduced. At this point, the integer part serves as the basis for profit and loss calculations. The waxing and waning of midnight is calculated, where the complete chapter represents degrees, while the remainder represents minutes. Multiply the total number of days by the minutes and the remainder; the remainder is processed according to the number of days in a week, and once the minutes are full, process according to the degrees. Finally, add the profit and subtract the loss to obtain the final degrees and remainder of midnight.
Next, let's calculate the daily decay. Multiply the remaining days in the calendar by the column decay, similar to dividing the total days in a week by a certain number, and the remainder is left, allowing us to know the daily decay specifics. Then multiply the column decay by the week void to get a constant. At the end of each calendar cycle, add the decay value to this constant; if it exceeds the value of the column decay, subtract it, and then proceed to calculate the decay value for the next calendar cycle.
Then, adjust the calendar day and minutes according to the decay value. If the minutes are either exceeded or insufficient, adjust the chapter and degrees. Multiply the total number of days by the minutes and the remainder, then add the daily decay value to the fixed degrees of midnight to calculate the degrees for the following day. If the number of days in the calendar cycle is not equal to the number of days in a week, subtract 1338 from the total, then multiply by the number of days. If it equals the number of days in a week, add the remainder of 837, divide by the smaller number 899, then add the previous decay value, and repeat the earlier calculations.
Next, subtract or add the profit and loss rate from the decay value to obtain the variable profit and loss rate, then use it to calculate the profit and loss rate at midnight. If the profit and loss is insufficient at the end of the calendar cycle, subtract it in the opposite direction, move to the next calendar cycle, and the method for handling the remainder is the same as described above.
Then calculate the degree of twilight. Multiply the fraction of monthly operation by the nightfall measure of the nearest solar term, then divide by 200 to obtain the Ming minutes. Subtract the Ming minutes from the monthly operation fraction to obtain the dusk minutes. The minutes are analogous to the degrees of the year; multiply the total number of days by the minutes, add it to the degree of midnight, and you can get the degree of twilight. If the remainder exceeds half, keep it; otherwise, discard it.
Finally, let's look at the operation of the moon. The moon's movement is represented by four tables and three paths, which are interwoven in the sky. Divide the moon's operation ratio by the number of days in a week, and you can get the number of days in the calendar. Multiply the number of days in a week by the new moon conjunction, similar to how the moon aligns once, to get the conjunction minutes. Multiply the total number of days by the conjunction number, process the remainder based on the number of conjunctions, and get the retreat minutes. According to the lunar week, you can calculate the daily progress, and the number of conjunctions represents the difference.
The calculation of the decay, profit and loss rate, and the number of the Yin and Yang calendar is as follows:
One day, subtract one, add seventeen, initial;
Two days (limit of twelve hundred and ninety, differential of four hundred and fifty-seven.) This represents the previous limit.
Subtract one, add sixteen, seventeen;
Three days, subtract three, add fifteen, thirty-three;
Four days, subtract four, add twelve, forty-eight;
Five days, subtract four, add eight, sixty;
Six days, subtract three, add four, sixty-eight;
Seven days, subtract three (insufficient subtraction, reverse profit to add, meaning adding one, should subtract three, is insufficient)
Add one, seventy-two;
Eight days, add four, subtract two, seventy-three;
(When exceeding the extreme loss, it indicates that the moon has traversed half a week; the degree has surpassed the extreme, thus it should be deducted.)
Nine days, add four, subtract six, seventy-one.
Ten days, add three days, subtract ten days, equal to sixty-five.
Eleven days, add two days, subtract thirteen days, equal to fifty-five.
Twelve days, add one day, subtract fifteen days, equal to forty-two.
Thirteen days, (limit is three thousand nine hundred and twelve, differential is one thousand seven hundred and fifty-two.) This is the final deadline.
Add one day (start of the calendar, calculate daily), subtract sixteen days, equal to twenty-seven.
For the daily count (five thousand two hundred and three), subtract the lesser amount from the lesser amount, equal to eleven.
Less big law, four hundred and seventy-three.
Calendar cycle: 175,565.
Difference rate: 1,986.
New moon conjunction: 18,328.
Micro-difference: 914.
Micro-difference: 2,209.
Subtract the accumulated months from the first month, then multiply separately by the new moon conjunction and micro-difference. Subtract the micro-difference from the conjunction if it exceeds; subtract the cycle if it exceeds. The remaining part that does not complete the calendar cycle is the date in the solar calendar; if it completes, subtract it, and the remaining is the date in the lunar calendar. The remainder is treated as a day similar to a monthly cycle, but this part is not included in the calculations; the resulting month conjunction enters the calendar, and the remaining part that does not complete a day is the day remainder.
Add two days: the day remainder is 2,580, the micro-difference is 914. Calculate the days according to this method; subtract if it reaches 13, and the remaining is processed as days. The lunar and solar calendars finally alternate; the point at which the calendar starts, before the deadline, is the pre-limit remainder; after the deadline, it is the post-limit remainder, with the month running in between.
Calculate the size of the gain or loss separately for the late and early calendars. Multiply by the conjunction to get the micro-difference; add or subtract the gain or loss to the lunar and solar day remainder, adjusting the date if the day remainder is insufficient. Multiply the determined day remainder by the gain or loss rate, as if a month cycle is obtained, and use the gain or loss as the additional fixed number.
Multiply the difference rate by the new moon remainder, as if using the micro-difference to get one, and subtract from the calendar day remainder. If insufficient, add a month cycle and subtract again, then subtract one day. Then add the day's fraction to its fraction, simplify the micro-difference with the conjunction to get the fraction, which marks the entry into the calendar at midnight.
To find the second day, add one day: the day remainder is 31, the fraction is 31. Subtract the fraction from the remainder as with the conjunction; subtract a full month cycle from the remainder, add one day. The calendar concludes, and you subtract the full day's fraction, marking the start of the new calendar. If the day's fraction is not complete, keep it, add the remainder of 2,702, and the fraction is 31, which is the entry into the next calendar.
Multiply the total by the midnight gain or loss and remainder for both the late and early calendars. Subtract half a week from the remainder if it is full; add or subtract the gain or loss to the lunar and solar day remainder, adjusting the date if the day remainder is insufficient. Multiply the determined day remainder by the gain or loss rate, as if a month cycle is obtained, and use the gain or loss as the midnight fixed number.
Using the profit and loss ratio multiplied by the recent solar term's nocturnal leak, one two-hundredth represents brightness, and subtracting the profit and loss ratio yields dusk; then, using half of the nocturnal profit and loss as the constant for dawn and dusk. This passage discusses ancient astronomical calculations, which may seem quite complex. Let's break it down step by step. First, it says to calculate the angle of the moon's position relative to the ecliptic. The method involves first calculating the number of days from a specific point in time, then dividing by 12, and subsequently dividing the remainder by 3. If the remainder is 1, it is called "strong"; if it is less than 1, it is called "weak," to determine the moon's position. "Strong positive values and weak negative values, strong and weak merge, same name merge, different name cancel." This sentence means that when calculating, positive and negative should be distinguished, and the same symbols should be added, while different symbols should be subtracted.
Next, it outlines the time span from the Ji Chou year to the Bing Xu year, a total of 7,378 years, and lists the stem-branch calendar years during this period. Then it starts to introduce the calculation method of the five visible planets (Jupiter, Mars, Saturn, Venus, Mercury), employing numerous technical terms, including "orbital period," "day rate," "chapter year," "chapter month," etc., which are coefficients used to calculate the trajectories of the planets. The calculation process is very complex, involving many multiplication and division operations, as well as concepts such as "big remainder," "small remainder," "entering month and day," "day remainder," "degree," "degree remainder," and so on, all of which are intermediate results generated in the calculation process.
Finally, it lists a series of specific numerical values, such as "record month," "chapter leap," "chapter month," "year in the middle," "common law," "day law," "meeting number," "week day," "dou fen," etc., as well as the specific parameters of Jupiter: "orbital period," "day rate," "conjunction number," "month remainder," "conjunction law," "day degree law," "new moon big remainder," "new moon small remainder," "entering month and day," "day remainder," "new moon virtual minute," "dou fen." These numbers are all involved in complex calculation formulas, ultimately obtaining the trajectories and positions of the five planets. In summary, this passage describes a set of ancient astronomical calendar calculation methods, demonstrating its complexity.
The core of this text lies in calculating the positions of planets, especially Jupiter. It utilizes a large number of parameters and formulas, the meanings and derivation processes of which require an in-depth understanding of ancient astronomical calendars to comprehend. The terms mentioned in the text, such as "circumferential rate," "solar coefficient," "universal method," and "solar method," are all proportional coefficients used to convert different time units and angle units. Meanwhile, "great surplus at new moon," "small surplus," "new moon day," and "solar surplus" are intermediate results generated during the calculation process, with the ultimate goal of determining the planet's position in the sky. The entire calculation process is quite tedious and requires a large number of multiplication and division operations.
In summary, this text showcases the complexity and precision of ancient astronomical calculations, as well as reflects the remarkable mathematical skills of ancient astronomers and their profound understanding of the laws of the universe. Although it is difficult for us to fully grasp the principles behind it today, we can appreciate the exploration and pursuit of astronomical knowledge by ancient scholars. The various parameters and formulas mentioned in the text also have certain reference value for modern astronomical research, helping us understand the evolution of ancient astronomical calendars.
The angle is thirty-three degrees, and the surplus is 2,956. Fire: circumferential rate 3,470, solar coefficient 7,271, total months 26, month surplus 25,627, total month method 64,733, solar degree method 2,006,723, great surplus at new moon 47, small surplus 1,157, new moon day 12, solar surplus 973,113, new moon phase division 300, dip division 494,115.
The following presents another set of data. The angle is forty-eight degrees, and the surplus is 1,919,706. Earth: circumferential rate 3,529, solar coefficient 3,653, total months 12, month surplus 53,843, total month method 67,051, solar degree method 278,581, great surplus at new moon 54, small surplus 534, new moon day 24, solar surplus 166,272, new moon phase division 923, dip division 511,705.
Next is the numerical value of gold. The degree is twelve, the remainder is 1,733,148. Gold: the weekly rate is 9,022, the daily rate is 7,213, the combined number of months is nine, the monthly remainder is 152,293, the combined monthly calculation is 171,418, the daily degree method is 531,958, the major lunar remainder is 25, the minor lunar remainder is 1,129, the day of the new moon is the 27th, the daily remainder is 56,954, the lunar void is 328, the dipper is 1,308,190.
Finally, the numerical value of the water element. The degree is 292, the degree remainder is 56,954. Water: the weekly rate is 11,561, the daily rate is 1,834, the combined number of months is one, the monthly remainder is 211,331, the combined monthly calculation is 219,659, the daily degree method is 680,429, the major lunar remainder is 29, the minor lunar remainder is 773, the day of the new moon is the 28th, the daily remainder is 641,967, the lunar void is 684.
First, let's calculate the total value, 1,676,345. The degree is fifty-seven, the degree remainder is 641,967. Then, multiply the data of the previous year by the weekly rate to get a full day rate, which we call "integrated sum"; the remaining part is called "combined remainder." Divide the weekly rate by the combined remainder; if the result is 1, it is the star combination of the previous year; if it is 2, it is the star combination of the previous two years; if nothing is obtained, it is the star combination of the current year. Subtract the weekly rate from the combined remainder to find the degree portion. The integrated sum of Venus and Mercury: odd numbers are in the morning, even numbers are in the evening.
Next, multiply the number of months and the monthly remainder by the integrated sum; if the result is a multiple of the combined monthly calculation, take the integer part as the month, and the remainder is the monthly remainder. Subtract the integrated month from the month; the remaining part is the month of entry. Then, multiply the leap month by the month of entry; if the result is a multiple of the leap month, subtract one leap month, and subtract the remaining part in the middle of the year; this part is called the combined month outside the standard calendar. If at the time of the leap month transition, use the new moon to make adjustments.
Then, multiply the month remainder using the common method, and multiply the new moon's remainder by the combined month method. Add these two results together, and simplify using the combined numbers. If the result is a multiple of the solar degree method, then you obtain the date of the star conjunction within the month. If it is not a multiple, the remainder is the solar remainder, which is recorded separately from the new moon calculation. Multiply the days of the week by the degree minutes; if the result is a multiple of the solar degree method, you get one degree, and the remainder is calculated using the method of the five preceding oxen. The above describes the method for determining star conjunctions.
Next, add the number of months together and the month remainders as well. If the result is a multiple of the combined month method, you obtain one month. If it does not exceed one year, that represents the star conjunction for the current year; if it exceeds one year, subtract one year from the total. If there is a leap month, consider that, and the remainder will be the star conjunction of the following year; if it exceeds one year again, that will be the star conjunction of the year after next. Venus and Mercury, when summed in the morning, yield the evening, and when summed in the evening, yield the morning.
Add the size of the new moon remainder and the size of the combined month remainder together. If it exceeds one month, add twenty-nine (for large remainders) or seven hundred seventy-three (for small remainders). If the small remainder exceeds the solar degree method, subtract it from the large remainder, using the same method as before. Add the date of entering the month and the solar remainder together, then add the date of entering the combined month and the remainder. If the result is a multiple of the solar degree method, you get one day; if the previous new moon small remainder exceeds the virtual division threshold, subtract one day; if the later small remainder exceeds seven hundred seventy-three, subtract twenty-nine days; if it is not enough, subtract thirty days. The remainder will indicate the date of the later conjunction within the month.
Finally, add the degrees together and the degree remainders as well. If the result is a multiple of the solar degree method, you get one degree.
Jupiter: Hidden for thirty-two days and visible for three hundred sixty-six days; hidden movement of five degrees, two million nine thousand nine hundred fifty-six minutes; visible movement of forty degrees (retrograde movement of twelve degrees, actual movement of twenty-eight degrees).
Mars: Hidden for one hundred forty-three days and visible for six hundred thirty-six days; hidden movement of one hundred ten degrees, forty-seven thousand eight hundred ninety-eight minutes; visible movement of three hundred twenty degrees (retrograde movement of seventeen degrees, actual movement of three hundred three degrees).
Saturn: Hidden for thirty-three days and visible for three hundred forty-five days.
This passage outlines ancient astronomical calculation methods, which may seem quite complex; let’s break it down sentence by sentence.
The first sentence, "Lurking for three degrees. 1,733,148 minutes." means that (a celestial body) lurked for three degrees and traveled a total of 1,733,148 minutes. These "degrees" and "minutes" are ancient astronomical measurement units.
The second sentence, "Appearing for fifteen degrees. (If six degrees of retrograde motion are subtracted, actual travel is nine degrees.)" means that (this celestial body) finally appeared for fifteen degrees.
The third to sixth sentences, "Venus: Hidden in the east for eighty-two days. 113,908 minutes. Appearing in the west. Lasting for 246 days. (If six degrees of retrograde motion are subtracted, actual travel is two hundred forty-six degrees.) Hidden for one hundred degrees. 113,908 minutes. Appearing in the east. (Daily movement as in the west. Hidden for ten days, retrograding eight degrees.)" These sentences describe the movement of Venus. "Hidden in the east for eighty-two days" means Venus hid in the east for eighty-two days, traveling 113,908 minutes; "Appearing in the west" means it appeared in the west, lasting for 246 days (minus six degrees of retrograde motion); the following two sentences describe another instance of Venus hiding and appearing in the east, with slightly different travel distances and times, and mentioning it "retreating eight degrees," indicating that Venus's movement is not always forward.
The seventh to ninth sentences, "Mercury: Hidden for thirty-three days. 612,505 minutes. Appearing in the west. Lasting for thirty-two days. (If one degree of retrograde motion is subtracted, actual travel is thirty-two degrees.) Hidden for sixty-five degrees. 612,505 minutes. Appearing in the east. Daily movement as in the west, hidden for eighteen days, retrograding fourteen degrees." These sentences describe the movement of Mercury, similar to Venus, also describing the time and travel distance of its appearance and hiding in the east and west, also including instances of retrograde motion.
From the tenth to the twelfth sentence, "According to the law of the sun and the remainder, adding the stars to the sun and the remainder, the remainder of the full sun and the law yield one, from the entire cycle as previously described, allowing the stars to align with the sun and the degrees. By the denominator of the star's movement multiplied by the degree seen, the remainder as the sun and the law yield one; the division continues, and any amount above half the law also yields one; and the sun plus the division it travels, the division fills its reference point yielding one degree. Contrary to the reference point, the division to be traveled is treated as the same reference point. Those left behind follow the previous, decreasing if contrary; the law is not exhausted, and the division is removed by the Dipper, using the reference point as the rate of travel, where the division has gains and losses, mutually assisting each other." This passage describes the specific method for calculating the movement of celestial bodies, using professional terms such as "sun degree," "denominator," "contrary," etc., which are very abstract and complex to explain. In simple terms, it is a set of ancient astronomical calculation formulas and steps used to calculate the trajectory and time of celestial bodies.
In the final paragraph, "Wood: The morning aligns with the sun, remaining in its path, sixteen days, one hundred seventy-four million two thousand three hundred twenty-three minutes; the planet moves two degrees and three hundred twenty-three million four hundred six hundred seven minutes, and the morning is seen in the east, after the sun. Following, fast, the sun travels eleven-fifths of fifty-eight minutes, and in fifty-eight days travels eleven degrees. Further following, late, the sun travels nine minutes, and in fifty-eight days travels nine degrees. Remaining stationary for twenty-five days before continuing. Contrary, the sun travels one-seventh, and in eighty-four days retreats twelve degrees. Further remaining for twenty-five days and then following, the sun travels nine-fifths of fifty-eight minutes, and in fifty-eight days travels nine degrees. Following, fast, the sun travels eleven minutes, and in fifty-eight days travels eleven degrees, in front of the sun, the evening sets in the west. Sixteen days, one hundred seventy-four million two thousand three hundred twenty-three minutes; the planet moves two degrees and three hundred twenty-three million four hundred six hundred seven minutes, and merges with the sun. In total, over three hundred ninety-eight days and three hundred forty-eight million four hundred sixty-six minutes, the planet completes a movement of forty-three degrees and two hundred fifty-nine thousand nine hundred fifty-six minutes." This passage describes the movement of Jupiter, including various states of movement such as direct motion, retrograde motion, and stationary, as well as detailed time and distance data. "In total" refers to Jupiter completing a full cycle of movement.
In conclusion, this text describes how ancient astronomers observed and calculated the movement patterns of Venus, Mercury, and Jupiter, involving a large number of professional terms and complex calculation methods, reflecting the intricacies of ancient astronomical observation and calculation.
Sun: In the morning, it appears together with the sun, and then it goes out of sight. After that, it moves smoothly for 71 days, covering 1489868 minutes, which is equivalent to the planet moving 55 degrees and 1242860.5 minutes. Then it appears in the east in the morning, behind the sun. While traveling smoothly, it moves 23 minutes and 14 seconds each day, covering 112 degrees over 184 days. It then continues to move smoothly but at a slower pace, traveling 23 minutes and 12 seconds each day, covering 48 degrees over 92 days. Then it stops for eleven days. It then moves retrograde, traveling 62 minutes and 17 seconds each day, retrograding 17 degrees in 62 days. It then stops again for eleven days, and then starts moving smoothly again, covering 48 degrees over 92 days, moving 12 minutes each day. Moving smoothly again, at a faster speed, it moves 14 minutes each day, covering 112 degrees over 184 days; at this point, it's in front of the sun, out of sight in the west at night. After 71 days, covering 1489868 minutes, which is equivalent to the planet moving 55 degrees and 1242860.5 minutes, it appears together with the sun again. This cycle completes in a total of 779 days, covering 973113 minutes, with the planet moving 414 degrees and 478998 minutes.
Mars: In the morning, it appears together with the sun, and then it goes out of sight. After that, it moves smoothly for 16 days, covering 1122426.5 minutes, which is equivalent to the planet moving 1 degree and 1995864.5 minutes. Then it appears in the east in the morning, behind the sun. While traveling smoothly, it moves 35 minutes and 3 seconds each day, covering 7.5 degrees over 87.5 days. Then it stops for 34 days. It then moves retrograde, traveling 17 minutes and 1 second each day, retrograding 6 degrees in 102 days. After 34 days, it starts moving smoothly again, covering 7.5 degrees over 87 days, moving 3 minutes each day. At this point, it's in front of the sun, out of sight in the west at night. After 16 days, covering 1122426.5 minutes, which is equivalent to the planet moving 1 degree and 1995864.5 minutes, it appears together with the sun again. This cycle completes in a total of 378 days, covering 166272 minutes, with the planet moving 12 degrees and 1733148 minutes.
Venus, when it aligns with the sun in the morning, first "hovers", which means its speed slows down, then "retrogrades", retrograding four degrees over five days, then it becomes visible in the east in the morning, positioned behind the sun. It continues to retrograde, moving back two-fifths of a degree each day, retreating six degrees in ten days. Then it "stays", remaining stationary for eight days. Then it "rotates", beginning to move forward, but at a slower pace, moving at a rate of 46.33 degrees per day, totaling 33 degrees over 46 days. Then the speed picks up, moving 91.15 degrees daily, reaching a total of 160 degrees in 91 days. After that, the forward speed increases, moving 91.22 degrees each day, covering 113 degrees in 91 days, at this time it is positioned behind the sun, reappearing in the east at dawn. Continuing forward, after 41 days and 56,954 minutes of travel, it traverses 50 degrees and 56,954 minutes, and ultimately aligns with the sun once more. From the first conjunction to the next, a total of 292 days and 56,954 minutes, the distance traveled by Venus remains consistent.
When Venus aligns with the sun at night, it first "hovers", then moves forward for 41 days and 56,954 minutes, covering 50 degrees and 56,954 minutes, then you can see it in the west at night, at this time it is positioned in front of the sun. Continuing forward, the speed increases, moving 91.22 degrees each day, covering 113 degrees in 91 days. Then the forward speed decreases, moving 15 degrees each day, covering 160 degrees in 91 days. Then its speed decreases further, moving 46.33 degrees each day, covering 33 degrees in 46 days. It "pauses", remaining motionless for eight days. Then it "rotates", beginning to "retrograde", moving back two-fifths of a degree daily, retreating six degrees in ten days, at this time it is positioned in front of the sun, appearing in the west at night. It "retrogrades", the speed increases, moving back four degrees in five days, and ultimately aligns with the sun once more. From the first conjunction to the final one, a total of 584 days and 113,908 minutes, the distance traveled by Venus remains consistent.
Mercury, when it aligns with the Sun in the morning, first "lies low," then "retrogrades," retreating seven degrees over nine days, after which it can be seen in the east, positioned behind the Sun in the morning. It "retrogrades" more, speeding up to "swift," retreating one degree each day. It "stays" put for two days without moving. Then it "rotates," beginning to move direct at a comparatively "slow" speed, moving approximately 0.89 degrees each day, covering eight degrees in nine days. After that, it speeds up to "swift," moving one and a quarter degrees each day, covering twenty-five degrees in twenty days, at which point it is behind the Sun and appears in the east in the morning. It continues to move direct; after sixteen days and 6,419,667 minutes, it has traveled thirty-two degrees and 6,419,667 minutes, ultimately meeting the Sun again. From one conjunction to the next, it takes a total of fifty-seven days and 6,419,667 minutes, and the degrees Mercury travels are the same.
Speaking of Mercury, it sets alongside the Sun, and then it seems to lie in wait, dutifully following the Sun. Specifically, every sixteen days, it moves thirty-two degrees and one six hundred forty-one thousand nine hundred sixty-seven minutes along the ecliptic. In the evening, you can see it in the west; it is always in front of the Sun.
If it moves quickly, it can travel one and a quarter degrees in a day, covering twenty-five degrees in twenty days. But if it moves slowly, it only travels seven-eighths of a degree in a day, covering eight degrees in nine days. Sometimes it simply stops, not moving for two days. Even more remarkably, it can also move backward! It can retrograde one degree in a day, and during this time, it is still in front of the Sun, hiding in the west by evening. If it retrogrades slowly, it can retreat seven degrees in nine days, ultimately meeting the Sun again.
From its conjunction with the Sun to the next, the entire cycle lasts one hundred fifteen days and six million two hundred fifty-five minutes, and this is how Mercury's orbit continues in a repetitive cycle.
