Let's first calculate the conjunction of the celestial bodies. Using the degrees of the zodiac, a full day counts as one degree, and any remainder is left over, recorded using the degrees of the five stars in front of the Ox. This is the method for calculating the conjunction of the celestial bodies. Add the months together, also add the remainders of the months; a full month's degrees count as a month. If it is a full month, subtract it. If there is a leap month, if applicable, note it down, and the remaining remainders are carried over to the next year; if it exceeds a full year again, carry it over to the following two years. For Venus and Mercury, adding the morning phase results in the evening phase, and vice versa. (This describes the method for calculating the conjunction cycle of planets, utilizing addition and subtraction as well as the concept of leap months.)
Next, calculate the remainders of the new moon and full moon. Add the remainders from the conjunction calculation to the remainders of the new moon and full moon; if it exceeds one month, add a large remainder of twenty-nine days and a small remainder of seven hundred seventy-three minutes. When the small remainder reaches the full day degrees, subtract it from the large remainder, using the same method as before. Then calculate the entry day of the month and the day remainder. Add the entry day of the month and the day remainder together; when the remainder reaches the full day degrees, count it as one day. If the small remainder from the previous conjunction reaches a full cycle, subtract one day; if the subsequent small remainder exceeds seven hundred seventy-three, subtract twenty-nine days; if it is not full, subtract thirty days. The remaining remainders are carried over to the next conjunction, which is the entry day of the month. Finally, sum the degrees and their remainders; when it reaches the full day degrees, count it as a full degree. (This section describes a more detailed calculation method, involving astronomical concepts such as new moons, entry days, and complex addition and subtraction operations.)
Jupiter: Hidden for thirty-two days, 3,484,646 minutes; appeared for three hundred sixty-six days; hidden running five degrees, 2,009,956 minutes; appeared running forty degrees. (Retrograde motion of twelve degrees, with an actual movement of twenty-eight degrees.)
Mars: Hidden for one hundred forty-three days, 97,313 minutes; appeared for six hundred thirty-six days; hidden running one hundred ten degrees, 47,898 minutes; appeared running three hundred twenty degrees. (Retrograde motion of seventeen degrees, with an actual movement of three hundred three degrees.)
Saturn: Hidden for thirty-three days, 16,672 minutes; appeared for three hundred forty-five days; hidden running three degrees, 173,348 minutes; appeared running fifteen degrees. (Retrograde motion of six degrees, with an actual movement of nine degrees.)
Venus: Morning visibility in the east for 82 days, 113,980 minutes; visible in the west for 246 days. (Retrograde motion 6 degrees, actual motion 246 degrees.) Morning visibility moving 100 degrees, 113,980 minutes; visible in the east. (Daily motion similar to the west, occulted for 10 days, retrograde motion 8 degrees.)
Mercury: Morning visibility for 33 days, 612,505 minutes; visible in the west for 32 days. (Retrograde motion 1 degree, actual motion 32 degrees.) Hidden motion for 65 degrees, 612,505 minutes; visible in the east. (Daily motion similar to the west, occulted for 18 days, retrograde motion 14 degrees.)
(This detailed section lists the time and degrees of hiding (retrograde) and appearance (direct motion) of each planet, containing a large amount of numerical information.)
Wow, this text looks complicated; let's break it down sentence by sentence. First, "By dividing the remainder of the day's motion by the divisor of the day's motion and adding the remainder of the degree when the star meets the sun, if the remainder can be divided evenly by the divisor of the day's motion, the result is one; following the previous calculation method, the degree when the star meets the sun can be calculated." Put simply, it is a complex division operation to calculate the position where the star appears.
Next, "By multiplying the denominator of the star's motion by the degree of appearance, if the remainder is not divisible by the divisor of the day's motion, and if the remainder exceeds half of the divisor, it is also considered as one; then add the day's motion to the star's motion, and when the degree reaches the denominator, add one degree; the denominators of direct and retrograde motions are different, so multiply the current denominator by the previous degree and divide by the previous denominator to get the current degree." This part is even more complex; it means: multiply the denominator of the star's motion by the degree of appearance, then divide the remainder by the divisor of the day's motion; if the remainder is not divisible, the remainder exceeding half of the divisor is also considered as one; then add the day's motion to the star's motion, and when the degree reaches the denominator, add one degree; the denominators of direct and retrograde motions are different, so multiply the current denominator by the previous degree and divide by the previous denominator to get the current degree. This resembles ancient astronomical calculation formulas, involving numerous variables and intricate calculation steps.
"If the celestial body stays, it inherits the previous angle; if it moves in retrograde, the angle is reduced; if the angle can't be divided evenly, the Dou asterism is used for division, using the current denominator as the ratio. The angles will increase or decrease, influencing each other. This part describes the adjustments and calculation methods of angles during the movement of celestial bodies, considering various situations of their motion. The last sentence explains the terminology in the calculations: '盈约满' (precise division calculations) refers to precise division calculations; '去及除之' (exhaustive division calculations) refers to exhaustive division calculations. In simple terms, it outlines two different division methods."
The description of Jupiter is relatively easier to understand. "Jupiter: in the morning, it aligns with the sun, proceeds forward, after 16 days and 1,742,323 minutes, the planet moves 2 degrees and 3,234,607 minutes, and is seen in the east after the sun. Moving forward quickly, it travels 11 minutes over 58 days, advancing 11 degrees. Then moving forward slowly, it travels 9 minutes, moving 9 degrees over 58 days. It remains stationary for 25 days before rotating. When moving backward, it travels 1/7 of a minute, retreating 12 degrees over 84 days. After staying for 25 days, it resumes its forward motion, traveling 9 minutes over 58 days, moving 9 degrees. Moving forward quickly, it travels 11 minutes, advancing 11 degrees over 58 days, before the sun sets in the west. After 16 days and 1,742,323 minutes, the planet moves 2 degrees and 3,234,607 minutes, aligning with the sun. Overall, one complete cycle lasts 398 days and 3,484,646 minutes, with the planet moving 43 degrees and 2,509,956 minutes." This passage describes the motion of Jupiter: Jupiter aligns with the sun, then moves forward quickly, slows down, then stops (stays), moves backward, stops again (stays), and then moves forward quickly before aligning with the sun again. This text provides specific data on Jupiter's movement, including time and angles, showcasing the periodicity and complexity of Jupiter's motion. In summary, this entire passage details ancient astronomical observations and calculations, which are quite complex and require a profound understanding of mathematics and astronomy to comprehend.
Sun: It rises in the morning alongside the sun, then disappears. It continues on its path for 71 days, traversing 1,489,868 minutes, which translates to a movement of 55 degrees and 242,860.5 minutes for the planet. It then appears in the east in the morning, behind the sun. While moving forward, it travels 14 minutes and 23 seconds each day, covering 112 degrees in 184 days. It then remains stationary for 11 days. It then moves backward, covering 17 degrees in 62 days while moving 17 minutes and 62 seconds each day. It stops for another 11 days, then moves forward again, covering 48 degrees in 92 days while moving 12 minutes each day. Moving forward again, its speed increases, covering 112 degrees in 184 days while moving 14 minutes each day. At this point, it is in front of the sun, disappearing in the western sky at night. After 71 days, it traverses 1,489,868 minutes, which corresponds to 55 degrees and 242,860.5 minutes, then appears with the sun again. In total, this entire cycle lasts 779 days and 973,113 minutes, covering 414 degrees and 478,998 minutes.
Saturn: It appears in the morning with the sun, then goes into hiding. It continues on its path for 16 days, traversing 1,122,426.5 minutes, which translates to a movement of 1 degree and 1,995,864.5 minutes for the planet. It then appears in the east in the morning, behind the sun. While moving forward, it travels 35 minutes and 3 seconds each day, covering 7.5 degrees in 87.5 days. It then stops for 34 days. It then moves backward, covering 6 degrees in 102 days while moving 1 minute and 17 seconds each day. After another 34 days, it moves forward again, covering 7.5 degrees in 87 days while moving 3 minutes each day. At this point, it is in front of the sun, disappearing in the western sky at night. After 16 days, it traverses 1,122,426.5 minutes, which corresponds to 1 degree and 1,995,864.5 minutes, then appears with the sun again. In total, this entire cycle lasts 378 days and 166,272 minutes, covering 12 degrees and 1,733,148 minutes.
Venus, when it meets the sun in the morning, first "hides," which refers to its retrograde motion. It moves back four degrees over the course of five days, then in the morning it can be seen in the east, behind the sun. Continuing to retrograde, it moves three-fifths of a degree each day, retreating six degrees in ten days. Then it "pauses" and remains still for eight days. Next, it "turns," starting its forward motion at a slower speed, completing forty-six thirty-thirds of a degree each day, totaling thirty-three degrees in forty-six days. Then the speed increases, moving one degree and ninety-one minutes each day, covering one hundred and six degrees in ninety-one days. The speed continues to increase, moving one degree and ninety-one minutes each day, covering one hundred and thirteen degrees in ninety-one days, at which point it runs behind the sun again, visible in the east in the morning. Finally, it continues moving forward for forty-one days, completing one fifty-fourth of a full circle, totaling fifty degrees and one fifty-fourth of a full circle, and eventually meets the sun. From one conjunction to the next, it is a total of two hundred and ninety-two days and one fifty-fourth of a full circle, and Venus covers the same distance.
When Venus meets the sun in the evening, it first "hides," this time moving forward, completing one fifty-fourth of a full circle in forty-one days, a total of fifty degrees and one fifty-fourth of a full circle. In the evening, it can be seen in the west, in front of the sun. Then it continues its forward motion, with the speed increasing, moving one degree and ninety-one minutes each day, covering one hundred and thirteen degrees in ninety-one days. The speed then begins to slow down, moving one degree and fifteen minutes each day, covering one hundred and six degrees in ninety-one days, and then continues moving forward. The speed slows down, covering thirty-three degrees in forty-six days. Then it "pauses" and remains still for eight days. Next, it "turns," starting to retrograde, moving three-fifths of a degree each day, retreating six degrees in ten days, at which point it appears in front of the sun, visible in the west in the evening. It "hides," which means it retrogrades, with the speed increasing, retreating four degrees in five days, and eventually meets the sun. From one conjunction to the next, it is a total of five hundred and eighty-four days and one eleven-thousandth of a full circle, and Venus covers the same distance.
Mercury, when it meets the sun in the morning, first "retreats," referring to its retrograde motion, moving back seven degrees. Then it can be seen in the east in the morning, positioned behind the sun. Continuing to retrograde, its speed increases, moving back one degree each day. Then it "pauses," remaining stationary for two days. After that, it "turns," starting to move forward at a slower speed, traveling eight ninths of a degree per day, covering eight degrees in nine days. Then its speed increases, moving one and a quarter degrees per day, taking twenty days to cover twenty-five degrees, at which point it is once again behind the sun and visible in the east in the morning. Finally, it moves forward for sixteen days, covering 32 degrees and 641,967 parts of a circle, ultimately meeting the sun. From one conjunction to the next, it takes a total of 57 days and 641,967 parts of a circle, with Mercury covering the same distance.
Well, what does all this mean? Let me explain it to you sentence by sentence. The first sentence, "Water: in the evening, meeting the sun, retreating, moving forward," means: Mercury, when it meets the sun in the evening, seems to retreat and then starts to move forward. The word "retreat" here refers to Mercury moving near the sun, being obscured by the sun's light, making it difficult to observe. "Forward" refers to the direction of Mercury's movement being the same as the sun's. Next, "Sixteen days, 641,967 parts of a day, the planet moves 32 degrees and 641,967 parts, and is seen in the west in the evening, before the sun," means: roughly sixteen days, or more precisely sixteen days plus 641,967 parts of a day, Mercury will move about 32 degrees, and then you can see it in the west in the evening, ahead of the sun. These ancient methods of calculating time and angles are remarkably precise. "Forward, fast, moving one and a quarter degrees per day, twenty days to cover twenty-five degrees and forward," means: when moving forward, it moves quite fast, covering one and a quarter degrees per day, taking twenty days to cover twenty-five degrees.
Further down, "At times, the sun travels eight-ninths of its usual distance, taking nine days to cover eight degrees. Sometimes it simply stops, remaining motionless for two days. It can also move in reverse, retreating one degree each day; at this time, it is still in front of the sun, disappearing from view in the western sky at dusk."
The last sentence, "When moving in reverse, it also slows down, taking nine days to retreat seven degrees before aligning with the sun again. From one conjunction to the next, it takes a total of one hundred and fifteen days, plus an additional six thousand one hundred and fifty-five minutes; this pattern applies to all planets," means: When it is moving backwards, it is also slow, it takes nine days to retreat seven degrees, and finally meets with the sun again. To be more precise, it takes one hundred and fifteen days and an additional fraction of a day; this describes Mercury's orbital period. This final sentence encapsulates the general duration of Mercury's complete orbit. The astronomical observations made by ancient astronomers were truly remarkable!
