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Set the celestial sphere at 365 degrees and 25 fen. Divide by 27 days; each day yields 13 degrees, with a remainder of 14 degrees and 25 fen.
Using the reduction method for subtraction (subtracting 14 degrees and 25 fen from 27), we obtain 75 parts, which represents the result after subtraction. After performing this subtraction three times to normalize, take 75 as the divisor. First, divide the integer part of the dividend, 27 days, multiplied by 100, yielding 2700. Then divide to get the integer part (where 36 serves as the denominator). Divide the numerator, 14 degrees and 25 fen, by 75, obtaining 19. Thus, it is 19/36. On the first day, the moon travels 13 degrees and 19/36; on the second day, 27 degrees and 2/36; on the third day, 40 degrees and 21/36; on the fourth day, 54 degrees and 4/36; on the fifth day, 67 degrees and 23/36; on the sixth day, 81 degrees and 6/36; on the seventh day, 94 degrees and 25/36.
Continuing this accumulation until the twenty-seventh day, one arrives at 365 degrees and 9/36. Therefore, 27 days correspond to the celestial sphere of 365 degrees and 1/4 degree. One-quarter degree corresponds to 25 ke within 100 ke; four sets of 25 ke make up 100 ke. According to the current combined calculation method, using 36 as the denominator, adding to 365 degrees and 9/36, four nines equal 36, thus combining to form one-quarter degree.
(New addition) In the case of the sixth year, there is a method derived from accumulated years. There are alternatively 354 days constituting one year, totaling 11 days and 55 ke less, which accounts for the surplus of accumulated Qi leading to intercalary months. Any intercalary month lacks a Zhongqi (Central Qi); these are all divisions of the preceding and following three Chen (two-hour periods), representing the numerical value of celestial degrees. The lunar image appears full or deficient according to its cycle, but the Moon itself does not actually lack substance. The Moon belongs to Taiyin (Greater Yin) and is the essence of Water; the Sun belongs to Taiyang (Greater Yang) and is the essence of Fire. When the Sun and Moon meet, they form the character "Ming" (Brightness), which embodies the Way of Heaven. Fire represents Yangming (Bright Yang) on the outside, and Water represents Yinming (Bright Yin) on the inside. Using Fire to illuminate and Water to reflect shapes allows their forms to be perceived. Vision in the eye is similar to the Sun shining; where light shines, images appear. Where sunlight cannot reach, images do not manifest and appear deficient; observing these images allows one to understand the phenomenon. Thus, when the waxing half-moon is in the south, the Sun is seen in the west setting in its lower half; when the waning half-moon is in the south, the Sun is seen in the east rising in its upper half. At Full Moon, the Sun and Moon face each other, resulting in a round and bright appearance. At New Moon, they share the same palace, making them invisible to the eye. Furthermore, although ice is translucent, if hung in a dark room at night without a torch providing light, how could its shape be clearly seen? From this, we know that although ice has internal brightness, without external illumination, its form cannot be seen; although the Moon shines internally, without the radiance of the Sun, its image cannot be manifested. Therefore, the Moon originally has no deficiency; it is merely due to the unequal speeds of the Sun and Moon's movements that the phases of waxing and waning occur.