"Han Yutong" is an ancient book created around 1610 and republished in 1648 in the late Ming and early Qing dynasties. Recently, some Western historians and pseudo-historians regard it as the pinnacle of ancient Chinese astronomy and geography. In fact, the book was compiled on the basis of Western scientific knowledge and technology brought by Western missionaries who came to China in 1589. The book is now in the National Library of China and the Library of Congress.
After the new moon, I see the difference between the rise and fall of the crescent moon sooner or later
Original text: Question: That is, after the New Year's Day, the moonlight grows longer, and it is thirteen degrees away from the sun every day, then the sun enters the horizon on the second day, and the moon is thirteen degrees away from the east of the sun, and the moon is thirteen degrees higher than the horizon.
Translation: Question: After the first day of the lunar calendar, the moon shines more and more light, and every day the moon is 13 degrees away from the sun, and the next day when the sun enters the horizon, the moon is 13 degrees away from the east side of the sun, which means that the moon is also 13 degrees higher on the horizon.
Original text: From the second day onwards, it is advisable for no one to see the moonlight, but now to see the light, or on the second day after the new day, or on the third day, or on the fourth day. Said: Because of the horizon and the ecliptic. Whoever dwells on the ground, and sees the moonlight, must see it when the moon wheel is twelve degrees higher than the horizon. Otherwise, no. The degree of the moon is the degree above the horizon. Whether the moonlight is seen or not, because of the height of the earth, not because of the distance from the sun.
Translation: From the next day, there should not have been a time when the moonlight could not be seen, but now it is only now, sometimes in the first two days, sometimes in three days, sometimes in four days, what is the reason for these differences? The reason why people can see the moonlight on the ground must be because the moon's orbit is 12 degrees above the horizon. If not, it is invisible. It turns out that the problem of degrees of the moon also has the problem of degrees from the ground level. Moonlight cannot be seen because of the height of the Moon above the ground level, not because of its angle from the Sun.