The full name of "Zhou Ti" is "Zhou Ti Suan Jing", which is the oldest astronomy and mathematical work. Tie, stock also, refers to the calculation method. According to legend, it was written in Zhougong Jidan, so it was called "Zhou Ti".
"Zhou Ti Sutra"
From Chapter 6 (excerpt)
The former Rong Fang asked Chen Zi and said: "Today I hear about the Master’s way. Knowing the height of the sun, the light of the light, the number of walks in a day, the number of distances and sights, the poverty of the four poles, the place of stars , The vastness of the heaven and the earth, and the master’s way, can all be known. Does his belief have it?"
Chen Zi said, "Yes."
Rong Fang said, "Although Fang is unconscious, I wish the Master please say it. If you are a Fang, you can teach this evil."
Chen Zi said, "Of course, this is the subject of arithmetic. The son's calculation is enough to know this. If you are sincere, think about it."
So Rong Fang went back and thought about it, and couldn't get it for a few days. When I saw Chen Zi again, he said, "Fang Sizhi can't get it. I dare to ask."
Chen Zi said: "Thinking is unfamiliar. This is also the technique of "looking at a distance to raise heights." It is wisdom that is inferior, but God is poor. Those who use the knowledge of the husband, Taoism, talk and appointment, are wise. If you ask a class and use MasterCard, you know. The arithmetic technique that Jinzi learned is to use wisdom. But it is still difficult, it is the wisdom of the son. Those who are difficult to understand in the art of the husband and the law will not only learn, but suffer from the failure of knowledge; if they are knowledgeable, they will suffer from their failures; if they are practiced, they cannot know. Therefore, the same skills should be learned, and colleagues should be respectful. The stupid wisdom of this group of scholars is divided by the wise and unscrupulous. Therefore, it is the quality of the sage to learn the wisdom. The husband who is in the same profession but can't enter the gods will not be able to study intensively because of the lack of wisdom. So it can’t be considered intensively. How can I think of a hidden son? Consolidate and think about it. "
Rong Fang returned to thinking about it, and couldn't get it for a few days. When I saw Chen Zi again, he said: "Fang Sizhi is very proficient. Wisdom is not as good, but God is poor, knowing cannot be obtained. I wish to say it eventually."
Chen Zi said: "Sit again, my words are you."
So Rong Fang sat down again and asked Chen Zizhi to say, "Six thousand miles south of the summer solstice, and 135,000 miles south of the winter solstice. You will be able to measure the shadows in the middle of the day. This is the number of heaven.
Press: Sun, 16,000 miles south of the summer solstice, 135,000 miles in the winter solstice.
Fig. Schematic diagram of a week
Zhou Ti is eight feet long, and the sundial (guǐ, sun shadow.) on the summer solstice is one foot six inches long. Those who are stubborn, share also. Those who are on the sundial, the sentence (gōu) is also. A thousand miles in the south, a sentence of one foot and five inches; a thousand miles in the north, a sentence of one foot and seven inches. The sundial is getting longer and longer.
Press: The pole is eight feet (about 184 cm), and the sun shadow during the summer solstice is one foot and six inches (about 36.8 cm). Going 1000 miles north and south, the sun shadow will shorten or lengthen by one inch (about 2.3 cm).
The phrase six feet is to take bamboo, one inch in the empty path, eight feet long, capture the shadow and look at it, the empty is covering the sun, and the sun should be the hole in the empty. From this point of view, the rate is 80 inches, and the diameter is one inch, so the sentence is the first and the 髀 is the stock.
Press: A bamboo with a diameter of one inch (2.3 cm) and a length of eight feet (184 cm). When looking at the sun, the bamboo tube can cover the size of the sun. The eighty-inch-long bamboo tube corresponds to an inch of sun shadow.
From 髀 to 60,000 li under the sun, there is no shadow. From this to the day, it is 80,000 li. According to the rate, eighty li is one li, one hundred thousand li is one thousand two hundred and fifty li. Therefore, the sundial has a diameter of one thousand two hundred and fifty miles.
Note: The suspected ancients first determined that the distance between the earth and the sun was one hundred thousand miles, and the sun was eighty thousand miles high, and then it was calculated that it was six thousand miles south to the sun. In addition: this paragraph calculates the diameter of the sun. The diameter of the sun (shadow) = 100000÷80 = 1250 miles.
If you seek evil (same as "oblique") to the sun, take the sun as the sentence, the sun high as the stock, multiply the sentence and the stock, and divide by the square, get the evil to the sun, from the side to the sun, ten Miles. "
Press: Use the Pythagorean theorem to calculate the distance between the diagonal lines: 10×10 = 8×8 + 6×6.
The method said: Zhou Ti is eight feet long, and the profit and loss of the sentence is thousands of miles. Therefore, it is said: Extremely, the sky is vast. Today, the stand table is eight feet high to look extremely high, and its sentence is one foot and three inches. From this perspective, it is from Zhou (where the state of Zhou is, referring to Hojing.) to the extreme north. "
Press: One foot and three inches = 103 inches. 103×1000 = 103000
Rong Fang said, "Who is Zhou Tui?"
Chen Zi said: "In ancient times, the emperor ruled the week. This number is from the week, so it is called the Zhou Ti. The one who is the one is also the table. The summer solstice is six thousand li to the south, and the winter solstice is 135,000 li to the south. Shadow. From this perspective, from the south to the summer solstice, 119,000 miles, and north to its midnight, the same is true. The common path, 238,000 miles, the path of the sun in the summer solstice, the week, Seventy-one thousand miles.
Press: The radius of the summer solstice road is 103000-16000 = 119000, the diameter is 238000
Circumference 238000 × 3 = 714000
From the middle of the summer solstice to the middle of the winter solstice, it is 119,000 miles, and the same goes for the north to the extreme. From the extreme south to the middle of the winter solstice, 238,000 miles, from the extreme north to midnight. Where the path is 476,000 miles, this winter solstice path is also one hundred forty-two8,000 miles.
Press: The diameter of the summer solstice is the same. Therefore, the total diameter of the first anniversary is 238000 × 2 = 476000 li, and the perimeter is 476000 × 3 = 1428000 li.
Figure 2 Schematic diagram of the four seasons of the sun
From the north to the extreme bottom on the spring and autumn equinox, it is 178,500 miles. From the extreme north to the middle of the night, it is also the same, with a path of 357,000 miles and a week of 1.71,000 miles. Therefore, it says: The path of the moon is always related to the place, and the path of the sun is also right with the place. From the south to the midday of the summer solstice, from the north to the midnight of the winter solstice, from the south to the midnight of the winter solstice, and from the north to the midnight of the summer solstice, the distance is 357,000 miles and the week is 1.71,000 miles.
Press: The midday of the spring and autumn equinoxes is between the summer and winter solstices.
Radius 178500 = 119000÷2 + 119000
Day and night on the vernal equinox, and even day and night on the autumnal equinox, there is often sunlight at the extreme bottom. At the autumn equinox day and night, and even at the vernal equinox, there is often no daylight. Therefore, when the day and night of the spring and autumn equinox are divided, the sunlight is extremely suitable, and the yin and yang are equally divided. The winter solstice and summer solstice are born from the convergent day, to the extreme of the length of day and night. At the spring and autumn equinox, the repair of yin and yang, the image of day and night. Day is yang, night is yin. From the vernal equinox to the autumnal equinox, the image of the day. From the autumnal equinox to the vernal equinox, the night is like. Therefore, during the spring and autumn equinox, the light shines under the north pole, and the sun shines at midnight to the south pole. This is the hour of the day and night. Therefore, it said: 167,000 miles on each side of the sun.
The distance one sees should be as light as the sun. From Zhou's point of view, it is 64,000 li to the north and 32,000 li to the south on the winter solstice. On the day of the summer solstice, the day of the winter solstice in the south is 48,000 li, the south is 6,000 li, the north is 151,000 li, and the north is 48,000 li. The night of the winter solstice is half daylight, and it is not as far as seven thousand li to the south and seventy-one thousand li below. The midday of the summer solstice and the midnight daylight are 96,000 li, crossing the extremes. The mid-day and midnight daylight of the winter solstice does not correspond to 142,000 li, nor to the extreme 71,000 li. On the day of the summer solstice, look straight from east to west, and from east to west during the week until Friday, 95,000 miles and a half. On the day of the winter solstice, there is no sun in the east and west. By calculation, from day to day to Tuesday, 144,557 miles and a half, whoever counts this way, the sun will converge. On the winter solstice and summer solstice, observe the number of laws and listen to the sound of the bell. Winter solstice day, summer solstice night. The difference was up to Nikko, and it was 810,000 miles from the four poles, and 1.43 million miles on Tuesday.
From Zhouzhinan to Rizhao thirty-two thousand miles, Zhoubei to Rizhao fifty-eight thousand miles, the east and the west are 391,683 miles and a half. Zhou is one hundred and three thousand miles in the middle of the sky, so it is strange that the east-west short diameter is 26,632 miles. Zhou Bei is fifty-eight thousand miles away. 135,000 miles on the winter solstice. During the winter solstice, the road runs for 476,000 miles, and the week is one hundred forty-two million miles. The four poles of the sun were strange in the week of 391,000 and 683. This method of radius. "