What method did the ancients use to determine the boundary of the territory and draw it into a map?

The story of Dayu's flood control is a household name. According to the Records of the Historian, he "left the rules and right the rules", holding surveying and mapping tools, "walking mountains and showing trees, setting mountains and rivers". According to legend, Hebo, the god of the Yellow River, once gave Dayu a slate engraved with a map of the Yellow River basin. These are the reflections of the map surveying and mapping at that time. After the flood control, Dayu traveled around the world, designated China's land as Kyushu, and inspected local products and land to determine tributes, thus forming the pre-Qin geographical masterpiece Yu Gong. Since then, "Kyushu" has become synonymous with the land of China, and "Gong Yu" has become a proper term for geographical works.

To draw a map, you must first measure it. The ancients developed many methods from simple to complex.

According to the Spring and Autumn Wei, Emperor Yan, one of the five emperors, traveled hundreds of thousands of miles to measure the earth. Dayu also sent Qiu Zhang to survey the whole territory of Shu Hai from east to west and from north to south. It can be seen that survey was one of the basic methods of geodesy at that time, so that thousands of years later, some people named the map "Yu Trace Map", which means the footprint of Dayu.

According to Liu Xin's Miscellanies of Xijing in the Western Han Dynasty, there is a kind of rail car that can calculate mileage, which was improved by Zhang Heng in the Eastern Han Dynasty. This kind of car adopts the principle of differential gear, which rings the drum once every ten miles and the bell once every ten miles, which greatly improves the speed of mileage measurement.

Vertical rod shadow measurement is a method to estimate the distance and position by measuring the length of sun shadow. The specific method is as follows: at noon that day, the watch poles with the same height (generally 8 feet high, equivalent to 1.88 meters) were erected in the north and south directions, and then the shadow of the watch poles was measured. According to "an inch of shadow is a thousand miles away" (the shadow of the sun is an inch, and the distance between the north and the south is calculated. According to Zhou Li, the shadow length from summer to the sun is/kloc-0.

"One inch of a thousand miles" is a rather rough empirical value, which was later denied by the theories and measurements of the southern astronomer He Chengtian, the Sui astronomer Liu Zhuo, the Tang astronomer monk and his entourage, and the Nangong theory.

As early as the Western Han Dynasty, Huainanzi recorded the basic method of measuring the height of the sun. When he arrived in the Three Kingdoms, Zhao Shuang, a native of the State of Wu, drew a map of the sun's height while taking notes on Zhou pian Shu Jing. The sun height map is a schematic diagram for calculating the sun height by measuring the sun shadow at two poles. Using the principle of similar triangles's side length ratio to measure the height of the sun and the long distance between the two places, it provides a method for indirect measurement. Mathematician Liu Hui said: "Anyone who looks extremely high and measures extremely deeply and knows its distance at the same time must use heavy difference." There are nine examples in his book gravity difference, including measuring the heights of islands, pine trees and buildings, measuring the size of cities, measuring the depth of valleys, and measuring the widths of estuaries and lakes.

After the Han Dynasty, the surveying tools such as armillary sphere, moment-covering and star-pulling board were invented one after another, which made the astronomical geodesic activities more active and the methods more precise. The methods commonly used in the pre-Qin period, such as stepping, surveying and vertical polar shadow surveying, still have vitality. During the Wanli period of the Ming Dynasty (1582), Matteo Ricci, an Italian missionary, came to China and brought western astronomical geodetic methods. In order to compile the calendar, in the second year of Chongzhen (1629), under the auspices of Xu Guangqi, assistant minister of the Ministry of Rites, the Western Bureau was established, which was attended by westerners coming to China and adopted western calculation methods, and carried out astronomical observations together with the Central Bureau which adopted China's traditional astronomical measurement methods. After five years of preparation, 10 kinds of new instruments, such as quadrant, astronomical clock, horizontal hanging armillary sphere, latitude and longitude celestial sphere, and timing telescope, have been manufactured, and practical observations with the contents of measuring time, azimuth, meridian and arctic height have been implemented. The trend of western methods replacing China and France has emerged. Western modern astronomical surveying and mapping methods were adopted in the national map surveying and mapping in the early and late Qing Dynasty.

Guyuan area map

Direction, Legend and Scale: How did the ancients draw maps?

The painted map of Guyuan House in the late Ming Dynasty is very strange. The whole map is radial, the painter stands in the center, and the map presents its scenes facing all directions. And it is different from the usual direction of going up north and down south. This picture is up east and down west, left north and right south. According to Su Pinhong, deputy director of the Ancient Books Museum of the National Library, it is easy to determine the direction according to the level of ancient science and technology, but the ancients often determined the direction according to actual needs, sometimes marked and sometimes not marked.

Guang Yu Tu, edited by Mindeiro Hongxian, is evenly divided with a square grid, like modern longitude and latitude lines. According to reports, this is an ancient auxiliary line for drawing maps on a scale, which is called "planning map". The length of the middle side of the square represents the actual mileage. According to records, this method began with the principle of "painting six bodies" put forward by Pei Xiu in Jin Dynasty. "Six-body" means "fraction", that is, today's scale; The second is "quasi-observation", which is used to determine the mutual orientation relationship between landforms and features; The third is "Daoli", which is used to determine the distance between the two roads; The fourth is "highly competitive"; The fifth is "square evil", that is, the fluctuation of ground slope; The sixth is "circuitous", that is, the conversion between the fluctuation of the site and the distance on the map. This is a milestone in the map history of our country. Pei Xiu once worked out the topographic abbot's map in the scale of one inch to a hundred miles, Jia Dan worked out the map of Hua Yi in the sea in the Tang Dynasty, and Shen Kuo in the Northern Song Dynasty worked out the map of states and counties in the world (also known as the map of guarding tombs) in the scale of two inches to a hundred miles. In Yuan Dynasty, the map of the whole country drawn by Zhu Siben in this way was more accurate than the previous one, which provided a reference for the drawing of Guang Yu Tu in Ming Dynasty.

Wide and modern maps are almost the same, but it is accurate and single. However, the full map of the summer resort in the Qing Dynasty, the map of Jiangxi Province, Wutai Mountain Scenic Area and the map of West Lake Palace, etc. With overlapping mountains, exquisite architecture and delicate brushwork, it is difficult to tell whether this is a landscape painting or a map. According to reports, this is the image drawing method of traditional map drawing in China.

Zheng He's nautical chart is a road map drawn according to Zheng He's voyage to the West. The whole map starts from Nanjing and extends to the east coast of Africa (now Mombasa, Kenya). The map shows the location of Asian and African countries, the distance and depth of the waterway.

The Ming court drew the Geographical Map of the Great World according to Matteo Ricci's hand-painted version. The map of the world brought by Matteo Ricci was marked and published in Chinese on 1584, and it was named "The Whole Map of Mountains and Seas". This exquisite map once aroused great interest of scholars at that time, but when they heard that China was only a part of the East, and the area occupied was so small that it was not in the center of the whole map, ministers were very angry. Matteo Ricci then projected the prime meridian, and later drew this map with Chinese painting in the center.

Matteo Ricci and later missionaries taught China people to use latitude and longitude positioning. The Complete Map of Mountain, Sea, Land and Air shows that the earth is round, which undoubtedly makes a revolutionary leap in China's view of the universe and China's map theory. During the Kangxi period of the Qing Dynasty, people completed the panorama of the Forbidden City in 10 years by means of field survey and projection of western longitude and latitude lines. This is a measured national map drawn by China under the guidance of scientific geography and scientific methods, and its significance is very far-reaching.