The map was drawn in ancient China. The following are several representative evolutionary histories from the Three Kingdoms period to the Yuan Dynasty. From the narration, we can know how the ancients measured and drew maps.
China also had the ability to draw nautical charts in the Song Dynasty. Of course, science developed rapidly after the Yuan Dynasty (for example, the hybrid seismograph can measure astronomy). At the same time, the development of foreign science is also wonderful ... (for example, the map of Taiwan Province Province drawn by the Dutch sailing around Taiwan Province Province).
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The first monograph on calculation —— Calculation Classics of Islands
The Book of Island Calculations was written by Liu Hui, a mathematician in the Three Kingdoms Period (3rd century BC). When he took notes for nine chapters of arithmetic, he wrote a volume of errors and attached it to the book.
Li Jiang, a mathematician in the Tang Dynasty, listed the heavy differences and named them "Calculating Classics on the Island", which was listed as one of the "Ten Books of Calculating Classics" in ancient China. The nine examples in this book all involve the problem of height measurement and its calculation. These nine examples are: measuring the height of islands (lookout island), measuring the height of pine trees on mountains (lookout pine), measuring the size of cities (lookout city), measuring the depth of gullies (lookout valley), measuring the height of towers above ground (lookout tower), measuring the width of rivers (lookout wave mouth), measuring the depth of clear water pools (lookout Qingyuan) and measuring the width of lakes (from mountains)
In order to solve these problems, Liu Hui put forward specific calculation methods, such as repeated table method, continuous cable method, cumulative distance method and so on. These methods boil down to one point, that is, gravity difference measurement. Gravity difference measurement is a theory and method to measure the height, distance and depth by using simple measuring tools such as moment, watch and rope, according to the proportional internal relationship between the corresponding sides of similar right triangle. Before Liu Hui, Zhao Shuang made a daily height map and put forward gravity difference's measurement theory for the first time when he was annotating the Classic of Weekly Parallel Calculations. In the book Calculation of Islands, Liu Hui skillfully used gravity difference's theory to put forward a variety of specific measurement and calculation methods, which popularized gravity difference's measurement theory.
Island Calculation is an enduring monograph on calculation. Gravity difference's surveying theory and method revealed in detail became the basic basis of ancient surveying, and built a bridge to realize the leap from direct surveying (step or quantity) to indirect surveying. Until today, the theory and method of weight difference measurement still have reference significance in some occasions.
What is "painting six bodies"
Six-body surveying and mapping is the six methods of surveying and mapping put forward by Pei Xiu, a cartographer in Jin Dynasty.
Pei Xiu (AD 224 ~ 27 1) was a well-known person in Hedong (present-day Shanxi). When Emperor Wu of Jin lost the lawsuit, he became prime minister. He looked up the old map left by Wei according to "the Sixth Army passed by, the region was far and near, the mountains and rivers were dangerous, the roads were circuitous and the roads were straight".
Because the old maps were sketchy and the place names changed a lot, he compiled the earliest atlas of China-regional map and topographic local map with the help of the guest scene. He summed up the experience of cartography in the past and put forward six principles of cartography, namely, "six aspects of cartography": one is "fraction", which reflects the ratio of area to length and width, 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 "Dao Li", which is used to determine the distance between the two places; The fourth is "competition", that is, relative elevation; The fifth is "square evil", that is, the fluctuation of ground slope; The sixth is "straightness", that is, the conversion between the fluctuation of the site and the distance on the map.
Pei Xiu believes that the six aspects of cartography are interrelated and extremely important in map making. If the map only has graphics and no scale, it is impossible to compare and measure the distance between the field and the map; If you draw according to the scale, regardless of accuracy, then the accuracy of the map here is ok, and there will be deviations elsewhere; With direction and no road, we don't know the distance between residential areas on the map, just like the barrier between mountains and seas can't be connected; With distance, we can't measure the slope of Fugui Mountain, so the number of paths will be contrary to the reality of distance, and the map is not accurate enough to be used.
The comprehensive application of these six principles has correctly solved the problems of map scale, orientation, distance and their transformation. Therefore, six-body cartography became the basis of China's cartography theory before the Ming Dynasty, and occupied an important position in the history of cartography in China and the world.
Ji Li Fang Hua
"Planning one by one" is a method of drawing maps in proportion. When drawing, the map is first covered with squares, and the length of each side in the square represents the field, which is equivalent to the squares on the modern topographic map; Then draw the map content according to the grid to ensure a certain accuracy. According to written records, this method began with the principle of "six-body diagram" put forward by Pei Xiu in Jin Dynasty. He once compiled a topographic abbot map with a scale of one inch and a hundred miles.
In the Tang Dynasty, Jia Dan compiled a map of foreigners in the sea at a speed of 100 miles per inch. In the Northern Song Dynasty, Shen Kuo compiled a map of counties and counties in the world (also known as the map of guarding tombs). In the Yuan Dynasty, Zhu Siben drew a national map-map by a planned method, and its accuracy exceeded that of predecessors. This method has been used for 1500 years until the early Qing Dynasty, which is of great significance in the history of cartography in China and the world.
Guo Shoujing's Surveying and Mapping Achievements in Yuan Dynasty
Guo Shoujing's greatest contribution to surveying and mapping is that he took the sea level along the coast of China as the datum of leveling. At that time, Guo Shoujing had set out from Mengmen Mountain (now Yichuan, Shaanxi Province to Jixian, Shanxi Province) to the east along Zhongtiao Mountain, surveyed the terrain along the old course of the Yellow River, and mastered the terrain changes in hundreds of miles north of the Yellow River.
This is a large-scale topographic survey in the middle reaches of the Yellow River. Large-scale investigation must solve the problem of unification and naturalization of local investigation data. According to "A Brief Introduction to Famous Officials in Yuan Dynasty", Guo Shoujing "tasted the difference between the sea level and the terrain of Gyeonggi, saying that the water of Gyeonggi is far from the sea, and its flow is steep, while the water of Gyeonggi is offshore, its flow is slow, and its word size is small. There is no such thing as water conservancy. "
This is the first time in the history books of China that a unified altitude system is established based on sea level, and the scientific concept of "altitude" is founded. This work is of great significance to the development of surveying and is an outstanding scientific achievement bred by the development of large-scale surveying in China.
Up to now, the leveling results of regional survey in all countries in the world are based on the average sea level at a certain point along the coast and are naturalized in the height system. In China, the average sea level of the Yellow Sea recorded by the tidal station of Qingdao Port over the years is taken as the benchmark, and the leveling origin is set in Qingdao as the benchmark of national elevation. This scientific method. Will continue to be used.