Chapter 10 Section 3 The Earliest Cartographic Theory——Pei Xiu’s Six Cartography

Pei Xiu (223-271 A.D.), styled Jiyan, was born in Wenxi (now Wenxi County, Shanxi).Born in a family of officials for generations, he loved reading since he was a child. He was able to write articles at the age of eight. When he was young, he was talented and became the staff of Minister Cao Shuang.Soon after Cao Shuang's defeat, he was appreciated by Sima Yi and Sima Zhao's father and son who were in charge of the power of the Wei State, and he went out with Sima Zhao.After Sima Yan established the Jin Dynasty, he was reused. In the fourth year of Taishi (268 A.D.), he served as Sikong (one of the most senior officials of the imperial court), in charge of the national household registration, maps, land, acres, taxes, etc.He died of illness three years later at the age of 48.

The most outstanding contribution of Pei Xiu in his life is the theory and practice of map drawing, especially the "six principles of map drawing" (six principles of map drawing) proposed by him when he wrote the preface to "Yugong Regional Map", which is the traditional Chinese cartography theory. It is an important basis for the Western surveying and mapping technology before it was introduced into China. Pei Xiu's "Six Styles of Cartography" are preserved in "Book of Jin·Pei Xiu Biography" and the related books "Yiwen Leiju" and "Beginners" compiled by the Tang Dynasty.In view of its great influence, the full text is now transcribed as follows:

There are six aspects of cartography: one is the division rate, so the degree of distinguishing the wide wheel is also.The second is to look forward, so it is the body of each other.The third is Daoli, so the number of where it comes from is determined.The fourth is called high and low, the fifth is called side evil, and the sixth is called tortuous and straightforward. These three are different according to the local conditions, so the school is also different in danger.If there is an image but no proportion, then there is no way to judge the difference between distance and distance; if there is a proportion but no perspective, even if it is in one corner, it will be lost to other places; The earth cannot be connected with each other; if there is a way, but there is no high or low, square, or straight, then the number of paths will be contrary to the reality of distance and nearness, and the correctness of hope will be lost.Therefore, with reference to these six factors, the distance and distance are determined by the ratio, each other is determined by the quasi-sight, the path is determined by the Tao, and the degree is determined by the calculation of high and low, side evil, and straightness.Therefore, despite the separation of steep mountains and huge seas, the vast distances of the precipices, and the causes of climbing and falling, all of them can be determined.Since the method of quasi-hope is correct, there is nothing hidden in the straight, straight, and near.

〔例句〕There are six principles of map making: one is the fraction (scale), which is used to distinguish the size of the range.The second is the quasi-look (orientation), which is used to determine the positional relationship between each other.The third is Daoli (road mileage), which is used to measure the distance between each other.The fourth is height (high and low terrain), the fifth is squareness (angle), and the sixth is straightness (curvature). These three aspects must be adjusted to local conditions, and the purpose is to correctly measure the horizontal straight-line distance of the curved road.If there are only images but no scale, then there is no way to distinguish distance from near.If you have a scale and don't pay attention to the direction, then even if you draw accurately in one direction, you will definitely make mistakes in other directions.Paying attention to mutual positions without specific road mileage, it is impossible to connect between closed locations such as mountains or seashores.If you have a specific road and cannot pay attention to correcting it from the three aspects of terrain height, angle and curvature, then the mileage of the road must not conform to the horizontal straight line distance, and it will also deviate from the correct orientation.Therefore, only by referring to these six principles, can the actual distance be determined through the scale, the exact relationship between each other through the azimuth, the specific route connecting each other through the road mileage, and the calculation of the height, angle and curvature of the terrain Find the horizontal straight line distance.Therefore, despite the barriers of mountains and seas, the huge differences in frontiers and foreign countries, the complexity of the terrain and the twists and turns of the roads, they can all be determined according to these principles.Once there is a way to determine the direction, it is impossible to determine the wrong position in any place, regardless of the straightness of the road and the distance.

Although the "six bodies of cartography" was proposed by Pei Xiu, it is actually the result of long-term accumulation of previous cartography experience and the theoreticalization of countless cartography practices.From the existing maps such as "Fangmatan Map", "Zhaoyu Map" and "Mawangdui Map", we can clearly see that mapmakers have successfully applied some or most of these principles.In the map production from the Western Jin Dynasty to the Qing Dynasty, most authors consciously used the "six elements of cartography".