Pei Xiu (224–271), courtesy name Jiyan, was a Chinese politician,
geographer, writer, and cartographer of the state of
Cao Wei in the
Three Kingdoms period and Jin dynasty of China. He was very much
trusted by Sima Zhao, and participated in the suppression of Zhuge
Dan's rebellion. Following Sima Yan taking the throne of the newly
established Jin dynasty, he and
Jia Chong had
Cao Huan deprived of his
position to accord to the will of heaven. In the year 267,
Pei Xiu was
appointed as the Minister of Works in the Jin government.
Pei Xiu outlined and analysed the advancements of cartography,
surveying and mathematics up until his time. He criticised earlier
Han dynasty maps for their lack of precision and quality when
representing scale and measured distances, although 20th century
archaeological excavations and findings of maps predating the third
century prove otherwise. There is also evidence that Zhang Heng
(78–139) was the first to establish the grid reference system in
1 As a cartographer
2 Written works
3 See also
As a cartographer
Further information: History of cartography § China
An early Western
Han dynasty (202 BCE – 9 CE) silk map found in tomb
Mawangdui Han tombs site, depicting the Kingdom of
Nanyue in southern China (note: the south direction is
oriented at the top, north at the bottom).
Pei Xiu is best known for his work in cartography. Although
professional map-making and use of the grid had existed in China
before him, he was the first to mention a plotted geometrical grid
reference and graduated scale displayed on the surface of maps to gain
greater accuracy in the estimated distance between different
locations. Historian Howard Nelson asserts that there is ample
written evidence that
Pei Xiu derived the idea of the grid reference
from the map of
Zhang Heng (78–139 CE), a polymath inventor and
statesman of the Eastern Han period. Robert Temple asserts that
Zhang Heng should also be credited as the first to establish the
mathematical grid in cartography, as evidenced by his work in maps,
the titles of his lost books, and the hint given in the Book of Later
Zhang Heng "cast a network of coordinates about heaven and
earth, and reckoned on the basis of it"). Xiu also created a set of
large-area maps that were drawn to scale. He produced a set of
principles that stressed the importance of consistent scaling,
directional measurements, and adjustments in land measurements in the
terrain that was being mapped.
The preface to Pei Xiu's written work was preserved in the 35th volume
of the Book of Jin, which is the official history for the Jin
dynasty and one of the Twenty-four Histories. It was written in the
Book of Jin that
Pei Xiu made a critical study of ancient texts in
order to update the naming conventions of geographic locations
described in old texts. His maps – drawn on rolls of silk –
were presented to Emperor Wu, who preserved them in the imperial
court's archives. Pei Xiu's maps have since been lost, decayed
or destroyed. Yet the oldest existing terrain maps from China date
to the fourth century BCE, found in a Qin tomb in present-day
Han dynasty maps from the second century BCE were found
earlier in the 1973 excavation of Mawangdui.
In 1697, the
Qing dynasty cartographer Hu Wei (胡渭) reconstructed
Pei Xiu's maps in his Yugong Zhuizhui (禹貢錐指, A Few Points on
the Vast Subject of the Yu Gong). Modern scholars have also used
Pei Xiu's writing to reproduce his works, and historians such as
Herrmann have compared
Pei Xiu to other great ancient cartographers
such as the Greek cartographer
The Yu Ji Tu, or Map of the Tracks of Yu Gong, carved into stone in
1137, located in the
Stele Forest of Xi'an. This three feet
squared map features a graduated scale of 100 li for each rectangular
grid. China's coastline and river systems are clearly defined and
precisely pinpointed on the map.
Yu Gong is in reference to the work
of the Chinese deity
Yu the Great
Yu the Great described in the geographical
chapter of the Book of Documents, dated fifth century BCE.
Pei Xiu wrote a preface to his maps with essential background
information regarding older maps in China. He also provided a great
deal of criticism about the existing maps from the
Han dynasty in his
time. Later Chinese ideas about the quality of maps made during the
Han dynasty and before stem from the assessment given by Pei Xiu,
which was not a positive one.
Pei Xiu noted that the extant Han
maps at his disposal were of little use since they featured too many
inaccuracies and exaggerations in measured distance between
locations. However, the Qin maps and
Mawangdui maps of the Han
dynasty discovered by modern archaeologists were far superior in
quality than those examined and criticised by Pei Xiu. It was not
until the 20th century that Pei Xiu's third century assessment of
earlier maps' dismal quality would be overturned and disproven. The
makers of the Han maps were familiar with the use of scale, while the
Qin map makers had pinpointed the course of rivers with some
accuracy. What these earlier maps did not feature was
topographical elevation, which
Pei Xiu would outline with his six
principles of cartography.
Pei Xiu's preface describes geographers in the Xia, Shang and Zhou
dynasties, although the earliest known geographical work was the Yu
Gong chapter of the Shu Ji or Book of Documents, compiled in the fifth
century BCE during the mid Zhou period.
Pei Xiu also referred to
Xiao He (died 193), who assembled the maps made during the fall of the
Qin dynasty. This was done after the founder of the Han dynasty, Liu
Bang (died 195 BC), had sacked the city of Xianyang.
Pei Xiu states:
The origin of maps and geographical treatises goes back into former
ages. Under the three dynasties (Xia, Shang and Zhou) there were
special officials for this (guoshi). Then, when the Han sacked
Xiao He collected all the maps and documents of the Qin. Now
it is no longer possible to find the old maps in the secret archives,
and even those
Xiao He found are missing. We only have maps, both
general and local, from the (Later) Han time. None of these employs a
graduated scale (fenlü) and none of them are arranged on a
rectangular grid (zhunwang). Moreover, none of them gives anything
like a complete representation of the celebrated mountains and the
great rivers; their arrangement is very rough and imperfect, and one
cannot rely on them. Indeed some of them contain absurdities,
irrelevancies and exaggerations, which are not in accord with reality,
and which should be banished by good sense.
Pei Xiu continues his preface with short background information on the
conquests by the Jin dynasty and the impressive maps commissioned by
Sima Zhao (211–264). He then described the methods he used to create
new maps while examining the ancient text of the
Yu Gong or Tribute of
Yu to create historical maps:
The assumption of power by the great Jin dynasty has unified space in
all the six directions. To purify its territory, it began with Yong
and Shu (
Gansu and Sichuan) and penetrated deeply into their regions,
though full of obstacles. Emperor Wen then ordered the appropriate
officials to draw up maps of Wu and Shu. After Shu had been conquered
and the maps were examined, with regard to the distances from one
another of mountains, rivers, and places, the positions of plains and
declivities, and the lines of the roads, whether straight or curved,
which the six armies had followed; it was found that there was not the
slightest error. Now, referring back to antiquity, I have examined
according to the
Yu Gong the mountains and lakes, the courses of the
rivers, the plateaus and plains, the slopes and marshes, the limits of
the nine ancient provinces and the sixteen modern ones, taking account
of commanderies and fiefs, prefectures and cities, and not forgetting
the names of places where the ancient kingdoms concluded treaties or
held meetings; and lastly, inserting the roads, paths and navigable
waters, I have made this map in eighteen sheets.
Pei Xiu outlined six principles that should be observed when creating
a map. He then defended his position and each of the six principles
with a short explanation as to how they provide better accuracy in
map-making and cartography. The first three principles outlined the
use of scale (fenlü), direction (zhunwang) and road distance (daoli),
while the last three principles are used to properly calculate
distances on uneven terrain as represented on a flat, two dimensional
Pei Xiu states:
In making a map there are six observable principles: (1) the graduated
divisions, which are the means of determining the map's scale; (2) the
rectangular grid (of parallel lines in two dimensions), which is the
way of depicting correct relations between various parts of the map;
(3) pacing out the sides of right-angled triangles, which is the way
of fixing the lengths of derived distances (i.e., the third side of
the triangle, which cannot be walked over); (4) (measuring) the high
and the low; (5) (measuring) right angles and acute angles; (6)
(measuring) curves and straight lines. These three principles are used
according to the nature of the terrain, and are the means by which one
reduces what are really plains and hills (literally cliffs) to
distances on a plane surface... If one draws a map without graduated
divisions, there is no means of distinguishing between what is near
and what is far. If one has graduated divisions, but no rectangular
grid or network of lines, then while one may attain accuracy in one
corner of the map, one will certainly lose it elsewhere (i.e. in the
middle, far from guiding marks). If one has a rectangular grid, but
has not worked upon the [third] principle, then when it is a case of
places in difficult country, among mountains, lakes or seas (which
cannot be traversed directly by the surveyor), one cannot ascertain
how they are related to one another. If one has adopted the [third]
principle, but has not taken account of the high and the low, the
right angles and acute angles, and the curves and straight lines, then
the figures for distances indicated on the paths and roads will be far
from the truth, and one will lose the accuracy of the rectangular
grid. However, if we examine a map prepared by the combination of all
these principles, we find that a true scale representation of the
distances is fixed by the graduated divisions. So also the reality of
the relative positions is attained by the use of paced sides of
right-angled triangles; and the true scale of degrees and figures is
reproduced by the determinations of high and low, angular dimensions,
and curved or straight lines. Thus even if there are great obstacles
in the shape of high mountains or vast lakes, huge distances or
strange places, necessitating climbs and descents, retracting of steps
or detours — everything can be taken into account and determined.
When the principle of the rectangular grid is properly applied, then
the straight and the curved, near and the far, can conceal nothing of
their form from us.
List of people of the Three Kingdoms
^ a b c d Needham, Volume 3, 538.
^ a b c d Hsu, 96.
^ Needham, Volume 3, 106–107.
^ Needham, Volume 3, 538–540.
^ Nelson, 359.
^ Temple (1986) 30.
^ Selin, Helaine (2008). Encyclopaedia of the History of Science,
Technology, and Medicine in Non-Western Cultures. Springer (published
March 17, 2008). p. 567. ISBN 978-1402049606.
^ Needham, Volume 3, 541.
^ a b c Needham, Volume 3, 540.
^ a b Hsu, 90.
^ Jacques Gernet (31 May 1996). A History of Chinese Civilization.
Cambridge University Press. pp. 339–.
^ a b Hsu, 97.
^ Needham, Volume 3, 500.
^ a b Needham, Volume 3, 539.
^ Hsu, 96–97.
^ Needham, Volume 3, 539–540.
Hsu, Mei-ling (1993). "The Qin Maps: A Clue to Later Chinese
Cartographic Development". Imago Mundi. 45: 90–100.
Needham, Joseph (1986). Science and Civilization in China. Volume 3,
Mathematics and the Sciences of the Heavens and the Earth. Taipei:
Caves Books Ltd.
Nelson, Howard (1974). "Chinese Maps: An Exhibition at the British
Library". The China Quarterly (58): 357–362.
Temple, Robert (1986). The Genius of China: 3,000 Years of Science,
Discovery, and Invention. New York: Simon and Schuster, Inc.
Prominent people of Cao Wei
Empresses and noble ladies
Empress Bian (Cao Mao's wife)
Empress Bian (Cao Huan's wife)
Princes and royal figures
Cao Ju (Prince of Fanyang)
Cao Ju (Prince of Pengcheng)
Cao Jun (Duke of Fan)
Cao Jun (Prince of Chenliu)
Cao Lin (Prince of Donghai)
Cao Lin (Prince of Pei)
Zhang Ji (Derong)
Zhang Ji (Jingzhong)
Other notable women
Other notable figures
Seven Sages of the Bamboo Grove