The Sea Island Mathematical Manual
- The Sea Island Mathematical Manual
"The Sea Island Mathematical Manual" or "Haidao suanjing" (海岛算经) was written by the Chinese mathematican Liu Hui of the Three Kingdoms era (220–280) as an extension of chapter 9 of The Nine Chapters on the Mathematical Art. [L. van. Hee, Le Classique d I'Ile Maritime: Ouvrage Chinois de III siecle 1932] During the Tang Dynasty, this appendix was taken out from "The Nine Chapters on the Mathematical Art" as a separate book, titled "Haidao suanjing"("Sea Island Mathematical Manual"), named after problem No 1 "Looking at a sea island".
This book contained many practical problems of surveying using geometry. This work provided detailed instructions on how to measure distances and heights with tall surveyor's poles and horizontal bars fixed at right angles to them. With this, the following cases are considered in his work:
#The measurement of the height of an island opposed to its sea level and viewed from the sea
#The height of a pine tree on top of a hill
#The size of a square city wall viewed at a long distance
#The depth of a ravine (using hence-forward cross-bars)
#The height of a building on a plain seen from a hill
#The breadth of a river-mouth seen from a distance on land
#The depth of a transparent pool
#The width of a river as seen from a hill
#The size of a city seen from a mountain
The 19th century British Protestant Christian missionary Alexander Wylie in his article "Jottings on the Sciences of Chinese Mathematics" published in "North China Herald" 1852, was the first person to introduce Sea Island Mathematical Manual to the West. French mathematician translated the book into French in 1932 [L. van. Hee, "Le Classique d I'Ile Maritime: Ouvrage Chinois de III siecle" 1932 ] . In 1986 Ang Tian Se and Frank Swetz translated Haidao into English.
After comparing the development of surveying in China and the West, Frank Swetz concluded that"in the endeavours of mathematical surveying, China's accomplishments exceeded those realized in the West by about one thousand years." [Frank J. Swetz: The Sea Island Mathematical Manual,Surveying and Mathematics in Ancient China 4.2 Chinese Surveying Accomplishments, A Comparative Retrospection p63 The Pennsylvania State University Press, 1992 ISBN 0-271-00799-0 ） ]
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