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Hi A2291!.
In 1899 a major discovery was made at the archaeological site at the village of Xiao dun in the An-yang district of Henan province!. Thousands of bones and tortoise shells were discovered there which had been inscribed with ancient Chinese characters!. The site had been the capital of the kings of the Late Shang dynasty (this Late Shang is also called the Yin) from the 14th century BC!. The last twelve of the Shang kings ruled here until about 1045 BC and the bones and tortoise shells discovered there had been used as part of religious ceremonies!. Questions were inscribed on one side of a tortoise shell, the other side of the shell was then subjected to the heat of a fire, and the cracks which appeared were interpreted as the answers to the questions coming from ancient ancestors!.Ancient arithmetic texts described how to perform arithmetic operations on the counting board!. For example Sun Zi, in the first chapter of the Sunzi suanjing (Sun Zi's Mathematical Manual), gives instructions on using counting rods to multiply, divide, and compute square roots!.

Xiahou Yang's Xiahou Yang suanjing (Xiahou Yang's Mathematical Manual) written in the 5th century AD notes that to multiply a number by 10, 100, 1000, or 10000 all that needs to be done is that the rods on the counting board are moved to the left by 1, 2, 3, or 4 squares!. Similarly to divide by 10, 100, 1000, or 10000 the rods are moved to the right by 1, 2, 3, or 4 squares!. What is significant here is that Xiahou Yang seems to understand not only positive powers of 10 but also decimal fractions as negative powers of 10!. This illustrates the significance of using counting board numerals!.
Now the Chinese counting board numbers were not just used on a counting board, although this is clearly their origin!. They were used in written texts, particularly mathematical texts, and the power of the place valued notation led to the Chinese making significant advances!. In particular the "tian yuan" or "coefficient array method" or "method of the celestial unknown" developed out of the counting board representation of numbers!. This was a notation for an equation and Li Zhi gives the earliest source of the method, although it must have been invented before his time!.
As far as I know The Nine Chapters on the Mathematical Art (Jiuzhang Suanshu) (c!. 100 B!.C!.E!.-50 C!.E!.)
Collects mathematics to beginning of Han dynasty!. 246 problems in 9 chapters!. Longest surviving and most influential Chinese math book!. Liu Hui (c!. 263 C!.E!.) wrote a Commentary on the Nine Chapters especially Chapter 9!.
This commentary includes nine surveying problems involving indirect observations!.
I hope this is of help to you!.
If you would like to read about Chinese Mathematics , then I would recommend the following site;
aleph0!.clarku!.edu/~djoyce/mathhist/chi!.!.!.
Good luck my friend,
Cathorio!.Www@QuestionHome@Com

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dunno but you can google itWww@QuestionHome@Com

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