Qin Jiushao: Shuxue Jiuzhang (Mathematics in Nine Categories) (1247)

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Qin Jiushao 秦九韶 or Ch'in Chiu-shao, ca. 1202–1261, was a Chinese mathematician, meteorologist, inventor, politician, and writer. He was born in Ziyang, Sichuan, his family came from Shandong province. He wrote Shushu Jiuzhang (Mathematical Treatise in Nine Sections) in 1247 AD.

Taken from: Chinese Maritime Activities and Socioeconomic Development C. 2100 B.C.1900 A.D

After the Customs' procedures and the reduction of the goods of the ship owner, there

remains 5,088 liang (1) of agalloch (2) eaglewood, 10,430 bags of pepper (40 jin (3) a bag), 212 cases of ivory.

These are the result of a joint investment of four partners: A, B, C, D. They also borrowed among themselves.

Person A claims to an official that his investment includes 200 liang (1) of gold, 4 bags of salt and 11 units of paper

currency. Person B invested 800 liang (1) of silver, 3 bags of salt and 88 units of paper currency. This totals 424,000

guan (1 guan = 1000 coins). It is known that Person A lent Person B the paper currency, Person B lent

person C the silver, Person C lent Person D the trade permit and Person D lent the gold to Person A.

If all the debts are to be paid and the foreign goods to be shared according to the original investment shares,

what where the original prices for silver, salt and trade permit? Proportionally, how much agalloch (2) eaglewood,

pepper and ivory does each person get?

(1) Liang: traditional Chinese weight unit, about 37.8 grams, the same as a tael.

(2) Agalloch = eaglewood: Agarwood or aloeswood, eaglewood or gharuwood is a fragrant dark resinous wood used in incense, perfume, and small carvings.

(3) jin(=chin). Also called catty is 604gr.