TheJiuzhang Suanshu(Nine Chapters on the Mathematical Art) is the longest surviving and one of the most important in the ten ancient Chinese mathematical books. The book was co-compiled by several people and finished in the early Eastern Han Dynasty (about 1st century), indicating the formation of ancient Chinese mathematical system. It became the criterion of mathematical learning and research for mathematicians of later generations ever since then.
Afterwards, theJiuzhang Suanshuhave been annotated by many mathematicians, the most famous ones including Liu Hui (in 263AD) and Li Chunfeng (in 656AD).The edition published by the Northern Song government in 1084 was the earliest mathematical book in the world. The book was introduced toKoreaandJapanduring the Sui and Tang dynasties (581-907). Now, it has been translated into several languages, including Japanese, Russian, German, English and French, and become the basis for modern mathematics.
The book is broken up into nine chapters containing 246 questions with their solutions and procedures. Each chapter deals with specific field of questions. Here is a short description of each chapter:
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Chapter I
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Chapter II
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Chapter III
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'Field measurement'
(Fang tian)
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'Cereals'
(Su mi)
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'Distribution by proportion'
(Cui fen)
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Method for calculation of areas of land
Deals with computation with fractions
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Concerns with proportions (for exchange of cereals, millet, or rice)
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Problems on proportional distribution
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Chapter IV
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Chapter V
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Chapter VI
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'What width?'
(Shao guang)
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'Construction consultations'
(Shang gong)
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'Fair taxes' (Jun shu)
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Finds the length of a side when given the area or volume
Finds the square root or cube root of a number
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Concerns with calculation for constructions of solid figures
Finds the volumes of various shapes of solid figures
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Deals with calculation on how to distribute grain and labor
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Chapter VII
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Chapter VIII
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Chapter IX
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'Excess and deficiency'
(Ying bu zu)
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'Rectangular arrays'
(Fang cheng)
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'Right Triangles'
(Gou gu)
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Uses of method of false position to solve difficult problems
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Problems on simultaneous linear equations
Introduces concept of positive and negative numbers
Addition and subtraction of positive and negative numbers
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Discusses the Gou gu theorem and properties of the right-angled triangle
Problems on similar right-angled triangles
Introduces general methods of solving quadratic equations
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The book's major achievements:
1. Devising a systematic treatment of arithmetic operations with fractions, 1,400 years earlier than the Europeans.
2. Dealing with various types of problems on proportions, 1,400 years earlier than the Europeans.
3. Devising methods for extracting square root and cubic root, which is quite similar to today's method, several hundred years earlier than the Western mathematicians.
4. Developing solutions for a system of linear equations, about 1,600 years earlier than the Western mathematicians.
5. Introducing the concepts of positive and negative numbers, more than 600 years earlier than the West.
6. Developing a general solution formula for the Pythagorean problems (problems of Gou gu), 300 years earlier than the West.
7. Putting forward theories of calculating areas and volumes of different shapes and figures.
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