Mathematical Treatise in Nine Sections
The Mathematical Treatise in Nine Sections (simplified Chinese: 数书九章; traditional Chinese: 數書九章; pinyin: Shùshū Jiǔzhāng; Wade–Giles: Shushu Chiuchang) is a mathematical text written by Chinese Southern Song dynasty mathematician Qin Jiushao in the year 1247. The mathematical text has a wide range of topics and is taken from all aspects of the society of that time, including agriculture, astronomy, water conservancy, urban layout, construction engineering, surveying, taxation, armament, military and so on.
This book contains nine chapters:
Da Yan type (Indeterminate equations);
Heaven phenomena
Area of land and field
Surveying
Taxation
Storage of grains
Building construction
Military matters
Price and interest.Each chapter contains nine problems, a total of 81 problems.
Apart from describing Chinese Remainder Theorem for the first time and providing a constructive proof for it, the text investigated:
Indeterminate equations
"Lin Long method" for numerical solution of algebraic equations, 570 years before Horner's method
Areas and volumes of geometric objects and
Linear systemLike many traditional Chinese mathematical works, the text reflects a Confucian administrator's concern with more practical mathematical problems, like calendrical, mensural, and fiscal problems.