The ''Mathematical Treatise in Nine Sections'' () is a mathematical text written by Chinese

Southern Song The Song dynasty (; ; 960–1279) was an imperial dynasty of China that began in 960 and lasted until 1279. The dynasty was founded by Emperor Taizu of Song following his usurpation of the throne of the Later Zhou. The Song conquered the rest ...

dynasty

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

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 Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ...

Taxation A tax is a compulsory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity) by a governmental organization in order to fund government spending and various public expenditures (regional, local, o ...

#Storage of grains #Building construction #Military matters #Price and

interest In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distin ...

. 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 *"Linglong method" (, roughly "method of harmoniously alternating evolution") for numerical solution of algebraic equations, 570 years before Horner's method *

Area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an op ...

s and

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...

s of geometric objects and *

Linear system In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction ...

Like many traditional Chinese mathematical works, the text reflects a

Confucian Confucianism, also known as Ruism or Ru classicism, is a system of thought and behavior originating in ancient China. Variously described as tradition, a philosophy, a religion, a humanistic or rationalistic religion, a way of governing, or ...

administrator's concern with more practical mathematical problems, like calendrical, mensural, and fiscal problems. The text existed in

manuscript A manuscript (abbreviated MS for singular and MSS for plural) was, traditionally, any document written by hand – or, once practical typewriters became available, typewritten – as opposed to mechanically printed or reproduced i ...

form in 1247, it was incorporated into The Yongle Encyclopedia in 1421; in 1787 the book was collected into Siku Quanshu, in 1842 appeared in woodblock printed edition. The 19th century British

Protestant Protestantism is a Christian denomination, branch of Christianity that follows the theological tenets of the Reformation, Protestant Reformation, a movement that began seeking to reform the Catholic Church from within in the 16th century agai ...

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 Mathematical Treatise in Nine Sections to the West. In 1971 Belgian sinologist

Ulrich Libbrecht Ulrich Libbrecht (10 July 1928, Avelgem – 15 May 2017) was a Belgian philosopher and author in the field of comparative philosophy. His magnum opus consists of four books in Dutch - called "Introduction to Comparative Philosophy". An abbrev ...

published his doctorate dissertation, ''Chinese Mathematics in the Thirteenth Century'', which earned him a degree cum laude at

Leiden University Leiden University (abbreviated as ''LEI''; nl, Universiteit Leiden) is a public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William, Prince of Orange, as a reward to the city o ...

.Ulrich Libbrecht: ''Chinese Mathematics in the Thirteenth Century'': "Shu-shu Chiu-chang" of Ch'in Chiu-shao, Dover Publications Inc.,

Notes

References

*Guo, Shuchun
"Qin Jiushao"
'' Encyclopedia of China'' (Mathematics Edition), 1st ed.
Siku Quanshu edition of the book - 數學九章 (四庫全書本)
{{Song dynasty topics Song dynasty literature Chinese mathematics Mathematics manuscripts 1247 works Treatises 13th-century Chinese books