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:
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:
Like many traditional Chinese mathematical works, the text reflects a Confucian administrator's concern with more practical mathematical problems, like calendrical, mensural, and fiscal problems.
The text existed in manuscript 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 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 published his doctorate dissertation, Chinese Mathematics in the Thirteenth Century, which earned him a degree cum laude at Leiden University.
Chinese classic texts or canonical texts or simply dianji (典籍) refers to the Chinese texts which originated before the imperial unification by the Qin dynasty in 221 BC, particularly the "Four Books and Five Classics" of the Neo-Confucian tradition, themselves a customary abridgment of the "Thirteen Classics". All of these pre-Qin texts were written in classical Chinese. All three canons are collectively known as the classics.
In mathematics and computer science, Horner's method is an algorithm for polynomial evaluation. Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. After the introduction of computers, this algorithm became fundamental for computing efficiently with polynomials.
Zhu Shijie, courtesy name Hanqing (漢卿), pseudonym Songting (松庭), was a Chinese mathematician and writer. He was a Chinese mathematician during the Yuan Dynasty. Zhu was born close to today's Beijing. Two of his mathematical works have survived. Introduction to Computational Studies, and Jade Mirror of the Four Unknowns.
The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE. This book is one of the earliest surviving mathematical texts from China, the first being Suan shu shu and Zhoubi Suanjing. It lays out an approach to mathematics that centres on finding the most general methods of solving problems, which may be contrasted with the approach common to ancient Greek mathematicians, who tended to deduce propositions from an initial set of axioms.
Qin Jiushao, courtesy name Daogu (道古), was a Chinese mathematician, meteorologist, inventor, politician, and writer. He is credited for discovering Horner's method as well as inventing Tianchi basins, a type of rain gauge instrument used to gather meteorological data.
The Gujin Tushu Jicheng, also known as the Imperial Encyclopaedia, is a vast encyclopedic work written in China during the reigns of the Qing Dynasty emperors Kangxi and Yongzheng. It was begun in 1700 and completed in 1725. The work was headed initially by scholar Chen Menglei (陳夢雷), and later by Jiang Tingxi.
Mathematics in China emerged independently by the 11th century BC. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system, algebra, geometry, number theory and trigonometry.
Yang Hui, courtesy name Qianguang (謙光), was a Chinese mathematician and writer during the Song dynasty. Originally, from Qiantang, Yang worked on magic squares, magic circles and the binomial theorem, and is best known for his contribution of presenting Yang Hui's Triangle. This triangle was the same as Pascal's Triangle, discovered by Yang's predecessor Jia Xian. Yang was also a contemporary to the other famous mathematician Qin Jiushao.
Huangdi Neijing, literally the Inner Canon of the Yellow Emperor or Esoteric Scripture of the Yellow Emperor, is an ancient Chinese medical text that has been treated as the fundamental doctrinal source for Chinese medicine for more than two millennia. The work is composed of two texts—each of eighty-one chapters or treatises in a question-and-answer format between the mythical Yellow Emperor and six of his equally legendary ministers.
The Siku Quanshu, variously translated as the Complete Library in Four Sections, Imperial Collection of Four, Emperor's Four Treasuries, Complete Library in Four Branches of Literature, or Complete Library of the Four Treasuries, is the largest collection of books in Chinese history. The complete encyclopedia contains an annotated catalogue of 10,680 titles along with a compendiums of 3,593 titles. The Siku Quanshu ended up surpassing the Ming dynasty's 1403 Yongle Encyclopedia in size, which was China's largest encyclopedia prior to the creation of the Siku Quanshu.
The Book on Numbers and Computation, or the Writings on Reckoning, is one of the earliest known Chinese mathematical treatises. It was written during the early Western Han dynasty, sometime between 202 BC and 186 BC. It was preserved among the Zhangjiashan Han bamboo texts and contains similar mathematical problems and principles found in the later Eastern Han period text of The Nine Chapters on the Mathematical Art.
Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra.
Chinese encyclopedias comprise both Chinese-language encyclopedias and foreign-language ones about China or Chinese topics. There is a type of native Chinese reference work called leishu that is sometimes translated as "encyclopedia", but although these collections of quotations from classic texts are expansively "encyclopedic", a leishu is more accurately described as a "compendium" or "anthology". The long history of Chinese encyclopedias began with the Huanglanleishu and continues with online encyclopedias such as the Baike Encyclopedia.
Tie Ban Shen Shu is an ancient form of divination from China, which is still in use in China, Taiwan, Singapore and the Chinese diaspora in Southeast Asia. Tie ban shen shu is regarded as among the most accurate and most difficult methods of personal fortune divination. Tie Ban is as well regarded as the collective Three Arts or Three Styles, Qi Men Dun Jia, Da Liu Ren and Tai Yi Shen Shu, China's highest metaphysical arts.
Yigu yanduan is a 13th-century mathematical work by Yuan dynasty mathematician Li Zhi.
Jigu suanjing was the work of early Tang dynasty calendarist and mathematician Wang Xiaotong, written some time before the year 626, when he presented his work to the Emperor. Jigu Suanjing was included as one of the requisite texts for Imperial examination; the amount of time required for the study of Jigu Suanjing was three years, the same as for The Nine Chapters on the Mathematical Art and Haidao Suanjing.
The Ten Computational Canons was a collection of ten Chinese mathematical works, compiled by early Tang dynasty mathematician Li Chunfeng (602–670), as the official mathematical texts for imperial examinations in mathematics.
Jade Mirror of the Four Unknowns, Siyuan yujian (四元玉鉴), also referred to as Jade Mirror of the Four Origins, is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie. Zhu advanced Chinese algebra with this Magnum opus.
Tianchi basins were meteorological measuring instruments used to gather and measure the amount of liquid precipitation over a period of time during the Song Dynasty. The instrument was devised by the Song Chinese mathematician and inventor Qin Jiushao in 1247.
Wu Zhen, courtesy name Tingzhen, was a Song dynasty historian from Chengdu who wrote 2 books enumerating mistakes found in New Book of Tang and Historical Records of the Five Dynasties, both history books by Ouyang Xiu. As pointed out in the 18th-century Siku Quanshu, Wu Zhen was "inclined to criticise for the sake of criticism".