Qin Jiushao

Qin Jiushao

Qin Jiushao (1208-1268), Han nationality, was born in Lu county (now Fanxian County, Henan Province). He is a famous mathematician in the Southern Song Dynasty. Together with Li Ye, Yang Hui and Zhu Shijie, he is known as the four masters of mathematics in the song and Yuan Dynasties.

He studied astrology, temperament, arithmetic, poetry, bow, sword, and architecture. He served as the magistrate of Qiongzhou and Si nongcheng. Later, he was demoted and died in Meizhou. In 1247, he completed his book "nine chapters of Shu Shu Shu", which includes the method of Da Yan seeking one (the solution to the problem of first-order Congruence Equations, also known as the Chinese remainder theorem), the method of three oblique quadrature and the method of Qin Jiushao (the number of positive roots of higher-order equations) Value method is an important contribution in the world. This paper presents an algorithm for solving the numerical solution of higher order polynomial equation of one variable positive and negative quadrature.

brief account of the author's life

Qin Jiushao, the word Daogu. Lu county (now Fanxian County, Henan Province) people. Ancient Chinese mathematician. He was born in the first year of Jiading (1208) and demoted to Meizhou in the second year of yuejingding (1261). He died in Meizhou in February of the fourth year of Xianchun (1268) at the age of 61.

Qin Jiushao's father, Qin Jiqi, was born as a Jinshi. He was an official, a doctor and a secretary. Qin Jiushao was intelligent and diligent. In the fourth year of song shaoding (1231), Qin Jiushao was a Jinshi in the examination. He successively held the posts of county captain, general judge, counsellor, prefectural governor, tongnong, and temple official. He served as an official in Hubei, Anhui, Jiangsu, Zhejiang and other places successively. He was demoted to Meizhou around 1261 and soon died in his office. In his spare time, he devoted himself to mathematics,

He collected a wide range of calendar, mathematics, astrology, temperament, construction and other information for analysis and research. In 1244-1247, when he was filial to his mother, he combined his long-term accumulated mathematical knowledge and research results and wrote the famous masterpiece "nine chapters of Shu Shu" and created "Da Yan Qiu Yi Shu". It is called "Chinese Remainder Theorem". His theory of "positive and negative prescription" is called "Qin Jiushao procedure". Almost all countries in the world have come into contact with his theorems, laws and problem-solving principles in mathematics courses from primary school, middle school to university.

Sutton, a famous American historian of science, called Qin Jiushao "one of the greatest mathematicians of his nation, his time, and indeed of all times".

Qin Jiushao was a native of Lu county (now Fanxian County, Henan Province). His father was Qin Jizhe, whose name was Hongfu. He was a Jinshi in the fourth year of Shaoxi (1193), and later served as the governor of Bazhou (now Bazhong, Sichuan). In March of 1219, the 12th year of Jiading, soldiers Zhang Fu and Mo Jian of Xingyuan (now Hanzhong, Shaanxi) launched a mutiny. After entering Sichuan, they captured Lizhou (now Guangyuan), Langzhou (now Langzhong), Guozhou (now Nanchong), Suining (now Suining), Puzhou (now Anyue) and other places. When the mutinous army occupied Bazhou, Qin Jizhe abandoned the city and fled, and arrived at Lin'an (now Hangzhou), the capital of the Southern Song Dynasty, with his family. In Lin'an, Qin Jizhe was a doctor and Secretary of the Ministry of industry. In June of the first year of Baoqing (1225), he was appointed governor of Tongchuan and returned to Sichuan.

Qin Jiushao lived in his hometown when he was a child. At the age of 18, he was "the head of a righteous soldier in the village" and later moved to Kyoto with his father. He is a very intelligent man, attentive and studious. When his father was a doctor and Secretary of the Staff Department, it was time for him to study hard and accumulate knowledge. The doctor of the Ministry of industry is in charge of the construction, while the Secretary province is in charge of the books. Therefore, he has the opportunity to read a large number of ancient books, visit experts in astronomy, calendar and architecture, ask about astronomy, calendar and civil engineering, and even go deep into the construction site to understand the construction situation. He also studied mathematics from a hermit who was proficient in mathematics. He also learned parallel Li poetry from famous poet Li Liu and reached a higher level. Through this stage of study, Qin Jiushao became a learned and versatile young scholar. At that time, people said that he was "extremely skillful in his nature, and he studied everything from astrology, temperament, arithmetic to construction" and "games, balls, horses, bows and swords."

In 1225, Qin Jiushao followed his father to Tongchuan (now Santai County, Sichuan). The Mongolian army has invaded Gansu and Shaanxi, and the struggle against Mongolia (yuan) in the north is in full swing. The court of the Southern Song Dynasty "recruited 5000 righteous soldiers and made an agreement with the people, saying:" when the enemy arrives, the officers and soldiers will defend the original fort, the people will protect the Shanzhai, and the righteous soldiers will be guerrillas. " Civilian armed forces have been established in various places. Qin Jiushao, a military expert, served as the "righteous soldier head" of the civilian armed forces to maintain local public order.

A few years later, Li and Liu invited him to the Academy of Southern Song Dynasty to collate books and documents, but he did not make the trip. In 1236, Yuanbing invaded Sichuan Province, and wars were still frequent in the Jialing River Basin. Qin Jiushao had to take part in military activities frequently. Later, he wrote in the preface to the book of nine chapters: "when Di was suffering from disease, he could not help thinking that it was all between the stone and the stone. After ten years of sacrifice, his heart was withered and depressed", which truly reflected this turbulent life. As a result of the advance of Yuan soldiers and the collapse of soldiers, Tongchuan was no longer able to live in peace. So he went out to the east of Sichuan again, served as the general judge of Qizhou (now Qichun in Hubei Province) and the garrison of Hezhou (now Hexian in Anhui Province), and finally settled in Huzhou (now Wuxing in Zhejiang Province). When Qin Jiushao was in charge of Hezhou Prefecture, he used his power to sell salt to the common people. After settling down in Huzhou, the residence built was "extremely grand" and "later was a row of houses, which was used to be a place for Xiuji and orchestral". According to reports, he lived in Huzhou in luxury and "spent nothing". In August 1244, Qin Jiushao took tongzhilang as the judge of Jiankang prefecture (now Nanjing, Jiangsu Province). In November, he left his post because of his mother's death and returned to Huzhou to keep filial piety. During this period, he devoted himself to the study of mathematics, and completed the famous mathematical work "nine chapters of Shu Shu" in September 1247. Due to his rich knowledge and achievements in astronomy and calendar, he was summoned by the emperor to expound his views, and presented a draft and mathematical outline (i.e. nine chapters of the book of numbers).

In the second year of Baoyou (1254), Qin Jiushao returned to Jiankang and took up the post of system envoy along the Yangtze River. After that, he tried his best to curry favor with and bribe Jia Sidao, a powerful official of the current Dynasty. He was appointed as the governor of Qiongzhou in the sixth year of Baoyou's reign (1258), but he was removed three months later. Liu Kezhuang, a contemporary, said that Qin Jiushao "only went to the county (Qiongzhou) for a hundred days, and the people of the county were not tired of his greed. He wrote songs to cry for the dead to go quickly." Zhou Mi also said that he "went to the county for a few months, and he was very rich.". It seems that because of his corruption in Qiongzhou, the people are extremely dissatisfied. After returning to Huzhou from Qiongzhou, Qin Jiushao took refuge with Wu Qian and got his appreciation. They had a close relationship. Wu Qian planned to serve as the chief of the Si Nong temple in the first year of Kaiqing (1259) and the Linjiang army in the first year of JINGDING (1260). During this period of time, Qin Jiushao was keen on seeking official positions, pursuing fame and wealth, and had no remarkable achievements in science. Wu Jiunan Shao was also involved in the fierce internal struggle for the removal of officials. In about 1261, he was demoted to Meizhou to be a local official. He "kept on governing in Meizhou" and soon died.

Qin Jiushao's main achievement in mathematics is that he systematically summarized and developed the numerical solution of higher-order equation and the solution of first-order congruence group, and put forward quite complete "positive and negative square method" and "Da Yan seeking one method", which reached the highest level of mathematics in the world at that time.

The Qin Jiushao memorial hall built in Anyue is magnificent and magnificent.

Life story

Qin Jiushao (1208-1268) was born in Fanxian County, Henan Province.

The spring of 1208, the first year of Jiading, was born in Puzhou,

In October 1229, the second year of shaoding, Qin Jiushao promoted the county captain of Qi county,

In August of the fourth year of shaoding (1231), Qin Jiushao took part in Wei liaoweng's efforts to suppress the barbarians in Luzhou and repair the battlements of the city buildings,

In the fifth year of shaoding (1232), Qin Jiushao met Wu Qian when Wei liaoweng led Wu Qian to inspect tongchuanfu road and Chengdu Fu Road. Wei liaoweng and Wu Qian went with Qin Jiushao to visit Xu Yi who was ill.

In 1236, Qin Jiushao was promoted to Tongtan in Qizhou, Hubei Province,

In the autumn of 1237, the first year of Jiaxi reign, Qin Jiushao knew Hezhou (now Hexian County, Anhui Province)

In the second year of Jiaxi reign (1238), Qin Jiushao returned to Lin'an for Ding Fuyou. During Ding Fuyou's period in Hangzhou, Qin Jiushao found it inconvenient for people on both sides of Xixi River to cross the river. He designed and built a bridge on Xixi River, named "Xixi bridge". Mathematician Zhu Shijie named the bridge "Daogu bridge" in memory of Qin Jiushao.

In the third year of Jiaxi reign (1239), after Qin Jiushao had dealt with his father's affairs in Hangzhou, he went back with his mother and his wife to Huzhou west gate. His father's early house continued to worry about his father. Qin Jiushao and Wu Qian of zhiqingyuan prefecture (Ningbo, Zhejiang Province) began to rebuild his father's house during his father's worry period in Huzhou.

In June of the third year of Chunyou, Wu Qian returned to Huzhou to worry about his mother Ding. Qin Jiushao had even closer contacts with Wu Qian, who was robbed of his official position.

In the fourth year of Chunyou (1244), Qin Jiushao took the post of tongzhilang as the general judge of Jiankang (Nanjing) government. In November, Qin Jiushao was relieved of his mother's worries and left his post. He returned to Huzhou to keep watch for his mother, who was nearly 80 years old. He devoted himself to the research and application of mathematical achievements in practice and wrote a book "mathematical outline". At this time, Wu Qian was also in Huzhou, where they had a close relationship.

In the eighth year of Chunyou (1248), mathematical outline was recommended to the imperial court.

In 1249, Chen Zhensun, a bibliographer, consulted Qin Jiushao when compiling bibliography.

In the 10th year of Chunyou (1250), Qin Jiushao left the post of general judge of Jiankang and took up the post of governor of Suzhou.

In 1254, Jiushao served as the magistrate of Jiangning (Nanjing, Jiangsu Province) government and the counsellor of the system and establishment department along the Yangtze River, managing the grain roads of the ten prefectures in the south of the Yangtze River.

In the sixth year of Baoyou's reign (1258), Qin Jiushao was recommended by Jia Sidao to Li zengbo as the governor of Qiongzhou

Chinese PinYin : Qin Jiu Shao