Mathematics was one of the most developed basic science disciplines in ancient China，and "Jiu Chapter" was the most important mathematical classic in ancient China。

Biography of "Nine Chapters" contains the Western Han Dynasty "Nine Chapters of 筭 筭"、Three Kingdoms Wei Liu Hui Note and Tang Lichunfeng and other comments:。It has two meanings: narrow and general。Said narrowly，Only the Western Han Dynasty Zhang Cang (? - 1)、Geng Shouchang (1st Century) and other compiled "Nine Chapter 筭 筭 筭" This article。Generally speaking，It also includes comments such as Liu Hui Note and Li Chunfeng。Liu Hui calculated the period of the circularity in the Nine Chapter 筭 ■ ■ = 3.14，and March 14, it is designated as "International Mathematics Day".。

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"Nine Chapter 筭 筭 筭 筭，Volume One Field，There are various area formulas and the earliest and most complete scores in the world。Volume two corn，The proportional algorithm based on today's surgery (today's third rate method) as the main body。Volumes three declines，It is the proportional allocation algorithm，There are also a number of problems that can be attributed to the surgical proportion today。Volume Four Shao Guang，Is the inverse transport calculation of area and volume problem，The most important thing is to propose the world's earliest opening square and open cubic program。Volume Six average，It is the allocation algorithm of various volume formulas and the workload of earthwork。Volume Six average，Is a reasonable burden algorithm for tax，There are various arithmetic problems。Volumes Seven Ying Insufficient，Is the algorithm for profit and loss and its application in other calculation problems。Volume Eight Party Act，Is the linear equation group of today's linear formula，There is also the method of positive and negative number addition and subtraction and method of the equation。Rolling nine pyracuses，Is the Pythagorean theorem、Jieqiao stocks、Pythagorean Rongfang、Pythagorean Rongyuan and Simple Testing Questions。It established the basic framework of Chinese classical mathematics。

"Nine Chapters" contains nearly a hundred very abstract art texts that are formulas、Solution and 246 example questions。Where the scores are four operating standards、ratio bet365 Play online games and ratio allocation algorithm、Insufficient algorithm、Opening method、Linear equation group solution、The rules of positive and negative number plus and subtraction and some solution clue forms are all ahead of other cultural traditions for hundreds or even thousands of years，It is a major achievement with global significance。

The academic "Nine Chapter 筭 筭" is a saying in the application problem。This summary is not accurate，Actually its main part is not a question、Answer、Question set of one technique，but the form of algorithm rate example。

The relationship between the articles and topics of "Nine Chapters"，Generally speaking, there are several situations。

1. Abstracts of a class of problems, one or more example questions。This kind of content is often a question, one or one technique，or even counting questions。There are different situations here。

(1) Give one or more example questions，Then give one or more abstract art text。In example, there are only questions and answers，No art text。For example, Fang Tianzhang listed the three score -plus examples and gave the "combined score", which is the score plus law。Fang Tianzhang，2 men's scriptures、Its rate of surgery and reversal，Shao Guangzhang Kai Fangshu、Open Circle、Kai Cube and Kai Circle，Commercial Gongzhang except for the techniques of city walls and other techniques and their children's examples and their example questions，Both losers 4 techniques，Insufficient chapters of two profits and two inadequate techniques and one technique、，Pythagin chapter pythagy、Pythagorean Rongfang、Pythagorean Rongyuan and Test Yiyi 5，All belong to this situation，A total of 71 techniques、102 example questions。

(2) Give abstract art text，List a few more example questions。Example only questions and answers，No art text。Shang Gong Zhangchengyuan and other techniques、刍，Insufficient Zhang Ying Insufficient and its surgery belongs to this situation，A total of 4 techniques、14 example questions。

(3) Give abstract general technique，Several example questions。Examples include topics、Answers and Application of Application。corn chapter today has surgery and its 31 examples，During the decaying division、Returning to decay and 9 example questions，Shao Guangzhang Shao Guangshu and its 11 examples，11 general calculation problems solved with lack of profit，and Formula Chapter Division、Positive and negative、profit or loss and its 18 examples，A total of 7 techniques (no surgery is not included)，80 example questions。

These three situations have a total of 82 techniques、Bet365 app download 196 questions，About 80%of the book。Here，The text is the center，Is the main body，Very abstract and rigorous，and have universal，Instead of replacing modern symbols is the formula or computing program。The topic is to appear as an example and attach it to the art text。We call it the form of the example of the literary system。

2. The form of the application problem set

This kind of content is often one question and one technique。The degree of abstraction of its art text is also different。

(1) Abstract art text on a question。For example, the uniform loses "凫 geese" question，Although its art text has not left the number of days, this object，But there is no specific number of numbers，Adapt to the same problem。Losses Changan to Qi、牝 牝、矫、fake field、Cheng Geng、Wuxu Pond and other questions，Pythagofa chapter holding the pole to leave home and other questions。

(2) Calculating grass。Non -decaying topics of the Dayson，Most of the topics of the non -equalization of the average infusion，Most of the pyrothebuk -shaped problems of Pythagin Chapters and the subjects of "Four Four Shows" and other topics are calculated in specific numbers，It exists independently for not being able to leave the question。

There are 50 questions in this part，All the non -decaying classification problems of the decay chapter、Utilized seal atypical input problems，and the unlocking shares of the hook clue chapter and the four tables and the distance。They all focus on the topic，The art text is just the solution of the topic or the calculation of fine grass。

Sorry to be metaphorized，Can't summarize "Nine Chapters" as "one question、Answer、A Skills "application problem set。We think，At least there are at least three different styles of books in the history of mathematics，One is to form a axiomatic system like Eu Jioli "Original"; the second is the application problem set like Danfan's "arithmetic"，China's "Sun Tzu Being" and other works are the same; the main part of "Nine Chapter" is different from these two，but the third type，That is the form of the algorithm uniformity example。

It is not difficult to see，The technique of "Nine Chapters" is not a level。It can be divided into three levels at least: First, very abstract of a type of problem、Rigid and universal algorithm。Second is a more abstract algorithm of a question。Third is the calculation of specific problems。

　　The compilation of "Jiu Chapter"

The compilation of "Nine Chapters" not only involves "Nine Chapter 筭 筭" itself，and the positioning of some historical figures such as Zhang Cang，It is also related to the understanding of pre -Qin Bet365 app download Mathematics，It is a major problem in the study of Chinese mathematics history。The name of "Nine Chapters" is first preluded in the existing historical materials in the East Han Dynasty and the second year (179).、In the inscription of power，It has become the classic of the official standardized measurement device in the 2nd century，Explain that its compilation is much more early。

(1) "Nine Chapter 筭 筭。The compilation of "Nine Chapters" is mainly based on the following sayings。Liu Hui "Nine Chapter 筭 · · Preface" said: "Zhou Gong's gift has nine numbers，From time to time，then "Chapter Nine" is 矣。Burning Burning Book of Qin Burning in the Passion，By Scripture Disposal。From time to time，Hanbei Pinghou Zhang Cang、Geng Shouchang of Daji Nongzhong, Geng Shouchang, is a good fortune -telling world。Cang and others due to the remains of the old text，Each name is deleted。Therefore, the school's purpose is with ancient or different，and those who are mentioned as close words。"This means，"Nine times" has developed into "Nine Chapter 筭 筭"，Disposal due to the Burning Book of Burning Qin，Zhang Cang in the Western Han Dynasty、Geng Shouchang collects relics，Delete and supplement it one after another。This is the earliest record of the compilation of "Nine Chapters" in existing historical materials。

Tang Yanben's "Xia Houyang Sutra"、Jiaxian in the Northern Song Dynasty、Southern Song Rongyu、Yuan Mo Ruo and others believe that "Nine Chapter 筭 筭" is written by Huangdi or Lishou。Qing Daizhen "Changan in the book、The name of the forest "，and "Shanglin Garden in Wudi"，Negative Zhang Cang deletes "Nine Chapter 筭 筭"，I believe that the editing of "Nine Chapters" is after the middle of the Western Han Dynasty。Qian Baodi pushed it to the lower half of the century AD。

Dai Zhen、Qian Baodi, etc. Although there are different degrees of research，​​But none of them are enough to overthrow the historical material that Liu Hui's assertion，For example, Shanglinyuan，Qin Shihuang era。Liu Hui went to Gu Weiyuan，Not only the reliable statement of the compilation of "Nine Chapters" in "Nine Chapters"，And can see more information than Dai Zhen and others。

(2) "Nine Nine" and "Nine Chapter 筭 筭"。No matter how much people compiled the compilation of "Nine Chapters"，But do not deny that "Nine Chapter 筭 筭" is connected with "Nine times"。"Zhou Li · Di Guan Situ" records that nine are one of the six basic education received by noble children。But do not deny that "Nine Chapter 筭 筭" is connected with "Nine times"、corn、Differential、Shao Guang、Business Gong、Bet365 lotto review Both lost、Formula、Insufficient winning、beside me。There is a weight difference today、Xi Yan、Piberbuki also。​​"" Xi Yan "is Yanwen。Zheng Zhong believes that "Fangtian" to "beside the main" is a mathematical category inherent in the pre -Qin Dynasty，"Differential" and "Pythake" is developed by the Han Dynasty。

The "Nine Nine" in the early years of the Western Zhou Dynasty developed to the Spring and Autumn and Warring States，Nine branches that Er Zheng said。The algorithm is mostly abstract，It is a reflection of strong abstract thinking ability of pre -Qin people。Actually，Pre -Qin classics and unearthed cultural relics have several nine -nine clues。"Shang Jun Book" said that "the master wants to govern the people" must be "trial"。"Pipe" loading the tube and proposed "the place to decline its politics"。Measure the area of ​​the field with a square is the most intuitive，When the land is not a square，"Mozi" and "Mencius" all have records of "long -term complement"，This is the content of Shao Guangshu。"Pipe" when it comes to the water and water engineering, the "Cheng Gong" must be distinguished by the four seasons, that is, the standard workload。"Pipe" also said, "，Ruowang Table，If the evil person can know "，It should be a way to be near。

Comparison of the name of the pre -Qin "Nine times" and the name of "Nine Chapters"，Only the difference、Insufficient winning、There are three differences on the side。Among them, the meaning of the first two is the same。"Side" and "Pythagorean" are largely different，But according to the prompt from Jia Xian in the Northern Song Dynasty，It is necessary to include Pythagorean、Pythagorean Rongfang、Pythagorean Rongyuan and Simple Testing Problems (mainly Testing the Fang Fang Question) and other content。

Analysis of the system of "Nine Chapters of 筭 筭" before，Among them, the three situations that adopt the form of surgical literary system cover Fang Tian、corn、Shao Guang、Business Gong、Not enough、Formula and other six chapters and the problems of the decay chapters、The average losing problem of the average loser and the pyrata of Pythagin Seed、Pythagorean Rongfang、Pythagot Rongyuan、Testing Yi and other questions。and the content of the application problem set is the problem of non -decaying classification of the remaining dying chapters、A non -homogeneous infusion problem in the average infusion，and problems such as hooks and hooks and four tables of hooksticks。This part of this part is not only sorbous、The part of the style of the style is completely different，Bet365 lotto review and Dayson、The nature of these topics in the loser is uncoordinated with the name of the name，There are also large differences in compilation thoughts，is obvious complement。So if these three chapters are removed，and restore the title of the "Essentials"，The remaining content of "Nine Chapters" is not only consistent with the title，The form of the example of the system of surgical literary system，and amazing consistent with the "nine number" said by Er Zheng。This irrefutable proof，The "nine numbers" that Zheng Zhong said did exist during the Spring and Autumn and Warring States Periods，Liu Hui said, "The flow of nine times，Then "Chapter Nine" is a 矣 "。In other words，In the pre -Qin，Indeed, there is a main part of the main part of the "Nine Disted" developed from the "Nine Digitals" as the basic content，"Nine Chapter 筭 筭" in the form of the body of the system of surgery。

(3) The age reflected in the price in "Nine Chapters"。The "Qin and Han Law History Examination theory" in Japan's "Qin and Han Law History Examinations" tests the era of prices reflected in the prices in "Nine Chapters"。He thinks，"Nine Chapter 筭 筭" basically reflects the Warring States Period、Qin Shi's price "。Especially the similarity of labor income is of great significance to confirm the above conclusions。So，"Jiu Chapter" reflects the price level of the Warring States Period and the Qin Dynasty as a whole，instead of the price level of the Han Dynasty。This provides new evidence for Liu Hui's statement。It's just that Hori still follows "Nine Chapters" in the first century AD，Make it difficult to discuss it。

(4) Liu Hui's discussion about the compilation of "Nine Chapters" is correct。The most important argument for Liu Hui about Zhang Cang's deletion of "Nine Chapters" is the same as Emperor Hanwu.。In fact，"Salt and Iron Theory" mentioned in both the average infusion，The average losses of ancient times are similar to the average transmission method of "Nine Chapters"，The average loser of the present, which was implemented when Emperor Hanwu, was different from this。Bamboo Slip unearthed in the Bamboo Slip unearthed at the same time and "Book of Books"。Fuyang Shuangu Duki Western Hanwen Emperor Western Hanwen Emperor's Classic of Mathematics Works on the tomb，There is a question in the first question of the first question。This has fundamentally overturned Dai Zhen and others on the argument that Liu Hui discussed。

other，Liu Hui has the rigorous learning style of seeking truth from facts，If he did not see Zhang Cang and others Bet365 app download delete the "Nine Chapter 筭 筭", it is indeed recorded，The compilation of "Nine Chapters" is a serious question，Is it absolutely impossible to make an open river。

Zhang Cang and others to organize the guiding ideology of "Nine Chapter 筭 筭" is the Confucianism。Xunzi、Zhang Cang、Jia Yi is the teacher -student relationship of the biography。Jia Yi is the main representative of Confucianism in the early Western Han Dynasty，It can be seen that Zhang Cang believes that he believes in Confucianism。"Xunzi · Confucian Effect" divides the learning into Wenwen、see、Knowing、Four layers of line，"Learning to do it and stop"。"Nine Chapter 筭 筭 筭" has more than calculation，Taking algorithm as the center，The algorithm is based on solving actual problems as the fundamental purpose，Show the style of "seeking truth from facts"，It is the materialist thought of Xunzi。

　　(The author is a researcher at the Institute of Natural Sciences of the Chinese Academy of Sciences)