Nine Chapters of Arithmetic is the first mathematical monograph in ancient China, and it is the most important of the ten classic computational works formed around the first century. Its author can no longer be examined. It is generally believed that it has gradually become the final version after several generations of supplement and modification. Zhang Cang and Geng Shouchang in the Western Han Dynasty had been supplemented and sorted out, and they were generally finalized at that time. The last book was in the early years of the Eastern Han Dynasty at the latest, and most of them were Notes to Nine Chapters written by Wei Yuan, Jing Yuan and Liu Hui in the Three Kingdoms Period (263).

The mathematical achievements of "Nine Chapters Arithmetic" are various:

(1), the main achievements in arithmetic are fractional operation, proportional problem and "remainder" algorithm. Nine Chapters Arithmetic is the earliest book in the world that systematically describes fractional operation. The second, third and sixth chapters have many problems of proportion, which are also relatively early in the world. The algorithm of "insufficient profit" needs to give two assumptions, which is a creation. In medieval Europe, it was called "double law". Some people think it came from China through the Arab countries in the Middle Ages.

(2) Nine Chapters Arithmetic summarizes a lot of geometric knowledge in production and life practice, and puts forward many formulas for calculating area and volume, as well as the application of Pythagorean theorem in square field, quotient work and Pythagorean chapter.

③ Algebra content in Nine Chapters Arithmetic is also very rich, which has the advanced level in the world at that time.

1. square root and publisher

(2) The addition of two numbers with different symbols is actually subtraction, that is, division of different names. If the absolute value of a positive number is large, then its sum is positive, that is, "nothing is positive." If the absolute value of a negative number is large, then its sum is negative, that is, "nothing is negative." Symbolize as

(1) if a & gtb≥0,

Then a+(-b)=[b+(a-b)]+(-b)=a-b,

Or (-a)+b=[(-b)-(a-b)]+b=-(a-b).

2 if b & gta≥0,

Then a+(-b)=a+[(-a)-(b-a)]=-(b-a),

Or (-a)+b = (-a)+[a+(b-a)] = b-a, which was unmatched by other books at that time.