At about the same time as the "Zhou Ji Sutra of Arithmetic", there is also a mathematical treatise, which is called "Nine Chapters of Arithmetic" in the history of science, which is the first and most important mathematical treatise in China. Written in the early years of the Eastern Han Dynasty, the Nine Chapters of Arithmetic contains solutions to 246 practical problems, including arithmetic, elementary algebra, and elementary geometry.
The four fractional arithmetic, the proportional algorithm, and the use of the Pythagorean theorem to solve some measurement problems were all the world's highest scientific work at that time. The record of the concept of negative numbers and the law of addition and subtraction of positive and negative numbers is also the earliest in the history of mathematical sciences in the world.
The book also describes many problems such as open squares, open squares, numerical solutions of one-dimensional quadratic equations, and simultaneous one-dimensional equations. "Nine Chapters of Arithmetic" has a great influence on the history of ancient mathematics in China, and also occupies an important position in the history of mathematics in the world.
The Nine Chapters of Arithmetic can be roughly divided into 9 aspects:
1) Land surveying. The book lists right triangles, trapezoids, triangles, circles, arcs, and rings, and gives methods for calculating the area of these shapes.
2) Percentages and proportions, according to the proportional relationship to find the answer to the question.
3) Arithmetic and geometric progressions.
4) Solve the problem of finding the length of other sides when the area and length of one side of the figure are known. There are also problems such as finding square roots, cubic roots, etc.
5) Measurement and calculation of the volume of three-dimensional figures, including walls, city walls, embankments, waterways and rivers.
6) Solve mathematical problems in the collection of taxes. There are also issues related to the time it takes for people to transport grain from the production area to the capital to pay taxes, and there is also the issue of taxation according to population.
7) The problem of excess and insufficiency. That is, to solve the problem of ax+b=0.
8) Solve equations and indefinite equations.
9) The nature of a right triangle.
In the chapter "The Nature of Right Triangles", there is such a question:
A pool, one zhang in length and one zhang in width, there is a reed born in the pool**, the reed is one foot high out of the water, let the reed fall to the edge of the pool, just the tip of the reed and the edge of the pool. Q: How deep is the water? This problem was later found in Indian mathematical writings and then spread to medieval Europe. This can only be solved by utilizing similar right-angled triangles.
The influence of the Nine Chapters of Arithmetic on the occurrence of ancient Chinese mathematics is as profound as the influence of the ancient Greek Euclid's Geometry on Western mathematics.
For more than a thousand years since, it has been used directly as a textbook. Japan and North Korea have also used it as a textbook. Scholars of all generations have attached great importance to the study of this arithmetic, and in the early mathematical works of Europe and Arabia, the algorithm for the problem of excess and deficiency is called the "Chinese algorithm", which shows its originality.