Qin's positive and negative balance method puts forward the principle that "quotient is always positive, real is often negative, from positive to negative, and profit is often negative", and gives a unified operation rule by pure algebraic addition, which is extended to any high-order equation.
Qin's "pros and cons" are called "Qin scheme". Countries all over the world start from primary school? When I was in middle school, I almost came into contact with his theorem in college math class? Laws and principles for solving problems.
This achievement is the highest achievement of medieval mathematics, which is five or six hundred years earlier than the same solution of Horner 18 19 in England.
Qin also improved the solution of linear equations, and eliminated them by mutual multiplication, which is completely consistent with the current addition, subtraction and elimination methods. At the same time, a rough calculation formula is given, which can be extended to the solution of general linear equations.
In Europe, it was first given by Bourdieu in 1559, more than 300 years later than Qin. Bourdieu used a very incomplete method of addition, subtraction and elimination to solve linear equations, and the theoretical integrity was not as good as Qin's.
The method of solving a kind of large-scale problems in ancient China. Qin systematically expounded the solution of this kind of problem, which is called "large extension technique", that is, the first congruence group solution in modern number theory.
This achievement is the highest achievement of medieval mathematics, which is more than 500 years earlier than the congruence theory established by the famous western mathematician Gauss in 180 1, and is called "China's remainder theorem" by the west. Qin not only won great honor for China, but also made outstanding contributions to world mathematics.
Qin also pioneered the "three-oblique quadrature method" and gave a formula for calculating the area of three sides of a known triangle. Some empirical constants are also given, such as "firm three penetrating four soil five, millet rate fifty, wall method half", which still has practical significance even now.
In Deductive Reciprocity, Qin also gave a clever and universal operation method for the mixed proposition of distribution ratio and chain ratio, which is still meaningful today.