Zu Xuan used a principle when calculating the volume of a sphere: "If the potential is the same, the product cannot be different". "Force" is the cross-sectional area and "potential" is the three-dimensional height. It means two solids with the same height. If the cross-sectional area at the same height is equal, the volume is equal.
More specifically, two solids between two parallel planes are cut by any plane parallel to these two planes. If the areas of two sections are equal, the volumes of two solids are equal. In China, the above principle is called "the principle of founding fathers", while abroad, it is usually called "the principle of cavalieri".
Extended data:
The significance of the principle of ancestral pestle;
A straight line consists of points, and the points represent the length of the straight line; A surface is composed of lines or points, and the number of points indicates the size of the area; Geometry is made up of faces, lines and finally points. Points also indicate the size of the volume. In order to make the volumes of the two geometries equal, that is, to make the number of points that make up the two geometries the same, the ancestor principle is applied to them.
Two geometric bodies are sandwiched between two parallel planes, which can be understood as the height between the parallel planes of these two geometric bodies is equal. The distance between two parallel planes is fixed. If distance is regarded as a line segment, there are countless points on this distance. After passing through a point, a section parallel to two parallel planes can be drawn.
If the cross-sectional areas of two geometric bodies cut by parallel sections passing through each point are equal, it means that the two geometric bodies have the same number of points on every two sections at the same height.
There are countless cross-sections, and the number of points on the cross-sections of every two geometric bodies with the same height is the same, that is to say, the number of points of the two geometric bodies is the same, that is, the volume is the same. Therefore, we can use this kind of thinking to understand the principle of Chengzu.
Baidu Encyclopedia-The Principle of Being an Ancestor