1.祖暅原理介绍及其推广.我国齐梁时代的数学家、祖冲之的儿子祖咂提出这样一个原理:两个等高的几何体若在所有等高处的水平截面的面积相等,则这两个几何体的体积相等,这个原理称为“祖咂原理”.例如,将底面半径为R、高为屁的圆柱体和半径为R的半球体按如图1的方式放置,从圆柱体中“挖去”一个底面半径为R、高为R的倒置圆锥.现有一平行于底面且与底面距离为h的平面截这两个几何体(0≤h≤R),所得截面分别为圆环和 1. The introduction of ancestral principles and its promotion.Chinese mathematicians in Qiliang era, son of ancestor Zu-zhong proposed such a principle: two equal geometry if the horizontal section of equal height at all equal areas, the two For example, a cylinder with a bottom radius R, a high fart, and a hemisphere with radius R is placed as shown in Fig. 1, and the cylinder from the cylinder In the “dug into ” an inverted cone with a bottom radius R and a height R. There is a plane parallel to the bottom and distance h from the bottom of the two geometric bodies (0≤h≤R), the resulting cross sections are Ring and