刘徽的体积理论主要集中在他为《九章算术》所作的注文中(263)。由于他所处理的几何体的种类以及所使用的方法都有超出《几何原本》的地方,所以他的体积理论为越来越多的人所注意。本文的目的是介绍刘徽体积理论中的几个基本原理,即出入相补原理、刘徽原理、刘徽——祖暅原理以及一些应用。 Liu Hui’s volume theory mainly focused on his annotations for the “Nine Chapters of Arithmetic” (263). Since the type of geometry he is dealing with and the methods used are beyond the “geometry”, his volume theory has attracted more and more attention. The purpose of this paper is to introduce several basic principles in Liu Hui’s volume theory, namely, the principle of in and out complementarity, the principle of Liu Hui, the principle of Liu Hui, the ancestral hall, and some applications.