The Chinese concept of Cavalieri's principle and its applications
Put in modern language of calculus, that the volume of solid is \(\int^{b}_{a}A(x)dx\) is called Cavalieri principle. In the third century, while attempting to derive the volume of a sphere, Liu Hui applied a similar principle to determine the ratio of a sphere and a solid circumscribing the sphere. The solid is formed by the intersection of two perpendicular cylinders circumscribing the sphere and is called mou he fang gai. Liu Hui left unresolved the problem of finding the volume of the mou he fang gai. In the fifth century Zu Geng, also applying Cavalieri's principle, solved this problem and thus derived the volume of a sphere. This shows that the principle was known and applied over a mellenium before Cavalieri. A discussion on Mei Wending's and Xu Youren's work on areas and volumes shows that while Mei's work was stated mostly without proof and was influenced by a transmission from the West, Xu's work was a continuation of Zu's tradition.
scientific article; zbMATH DE number 3950442