摘要
本文拟就《九章算术》环田两问的经文及注文提出一些看法,即:1.刘徽可能把环田的中、外周拉直,使之变成与之等积的等腰梯形,再割补成等积的长方形,用以证明环田面积算法;2.刘徽及李淳风在第38问注文中,错误地使用了公式,得到环缺形之径的错误结论,这不能不说是刘、李二人的疏忽;3.所谓"环田密率公式",似应补充必要的依据。
This paper attempts to give the following views on the texts and commentaries of the two ring area problems in Nine Chapters on the Mathematical Art: 1. Liu Hui's possible method for demonstrating a formula for the ring area is to change interior and exterior perimeters into two-line segments so that the ring area forms an isosceles trapezoid and then a rectangle by dissecting. 2. Liu Hui and Li Chunfeng made mistakes in their commentaries on Problem 38 to find the width of a ring area by the formula for circular areas. 3. It seems necessary to provide requisite basis for 'the ring area precise formula'.
出处
《自然科学史研究》
CSCD
1993年第4期324-332,共9页
Studies in The History of Natural Sciences
