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By: Tao Steven Zheng (郑涛)

【历史纵横】

《缀术》是南北朝时期祖冲之（公元429年 ~ 501年）、祖暅（约公元450年 ~ 520年）父子合撰的数学著作。此书汇集了他们的数学研究成果，比如计算圆周率与球的体积公式。《缀术》在唐代成为国子监算学课本之一。当时的学生需要四年时间学习，而且被认为非常深奥，以致“学官莫能究其深奥，故废而不理”（《隋书·律历志》）。因此，《缀术》终于北宋时期佚传。本节选来自沈括（公元1031 ~ 1095年）的《梦溪笔谈》。

【Historical Note】

The Zhui Shu (Method of Interpolation) is a mathematics text written during the Northern and Southern dynasties (386 – 589 AD) by Zu Chongzhi (429 – 501 AD) and his son Zu Geng (c. 450 – 520 AD). The book is a compilation of their mathematical findings, such as the calculation of π and the precise volume of the sphere. During the Tang dynasty, the Zhui Shu was included into the mathematics curriculum at the Guozijian (Imperial Academy). The book is said to require four years of study, and was considered to be so abstruse that “students could not study its profundity, so it is abandoned and ignored.” Unfortunately, the Zhui Shu was lost during the Northern Song Dynasty. This excerpt is a description of the Zhui Shu taken from the Mengxi Bitan, written by Shen Kuo (1031 – 1095 AD).

 【原文】 《梦溪笔谈·卷18技艺3》 审方面势，覆量高深远近，算家谓之“軎术”。軎文象形，如绳木[1]所用墨斗[2]也。求星辰之行，步气朔消长，谓之“缀术”。谓不可以形察，但以算数缀之而已。北齐祖亘[3] 有《缀术》二卷 [4] 。 【英译】 Mengxi Bitan (Volume 18 Jiyi 3) Mathematicians call the method of surveying terrain, their heights and distances weishu. The character wei (軎) is a pictograph, which looks like a cord through the carpenter’s ink marker. The method of computing the movements of stars and the changes of the lunar calendar is called zhuishu. The name of this method suggests that the movement of celestial bodies cannot be known by their outward shapes and movements; rather, the movements can only be interpolated via a series of linked mathematical computations. During the Northern Qi dynasty, Zu Geng authored the Zhui Shu in two volumes.

【注释】

[1] 绳木：绳子。

Cord, rope, string.

[2] 墨斗：中国木匠用的工具，由墨仓、线轮、墨线、墨签构成。

Ink marker, a tool used by Chinese carpenters for marking lines.

[3] 祖亘：祖暅 [gèng] （约公元 456年—536 年），一作祖暅之，是中国南北朝时期数学家、天文学家。

Zu Geng (c. 456-536), or Zu Gengzhi, was a Chinese mathematician and astronomer during the Northern and Southern Dynasties.

[4] 据《隋书·经籍志》，《缀术》有六卷。

According to Sui Shu (Book of Sui), the Zhui Shu has six volumes.

【今译】