沈括 著

【原文】?

《夢溪筆談·卷18技藝3》

審方面勢，覆量高深遠近，算家謂之“軎術”。軎文象形，如繩木[1]所用墨斗[2]也。求星辰之行，步氣朔消長，謂之“綴術”。謂不可以形察，但以算數(shù)綴之而已。北齊祖亙[3] ?有《綴術》二卷 [4] 。

【注釋】

[1] 繩木：繩子。

[2] 墨斗：中國木匠用的工具，由墨倉、線輪、墨線、墨簽構成。

[3] 祖亙：祖暅 [gèng] （約公元 456年—536 年），一作祖暅之，是中國南北朝時期數(shù)學家、天文學家。

[4] 據(jù)《隋書·經(jīng)籍志》，《綴術》有六卷。

【今譯】

推求方位和地勢，測量高低和遠近，算學家稱它為“軎術”。是個象形字，像在木頭上劃直線用的墨斗。求天體的運行，推算節(jié)氣朔望的盈縮變化，叫作“綴術”。這是指不可以用形體來考究，只能用算學的方法把它們連綴起來計算而已。北齊祖亙（祖暅）著有《綴術》二卷。

【英譯】

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[1] authored the Zhui Shu ?in two volumes[2].

【Notes】

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

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

【歷史縱橫】

《綴術》是南北朝時期祖沖之（公元429年 ~ 501年）、祖暅（約公元450年 ~ 520年）父子合撰的數(shù)學著作。此書匯集了他們的數(shù)學研究成果，比如計算圓周率與球的體積公式。《綴術》在唐代成為國子監(jiān)算學課本之一。當時的學生需要四年時間學習，而且被認為非常深奧，以致“學官莫能究其深奧，故廢而不理”（《隋書·律歷志》）。因此，《綴術》終于北宋時期佚傳。本節(jié)選來自沈括（公元1031 ~ 1095年）的《夢溪筆談》。

【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).

Article by Tao Steven Zheng（鄭濤）?