References

• 《四庫全書總目提要·卷107 子部·天文算法類二》

Source: The 'Wujing Suanshu' (五經算術), translated as "Five Classics Arithmetic," is a mathematical treatise attributed to Zhen Juan of the Northern Zhou dynasty. The work was later annotated by Li Chongfeng, a prominent Tang dynasty scholar and compiler of official mathematical texts. Though its original authorship is not explicitly recorded in early catalogs like the 'Sui Shu·Jing Ji Zhi' (隋書·經籍志), analysis of the text's annotations confirms Zhen Juan's role as compiler, given his distinctive use of the phrase "Zhen Juan an" ("Judgment of Zhen Juan") in mathematical explanations. The treatise was recognized as part of the Tang dynasty's official curriculum for mathematical scholars, alongside works such as the 'Zhou Bi Suan Jing' (周髀算經). Zhen Juan, noted for his expertise in arithmetic and serving as Sili Jiaoyue and governor of Hanzhong during the Northern Zhou, previously annotated classical mathematical texts like the 'Zhou Bi'. The 'Wujing Suanshu' draws on passages from the 'Shangshu', 'Xiaojing', 'Shijing', 'Yijing', 'Lunyu', 'Three Li' (礼记), and 'Chunqiu', applying mathematical reasoning to resolve ambiguities in these texts. Its methodology, rooted in Zhen Juan's annotations, emphasizes systematic calculation to clarify classical interpretations. The Tang dynasty's inclusion of the 'Wujing Suan' as one of ten canonical mathematical works, studied alongside the 'Zhou Bi', underscores its scholarly significance. Li Chongfeng's annotations, commissioned during the Zhenguan era, preserved the text's structure and clarified its applications in calendrical calculations and pitch measurement theory (e.g., resolving discrepancies in descriptions of the twelve 'lv' 律 pitches). The treatise also addresses textual corruptions in later editions of historical sources, such as errors in the 'Houhanshu·Zhi' regarding musical scales and the 'Yue Ling Zhangju' on pitch lengths. Lost during most of history, the 'Wujing Suanshu' survives fragmented but intact within the Yongle Dadian (永樂大典), edited in 1403. Its critical value lies not only in its mathematical rigor but also in its role as a tool for philological and historical verification, exemplified by its corrections of textual errors in works like the 'Lüshi Chunqiu' and the 'Houhanshu'. For instance, it clarifies that the central pitch " Huangzhong" (黃鐘) refers to the clearest (清律) rather than longest (浊律) tuning, a distinction critical to understanding ancient Chinese music theory. The text's detailed derivations of arithmetic rules for calculating calendar intercalations and architectural proportions further highlight its dual function as both mathematical manual and philological resource. By synthesizing technical calculations with classical exegesis, the 'Wujing Suanshu' remains a seminal work in the history of Chinese scholarship, bridging the fields of mathematics, historiography, and textual criticism. Its annotations by Li Chongfeng+#8194;and its preservation within the 'Yongle Dadian' ensured its influence endured into later scholarly traditions. ==References== * 《四庫全書總目提要·卷107 子部·天文算法類二》