從《張丘建算經》看北魏平城時期的若干問題

Problems in Pingcheng Period of the Northern Wei, basing on Zhangqiujian Suanjing

《張丘建算經》是中國中古時期算學重要的經典著作之一，中國數學史專家郭書春引用算經的計算題，認為《張丘建算經》中的算題，不應該是晉朝人生活和賦稅規範下的狀態；並參考近人錢寶琮和馮立升的考據，而認定成書時間，應該屬於北魏孝文帝即位之前的平城時期。事實上，北魏定都平城，確立平城時代的開始，是在道武帝天興元年（398）秋七月，該年正值東晉安帝隆安二年（398），因此本文就此透過這樣的時空環境，以魏晉南北朝史學界較少引用的《張丘建算經》上中下三卷，來討論北魏孝文帝即位之前的平城時期（398～470），史料中可以相互印證的若干問題。

「Zhangqiujian Suanjing」《張丘建算經》is one of the masterpieces in MedievalChina. China Mathematics, Shu-chun Guo （郭書春）considered those calculationproblems in「Zhangqiujian Suanjing」should not be the situation of the living andtaxation types in Jin Dynasty. He also confirmed the age of it should be the Pingchengperiod of the Northern Wei, before the Thenthronement of the Emperor Xiaowen,based on the archival studies by modern historians Baocong Qian（錢寶琮）andLisheng Feng（馮立升）. Nevertheless, the time for the Northern Wei ‘s relocation itscapital in Pingcheng（平城）, so-called “ the Pingcheng Period “（AD 398～494）, wasthe first year of Tianxing of the regime of Daowu Emperor（AD398）, and wasoverlapped by the period of Eastern Jin Longan （隆安, AD397～401）regime of JinAn Emperor （晉安帝）. Therefore, my article tries to clarify archival studies duringboth of these two regimes which may prove certain new historical explanation for「Zhangqiujian Suanjing」.