The Grand Astrologerʼs platform and ramp: Four problems in solid geometry from Wang Xiaotongʼs ‘Continuation of ancient mathematics’ (7th century AD)

Wang Xiaotongʼs Jigu suanjing is primarily concerned with problems in solid and plane geometry leading to cubic equations which are to be solved numerically by the Chinese variant of Hornerʼs method. The problems in solid geometry give the volume of a solid and certain constraints on its dimensions, and the dimensions are required; we translate and analyze four of these. Three are solved using dissections, while one is solved using reasoning about calculations with very little recourse to geometrical considerations. The problems in Wang Xiaotongʼs text cannot be seen as practical problems in themselves, but they introduce mathematical methods which would have been useful to administrators in organizing labor forces for public works.

摘要王孝通的《緝古算術》主要在處理立體與平面幾何中使用到三次方程式的問題，而這些方程式是用中國版的霍納法求出數值解。立體 幾何的問題是給定立體體積與外部尺寸的某些限制，然後再求解外 部尺寸；本文翻譯且分析四個問題。其中三題是用分割法求解 ，另一題則是用關於計算的推理求解，並且很少觸及幾何上的考量。王 孝通著作中的問題本質上不能看成實用問題，但這些問題介紹的數學方法對於官吏組織勞動力進行公共工程很有幫助。(英家銘譯)