《数书九章》方程章及其算筹思想:以“遥度圆城”为例

The equation chapter of Mathematical Treatise in Nine Sections and its thought of calculating and raising funds:based on"Yaodu Yuancheng"

中国古代算法思想中的"方程"源于"算筹".13世纪秦九韶提出正负开方术,并将其用于求解一元高次方程,为数值解多项式方程奠定了重要的发展基础.本文以《数书九章》第八卷"遥度圆城"为例,探讨了秦九韶正负开方术求解高次方程正根的解法,剖析了古今算法高次方程的求解步骤,验证了玲珑10次方程来历的猜想,并结合古今算法的差异和优势,探究如何树立正确的数学史观.

The ancient Chinese algorithm thought contained in"equation"originates from"counting chips".In the 13th century,Qin Jiushao proposed positive and negative square method to solve higher order equations,which laid an important foundation for numerical solution of polynomial equations.In the case of the eighth chapter of The equation chapter of Mathematical Treatise in Nine Sections based on"Yao du Yuan cheng",the steps of ancient and modern algorithms to solve higher order equations are deeply analyzed,and the differences and advantages of ancient and modern algorithms and how to establish a correct view of ancient mathematics history are explored.