One Quadratic Equation, Different Understandings: the 13th Century Interpretations by Li Ye and Later Commentaries in the 18th and 19th Centuries
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The Chinese algebraic method, the \textit{tian yuan shu}, was developed during Song period (960--1279), of which Li Ye's works contain the earliest testimony. Two 18th century editors commentated on his works: the editor of the \textit{Siku quanshu} and Li Rui, the latter responding to the former. Korean scholar Nam Byeong-gil added another response in 1855. Differences can be found in the way these commentators considered mathematical objects and procedures. The conflicting nature of these commentaries shows that the same object, the quadratic equation, can beget different interpretations, either a procedure or an assertion of equality. Textual elements in this paper help modern readers reconstruct different authors' understandings and reconsider the evolution of the definition of the object we now call `equation'.
Abstract
The Chinese algebraic method, the \textit{tian yuan shu}, was developed during Song period (960--1279), of which Li Ye's works contain the earliest testimony. Two 18th century editors commentated on his works: the editor of the \textit{Siku quanshu} and Li Rui, the latter responding to the former. Korean scholar Nam Byeong-gil added another response in 1855. Differences can be found in the way these commentators considered mathematical objects and procedures. The conflicting nature of these commentaries shows that the same object, the quadratic equation, can beget different interpretations, either a procedure or an assertion of equality. Textual elements in this paper help modern readers reconstruct different authors' understandings and reconsider the evolution of the definition of the object we now call `equation'.
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