《四元玉鉴》卷首“三图”的代数意义

A study on significance of algebra in "three graphics" of the head for precious mirror of Si-Yuan Yu-Jian

目的揭示朱世杰(1300前后)通过“三图”引出的代数恒等变换思想和方法。方法运用几何图形和数理分析相结合的方法分析“三图”的几何性质和代数意义。结果“三图”不仅具有几何意义,还具有深刻的代数意义,它是几何和代数的高度统一。结论“三图”所表达的代数恒等关系、思想和方法广泛应用于四元术中,为突破四元向更高元方程发展提供了可能性,其重要的代数思想需要进一步研究和挖掘。

Aim To reveal ZHU Shijie＇s thoughts and methods of algebra identical transformation in ＂three graphics＂. Methods Aanalyze geometric properties and algebra significance in ＂three graphics＂ by geometric graphics and mathematical analysis. Results There are profound geometric and algebraic significance in ＂ three graphics＂ and it is the unification of geometric and algebra. Conclusion The relations, thoughts and methods in in ＂ three graphics＂ have been adapted for four elemments algerbra, offered possible breakthrough of four elemments and de- velopment of higher multivariate equations. The algebraic significance should be further studied.