摘要：本文对高等几何中的对偶原理及其相关命题、定理、性质进行了归纳整理，主要研究内容是通过运用对偶原理从已有命题转化为其对偶命题，并得到相应的初等几何命题，中学几何命题；对已有的对偶命题来进行进一步的推广和研究以及在其他数学分支和其他学科中的应用，体现高等几何的一些思想观点和方法。从而阐明对偶原理在较高观点上处理中学几何问题，提高命题推广能力所起的作用。
关键词：对偶原理；高等几何；几何学；中学几何
Abstract：The article has generalized the these，complexions of the principle of the duality in the advanced geometric. The main goal is translating the predecessor principle into the duality these，and get the corresponding elemental geometric these by applying the principle of duality. The other aim is embodying some important thoughts and approaches of advanced geometric by making more explorations and promotions of the predecessor principle of the duality ,and the applying of the principle of the duality in other denomination of the math and science. The eventually purpose is that present the influence of the duality principle on the dealing the elemental geometric questions and promotion ability of the other principles.
Key Words：principle of the duality； higher geometry； geometry；middle school geometry
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