球面三角形的梅涅劳斯定理、塞瓦定理与等距共轭点——平面三角形的切心(热尔岗点)和界心(奈格尔点)在球面三角形上的推广

Menelaus’ Theorem, Ceva’s Theorem and Isometry Conjugate Points in Spherical Triangle—Spreadof Gergonne Point and Nagel Point from Plane Triangle toSpherical Triangle

摘要: 本文利用球面三角形的梅涅劳斯定理与塞瓦定理给出球面三角形的等距共轭点之概念，最后把平面三角形的切心(热尔岗点)和界心(奈格尔点)推广至球面三角形上。

Abstract: In this paper, the concept of isometry conjugate points in spherical triangles is given by using Menelaus’ theorem and Ceva’s theorem, the Gergonne point and the Nagel point in plane triangle are spreaded to spherical triangle in the end.