1问题的提出我们知道,将平面几何中著名的蝴蝶定理作推广便得坎迪定理(见文[1]定理7.3.1)如图1,过圆的弦AB上的任一点M,引任意两条弦CD和EF,连结ED和CF交AB于P和Q,若AM=a,BM=b,PM=x,QM=y,则1a-1b=1x-y1(*)特别地,a=b时,即得蝴蝶定理.图1在坎迪定理中,我们是过点M作两条相交弦CD 1 The question is raised. We know that the Candi theorem is obtained by generalizing the famous butterfly theorem in plane geometry (see [1] Theorem 7.3.1). Figure 1. Any point M on an over-circular string AB. Two strings CD and EF, link ED and CF to AB and P and Q, if AM=a, BM=b, PM=x, QM=y, then 1a-1b=1x-y1(*) In particular, a =b, that is, butterfly theorem. Figure 1 In Candi’s theorem, we are over the point M for two intersecting strings CD