在比例和的圓舞曲：當內切錐線遇上截線比例和~[\ref{[1]}]中，介紹了實數體歐氏空間下多邊形相切的二次曲線會滿足一個有關交比及平方根的恆等式。而交比、相切及二次曲線都是在任意設射影空間都存在的概念，但平方根卻不是任意體中都存在的。因此本文將透過交比的運算、射影變換、Brianchon定理等純射影幾何的定理和工具，證明並推廣此恆等式至任意體下的射影空間，並對原文中平方根的選取予以修正。

In bibliography~[\ref{[1]}], they claim a equation about relation between square root of cross ratio and a conic inscribed in a polygon in real Euclidean space.Cross ratio,tangent,and quadric curve are defined on any projective space but square root can not be defined in some field.In this paper, I'll proof and generalize this identity by pure projective geometry like property of cross ratio, projective transformation, Brianchon's theorem, and so on.Finally, I'll correct the way to determine sign of square root in original paper.