Theorem. For two points $A,B\in H_{\mathrm{pr}}^n$ let $X$, $Y$ be the points of intersection of the line $AB$ with the quadric $Q=\{[x]:\langle x,x\rangle_{n,1}=0\}$, such that $\{A,Y\}$ and $\{B,X\}$ separate each other. Then \[d_{\mathrm{pr}}(A,B)=\frac12\log\cr(B,X,A,Y)\,.\]        Proof. Remember that $\cr(q,1,0,\infty)=q$. If we … Continue reading Lecture 19