Coxeter- Exercise 2.5.6
- Pinyi Yao
Draw one random lines b through O and one random line c throught E. We get D=b·e. Connect D and G, we get line d. Draw another line e through O, we get I=e·c and H=e·d. Connect E and H, we get J=EH·OD. Connect J and I, we can see that it goes throught point C. Measuring from O, we have the distances 10,12,15 in "harmonic progression." (Their reciprocals are in "arithmetic progression.") Measuring from C, we have another harmonic progression 3,5,15.