Home⇨circularsaw3⇨

circularsaw3 with line A projected to infinity

This pseudoline arrangement is a uniform variation of Ceva's theorem, which has an easy to prove slope constraint (as a line arrangement, with line 0 projected to infinity). Carroll, [2000d] shows: 

   sin(θF-θE)sin(θD-θC)sin(θB-θA) < sin(θF-θA)sin(θE-θD)sin(θC-θB)

Line Order At Infinity

E< F< D< C< B< 0

Bases

Positively Oriented

EFD, EFC, EFB, EF0, EDB, ECB, FDB, FCB, DCB,

Negatively Oriented

EDC, ED0, EC0, EB0, FDC, FD0, FC0, FB0, DC0, DB0, CB0,

Not Bases

The Pseudolines