?? so consider ac=bb .... ?? ....

a = x+y

c = x-y

xx - yy = bb

bb + yy = xx

?? inverting a leaves out x+y = 0 ...

?? inverting c leaves out x = y ... ????....

?? inverting both should leave a torus ??? .... ??? ..... ??? hmmm, so perhaps it does ... ?? 4 half-cones in a double cone ... ?????? ..... ??? blowing up apex ... ???? ....

?? for b = 0, ac = bb as cross ...

?? "forgetting b" ... ?? "ramification" at bars of cross ?? ... ??? ... ?? real vs complex ... ???? ....