|
the orthogonality theorem (1) The i-lines C(a,α,b), C(c,γ,d) are orthogonal if and only if ad + bc=α*γ + αγ*. (2) If i-lines L and M are orthogonal and i is an inversive transformation, then i(L) and i(M) are orthogonal. (3) If L and M are distinct i-lines, then iL(M) = M if and only if L and M are orthogonal. The proof is somewhat lengthy.
|