Finally, if is disjoint from a, then Iq ◦ Ip and Is ◦ Ir are elliptics with the center
p◦ ∩ q◦ =
◦ = r ◦ ∩ s◦. Their composition is again an elliptic with the same center,
or identity. If it has a fixed point x ∈ C, then it must be the identity, and the theorem
is proved.