Adrian van Roomen's solution of Apollonius Tangency Problem

Adrian van Roomen published (Problema Apolloniacum) in 1596, Wurzberg.
Van Roomen used the geometric fact that centers of circles tangent to two circles are located on two conic sections. Hence, given three circles there exist four sets of three conic sections. The four common cords are concurrent in the radical center of three given circles. If a common cord is parallel to an asymptote of a conic section, then a center is at infinity.