Clifford's circle chain theorem in the ordinary Euclidean plane refers to a "chain of theorems" of increasing complexity. Every one of this infinite sequence of theorems must be true for the whole to be true. It begins with two circles passing through a common point O (n=2). The next theorem in the chain is for the case of three circles through a common point O (n=3) and so forth for n=4,5,6, ... If one takes the point O to infinity the n circles become n straight lines (circles with infinite radii.) The following shows interactive diagrams for the cases n=2, ... ,8 circles through O.
R. Penrose The Mathematics of William Kingdon Clifford: A Personal Reflection, in M. Chisholm Such Silver Currents - The Story of William and Lucy Clifford 1845-1929, Lutterworth, Cambridge 2002.
Soli Deo Gloria. Created with Cinderella by Eckhard Hitzer (Fukui).