r 
[1.85 
185] NOTE ON THE ‘ CIRCULAR RELATION’ OF PROF. MOBIUS. 
119 
such that the circles a', ¡37', <o' pass 
a' through (BO', P'), 
/3' „ (O', A', P), 
» (A', B\ C). 
We may construct in this manner two figures, such that to three points of the first 
figure there correspond in the second figure three points which may be taken at 
pleasure, but these once selected to every other point of the first figure there will 
correspond in the second figure a perfectly determinate point. And the two figures 
will be such that whenever in the first figure four or more points lie in a circle, 
then in the second figure the corresponding points will also lie in a circle. The 
relation in question is due to Prof. Mobius, who has termed it the Kreis-verwandschaft 
(circular relation) of two plane figures. See his paper Grelle, t. lii. [1856], pp. 218—228, 
extracted from the Berichte of the Royal Saxon Society of Sciences of the 5th Feb. 
1853, [and Werke, t. ii. pp. 207—217].