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UNIVERSITY OF COLORADO STUDIES 



The circles of the first pencil we assume tangent to the >>-axis 

 (x = o), and those of the second tangent to the line. 



x — a 



y—b ' 

 or x — yk — a + bk = o 



(i7) 



at the point (a, b). 



Fig. 2 



Now, any two circles of a pencil of circles determine all the other 

 circles of the pencil, as indicated in formula (16). We may also choose 

 special circles of these pencils, for instance, the tangents at their double 

 points and the zero-circles in these points. Thus we have 



