The first case above is that of disc<0. The involution has no

The second case has disc>0. The involution has two real fixed points Q and Q', resulting by solving the equation c*x

There is an inverse to this procedure of definition of a circle bundle out of an involution. Having a bundle of circles and an arbitrary line one can define an involution induced by the bundle on the line. This is discussed in Involution2.html .

The deeper reason of the validity of this property is the Desargues Involution theorem, of which this is a particular case. In fact it is a particular case of that theorem applied to a circle bundle considered as a conic bundle of non-intersecting type (the member-conics are

DesarguesInvolution.html

DesarguesInvolutionComplex.html

HomographicRelation.html

Involution2.html

Involution3.html

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