THE CONIC OF CENTERS S~2 OF A PENCIL P~2_(1=2=3,4)

摘要

In the paper the author presents further results of the earlier research on the pencils of osculary tangent conies. The definition of a special quadratic transformation "E" will be given, in which circle n~2 is a basis of transformation, while the center of transformation W lies on the same circle itself. It has been proved that all lines that do not pass through point W will transform into osculary conies passing through the three points 1=2=3 coinciding with the center W. The centers of these conies make also a conic, which has been denoted with s~2 and called a "conic of centers". In the work such special cases will be discussed, where dependent on the base quadrangle 1=2=3,4 layout the conic of centers s~2 will be a hyperbola, an ellipse or a parabola. Two theorems have been formulated and proved.