(untitled) (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 1996)
Consider in the projective plane a curve k of second order and a point P, which is nonsingular for k. To an arbitrary point M, different from P, let correspond its polar-conjugate point M^′ with respect to k, which lies on the line MP. We call this transformation a generalized inversion. Also, we call quadratic transformation of the projective plane π a map of π into π if the coordinates of the image M^′ of M are homogeneous functions of second order of the coordinates of M. We prove that any invertible quadratic transformations S allows the presentation S=π_2Jπ_1, where π_1 and π_2 are linear transformations and J is a generalized inversion.