Appell Transformation

A Homographic transformation

$$x_1 = {ax+by+c\over a''x+b''y+c''}$$

$$y_1 = {a'x+b'y+c'\over a''x+b''y+c''}$$

with $t_1$ substituted for $t$ according to

$$k\,dt_1={dt\over(a''x+b''y+c'')^2}.$$

References

Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet ``Mathematical Encyclopaedia.'' Dordrecht, Netherlands: Reidel, pp. 210-211, 1988.