Theorems Connected with Inversion

The square of the tangent from a point P to a circle S , divided by the diameter of S , will, in what follows, be denoted by ( PS ). If S open out into a straight line, it is easily seen that ( PS ) equals in the limit the perpendicular distance of P from this line; accordingly the length of the perpendicular from a point P on a straight line S will be denoted by the same symbol ( PS ).