Googling around confirms that nineteenth century mathematicians were fond of involutions and imaginary points. See, for example, this article in Encyclopedia Brittanica in 1891, or these pages from a book published in 1913.

You can read an alternative description of the polar line on Wikipedia.

Rob Lewis has set up a demo on Geogebra.

• Install the program here.
• Save Rob's data, Involution.ggb (right click on the link).

Alternatively, you can go see the construction in a web app here, but the web app is really slow.

Rob explains that the points a and b are the two solutions (x,y) to the equation c=e, according to the naming scheme on the left side of the window.