Strip Brightness in a Spherical System My question concerns the following problem, published in Galactic Dynamics by Binney and Tremaine and based on a work by Schwarzschild.
Specifically, I am having difficulties in deriving the given result in part (c), which I suppose is due to the confusion surrounding the definition of strip brightness. Could someone please explain, with the aid of a diagram if possible, how $x$ is related to the projection, $R$, of the  radius $r$ onto the plane of the sky? I am having trouble visualising what $x$ is measuring here.
It is the luminosity in a straight strip like this:

(Credit: West 29 / CC BY-SA from here)
where the center of the strip passes a distance $x$ from the center of the circle at closest approach.  So starting from the center and moving out, each successive strip would have a progressively larger value of $x$, but $x$ is a constant for a given strip (with $x = 0$ for the center strip).
The only differences from the picture are that (a) the strips have an infinitesimal width $dx$, and (b) they are infinite in length rather than the finite circle shown here.