Ain't got the books with me but I'll have a shot at it anyway. Very interesting question and I have to admit I didn't really know the answer. I've always taken it as gospel - not a good thing!
In a glide, you're getting rid of altitude to compensate for the energy loss created by drag. Set up an equation for the work done by drag and by gravity.
dW = m*g*dh - dt*V*D
D = m*g*cos(ga)/(L/D), as L will then equal m*g*cos(ga)
where ga is the glide angle.
The ground distance travelled, ds is dt*V*cos(ga). As the work done on the aircraft will sum up to zero, we end up with
m*g*dh - dt*V*m*g*cos(ga)/(L/D) = 0
m*g * (dh - ds/(L/D)) = 0
divide by m*g as it can't be zero
dh = ds/(L/D)
ds/dh = L/D
I thought I was doing good trying to avoid those airport hotels... and look at me now.