The four equations are the immediate offspring of plugging in values for x and y and z into that first equation I posted: (x-x')^2+(y-y')^2=m(z-z')^2. So for the equation for the top left corner (x'=-1, y'=1, z'=whatever height value was given), we plug those values into the above equation. Alas, I saw symmetry where there was none, and so I set m=1 which allowed much cancelling out. But even without m==1, when you multiply out the squares and then subtract any two equations, all the squares cancel out.