Einstein's spherical front: Please recalculate it!

Max Born

Why did Einstein believe to get a spherical wave in the moving system?

From Einstein, 1905, "On the Electrodynamics of moving Bodies" "At the time t′ = t = 0, when the origin of the coordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity c in system S. If (x, y, z) be a point just attained by this wave, then x²+y²+z² = c²t². Transforming this equation with the aid of our equations of transformation we obtain after simple calculations x′² +y′²+z′² = c²t′². The wave under consideration is therefore no less a spherical wave with velocity of propagation c when viewed in the moving system. This shows that our two fundamental principles are compatible.”
The moving System S' is the red marked. Please check out, by using the -slider, which changes the -ratio, what Einstein could have meant. After changing the -value, use the "set L" button to set the time needed accurately to travel . The "set U" button may be used to get nice numbers, e.g. the dx-value of 100.