The equation of the tangent to an ellipse at point x₀, t₀ is

Our ellipse is this:

which means that α = cT, β = T, x₀ = x', y₀ = t', y = t. So the above formula becomes:

We want the x coordinate of the point of intersection of this line with the x axis of the graph, so, setting t = 0, we get:

Now, going back to the Lorentz transformation, the equation of the x axis of the Moving Body, (produced by setting t' = 0), is:

We want the x coordinate of the point of intersection of this line with the x axis of the Stationary Body at t = T, so we have:

So we see that the point of intersection of the unadjusted Lorentz x axis of the Moving Body with the x axis of the Stationary Body at t = T has the same x coordinate as the intersection of the adjusted x axis with the x axis of the Stationary Body at t = 0, and therefore it can be considered its projection.