2 Pa(Pb(x)) = Pa(x) + Pb(x) - Pab(x)
Here Pab is the projection
onto a versor. The result is due to Tim Bouma.
I have not put any labels to clutter the figure, but follow the red and
green arrows to get the two composite projections. The blue parallellogram
is spanned from Pa(x)/2 and Pb(x)/2, and the
final connections to the results use half the versor projections.
You can drag x and a or b to get a feeling for the construction. Make sure you do the special cases where a and b make
an angle of 90 degrees, and of 0 degrees.
Created with Cinderella