>> When *I* apply Pythagoras, I don't pretend the speed of light along 
>> the hypotenuse is the same as it is along the adjacent.
>> I compute sqrt(c^2 + v^2), not c as a relativist does.
>> Androcles
>
> The velocity is c, the *component* of that velocity along y is
> sqrt(c^2 - v^2)

Less than c,  contradicting  c invariant.
You forgot to mutter "inertial frame".
Androcles.