https://en.m.wikisource.org/wiki/The_Foundation_of_the_Generalised_Theory_of_Relativity
https://en.m.wikipedia.org/wiki/Geodesics_in_general_relativity
In his 1915 paper Einstein derives the equations of geodedics, he uses the principle of least action and a centain point he uses as (delta)lambda the length of the geodedics and he obtains a result that is correct, but isn't that a geodedic "orthogonal" to the original? On Wikipedia the proof starts with (delta)lambda and ends with (delta)tau which are linear elements that pass through the same point, in Einstein's book instead he uses (delta)s but isn't that "wrong"? He had to use another parameter right? Mathematically nothing is wrong.