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\section{Gaussian Coordinates}  Two neighbouring points P and P' on the surface then correspond to the co-ordinates  $$  P: u, v (u, v) \\  P': u (u  + du, v + dv, dv),  $$  where du and dv signify very small numbers. In a similar manner we may indicate the distance (line-interval) between P and P', as measured with a little rod, by means of the very small number ds. Then according to Gauss we have