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