Fig. VI
We must now pass to the curvature of a surface. At a point
on the surface where the curvature is to be computed we trace a normal to the surface. Then through this normal we trace a plane, which of course intersects the surface along a plane curve. We assume this normal plane to revolve round the normal as axis and we thus obtain a series of plane curves of intersection defined by the normal plane and surface. Each one of these curves passing through the point
possesses a definite curvature at
, and this curvature can be computed through the medium of the corresponding osculating circle.
Here a geometrical fact is evidenced. It is found that in the general case there exist two remarkable positions of the intersecting normal plane, perpendicular to one another and therefore sectioning the surface along two curves (1) and (2) orthogonal to each other at