I am teaching a class on elementary differential geometry and I would like to know, for myself and for my students, something more about the history of Euler Theorem and Euler equation: the curvature of a normal section is determined by the principal curvatures and the angle that the tangent to the curve makes with a principal direction via Euler equation.
This gives a rather rigid, albeit infinitesimal, description of the geometry of a surface at a point. I have been wondering how Euler might have thought that something like this should be true. Does it come from linear algebra and results about eigenvalues and eigenvectors of symmetric matrices?
