A historical walk along the idea of curvature, from Newton to Gauss passing from Euler

From Newton ”Method of fluxions” to Gauss’ Theorema Egregium, the notion of curvature notably evolved from its appliance to a curve in a plane, to the one about a surface in space. Euler was the first mathematician who tried to define the curvature of a surface, although employing the curvature of a curve by comparing a plane section of the surface and a circumference. Later, Gauss changed Euler’s definition to overcome its limitations by defining it through the comparison between the linear element of the surface and the spherical one.