Where in Eulers writings can I find a proof of his homogeneous function theorem: $y$ is a homogeneous function of degree $k$ in $x_1,\ldots,x_n$ iff $ky = \sum_{i=1}^n x_i\frac{\partial y}{\partial x_i}$? None of the sources I've seen cite him.
I'm curious because in his Introduction to the analysis of the infinite he defines a homogeneous function as one "in which each term has the same degree" and goes on to discuss several examples (not just polynomials). But I don't see him writing down the "modern" definition $$f(\lambda{\bf x})=\lambda^k f({\bf x})$$ and wonder how he would prove the result without this. (I know he used function notation, but very rarely.)
