In linear elasticity, the governing PDE is the equilibrium equations (absent of vibration considerations):
$$ -\nabla \cdot \sigma = F $$
Is this equation simply derived from the sum of forces and moments?
In most linear elasticity papers, I see these governing equations. Is there an original source for where these equations came from? I'm looking for a more fundamental citation, but it seems so ubiquitously used and known that it's difficult for me to find the original source.