Does this form of reasoning have a name. I often see it but am a little confused on how to read/understand it and wanted to look more into it but don't know what to call it
Ex. Let's call the force law between the objects $F(m_1,m_2,r)$. We know that if we put the body $m_1$ in free fall, the acceleration doesn't depend on the mass, so
$$F(m_1,m_2,r)=m_1G(m_2,r)$$ So that the mass will cancel in Newton's law to give a universal acceleration. This gives you the relation
$$F(\lambda m_1,m_2,r)=\lambda F(m_1,m_2,r).$$
Source: Combining Proportions to get Newton's Law of Universal Gravitation