I am unaware of any other method for analyzing elastic collisions other than applying both conservation of momentum and conservation of energy. Since Newton didn't have conservation of kinetic energy to use as a tool was he unable to analyze elastic collisions? PS In the Scholium at the end of the axioms (right before Book I) of the Principia Newton writes about experiments he did with colliding spherical pendulums made of different materials. He mentions how steel spheres rebound with nearly the same velocity while other materials like compressed wool spheres had only a fraction of their initial velocity. He used these observations as evidence for the third law.