# Equation for the conservation of vis viva

How did Christiaan Huygens come across the fact that the quantity $mv^2$ is conserved during motion? I would like to know his thought process and how he derived or proved this result.

Huygens considered the impact in two different inertial systems, one of them being the centre-of-mass system. There he found that for both cases the vis viva was conserved. He wrote the equation already in modern form: $m_1v_1^2 + m_2v_2^2 =m_1v_1'^2 + m_2v_2'^2$