Significance
In any collision, explosion or separation, the total momentum before equals the total after — Wallis, Wren and Huygens each derived it for the Royal Society in 1668, twenty years before the Principia. It follows from the third law and is what makes a rocket work in vacuum: exhaust goes one way, the ship the other, and the sum stays what it was. Noether's theorem later showed it is the symmetry of space under translation.