Euler’s first law is p = mv, where v is the velocity of the center of mass of a body.

The definition of momentum given by newton in the Principia is as follows: “The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly.
The motion of the whole is the sum of the motions of all the parts ; and therefore in a body double in quantity, with equal velocity, the motion is double ; with twice the velocity, it is quadruple,”

Aren’t these two things the same? What new insights if any did euler’s first law bring about?