We shall see later that it is implied in Newtons statement of his Second Law of motion.
The statement that the increase of momentum is equal to the impulse is (it may be remarked) equivalent to Newtons own formulation of his Second Law.
Newtons Second Law asserts that change of momentum is equal to the impulse; this is a statement as to equality of vectors and so implies identity of direction as well as of magnitude.
In the case of a particle falling directly towards the earth from rest at a very great distance we have C=o and, by Newtons Law of Gravitation, p/ai=g, where a is the earths radius.
The product mu of the mass into the velocity is called the momentum or (in Newtons phrase) the quantity of motion.