Dear Josh,

Because, there was a vague, confusing, philosophical use of the term "energy of

motion" that predated Newton and he wanted his audience to connect. People also

used the term "momentum" and often used the two terms indistinglishably.

Newton's work was clear.

Newton did his calculus in Principia in a rather implict way so that it

would look more like proofs in euclidean geometry. He did this because he was

expecting to be criticized for his new tool of calculus ( fluxions).

By using previous terms, he made his work less radical appearing.

But, the intelligent reader of his time understood how radical it was.

Good historical question!

best

penny

Although, Newton derives it as a first integral of the equation of motion, he

never uses the term "first integral" for that would be using calculus (

fluxions) in an explicit way. He thought people like Hooke would have villified

him.