  It is important to recognize that, in calling the referents of the defined terms “quantities,” Newton is assigning them to the ontological category of quantity in Aristotle's sense. Thus force and motion are quantities that have direction as well as magnitude, and it makes no sense to talk of forces as individuated entities or substances. Newton's laws of motion and the propositions derived from them involve relations among quantities, not among objects. In place of “no entity without identity,” we have “no quantity without definite  proportions;”[19] and the demand on measurement is to supply values that unequivocally yield an adequate approximation to these definite proportions.