Newton's formulation of his II Law of Motion into the Principia is not "symbolic"; see:
The first "algebraic" formulation of Newton's law of motion is due to:
XXII. [...] after having decomposed all the forces acting on the body into the three perpendicular components $P, Q, R$ [...] the movement of the body will be described by the three following formulae:
$$I. \ \ 2M ddx=P dt^2 \ \ \ II. \ \ 2M ddy=Q dt^2 \ \ \ III. \ \ 2M ddz=R dt^2.$$
An early example of dependency between physical magnitudes is Aristotle (wrong) law of motion:
If, then, $A$ is the mover, $B$ the moved, $C$ the distance moved, and $D$ the time, then in the same time the same force $A$ will move $\dfrac 1 2 B$ twice the distance $C$, and in $\dfrac 1 2 D$ it will move $\dfrac 1 2 B$ the
whole distance $C$; for thus the rules of proportion will be observed [Physics, Book VII, 249b27-250a9].