Warning. This is an attempt at an answer out of curiosity rather than an expert answer.

Newton has the following passage in "Recomputation of surfaces of least resistance," (1694) (see Whiteside*, pp. 470-471):

Unde $aabb - 2aabx+aaxx+ bbxx = aay + xxy$

[capiendo fluxiones]

$- 2aab\dot x + 2aax\dot x+2bbx\dot x =2x\dot xy + aa\dot y+xx\dot y$

Whiteside (ibid) writes: "The dotted letters in immediate sequel are Newtonian fluxions; that is, $\dot x = \frac {dx}{dt}$ and $\dot y = \frac {dy}{dt}$ where t is some independent variable of ‘time’."

I'd like to add that I don't think that interpreted in the context (whether historical or modern), something like $x=x(t)$ (say in parametric equations) or $y=y(x)$ (say when** $y$ represents the distance from the $x-axis$ at a certain $x$), would be an "abuse of the notation".

*The mathematical papers of Isaac Newton Volume VI 1684-1691

** I am pretty sure I have seen something like this in historical texts, but I couldn't remember where.

Warning. This is an attempt at an answer out of curiosity rather than an expert answer.

Newton has the following passage in "Recomputation of surfaces of least resistance," (1694) (see Whiteside*, pp. 470-471):

Unde $aabb - 2aabx+aaxx+ bbxx = aay + xxy$

[capiendo fluxiones]

$- 2aab\dot x + 2aax\dot x+2bbx\dot x =2x\dot xy + aa\dot y+xx\dot y$

Whiteside (ibid) writes: "The dotted letters in immediate sequel are Newtonian fluxions; that is, $\dot x = \frac {dx}{dt}$ and $\dot y = \frac {dy}{dt}$ where t is some independent variable of ‘time’."

I'd like to add that I don't think that interpreted in the context (whether historical or modern), something like $x=x(t)$ (say in parametric equations) or $y=y(x)$ (say when** $y$ represents the distance from the $x$-axis at a certain $x$), would be an "abuse of the notation".

*The mathematical papers of Isaac Newton Volume VI 1684-1691

** I am pretty sure I have seen something like this in historical texts, but I couldn't remember where.