History of the study of rational points on the circle

Question

What is the first known instance of a mathematician parameterizing rational points on the unit circle by the slopes of rational lines going through a rational point on the circle?

Answer 1

I believe this has to be Diophantus, who uses this method to find rational solutions to second degree equations in $x$ and $y$. Thomas Heath summarizes (p. 68) some of these results by saying that Diophantus solves the equation $$Ax^2+c^2=y^2$$ by putting $y=mx\pm c$, obtaining $$x=\pm{2mc \over A-m^2}$$ Of course, Diophantus would only consider the positive solution.

Btw, the Wikipedia article on Pythagorean Triplets describes how Euclid's formula can be found by rational parametrization of points on the unit circle, but this is not the method that Euclid used.