[math-fun] Babylonian trig

I'm still trying to understand what all the fuss is about. Apparently, the Babylonians could do trig w/o angles. I get it: angles (implicitly) require complex exponentials. Perhaps they knew about Gaussian integers, but probably not. But w/o angles, you still need some graded rational approximations to slope; perhaps continued fractions will do? So here's my question (RWG knows this already): Given a continued fraction stream of approximations to a/c, compute the continued fraction stream of approximations to (b/c)=sqrt(1-(a/c)^2).