That's crazy, was it an empirical result or did he prove it rigorously? About a year ago I was banging my head against a wall trying to derive a function that would remap uniform angles to a uniform sampling over the integral of the changing slice circumference, and it just turned into a nasty mess I couldn't simplify. Can't believe that the function I was looking for was cosine!

That's crazy, was it an empirical result or did he prove it rigorously?

I'm not an expert in the history of mathematics, but I believe he proved it with a degree of rigor that was satisfactory for his time.