So, I was just reading about the Secant Method and came across the sentence that it:
"developed independently of Newton's method, and predates it by over 3,000 years.".
This would mean that it was first used some time around $1300$ BCE. Which was well before the developments of Cartesian co-ordinate systems and probably even before basic algebra, though they may have had some form of it.
So my question is: how could the ancient Babylonians possibly come up with a root-finding algorithm with such a limited set of mathematical tools at their disposal? Did they just do it by trial and error or can someone show me how they can derive the method as the Babylonians did?
Thanks very much,