Joanna Papakonstantinou wrote a PhD thesis on the historical development of BFGS and the secant method back in 2009: https://scholarship.rice.edu/handle/1911/6

Joanna Papakonstantinou wrote a PhD thesis on the historical development of BFGS and the secant method back in 2009: https://scholarship.rice.edu/handle/1911/61898 https://scholarship.rice.edu/handle/1911/61898 Part of that thesis discusses the Babylonian use of the rule of the double false position and it's application to solving quadratics, which can be used to get the square root. Anyway, I'm not an expert in this history, but I believe she includes references to the related texts for those interested.