Origin and Evolution of the Secant Method in One Dimension

Abstract Many in the mathematical community believe that the secant method arose from Newton's method using a finite difference approximation to the derivative, most likely because that is the way that it is taught in contemporary texts. However, we were able to trace the origin of the secant method all the way back to the Rule of Double False Position described in the 18th-century b.c. Egyptian Rhind Papyrus, by showing that the Rule of Double False Position coincides with the secant method applied to a linear equation. As such, it predates Newton's method by more than 3,000 years. In this paper, we recount the evolution of the Rule of Double False Position as it spanned many civilizations over the centuries leading to what we view today as the contemporary secant method. Unfortunately, throughout history naming confusion has surrounded the Rule of Double False Position. This naming confusion was primarily a product of the last 500 years or so and became particularly troublesome in the past 50 years, creating confusion in the use of the terms Double False Position method, Regula Falsi method, and secant method. We elaborate on this confusion and clarify the names used.