1995/12/01 by Tjalling Ypma · 7 citations
Mathematics · Arts and Humanities · #History and Theory of Mathematics #Historical Philosophy and Science #Architecture and Art History Studies
paper · doi:10.1137/1037125
openalex publication_date 1995/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
This expository paper traces the development of the Newton-Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, and Thomas Simpson. It is shown how Newton's formulation differed from the iterative process of Raphson, and that Simpson was the first to give a general formulation, in terms of fluxional calculus, applicable to nonpolynomial equations. Simpson's extension of the method to systems of equations is exhibited.