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.
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Copyright 1995 Society for Industrial and Applied Mathematics
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Stable URL: http://www.jstor.org/stable/2132904
Ypma, Tjalling J., "Historical Development of the Newton-Raphson Method" (1995). Mathematics. Paper 93.