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Thomas Simpson and ‘Newton's method of approximation’: an enduring myth

Published online by Cambridge University Press:  05 January 2009

Nick Kollerstrom
Nick Kollerstrom
Affiliation:
Department of History and Philosophy of Science, University CollegeLondon.
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Extract

A resurgence of interest has occurred in ‘Newton's method of approximation’ for deriving the roots of equations, as its repetitive and mechanical character permits ready computer use. If x = α is an approximate root of the equation f(x) = 0, then the method will in most cases give a better approximation as

where f′(x) is the derivative of the function into which α has been substituted. Older books sometimes called it ‘the Newton–Raphson method’, although the method was invented essentially in the above form by Thomas Simpson, who published his account of the method in 1740. However, as if through a time-warp, this invention has migrated back in time and is now matter-of-factly placed by historians in Newton's De analysi of 1669. This paper will describe the steps of this curious historical transposition, and speculate as to its cause.

Type
Research Article
Information
The British Journal for the History of Science , Volume 25 , Issue 3 , September 1992 , pp. 347 - 354
Copyright
Copyright © British Society for the History of Science 1992

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Thomas Simpson and ‘Newton's method of approximation’

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