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Joseph Raphson was an English mathematician known best for the Newton–Raphson method. Little is known about his life, and even his exact years of birth and death are unknown, although the mathematical historian Florian Cajori provided the approximate dates 1648–1715. Raphson attended Jesus College at Cambridge, graduating with an M.A. in 1692.[1] He was made a Fellow of the Royal Society on 30 November 1689, after being proposed for membership by Edmund Halley.

Raphson's most notable work is Analysis Aequationum Universalis, which was published in 1690. It contains a method, now known as the Newton–Raphson method, for approximating the roots of an equation. Isaac Newton had developed a very similar formula in his Method of Fluxions, written in 1671, but this work would not be published until 1736, nearly 50 years after Raphson's Analysis. However, Raphson's version of the method is simpler than Newton's, and is therefore generally considered superior. For this reason, it is Raphson's version of the method, rather than Newton's, that is to be found in textbooks today.

Raphson was a staunch supporter of Newton's, in contrast to Gottfried Leibniz's claim to be the sole inventor of Calculus. In addition, Raphson translated Newton's Arithmetica Universalis into English. The two were not close friends, however, as is evidenced by Newton's inability to spell Raphson's name either correctly or consistently.

Raphson seems to be the one, who coined the word pantheism, in his work De spatio reali, which was published in 1697[2], where it may have been found by John Toland.


1. ^ Ralphson, Joseph in Venn, J. & J. A., Alumni Cantabrigienses, Cambridge University Press, 10 vols, 1922–1958.
2. ^ Ann Thomson; Bodies of Thought: Science, Religion, and the Soul in the Early Enlightenment, 2008, page 54.

* David J. Thomas; Judith M. Smith. 'Joseph Raphson, F.R.S.', Notes and Records of the Royal Society of London, Vol. 44, No. 2. (Jul., 1990), pp. 151–167.

External links

* O'Connor, John J.; Robertson, Edmund F., "Joseph Raphson", MacTutor History of Mathematics archive, University of St Andrews, .


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