Editing Thomas Simpson (section)

==Work==
[[File:Simpson - Miscellaneous tracts on some curious and very interesting subjects in mechanics, physical-astronomy and speculative mathematics, 1768 - 598998.tif|thumb|''Miscellaneous tracts'', 1768]]

The method commonly called [[Simpson's Rule]] was known and used earlier by [[Bonaventura Cavalieri]] (a student of Galileo) in 1639, and later by [[James Gregory (astronomer and mathematician)|James Gregory]];<ref>{{cite journal | url=https://www.jstor.org/stable/30037470 | jstor=30037470 | doi=10.2307/30037470 | last1=Velleman | first1=Daniel J. | title=The Generalized Simpson's Rule | journal=The American Mathematical Monthly | date=2005 | volume=112 | issue=4 | pages=342–350 }}</ref> still, the long popularity of Simpson's textbooks invites this association with his name, in that many readers would have learnt it from them.

In the context of disputes surrounding methods advanced by [[René Descartes]], [[Pierre de Fermat]] proposed the challenge to find a point D such that the sum of the distances to three given points, A, B and C is least, a challenge popularised in Italy by [[Marin Mersenne]] in the early 1640s. Simpson treats the problem in the first part of ''Doctrine and Application of Fluxions'' (1750), on pp.&nbsp;26–28, by the description of circular arcs at which the edges of the triangle ABC subtend an angle of pi/3; in the second part of the book, on pp.&nbsp;505–506 he extends this geometrical method, in effect, to weighted sums of the distances. Several of Simpson's books contain selections of optimisation problems treated by simple geometrical considerations in similar manner, as (for Simpson) an illuminating counterpart to possible treatment by fluxional (calculus) methods.<ref>Rogers, D. G. (2009). [http://turing.une.edu.au/~ernie/Archive/Creases2009MT.pdf Decreasing Creases] {{webarchive|url=https://web.archive.org/web/20131104003416/http://turing.une.edu.au/~ernie/Archive/Creases2009MT.pdf |date=4 November 2013 }} Mathematics Today, October, 167–170</ref> But Simpson does not treat the problem in the essay on geometrical problems of maxima and minima appended to his textbook on Geometry of 1747, although it does appear in the considerably reworked edition of 1760. Comparative attention might, however, usefully be drawn to a paper in English from eighty years earlier as suggesting that the underlying ideas were already recognised then:
* J. Collins A Solution, Given by Mr. John Collins of a Chorographical Probleme, Proposed by Richard Townley Esq. Who Doubtless Hath Solved the Same Otherwise, ''Philosophical Transactions of the Royal Society of London'', 6 (1671), pp.&nbsp;2093–2096.

Of further related interest are problems posed in the early 1750s by J. Orchard, in ''The British Palladium'', and by T. Moss, in ''The Ladies' Diary; or Woman's Almanack'' (at that period not yet edited by Simpson).