Editing Method of Fluxions

{{short description|Book by Isaac Newton}}
{{Infobox book
| name           = Method of Fluxions
| image          = The method of fluxions and infinite series cover.jpg
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| caption        = Cover of book published in 1736
| author         = Isaac Newton
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| language       = English
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| genre          = Mathematics
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| publisher      = Henry Woodfall
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| pub_date       = 1736
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| pages          = 339
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'''''Method of Fluxions''''' ({{langx|la|De Methodis Serierum et Fluxionum}})<ref>[https://books.google.com/books?id=WyQOAAAAQAAJ The Method of Fluxions and Infinite Series]: With Its Application to the Geometry of Curve-lines. By Sir Isaac Newton, Translated from the Author's Latin Original Not Yet Made Publick. To which is Subjoin'd, a Perpetual Comment Upon the Whole Work, By John Colson, Sir Isaac Newton. Henry Woodfall; and sold by John Nourse, 1736.</ref> is a mathematical treatise by [[Isaac Newton|Sir Isaac Newton]] which served as the earliest written formulation of modern [[calculus]]. The book was completed in 1671 and posthumously published in 1736.<ref>{{Cite web |last=Sastry |first=S.Subramanya |title=The Newton-Leibniz controversy over the invention of the calculus |url=http://pages.cs.wisc.edu/~sastry/hs323/calculus.pdf |website=[[University of Wisconsin–Madison]] Computer Sciences User Pages}}</ref>
==Background==
[[Fluxion (mathematics)|Fluxion]] is Newton's term for a [[derivative]]. He originally developed the method at [[Woolsthorpe Manor]] during the closing of [[University of Cambridge|Cambridge]] due to the [[Great Plague of London]] from 1665 to 1667. Newton did not choose to make his findings known (similarly, his findings which eventually became the ''[[Philosophiae Naturalis Principia Mathematica]]'' were developed at this time and hidden from the world in Newton's notes for many years). [[Gottfried Leibniz]] developed his form of calculus independently around 1673, seven years after Newton had developed the basis for differential calculus, as seen in surviving documents like “the method of fluxions and [[Fluent (mathematics)|fluents]]..." from 1666. Leibniz, however, published his discovery of differential calculus in 1684, nine years before Newton formally published his fluxion [[notation]] form of calculus in part during 1693.<ref>{{Cite web |last=Sastry |first=S.Subramanya |title=The Newton-Leibniz controversy over the invention of the calculus |url=http://pages.cs.wisc.edu/~sastry/hs323/calculus.pdf |website=[[University of Wisconsin–Madison]] Computer Sciences User Pages}}</ref>

==Impact==
The calculus notation in use today is mostly that of Leibniz, although [[Newton's notation|Newton's dot notation]] for differentiation <math>\dot{x}</math> is frequently used to denote derivatives with respect to time.

==Rivalry with Leibniz==
Newton's ''Method of Fluxions'' was formally published posthumously, but following Leibniz's publication of the calculus a [[Leibniz–Newton calculus controversy|bitter rivalry]] erupted between the two mathematicians over who had developed the calculus first, provoking Newton to reveal his work on fluxions.

==Newton's development of analysis==
For a period of time encompassing Newton's working life, the discipline of [[Mathematical Analysis|analysis]] was a subject of controversy in the mathematical community. Although analytic techniques provided solutions to long-standing problems, including problems of [[Quadrature (geometry)|quadrature]] and the finding of tangents, the proofs of these solutions were not known to be reducible to the synthetic rules of Euclidean geometry. Instead, analysts were often forced to invoke [[infinitesimal]], or "infinitely small", quantities to justify their algebraic manipulations. Some of Newton's mathematical contemporaries, such as [[Isaac Barrow]], were highly skeptical of such techniques, which had no clear geometric interpretation. Although in his early work Newton also used infinitesimals in his derivations without justifying them, he later developed something akin to the [[Limit of a function#(ε, δ)-definition of limit|modern definition of limits]] in order to justify his work.<ref>{{cite journal|last=Kitcher|first=Philip|title=Fluxions, Limits, and Infinite Littlenesse. A Study of Newton's Presentation of the Calculus|journal=Isis|date=Mar 1973|volume=64|issue=1|pages=33–49|jstor=229868|doi=10.1086/351042|s2cid=121774892}}</ref>

==See also==
{{div col|colwidth=22em}}
* [[History of calculus]]
* [[Calorimetry]]
* [[George Berkeley]]
* [[Leonhard Euler]]
* [[Non-standard analysis]]
* [[Newton's method]]
* [[Charles Hayes (mathematician)]]
* [[John Landen]]
* [[John Colson]]
* [[Leibniz–Newton calculus controversy]]
* [[Joseph Raphson]]
* [[Time in physics]]
* [[William Lax]]
{{div col end}}

==References and notes==
{{reflist}}

==External links==
*[https://archive.org/details/methodoffluxions00newt ''Method of Fluxions''] at the [[Internet Archive]]

{{Isaac Newton}}

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[[Category:1671 non-fiction books]]
[[Category:1736 non-fiction books]]
[[Category:1671 in science]]
[[Category:1736 in science]]
[[Category:History of mathematics]]
[[Category:Mathematics books]]
[[Category:Books by Isaac Newton]]
[[Category:Differential calculus]]
[[Category:Mathematics literature]]
[[Category:Books published posthumously]]
[[Category:Treatises]]