Editing Method of Fluxions (section)

==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>