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Newton Papers : Fluxions. The items in Add. 3960 were composed in different periods, from the mid 1660s [Add. 3960.12] to the early 1690s and early 1700s, when Newton planned to write a treatise on the calculus, what he termed ‘the methods of series and fluxions’.
This chapter explores the analytical method of fluxions, as stated in De Methodis. Newton’s method of fluxions can be divided into two parts: The direct and the inverse. Newton considered the techniques of the direct method to be perfected, as presented in his treatise De Methodis.
And after several examples of squaring Curves by this method, he described the method of fluxions for finding the Areas, Lengths, convex surfaces, solid contents & centers of gravity of curvelines & curvilinear figures.
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The discretized systems of nonlinear equations are treated by using the Newton method, and the associated linear subproblems are solved by means of a monolithic (geometrical) multigrid method...
