The Mathematical Papers of Isaac Newton Volume 4, 1674}}}1684 [Paperback]

This volume reproduces the texts of a number of important, yet relatively minor papers.This volume reproduces the texts of a number of important, yet relatively minor papers, many written during a period of Newton's life (16771684) which has been regarded as mathematically barren except for his Lucasian lectures on algebra (which appear in Volume V).This volume reproduces the texts of a number of important, yet relatively minor papers, many written during a period of Newton's life (16771684) which has been regarded as mathematically barren except for his Lucasian lectures on algebra (which appear in Volume V).This volume reproduces the texts of a number of important, yet relatively minor papers, many written during a period of Newton's life (167784) which has been regarded as mathematically barren except for his Lucasian lectures on algebra (which appear in Volume V). Part 1 concerns itself with his growing mastery of interpolation by finite differences, culminating in his rule for divided differences. Part 2 deals with his contemporary advances in the pure and analytical geometry of curves. Part 3 contains the extant text of two intended treatises on fluxions and infinite series: the Geometria Curvilinea (c. 1680), and his Matheseos Universalis Specimina (1684). A general introduction summarizes the sparse details of Newton's personal life during the period, one  from 1677 onwards  of almost total isolation from his contemporaries. A concluding appendix surveys highlights in his mathematical correspondence during 16746 with Collins, Dary, John Smith and above all Leibniz.Part I. Researches in Algebra, Number Theory and Trigonometry: 1. Approaches to a General Theory of Finite Differences; 2. Problems in Elementary Number Theory; 3. Codifications of Elementary Plane and Spherical Trigonometry; 4. Miscellaneous Notes on Annuities and Algebraic Factorization; Part II. Researches in Pure and Analytical Geometry: 1. Miscellaneous Problems in Elementary Geometry; 2l$