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Full Description
This volume reproduces the texts of a number of important, yet relatively minor papers, many written during a period of Newton's life (1677-84) 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 1674-6 with Collins, Dary, John Smith and above all Leibniz.
Contents
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; 2. Researches into the Greek 'Solid Locus'; 3. Miscellaneous Topics in Analytical Geometry; Part III. The 'Geometria Curvilinea' and 'Matheseos Universalis Specimina': 1. The 'Geometry of Curved Lines'; 2. Specimens of a Universal System of Mathematics; Appendix.
