The Mathematical Papers of Isaac Newton:, Volume 4; Volumes 1674-1684

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Cambridge University Press, Jan 3, 2008 - Mathematics - 722 pages
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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.
 

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Contents

141r144r A first
3
82r84r Tabular computation of differences and their use
4
the series is assumed and its coefficients are then successively determined term by term from
5
68v A configuration illustrating linesegments determinable one from another by simple
10
Newtons ignorance of Briggs and Harriot 4 Possible
13
3r4v A discarded sheet from Newtons epistola posterior to Leibniz
32
deriving centraldifference interpolation formulas 1 A detailed tabulation of unit
64
3 Lemma
72
39r40r A first draftpreliminary revise of the third
343
2 Observations on asymptotes and diameters in the general cubic curve 1 private
351
THE GEOMETRIA CURVILINEA AND MATHESEOS
407
are examined most simply and clearly by Euclidean geometry augmented by fluxional
410
Newtons attack on Cartesian algebraic analysis 409 The theory
413
Its sudden abandonment after Halleys visit to Cambridge in August 1684?
419
Definitions of fluxional increment and decrement 424 Axioms and postulates
426
mented right triangle 428 The model abandoned and the theorems restated in abstract
442

91v The resolution of geometrical questions regarding numbers
110
CODIFICATIONS OF ELEMENTARY PLANE AND SPHERICAL
116
33r44v The elaborated augmented compendium ofTrigono
164
derivation from the collapsed net of standard theorems relating
184
MS Wharton 592 Whartons transcript
191
MISCELLANEOUS NOTES ON ANNUITIES AND ALGEBRAIC
203
Tabulation of results and examination of their pattern 207 The quadratic factori
212
Newtons early knowledge not profound of classical geometry 217 His study of Pappus
229
problems 1 Various ways ofgiving determining a triangle by a simple relationship
268
RESEARCHES INTO THE GREEK SOLID LOCUS
274
passim Solution of the Ancients problem of the 4line solid
286
considering their points at infinity
335
on the fluxions of the sides basesegments and perpendiculars of a general scalene
462
61v A first sketch
504
53v Two trivial variants on Proposition 20
518
of the Geometria
524
13r14r The revised computation of series Chapter
592
Chapter 2 on transmuting series whose alternate terms have the same sign The basic
616
Examples of this 622 General observations on the relative efficacy of ways of deriving
633
llr12v Preliminary versions of Chapter 2 of the
652
and November 1676 mark the opening and close of Newtons mathematical
667
manuscripts and his debt therein to Wallis 672 The central passages in the epistola borrow
674
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About the author (2008)

Born at Woolsthorpe, England, Sir Isaac Newton was educated at Trinity College, Cambridge University, where he graduated in 1665. During the plague of 1666, he remained at Woolsthorpe, during which time he formulated his theory of fluxions (the infinitesimal calculus) and the main outlines of his theories of mechanics, astronomy, and optics, including the theory of universal gravitation. The results of his researches were not circulated until 1669, but when he returned to Trinity in 1667, he was immediately appointed to succeed his teacher as professor of mathematics. His greatest work, the Mathematical Principles of Natural Philosophy, was published in 1687 to immediate and universal acclaim. Newton was elected to Parliament in 1689. In 1699, he was appointed head of the royal mint, and four years later he was elected president of the Royal Society; both positions he held until his death. In later life, Newton devoted his main intellectual energies to theological speculation and alchemical experiments. In April 1705, Queen Anne knighted Newton during a royal visit to Trinity College, Cambridge. He was only the second scientist to have been awarded knighthood. Newton died in his sleep in London on March 31, 1727, and was buried in Westminster Abbey. Because of his scientific nature, Newton's religious beliefs were never wholly known. His study of the laws of motion and universal gravitation became his best-known discoveries, but after much examination he admitted that, "Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done.

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