The Mathematical Papers of Isaac Newton:

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Cambridge University Press, Jan 3, 2008 - Mathematics - 772 pages
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When Newton left Cambridge in April 1696 to take up, at the age of 53, a new career at the London Mint, he did not entirely 'leave off Mathematicks' as he so often publicly declared. This last volume of his mathematical papers presents the extant record of the investigations which for one reason and another he pursued during the last quarter of his life. In January 1697 Newton was tempted to respond to two challenges issued by Johann Bernoulli to the international community of mathematicians, one the celebrated problem of identifying the brachistochrone; both he resolved within the space of an evening, producing an elegant construction of the cycloid which he identified to be the curve of fall in least time. In the autumn of 1703, the appearance of work on 'inverse fluxions' by George Cheyne similarly provoked him to prepare his own ten-year-old treatise De Quadratura Curvarum for publication, and more importantly to write a long introduction to it where he set down what became his best-known statement of the nature and purpose of his fluxional calculus.
 

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Contents

LIST OF PLATES
lvi
477r A fleshedout
1
THE DE QUADRATURA AMPLIFIED AS AN ANALYSIS
5
The twin problems of Johann Bernoullis Programma of New Years Day solved by Newton
7
constructing the radius of curvature at a general point of an ellipse 161 3 Add
8
Machins ineffective attempt 1718 to extend this to a general centralforce field
13
literal truth of Leibniz standpoint was soon lost from sight 28 The text of the De Quadratura
14
nomical daytoday arithmetical computations of the period 36 More sustained reworkings
43
115v116v A first
227
THE METHOD OF FINITE DIFFERENCES 1710
236
the text as printed by Jones in his 1711 Analysis Pro
246
From these there is given the curve of parabolic kind which shall pass
252
QUANTITATES FLUENTES ET EARUM MOMENTA 1712
258
Appendix Prior computations and drafts for the Analysis 1 private Calculation
300
PROPOSITION X OF THE PRINCIPIAs SECOND BOOK
312
1 Tottering steps towards achieving a valid resolution of this basic problem in the resisted
326

that the calculus of fluxions was not begotten before the calculus of differences sent privately
58
to observed reality 386 Including Rule 7 the rule of false position employed
64
descent to differentiodifferentials which might be put to the English to test their mathe
66
THE TWIN PROBLEMS OF BERNOULLIS 1697 PROGRAMMA
72
The full Latin text of Bernoullis printed Programma of New Years
80
THE de quadratura curvarum REVISED
92
Given any relationship of fluents to find that of their fluxions 92
102
207 + 7 88209211
110
its limitincrement is expanded as a Taylor series 112 The dotsymbols for fluxions
118
3 The final text of the augmented introduction and refurbished concluding portion
129
61v A rough draft of the terminal scholium
166
algebra symbolic arithmetic uses
188
113r114v117r118r On the construction of geometrical problems
212
115r116r A first
220
the semicircle 326 If carried through these would determine the resistance to be twice
337
and gravity are conceived to act over infinitesimalmoments of time not continuously
369
Initial attempts by Newton late September 1712 to locate the defect in
413
for ascertaining the curvature radius in partial derivatives
423
Appendix The wouldbe General Solution turned by Newton into Latin 1 Add
435
3 A first full rendering in Latin of Newtons Method of Solution 437 4 private
441
minor complements to the arithmetica
460
28r Deriving the Cartesian equation of the nodal cubic described by
468
public his early mathematical papers content in England as Leibniz in Germany to
471
plagiarism from the Principia in his 1689 Acta essays 499 Attempts by Chamberlayne
503
4rff
510
challengeproblem on constructing orthogonals to a family of curves
523
N B Unless otherwise specified citations here and below are of manuscripts in
539
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Harold M. Edwards
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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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