The Mathematical Papers of Isaac Newton:

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Cambridge University Press, Jan 3, 2008 - Mathematics - 626 pages
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The main part of the third volume of Dr Whiteside's annotated and critical edition of all the known mathematical papers of Isaac Newton reproduces, from the original autograph, Newton's elaborate tract on infinite series and fluxions (the so-called Methodus Fluxionum), including a formerly unpublished appendix on geometrical fluxions. Ancillary documents include, in Part 1, papers on the integration of algebraic functions and, in Part 2, short texts dealing with geometry and simple harmonic motion in a cycloidal arc. Part 3 reproduces, from both manuscript versions of Newton's Lectiones Opticae and from his Waste Book, mathematical excerpts from his researches into light and the theory of lenses at this period. An appendix summarizes mathematical highlights in his contemporary correspondence.
 

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Contents

and composite curves influence of James Gregory and Barrow 128 Mode 2 focus
4
Barrow reports on a new Newtonian treatise of infinite series December 1670 3 Newton
13
538r Newtons citation of the 1671 tract in a draft preface
20
PRELIMINARY SCHEME FOR A TREATISE ON FLUXIONS
28
to infinite series by division 38 Examples of reduction by extracting roots as infinite
60
Newton generalizes Gregorys concept of a double series convergens
68
modified Huddenian multipliers in simple cases 74 Geometrical justification and Ferma
78
Use of inverse Huddenian multipliers to determine finite solutions by inspection
104
fluxion of the area of a rectangle and triangle as one side flows parallel to itself
344
That of the area generated by a rotating radius vector 346 That of an arc intercepted
350
THE QUADRATURE OF CURVES DEFINED BY POLYNOMIALS
373
PART 2
383
INTRODUCTION
389
Brounckers first attempts to confirm Huygens result JanuaryFebruary 1662 395 Hookes
400
RESEARCH INTO THE ELEMENTARY GEOMETRY
408
cycloid is proportional to the distance of fall along it to its lowest point 420 Hence
424

solutiones particulares of two de Beaune equations 108 Examples where series solution
110
Example 2 is the general cycloid
146
the curvature is that of the osculating circle 150 Possible defining symptoms
180
of inequability of curvature by the ratio of the fluxion of the curvature radius to that of
194
general observations 198 Examples in geometrical
202
exemplified in the cycloid and sinusoid 204 Cavalierian areapreserving convolu
208
their conversion to common form
232
and y dzXli1e +fzvf h + izvv in terms of the areas s and a of these 244 Observations
262
correctly choosing bounds 264 Similar tables might be constructed
268
simple examples 116 List of nine problems to which
289
The cissoid and conchoid 270 The quartic y2c2 z2 z2 + bz c2 272 The quadra
290
3346 An intended addendum on geometrical fluxions
338
RESEARCHES IN GEOMETRICAL OPTICS
433
of elemental coloured rays each separately refracted 438 The preamble to his first lecture
441
Pembertons or Jones? editorial description of the Opticas Pars prima
449
the resulting quartic is solved in Cartesian style
462
MISCELLANEOUS RESEARCHES INTO REFRACTION
514
72v73r insert
536
strong enough to cause a sensible Bow
544
428 6fr3970 9 615r617r The general problem
552
NEWTONS MATHEMATICAL CORRESPONDENCE
559
I could give exacter solutions
567
INDEX OF NAMES
573
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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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