The Mathematical Papers of Isaac Newton:, Volume 7; Volumes 1691-1695

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Cambridge University Press, Jan 3, 2008 - Mathematics - 764 pages
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Newton's mathematical researches during the last five years of his stay in Cambridge before leaving in April 1696 to take up his duties at the Mint in London have three main centres of interest: methods of fluxions and series, classical pure geometry, and Cartesian analytical geometry. Part 1 reproduces Newton's advances at this time in further extending the techniques of his combined calculus of fluxions and fluent, and of expansion into infinite series. Part 2 gives publication of Newton's lengthy excursions in the early 1690s into the modes of geometrical analysis used by the 'ancient' geometers, based - by way of Commandino's Latin translation - on the account of this little understood field of the Greek 'topos analuomenos' which was given by Pappus in the prolegomenon to the seventh book of his Mathematical Collection. Part 3 gives prominence to the final text of the Enumeratio Linearum Tertii Ordinis which Newton put together in June 1695.
 

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Contents

LIST OF PLATES xlviH
xlviii
given a fluxional equation to determine the corresponding fluent relationship 70 The
1
Appendix Variant preliminary drafts for the final Liber secundus 1 Add 3962
3
Newton employs Oughtredian notation for the sum and difference
4
62r63r A first reshaping of Proposition IV of the 1691 De quadratura to be the
10
subordinate kinds 487 Hyperbolic and parabolic branches and the deficient curves
11
John Craiges visit to Cambridge in 1685 to talk of the quadrature of curves 3 Newton shows
18
31r40r56r56v38ar38br + private The unfinished preliminary text
24
on the equality of the products of alternate intercepts cut in the extended sides of a given
276
an incomplete opening and a Chapter 2 1 Add
294
is the universal Apollonian sectio spatii 314 Porism 11 is the Fermatian extension 316
336
A yet more general Porism 12 effecting the same by an arbitrary 11 correspondence
350
of the Arithmetica again 362 Ways in which a quadrilateral may be given both in species
380
further sorts of postulate which can be made
394
THE FINAL GEOMETRIC LIBRI DUO
402
segments of a triangle 452 Further such theorems but it is enough to have disclosed
460

for compounding quadratures of related
32
where by distinguishing related groups of terms in it the equation is seen to be directly
80
cannot distinguish between a general fluxional derivative and a particular value of it
98
by means of the preceding to solve problems Testing for maxima
114
Again instanced in the ellipse 116 The converse construction of properties of curves
128
University Library Cambridge
130
whose equations are trinomial 130 Newton for the first time introduces his standard
143
1059
160
Two reworked propositions on the fluxions and fluents of complex
164
The restyled excerpts from the De quadratura communicated to Wallis
177
PART 2
183
a comprehensive modern treatise on curves 193 The distinction of curves into grades
199
27r28r A preliminary account ofAnalysis Geometrica
222
PART 3
241
FIRST ESSAYS AT A MULTIPARTITE GEOMETRIA
248
where the ordination angle also is permitted to vary 502 And yet more complicatedly
503
CARTESIAN ANALYSIS OF HIGHER PLANE CURVES
563
David Gregorys thoughts in 1698 of editing the tract soon abandoned Newtons
566
IMPROVED ENUMERATION OF THE CUBIcs SPECIES
579
lr14r The finished enumeration into 72 species Division of straight
602
The four monodiametral ones species 2831 and the unique tridiametral instance
616
The seven monodiametral ones species 3945 620 The seven parabolic hyperbolas
635
16v A first
648
AND QUARTIC CURVES
656
44r42r42v Determining the simplest forms of general Cartesian
663
second f double point as origin 666 The defining equation of 106 terms when sub
670
derived from first principles by supposing a cubic approximating parabola 675 3 Add
679
2 Determining the slope of the apparent path of the comet of 16801 at its sighting
686
611r Case 5 where there are seven
702
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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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