The Mathematical Papers of Isaac Newton:, Volume 5; Volumes 1683-1684

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Cambridge University Press, Jan 3, 2008 - Mathematics - 664 pages
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The fifth volume of this definitive edition centres around Newton's Lucasian lectures on algebra, purportedly delivered during 1673-83, and subsequently prepared for publication under the title Arithmetica Universalis many years later. Dr Whiteside first reproduces the text of the lectures deposited by Newton in the Cambridge University Library about 1684. In these much reworked, not quite finished, professional lectiones, Newton builds upon his earlier studies of the fundamentals of algebra and its application to the theory and construction of equations, developing new techniques for the factorizing of algebraic quantities and the delimitation of bounds to the number and location of roots, with a wealth of worked arithmetical, geometrical, mechanical and astronomical problems. An historical introduction traces what is known of the background to the parent manuscript and assesses the subsequent impact of the edition prepared by Whiston about 1705 and the revised version published by Newton himself in 1722. A number of minor worksheets, preliminary drafts and later augmentations buttress this primary text, throwing light upon its development and the essential untrustworthiness of its imposed marginal chronology.
  

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Contents

between given quadratic cubic and quartic equations two by two 126 Elimination
4
his concept of a universal arithmetick mirroring
15
Whiston V preface to the 1707 editio princeps Certain exaggerations stemming
21
that of an Apollonius circle 230 Problems 278
27
resolving a quartic algebraic polynomial into surd quadratic factors 29 His concluding
30
5r6v Delimitation of the roots of equations and their factoriza
42
the analysis despite minor differences structurally the same as Descartes 270
46
23r Newtons derivation of theHeronian formula for a triangles
50
construction of a parabola through four points by determining its Cartesian equation
306
where two globes simultaneously released fall under simple
332
possibility of multiple real roots 338 An equation can have as many roots as it
350
diminishing them by a given quantity 352 Eliminating first or second terms from
366
Determining rational roots of a numerical equation by finding its factors 368 Isolating
372
Exemplified in equations of fourth fifth and seventh degree 376 The technique can
384
computation of an equations root is easy geometrical constructions for effecting
424
complicated algebraic curves 426 On this basis Newton urges the superiority of
434

PART 2
131
two arith
142
script
156
metrical relationships into algebraic equivalents 158 The same derived algebraic equation
162
Euclidean propositions useful to this end 164 Their application to Schootens problem
168
Reducing the algebraic equivalent to a single equation 172 Different
182
algebraic determi
192
Schootens fishpond promenade 194 Problem 10 to cut off a given area
204
the Newtonian geometrical model for anglesection and the algebraic
212
the full cubic 438 Proof of the method 440 An equivalent circular neusis used to construct
448
The circular neusis used to trisect an angle 45860 The equivalent rectilinear neusis
462
braically higher curves 474 The parabola is geometrically less simple than the ellipse
488
2V Two draft outlines of Newtons
518
THE ARITHMETICS UNIVERSALIS LIBER PRIMUS
533
which ensues in algebraic reduction from choosing as base variable one related in
614
the reduced Apollonian circletangency problem 61618 Variant ways
620
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Galois Theory
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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