The Mathematical Papers of Isaac Newton:

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Cambridge University Press, Jan 3, 2008 - Mathematics - 664 pages
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This volume reproduces mathematically significant extracts from the extant manuscript record of Newton's researches during 1684-5 into the dynamical motion of bodies under the deviating action of a central force, and his subsequent struggles thereby to explain the observed motions of solar comets and of the moon. The short tract De motu Corporum, which Newton initially composed on this topic in the early autumn of 1684, was primarily built around his earlier proof that in the absence of external perturbation a planetary eclipse may be traversed under an inverse-square force pull to its solar focus, but also discussed the simplest case of resisted ballistic motion. In epilogue, excerpts from his abandoned grand scheme for revising the Principia in the early 1690s detail Newton's planned refinements to his printed exposition of central force, both simplifying and extending it, introducing therein a novel general fluxional measure of such force - but failing adequately to apply it to the primary case of conic motion.
  

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Contents

3 Computation of the hourly rate of motion of the moons apogee and of its mean
3
is so constructed 24252 The name conic is taken in its broadest sense and includes
4
the disturbing central force which effects a given rotation of orbit 35860 Proposition
6
the influence upon him
8
Additions and corrections to the scholium to Proposition XXXI
17
is at first reluctant to take up Hookes notion 9 Newton initially suggests a spiral path of fall
22
FUNDAMENTAL INVESTIGATIONS ON THE MOTION OF BODIES
30
derivation of the sinelaw
65
that stated for the Borellian case of constant gravity is only loosely accurate 14850
162
The gravitational attraction of a thin circular ring upon an externalinternal
206
48v55r40r47r88r103r32r39r80r87r72r79v Articles IVX
229
repeats Newtons earlier construction of the distance
259
repeats the previous exact construction of the parabolic case 2
308
restates Wrens construction of the elliptical case by means of
322
APPROACHES TO THE SOLUTION OF PARTICULAR PROBLEMS
456
THE DE MOTU GORPORUM LIBER PRIMUS REMODELLED
538

30515 Resisted oscillation in a cycloidal pendulum
96
the last ratios of arc chord and tangent as their included contact angle vanishes
114
repeats the earlier derivation
132
the law of force to its centre inducing motion in an ellipse is again shown
146
facing p 46 Revised corollaries to the new Proposi
565
INDEX OF NAMES
611
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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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