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Sir Isaac Newton PRS MP
(25 December 1642 – 20 March 1727
[NS: 4 January 1643 – 31 March
1727])
[1] was an English
physicist,
mathematician,
astronomer,
natural philosopher,
alchemist and
theologian, who has been "considered by many to be the
greatest and most influential
scientist who ever lived."
[7] His monograph
Philosophiæ
Naturalis Principia Mathematica, published in 1687, lays the foundations
for most of
classical mechanics. In this work, Newton
described
universal gravitation and
the three
laws of motion, which dominated the scientific view of the physical
universe for the next three centuries.
Newton showed that the motions of objects on
Earth and of
celestial bodies are governed by the same
set of natural laws, by demonstrating the consistency between
Kepler's laws of planetary
motion and his theory of gravitation, thus removing the last doubts about
heliocentrism and advancing
the
Scientific Revolution.
The
Principia is generally considered to be one of the most important
scientific books ever written, due, independently, to the specific physical laws
the work successfully described, and for the style of the work, which assisted
in setting standards for scientific publication down to the present time. Newton
built the first practical
reflecting telescope[8]
and developed a theory of colour based on the observation that a
prism decomposes white light into the
many colours that form the
visible spectrum. He also formulated
an empirical law of cooling and
studied the
speed of
sound. In mathematics, Newton
shares the credit with
Gottfried Leibniz for
the development
of
differential and integral calculus. He
also demonstrated the
generalised binomial theorem, developed
Newton's method for
approximating the
roots of a function, and contributed to the
study of
power series.
Newton, although an
unorthodox Christian, was
deeply religious, and wrote more on
Biblical hermeneutics and
occult studies than on science
and mathematics. Newton secretly rejected
Trinitarianism, and feared
being accused of refusing
holy orders.
[9]
Mathematics
Newton's work has been said "to distinctly advance every branch of
mathematics then studied".
[19] His work on the
subject usually referred to as fluxions or calculus, seen in a manuscript of
October 1666, is now published among Newton's mathematical papers.
[20] The author of the
manuscript
De analysi
per aequationes numero terminorum infinitas, sent by
Isaac Barrow to
John Collins in June 1669, was
identified by Barrow in a letter sent to Collins in August of that year as:
[21]
Mr Newton, a fellow of our College, and very young ... but of
an extraordinary genius and proficiency in these things.
Newton later became involved in a dispute with
Leibniz over
priority in the development
of infinitesimal calculus. Most modern historians believe that Newton and
Leibniz developed
infinitesimal calculus independently,
although with very different notations. Occasionally it has been suggested that
Newton published almost nothing about it until 1693, and did not give a full
account until 1704, while Leibniz began publishing a full account of his methods
in 1684. (Leibniz's notation and "differential Method", nowadays recognised as
much more convenient notations, were adopted by continental European
mathematicians, and after 1820 or so, also by British mathematicians.) Such a
suggestion, however, fails to notice the content of calculus which critics of
Newton's time and modern times have pointed out in
Book
1 of Newton's
Principia itself (published 1687) and in its forerunner
manuscripts, such as
De motu corporum in gyrum ("On
the motion of bodies in orbit"), of 1684. The
Principia
is not written in the language of calculus either as we know it or as Newton's
(later) 'dot' notation would write it. But his work extensively uses an
infinitesimal calculus in geometric form, based on limiting values of the ratios
of vanishing small quantities: in the
Principia itself Newton gave
demonstration of this under the name of 'the method of first and last
ratios'
[22] and explained why
he put his expositions in this form,
[23] remarking also
that 'hereby the same thing is performed as by the method of indivisibles'.
Because of this, the
Principia has been called "a book dense with the
theory and application of the infinitesimal calculus" in modern times
[24] and "lequel est
presque tout de ce calcul" ('nearly all of it is of this calculus') in Newton's
time.
[25] His use of methods
involving "one or more orders of the infinitesimally small" is present in his
De motu corporum in gyrum of 1684
[26] and in his papers
on motion "during the two decades preceding 1684".
[27]
Newton had been reluctant to publish his calculus because he feared
controversy and criticism.
[28] He was close to
the Swiss mathematician
Nicolas Fatio de Duillier. In 1691,
Duillier started to write a new version of Newton's
Principia, and
corresponded with Leibniz.
[29] In 1693 the
relationship between Duillier and Newton deteriorated, and the book was never
completed.
Starting in 1699, other members of the
Royal Society (of which Newton was a member)
accused Leibniz of
plagiarism,
and the dispute broke out in full force in 1711. The Royal Society proclaimed in
a study that it was Newton who was the true discoverer and labelled Leibniz a
fraud. This study was cast into doubt when it was later found that Newton
himself wrote the study's concluding remarks on Leibniz. Thus began the bitter
controversy which marred the lives of both Newton and Leibniz until the latter's
death in 1716.
[30]
Newton is generally credited with the
generalised binomial
theorem, valid for any exponent. He discovered
Newton's
identities,
Newton's method, classified cubic plane
curves (
polynomials of degree three in two
variables), made substantial
contributions to the theory of
finite differences, and was the first to use
fractional indices and to employ
coordinate
geometry to derive solutions to
Diophantine
equations. He approximated partial sums of the
harmonic series by
logarithms (a
precursor to
Euler's summation formula), and was
the first to use
power
series with confidence and to revert power series. Newton's work on infinite
series was inspired by
Simon
Stevin's decimals.
[31]
He was appointed
Lucasian Professor of
Mathematics in 1669 on Barrow's recommendation. In that day, any fellow of
Cambridge or Oxford was required to become an ordained
Anglican priest. However, the terms of the Lucasian
professorship required that the holder
not be active in the church
(presumably so as to have more time for science). Newton argued that this should
exempt him from the ordination requirement, and
Charles II, whose permission was needed,
accepted this argument. Thus a conflict between Newton's religious views and
Anglican orthodoxy was averted.
[32]
Optics
From 1670 to 1672, Newton lectured on optics.
[34] During this period
he investigated the
refraction
of light, demonstrating that a
prism could decompose
white light into a
spectrum of colours,
and that a
lens and a
second prism could recompose the multicoloured spectrum into white light.
[35] Modern scholarship
has revealed that Newton's analysis and resynthesis of white light owes a debt
to
corpuscular
alchemy.
[36]
He also showed that the coloured light does not change its properties by
separating out a coloured beam and shining it on various objects. Newton noted
that regardless of whether it was reflected or scattered or transmitted, it
stayed the same colour. Thus, he observed that colour is the result of objects
interacting with already-coloured light rather than objects generating the
colour themselves. This is known as
Newton's
theory of colour.
[37]
From this work, he concluded that the lens of any
refracting
telescope would suffer from the
dispersion of light into colours (
chromatic
aberration). As a proof of the concept, he constructed a telescope using a
mirror as the
objective to bypass that problem.
[38]
Building the design, the first known functional reflecting telescope, today
known as a
Newtonian telescope,
[38]
involved solving the problem of a suitable mirror material and shaping
technique. Newton ground his own mirrors out of a custom composition of highly
reflective
speculum
metal, using
Newton's rings to judge the
quality of
the optics for his telescopes. In late 1668
[39]
he was able to produce this first
reflecting telescope. In 1671, the
Royal Society asked for a demonstration of his reflecting telescope.
[40] Their interest
encouraged him to publish his notes
On Colour, which he later expanded
into his
Opticks. When
Robert Hooke criticised some
of Newton's ideas, Newton was so offended that he withdrew from public debate.
Newton and Hooke had brief exchanges in 1679–80, when Hooke, appointed to manage
the Royal Society's correspondence, opened up a correspondence intended to
elicit contributions from Newton to Royal Society transactions,
[41]
which had the effect of stimulating Newton to work out a proof that the
elliptical form of planetary orbits would result from a centripetal force
inversely proportional to the square of the radius vector (see
Newton's law of
universal gravitation – History and
De motu corporum in gyrum). But
the two men remained generally on poor terms until Hooke's death.
[42]
Newton argued that light is composed of particles or corpuscles, which were
refracted by accelerating into a denser medium. He verged on soundlike waves to
explain the repeated pattern of reflection and transmission by thin films
(Opticks Bk.II, Props. 12), but still retained his theory of 'fits' that
disposed corpuscles to be reflected or transmitted (Props.13). Later physicists
instead favoured a purely wavelike explanation of light to account for the
interference patterns, and the
general phenomenon of
diffraction. Today's
quantum mechanics,
photons and the idea of
wave–particle duality bear only a
minor resemblance to Newton's understanding of light.
In his
Hypothesis of Light of 1675, Newton
posited the existence
of the
ether
to transmit forces between particles. The contact with the
theosophist Henry More, revived his interest in alchemy. He
replaced the ether with occult forces based on
Hermetic ideas of attraction and repulsion between
particles.
John
Maynard Keynes, who acquired many of Newton's writings on alchemy, stated
that "Newton was not the first of the age of reason: He was the last of the
magicians."
[43]
Newton's interest in alchemy cannot be isolated from his contributions to
science.
[5] This was at a
time when there was no clear distinction between alchemy and science. Had he not
relied on the
occult idea of
action at a distance, across a
vacuum, he might not have developed his theory of gravity. (See also
Isaac Newton's occult
studies.)
In 1704, Newton published
Opticks, in which he expounded his corpuscular
theory of light. He considered light to be made up of extremely subtle
corpuscles, that ordinary matter was made of grosser corpuscles and speculated
that through a kind of alchemical transmutation "Are not gross Bodies and Light
convertible into one another, ...and may not Bodies receive much of their
Activity from the Particles of Light which enter their Composition?"
[44]
Newton also constructed a primitive form of a frictional
electrostatic generator, using a glass
globe (Optics, 8th Query).
In an article entitled "Newton, prisms, and the 'opticks' of tunable
lasers
[45] it is
indicated that Newton in his book
Opticks was the first to show a diagram using a
prism as a beam expander. In the same book he describes, via diagrams, the use
of multiple-prism arrays. Some 278 years after Newton's discussion,
multiple-prism beam
expanders became central to the development of
narrow-linewidth tunable lasers. Also, the use of these prismatic
beam expanders led to the
multiple-prism dispersion
theory.
[45]
Mechanics and
gravitation
Further information:
Writing of Principia
Mathematica
In 1679, Newton returned to his work on (
celestial) mechanics, i.e., gravitation and
its effect on the orbits of
planets,
with reference to
Kepler's laws of planetary motion. This
followed stimulation by a brief exchange of letters in 1679–80 with Hooke, who
had been appointed to manage the Royal Society's correspondence, and who opened
a correspondence intended to elicit contributions from Newton to Royal Society
transactions.
[41]
Newton's reawakening interest in astronomical matters received further stimulus
by the appearance of a comet in the winter of 1680–1681, on which he
corresponded with
John
Flamsteed.
[46] After the
exchanges with Hooke, Newton worked out a proof that the elliptical form of
planetary orbits would result from a centripetal force inversely proportional to
the square of the radius vector (see
Newton's law of
universal gravitation – History and De motu corporum in gyrum). Newton
communicated his results to
Edmond Halley and to the Royal Society in
De motu
corporum in gyrum, a tract written on about 9 sheets which was copied
into the Royal Society's Register Book in December 1684.
[47] This tract
contained the nucleus that Newton developed and expanded to form the
Principia.
The
Principia
was published on 5 July 1687 with encouragement and financial help from
Edmond Halley. In this
work, Newton stated the
three universal laws of motion that
enabled many of the advances of the
Industrial Revolution which soon followed
and were not to be improved upon for more than 200 years, and are still the
underpinnings of the non-relativistic technologies of the modern world. He used
the Latin word
gravitas (weight) for the effect that would become known
as
gravity, and
defined the law of
universal
gravitation.
In the same work, Newton presented a calculus-like method of geometrical
analysis by 'first and last ratios', gave the first analytical determination
(based on
Boyle's law) of
the speed of sound in air, inferred the oblateness of the spheroidal figure of
the Earth, accounted for the precession of the equinoxes as a result of the
Moon's gravitational attraction on the Earth's oblateness, initiated the
gravitational study of the
irregularities in the motion of the moon,
provided a theory for the determination of the orbits of comets, and much
more.
Newton made clear his
heliocentric view of the solar system – developed
in a somewhat modern way, because already in the mid-1680s he recognised the
"deviation of the Sun" from the centre of gravity of the solar system.
[48] For Newton, it was
not precisely the centre of the Sun or any other body that could be considered
at rest, but rather "the common centre of gravity of the Earth, the Sun and all
the Planets is to be esteem'd the Centre of the World", and this centre of
gravity "either is at rest or moves uniformly forward in a right line" (Newton
adopted the "at rest" alternative in view of common consent that the centre,
wherever it was, was at rest).
[49]
Newton's postulate of an invisible
force able to act over vast
distances led to him being criticised for introducing "
occult agencies" into science.
[50] Later, in the
second edition of the
Principia (1713), Newton firmly rejected such
criticisms in a concluding
General Scholium, writing that it was enough
that the phenomena implied a gravitational attraction, as they did; but they did
not so far indicate its cause, and it was both unnecessary and improper to frame
hypotheses of things that were not implied by the phenomena. (Here Newton used
what became his famous expression
Hypotheses non fingo).
With the
Principia, Newton became internationally recognised.
[51] He acquired a
circle of admirers, including the
Swiss-born mathematician
Nicolas
Fatio de Duillier, with whom he formed an intense relationship. This
abruptly ended in 1693, and at the same time Newton suffered a
nervous breakdown.
[52]
Classification of
cubics
Besides the work of Newton and others on calculus, the first important
demonstration of the power of analytic geometry was Newton's classification of
cubic curves in the Euclidean plane in the late 1600s. He divided them into four
types, satisfying different equations, and in 1717
Stirling, probably with Newton's
help, proved that every cubic was one of these four. Newton also claimed that
the four types could be obtained by plane projection from one of them, and this
was proved in 1731.
[53]
Extracts Taken From:
http://en.wikipedia.org/wiki/Isaac_Newton
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