Isaac Newton

Sir Isaac Newton (; He was a key figure in the Scientific Revolution and the Enlightenment that followed. His book (Mathematical Principles of Natural Philosophy), first published in 1687, achieved the first great unification in physics and established classical mechanics. Newton also made seminal contributions to optics, and shares credit with the German mathematician Gottfried Wilhelm Leibniz for formulating infinitesimal calculus, although he developed calculus years before Leibniz. Newton contributed to and refined the scientific method, and his work is considered the most influential in bringing forth modern science.

In the , Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint for centuries until it was superseded by the theory of relativity. While this is the case, his laws still serve as excellent approximations for the vast majority of physical phenomena involving low speeds (much less than the speed of light) and weak gravitational fields. He used his mathematical description of gravity to derive Kepler's laws of planetary motion, account for tides, the trajectories of comets, the precession of the equinoxes and other phenomena, eradicating doubt about the Solar System's heliocentricity. Newton solved the two-body problem and introduced the three-body problem. He demonstrated that the motion of objects on Earth and celestial bodies could be accounted for by the same principles. Newton's inference that the Earth is an oblate spheroid was later confirmed by the geodetic measurements of Alexis Clairaut, Charles Marie de La Condamine, and others, convincing most European scientists of the superiority of Newtonian mechanics over earlier systems. He was also the first to calculate the age of Earth by experiment, and described a precursor to the modern wind tunnel. Further, he was the first to provide a quantitative estimate of the solar mass.

Newton built the first reflecting telescope and developed a sophisticated theory of colour based on the observation that a prism separates white light into the colours of the visible spectrum. His work on light was collected in his book Opticks, published in 1704. He originated prisms as beam expanders and multiple-prism arrays, which would later become integral to the development of tunable lasers. made the first theoretical calculation of the speed of sound, and introduced the notions of a Newtonian fluid and a black body. He was also the first to explain the Magnus effect. Moreover, he was the first to analyse Couette flow. In addition to his creation of calculus, Newton's work on mathematics was extensive. He generalised the binomial theorem to any real number, introduced the Puiseux series, was the first to state Bézout's theorem, classified most of the cubic plane curves, contributed to the study of Cremona transformations, developed a method for approximating the roots of a function, originated the Newton–Cotes formulas used for numerical integration, and further produced the earliest explicit enunciation of the general Taylor series. Additionally, Newton initiated the field of calculus of variations, formulated and solved the earliest problem in geometric probability, devised the earliest form of linear regression, and was a pioneer of vector analysis.

Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge; he was appointed at the age of 26. He was a devout but unorthodox Christian who privately rejected the doctrine of the Trinity. He refused to take holy orders in the Church of England, unlike most members of the Cambridge faculty of the day. Beyond his work on the mathematical sciences, Newton dedicated much of his time to the study of alchemy and biblical chronology, but most of his work in those areas remained unpublished until long after his death. Politically and personally tied to the Whigs, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–1690 and 1701–1702. He was knighted by Queen Anne in 1705 and spent the last three decades of his life in London, serving as Warden (1696–1699) and Master (1699–1727) of the Royal Mint, in which he increased the accuracy and security of British coinage. He was also the president of the Royal Society (1703–1727).

Early life

Isaac Newton was born (according to the Julian calendar in use in England at the time) on Christmas Day, 25 December 1642 (NS 4 January 1643) at Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, a hamlet in Lincolnshire. His father, also named Isaac Newton, had died three months before. Born prematurely, Newton was a small child; his mother, Hannah Ayscough, said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough (née Blythe). Newton disliked his stepfather and maintained some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: "Threatening my father and mother Smith to burn them and the house over them." Newton's mother had three children (Mary, Benjamin, and Hannah) from her second marriage.

The King's School

From the age of about twelve until he was seventeen, Newton was educated at The King's School in Grantham, which taught Latin and Ancient Greek and probably imparted a significant foundation of mathematics. He was removed from school by his mother and returned to Woolsthorpe by October 1659. His mother, widowed for the second time, attempted to make him a farmer, an occupation he hated. Henry Stokes, master at The King's School, and Reverend William Ayscough (Newton's uncle) persuaded his mother to send him back to school. Motivated by a desire for revenge against a schoolyard bully, whom Newton beat in a fight and humiliated, he became the top-ranked student, distinguishing himself mainly by building sundials and models of windmills.

University of Cambridge

In June 1661, Newton was admitted to Trinity College at the University of Cambridge. His uncle the Reverend William Ayscough, who had studied at Cambridge, recommended him to the university. At Cambridge, Newton started as a subsizar, paying his way by performing valet duties until he was awarded a scholarship in 1664, which covered his university costs for four more years until the completion of his MA. At the time, Cambridge's teachings were based on those of Aristotle, whom Newton read along with then more modern philosophers, including René Descartes and astronomers such as Galileo Galilei and Thomas Street. He set down in his notebook a series of "Quaestiones" about mechanical philosophy as he found it. In 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton obtained his BA degree at Cambridge in August 1665, the university temporarily closed as a precaution against the Great Plague.

Although he had been undistinguished as a Cambridge student, his private studies and the years following his bachelor's degree have been described as "the richest and most productive ever experienced by a scientist". The next two years alone saw the development of theories on calculus, optics, and the law of gravitation, at his home in Woolsthorpe. The physicist Louis Trenchard More writes that "There are no other examples of achievement in the history of science to compare with that of Newton during those two golden years."

Newton has been described as an "exceptionally organized" person when it came to note-taking, further dog-earing pages he saw as important. Furthermore, Newton's "indexes look like present-day indexes: They are alphabetical, by topic." His books showed his interests to be wide-ranging, with Newton himself described as a "Janusian thinker, someone who could mix and combine seemingly disparate fields to stimulate creative breakthroughs." William Stukeley wrote that Newton "was not only very expert with his mechanical tools, but he was equally so with his pen", and further illustrated how Newton's lodging room wall at Grantham was covered in drawings of "birds, beasts, men, ships & mathematical schemes. & very well designed". He also noted his "uncommon skill & industry in mechanical works".

In April 1667, Newton returned to the University of Cambridge, and in October he was elected as a fellow of Trinity. Fellows were required to take holy orders and be ordained as Anglican priests, although this was not enforced in the Restoration years, and an assertion of conformity to the Church of England was sufficient. He made the commitment that "I will either set Theology as the object of my studies and will take holy orders when the time prescribed by these statutes [7 years] arrives, or I will resign from the college." Up until this point he had not thought much about religion and had twice signed his agreement to the Thirty-nine Articles, the basis of Church of England doctrine. By 1675 the issue could not be avoided, and his unconventional views stood in the way.

His academic work impressed the Lucasian Professor Isaac Barrow, who was anxious to develop his own religious and administrative potential (he became master of Trinity College two years later); in 1669, Newton succeeded him, only one year after receiving his MA. Newton argued that this should exempt him from the ordination requirement, and King Charles II, whose permission was needed, accepted this argument; thus, a conflict between Newton's religious views and Anglican orthodoxy was averted. He was appointed at the age of 26.

As accomplished as Newton was as a theoretician, he was less effective as a teacher; his classes were almost always empty. Humphrey Newton, his sizar (assistant), noted that Newton would arrive on time and, if the room was empty, he would reduce his lecture time in half from 30 to 15 minutes, talk to the walls, then retreat to his experiments, thus fulfilling his contractual obligations. For his part Newton enjoyed neither teaching nor students. Over his career he was only assigned three students to tutor and none were noteworthy.

Newton was elected a Fellow of the Royal Society (FRS) in 1672. In 1672, and again in 1681, Newton published a revised, corrected, and amended edition of the Geographia Generalis, a geography textbook first published in 1650 by the then-deceased Bernhardus Varenius. In the Geographia Generalis, Varenius attempted to create a theoretical foundation linking scientific principles to classical concepts in geography, and considered geography to be a mix between science and pure mathematics applied to quantifying features of the Earth. While it is unclear if Newton ever lectured in geography, the 1733 Dugdale and Shaw English translation of the book stated Newton published the book to be read by students while he lectured on the subject.

Scientific studies

Mathematics

Newton's work has been said "to distinctly advance every branch of mathematics then studied". His work on calculus, usually referred to as fluxions, began in 1664, and by 20 May 1665 as seen in a manuscript, Newton "had already developed the calculus to the point where he could compute the tangent and the curvature at any point of a continuous curve". His work by 1665 amounted to a systematic calculus that unified differentiation and integration, which he applied to the dynamic analysis of algebraic and transcendental curves, an approach described by scholar Tom Whiteside as "radically novel, indeed unprecedented" and which later directly informed the theory of central-force orbits in the Principia. Another manuscript of October 1666, is now published among Newton's mathematical papers. Newton recorded a definitive tract of calculus in what is called his "Waste Book". Despite this, the notation of Leibniz is recognised as the more convenient notation, being adopted by continental European mathematicians, and after 1820, by British mathematicians.

The historian of science A. Rupert Hall notes that while Leibniz deserves credit for his independent formulation of calculus, Newton was undoubtedly the first to develop it, stating: Hall further notes that in Principia, Newton was able to "formulate and resolve problems by the integration of differential equations" and "in fact, he anticipated in his book many results that later exponents of the calculus regarded as their own novel achievements." Hall notes Newton's rapid development of calculus in comparison to his contemporaries, stating that Newton "well before 1690 . . . had reached roughly the point in the development of the calculus that Leibniz, the two Bernoullis, L'Hospital, Hermann and others had by joint efforts reached in print by the early 1700s".

Despite the convenience of Leibniz's notation, it has been noted that Newton's notation could also have developed multivariate techniques, with his dot notation still widely used in physics. Some academics have noted the richness and depth of Newton's work, such as the physicist Roger Penrose, stating "in most cases Newton's geometrical methods are not only more concise and elegant, they reveal deeper principles than would become evident by the use of those formal methods of calculus that nowadays would seem more direct." The mathematician Vladimir Arnold stated that "Comparing the texts of Newton with the comments of his successors, it is striking how Newton's original presentation is more modern, more understandable and richer in ideas than the translation due to commentators of his geometrical ideas into the formal language of the calculus of Leibniz."

His work extensively uses calculus in geometric form based on limiting values of the ratios of vanishingly small quantities: in the Principia itself, Newton gave demonstration of this under the name of "the method of first and last ratios" and explained why he put his expositions in this form, 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 and in Newton's time "nearly all of it is of this calculus." His use of methods involving "one or more orders of the infinitesimally small" is present in his De motu corporum in gyrum of 1684 and in his papers on motion "during the two decades preceding 1684".

It has been argued that Newton had an imprecise or limited understanding of limits. However, the mathematician Bruce Pourciau contends that in his Principia, Newton actually demonstrated a more sophisticated understanding of limits than he is generally credited with, including being the first to present an epsilon argument.

thumb|upright=0.75|Newton in 1702 by [[Godfrey Kneller]]

Newton had been reluctant to publish his calculus because he feared controversy and criticism. 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. In 1693, the relationship between Duillier and Newton deteriorated and the book was never completed. Starting in 1699, Duillier accused Leibniz of plagiarism. The mathematician John Keill accused Leibniz of plagiarism in 1708 in the Royal Society journal, thereby deteriorating the situation even more. The dispute then broke out in full force in 1711 when the Royal Society proclaimed in a study that it was Newton who was the true discoverer and labelled Leibniz a fraud; it was later found that Newton wrote the study's concluding remarks on Leibniz. Thus began the bitter controversy which marred the lives of both men until Leibniz's death in 1716.

Newton's first major mathematical discovery was the generalised binomial theorem, valid for any exponent, in 1664–65, which has been called "one of the most powerful and significant in the whole of mathematics." He discovered Newton's identities (probably without knowing of earlier work by Albert Girard in 1629), Newton's method, the Newton polygon, and classified cubic plane curves (polynomials of degree three in two variables). Newton is also a founder of the theory of Cremona transformations, and he made substantial contributions to the theory of finite differences, with Newton regarded as "the single most significant contributor to finite difference interpolation", with many formulas created by Newton. He was the first to state Bézout's theorem, and was also 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. He introduced the Puisseux series. He also provided the earliest explicit formulation of the general Taylor series, which appeared in a 1691-1692 draft of his De Quadratura Curvarum. He originated the Newton-Cotes formulas for numerical integration. Newton's work on infinite series was inspired by Simon Stevin's decimals. He also initiated the field of calculus of variations, being the first to formulate and solve a problem in the field, that being Newton's minimal resistance problem, which he posed and solved in 1685, later publishing it in Principia in 1687. It is regarded as one of the most difficult problems tackled by variational methods prior to the twentieth century. He then used calculus of variations in his solving of the brachistochrone curve problem in 1697, which was posed by Johann Bernoulli in 1696, and which he famously solved in a night, thus pioneering the field with his work on the two problems. He was also a pioneer of vector analysis, as he demonstrated how to apply the parallelogram law for adding various physical quantities and realised that these quantities could be broken down into components in any direction. He is credited with introducing the notion of the vector in his Principia, by proposing that physical quantities like velocity, acceleration, momentum, and force be treated as directed quantities, thereby making Newton the "true originator of this mathematical object".

Newton was probably first to develop a system of polar coordinates in a strictly analytic sense, with his work in relation to the topic being superior, in both generality and flexibility, to any other during his lifetime. His 1671 Method of Fluxions work preceded the earliest publication on the subject by Jacob Bernoulli in 1691. He is also credited as the originator of bipolar coordinates in a strict sense.

A private manuscript of Newton's which dates to 1664–66 contains what is the earliest known problem in the field of geometric probability. The problem dealt with the likelihood of a negligible ball landing in one of two unequal sectors of a circle. In analysing this problem, he proposed substituting the enumeration of occurrences with their quantitative assessment, and replacing the estimation of an area's proportion with a tally of points, which has led to him being credited as founding stereology.

Newton was responsible for the modern origin of Gaussian elimination in Europe. In 1669 to 1670, Newton wrote that all the algebra books known to him lacked a lesson for solving simultaneous equations, which he then supplied. His notes lay unpublished for decades, but once released, his textbook became the most influential of its kind, establishing the method of substitution and the key terminology of 'extermination' (now known as elimination).

In the 1660s and 1670s, Newton found 72 of the 78 "species" of cubic curves and categorised them into four types, systemising his results in later publications. However, a 1690s manuscript later analysed showed that Newton had identified all 78 cubic curves, but chose not to publish the remaining six for unknown reasons.

Newton briefly dabbled in probability. In letters with Samuel Pepys in 1693, they corresponded over the Newton–Pepys problem, which was a problem about the probability of throwing sixes from a certain number of dice. For it, outcome A was that six dice are tossed with at least one six appearing, outcome B that twelve dice are tossed with at least two sixes appearing, and outcome C in which eighteen dice are tossed with at least three sixes appearing. Newton solved it correctly, choosing outcome A, Pepys incorrectly chose the wrong outcome of C. However, Newton's intuitive explanation for the problem was flawed.

Optics

thumb|A replica of the reflecting telescope Newton presented to the [[Royal Society in 1672 (the first one he made in 1668 was loaned to an instrument maker but there is no further record of what happened to it).]]

In 1666, Newton observed that the spectrum of colours exiting a prism in the position of minimum deviation is oblong, even when the light ray entering the prism is circular, which is to say, the prism refracts different colours by different angles. This led him to conclude that colour is a property intrinsic to light – a point which had, until then, been a matter of debate.

From 1670 to 1672, Newton lectured on optics. During this period he investigated the refraction of light, demonstrating that the multicoloured image produced by a prism, which he named a spectrum, could be recomposed into white light by a lens and a second prism. Modern scholarship has revealed that Newton's analysis and resynthesis of white light owes a debt to corpuscular alchemy.

In his work on Newton's rings in 1671, he used a method that was unprecedented in the 17th century, as "he averaged all of the differences, and he then calculated the difference between the average and the value for the first ring", in effect introducing a now standard method for reducing noise in measurements, and which does not appear elsewhere at the time. He extended his "error-slaying method" to studies of equinoxes in 1700, which was described as an "altogether unprecedented method" but differed in that here "Newton required good values for each of the original equinoctial times, and so he devised a method that allowed them to, as it were, self-correct." Newton "invented a certain technique known today as linear regression analysis", as he wrote the first of the two 'normal equations' known from ordinary least squares, averaged a set of data, 50 years before Tobias Mayer, the person originally thought to be the oldest to do so, and he also summed the residuals to zero, forcing the regression line through the average point. He differentiated between two uneven sets of data and may have considered an optimal solution regarding bias, although not in terms of effectiveness.

He showed that coloured light does not change its properties by separating out a coloured beam and shining it on various objects, and that regardless of whether reflected, scattered, or transmitted, the light remains 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. His 1672 paper on the nature of white light and colours forms the basis for all work that followed on colour and colour vision.

thumb|Illustration of a [[dispersive prism separating white light into the colours of the spectrum, as discovered by Newton]]

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 reflective mirrors instead of lenses as the objective to bypass that problem. Building the design, the first known functional reflecting telescope, today known as a Newtonian telescope, involved solving the problem of a suitable mirror material and shaping technique. Newton grounded 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, he was able to produce this first reflecting telescope. It was about eight inches long and it gave a clearer and larger image. Newton reported that he could see the four Galilean moons of Jupiter and the crescent phase of Venus with his new reflecting telescope. which he later expanded into the work Opticks. When Robert Hooke criticised some of Newton's ideas, Newton was so offended that he withdrew from public debate. However, the two had brief exchanges in 1679–80, when Hooke, who had been appointed Secretary of the Royal Society, opened a correspondence intended to elicit contributions from Newton to Royal Society transactions,

In astronomy, Newton is further credited with the realisation that high-altitude sites are superior for observation because they provide the "most serene and quiet Air" above the dense, turbulent atmosphere ("grosser Clouds"), thereby reducing star twinkling.

thumb|upright|Facsimile of a 1682 letter from Newton to [[William Briggs (physician)|William Briggs, commenting on Briggs' A New Theory of Vision]]

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). Despite his known preference of a particle theory, Newton noted that light had both particle-like and wave-like properties in Opticks; he believed that corpuscles must interact with waves in a medium to explain interference patterns and the general phenomenon of diffraction.

In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. The contact with the Cambridge Platonist philosopher Henry More revived his interest in alchemy.

Newton contributed to the study of astigmatism by helping to erect its mathematical foundation through his discovery that when oblique pencils of light undergo refraction, two distinct image points are created. This would later stimulate the work of Thomas Young.

In 1704, Newton published Opticks, in which he expounded his corpuscular theory of light, and included a set of queries at the end, which were posed as unanswered questions and positive assertions. In line with his corpuscle theory, he thought that normal matter was made of grosser corpuscles and speculated that through a kind of alchemical transmutation, with query 30 stating "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?" Opticks has been referred to as one of the "earliest exemplars of experimental procedure". His design was probably built as early as 1677. It is notable for being the first quadrant to use two mirrors, which greatly improved the accuracy of measurements since it provided a stable view of both the horizon and the celestial body at the same time. His quadrant was built but appears to have not survived to the present. John Hadley would later construct his own double-reflecting quadrant that was nearly identical to the one invented by Newton. However, Hadley likely did not know of Newton's original invention, causing confusion regarding originality.

In 1704, Newton constructed and presented a burning mirror to the Royal Society. It consisted of seven concave glass mirrors, each about one foot in diameter. It is estimated that it reached a maximum possible radiant energy of 460 W cm⁻², which has been described as "certainly brighter thermally than a thousand Suns (1,000 × 0.065 W cm⁻²)" based on estimating that the intensity of the Sun's radiation in London in May of 1704 was 0.065 W cm⁻². As a result of the maximum radiant intensity possibly achieved with his mirror he "may have produced the greatest intensity of radiation brought about by human agency before the arrival of nuclear weapons in 1945." David Gregory reported that it caused metals to smoke, boiled gold and brought about the vitrification of slate. William Derham thought it be to the most powerful burning mirror in Europe at the time.

Newton also made early studies into electricity, as he constructed a primitive form of a frictional electrostatic generator using a glass globe, the first to do so with glass instead of sulfur, which had previously been used by scientists such as Otto von Guericke to construct their globes. He detailed an experiment in 1675 that showed when one side of a glass sheet is rubbed to create an electric charge, it attracts "light bodies" to the opposite side. He interpreted this as evidence that electric forces could pass through glass. Newton also reported to the Royal Society that glass was effective for generating static electricity, classifying it as a "good electric" decades before this property was widely known. His idea in Opticks that optical reflection and refraction arise from interactions across the entire surface is seen as a precursor to the field theory of the electric force. His theory of nervous transmission had an immense influence on the work of Luigi Galvani, as Newton's theory focused on electricity as a possible mediator of nervous transmission, which went against the prevailing Cartesian hydraulic theory of the time. He was also the first to present a clear and balanced theory for how both electrical and chemical mechanisms could work together in the nervous system. Newton's mass-dispersion model, ancestral to the successful use of the least action principle, provided a credible framework for understanding refraction, particularly in its approach to refraction in terms of momentum.

In Opticks, Newton introduced prisms as beam expanders and multiple-prism arrays, prismatic configurations that nearly 278 years later were incorporated into tunable lasers, where multiple-prism beam expanders became central to the development of narrow-linewidth systems. The use of these prismatic beam expanders led to the multiple-prism dispersion theory.

Newton was the first to theorise the Goos–Hänchen effect, an optical phenomenon in which linearly polarised light undergoes a small lateral shift when totally internally reflected. He provided both experimental and theoretical explanations for it using a mechanical model.

Science came to realise the difference between perception of colour and mathematisable optics. The German poet and scientist Johann Wolfgang von Goethe could not shake the Newtonian foundation but "one hole Goethe did find in Newton's armour, ... Newton had committed himself to the doctrine that refraction without colour was impossible. He, therefore, thought that the object-glasses of telescopes must forever remain imperfect, achromatism and refraction being incompatible. This inference was proved by Dollond to be wrong."

thumb|upright|Engraving of Portrait of Newton by [[John Vanderbank]]

Philosophiæ Naturalis Principia Mathematica

thumb|upright=1.25|Newton's own copy of [[Philosophiæ Naturalis Principia Mathematica|Principia with Newton's hand-written corrections for the second edition, now housed in the Wren Library at Trinity College, Cambridge]]

Newton had been developing his theory of gravitation as far back as 1665. In 1679, he returned to his work on celestial mechanics by considering gravitation and its effect on the orbits of planets with reference to Kepler's laws of planetary motion. 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. After his exchanges with Robert 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. He shared his results with Edmond Halley and the Royal Society in , a tract written on about nine sheets which was copied into the Royal Society's Register Book in December 1684. As part of this work, Newton also coined the term centripetal force. This tract contained the nucleus that Newton would develop and expand to form the Principia.

The was published on 5 July 1687 with encouragement and financial help from Halley. In this work, Newton stated the three universal laws of motion. Together, these laws describe the relationship between any object, the forces acting upon it and the resulting motion, laying the foundation for classical mechanics. His work achieved the first great unification in physics.

In the same work, Newton presented a calculus-like method of geometrical analysis using '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 Earth's spheroidal figure, 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. He provided the first calculation of the age of Earth by experiment, and also described a precursor to the modern wind tunnel.

Newton identified two "principal cases of attraction"—the inverse-square law and a central force proportional to distance—showing that both yield stable conic-section orbits and that spherically symmetric bodies behave as if their mass were concentrated at a point; in modern terms, this linear force law is mathematically equivalent to the force associated with the cosmological constant.

Through Book II of the Principia, Newton was an important pioneer of fluid mechanics, and later analysis has shown that of its 53 propositions almost all are correct, with only two or three open to question. Propositions 1–18 of the book are the first comprehensive treatment of motion under resistance proportional to velocity or its square, leading the scholar Richard S. Westfall to remark that 'almost without precedent, Newton created the scientific treatment of motion under conditions of resistance, that is, of motion as it is found in the world'. In Section IX of Book II, he formulated the linear relation between viscous resistance and velocity gradient that now defines a Newtonian fluid, despite his experiments giving little direct insight into viscosity. Newton also discussed the circular motion of fluids and was the first to analyse Couette flow, initially in Proposition 51 for a single rotating cylinder and extended in Corollary 2 to the flow between two concentric cylinders. Further, he was the first to analyse the resistance of axisymmetric bodies moving through a rarefied medium. He further determined the masses and densities of Jupiter and Saturn, putting all four celestial bodies (Sun, Earth, Jupiter, and Saturn) on the same comparative scale. This achievement by Newton has been called "a supreme expression of the doctrine that one set of physical concepts and principles applies to all bodies on earth, the earth itself, and bodies anywhere throughout the universe". 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.)

Newton was criticised for introducing "occult agencies" into science because of his postulate of an invisible force able to act over vast distances. 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 phenomenon 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 phenomenon. (Here he used what became his famous expression .)

With the , Newton became internationally recognised. He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier.

Other significant work

Newton studied heat and energy flow, formulating an empirical law of cooling which states that the rate at which an object cools is proportional to the temperature difference between the object and its surrounding environment. It was first formulated in 1701, being the first heat transfer formulation and serves as the formal basis of convective heat transfer, later being incorporated by Joseph Fourier into his work.

Philosophy of science

Of an estimated ten million words of writing in Newton's papers, about one million deal with alchemy. Many of Newton's writings on alchemy are copies of other manuscripts, with his own annotations. Some of the content contained in Newton's papers could have been considered heretical by the church. John Maynard Keynes was one of about three dozen bidders who obtained part of the collection at auction. Keynes went on to reassemble an estimated half of Newton's collection of papers on alchemy before donating his collection to Cambridge University in 1946.

All of Newton's known writings on alchemy are currently being put online in a project undertaken by Indiana University: "The Chymistry of Isaac Newton" and has been summarised in a book.

Bibliography

Reprinted, Dover Publications, 1960, , and Project Gutenberg, 2010.

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Digital archives

The Newton Project from University of Oxford
Newton's papers in the Royal Society archives
The Newton Manuscripts at the National Library of Israel
Newton Papers (currently offline) from Cambridge Digital Library
Bernhardus Varenius, Geographia Generalis, ed. Isaac Newton, 2nd ed. (Cambridge: Joann. Hayes, 1681) from the Internet Archive