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Isaac Newton

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Isaac Newton

Sir Isaac Newton, PRS (25 December 1642 (OS) – 20 March 1727 (OS) / 4 January, 1643 (NS) – 31 March 1727 (NS)) was an English physicist, mathematician, astronomer, inventor, philosopher and alchemist. A man of profound genius, he is widely regarded as one of the most influential scientists in history. He is associated with the scientific revolution and the advancement of heliocentrism.

Among his scientific accomplishments, Newton wrote the Philosophiae Naturalis Principia Mathematica, wherein he described universal gravitation and, via his laws of motion, laid the groundwork for classical mechanics. With Gottfried Leibniz he shares credit for the development of infinitesimal calculus. Newton was the first to promulgate a set of natural laws that could govern both terrestrial motion and celestial motion, and is credited with providing mathematical substantiation for Kepler's laws of planetary motion, which he expanded by arguing that orbits (such as those of comets) could include all conic sections (such as the ellipse, hyperbola, and parabola).

Newton was the first to realise that the spectrum of colours observed when white light passed through a prism is inherent in the white light and not added by the prism (as Roger Bacon had claimed in the 13th century), and also notably argued that light is composed of particles.

Newton also developed a law of cooling, proved the binomial theorem, and discovered the principles of conservation of momentum and angular momentum.

Newton is regarded by many as having "unrivalled mathematical genius" [see Dampier & Dampier]. The mathematician Joseph Louis Lagrange (1736-1813), Director of the Berlin Academy of Sciences, said this about Newton:

"Newton was the greatest genius that ever existed and the most fortunate, for we cannot find more than once a system of the world to establish." [See Shapley.]

Biography

Early years

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Newton was born in Woolsthorpe-by-Colsterworth (at Woolsthorpe Manor), a hamlet in the county of Lincolnshire. Newton was prematurely born and no one expected him to live; indeed, his mother, Hannah Ayscough Newton, is reported to have said that his body at that time could have fit inside a quart mug (Bell, 1937). His father, Isaac, had died three months before Newton's birth. When Newton was two years old, his mother went to live with her new husband, leaving her son in the care of his grandmother.

According to E.T. Bell (1937, Simon and Schuster) and H. Eves:

Newton began his schooling in the village schools and was later sent to Grantham Grammar School where he became the top boy in the school. At Grantham he lodged with the local apothecary, William Clarke and eventually became engaged to the apothecary's stepdaughter, Anne Storer, before he went off to Cambridge University at the age of 19. As Newton became engrossed in his studies, the romance cooled and Miss Storer married someone else. It is said he kept a warm memory of this love, but Newton had no other recorded 'sweethearts' and never married.
Engraving after Enoch Seeman's 1726 portrait of Newton

From the age of twelve until he was seventeen, Newton was educated at Grantham Grammar School. His family then removed him from school and attempted to make a farmer of him. However he was thoroughly unhappy with the work and eventually with the help of his uncle and of his schoolteacher, he managed to persuade his mother to send him back to school so that he might complete his schooling. This he did at the age of eighteen, achieving an admirable final report. His teacher said:

His genius now begins to mount upwards apace and shine out with more strength. He excels particularly in making verses. In everything he undertakes, he discovers an application equal to the pregnancy of his parts and exceeds even the most sanguine expectations I have conceived of him.

In 1661 he joined Trinity College, Cambridge, where his uncle William Ayscough had studied. At that time, the college's teachings were based on those of Aristotle, but Newton preferred to read the more advanced ideas of modern philosophers such as Descartes, Galileo, Copernicus and Kepler. In 1665 he discovered the binomial theorem and began to develop a mathematical theory that would later become calculus. Soon after Newton had obtained his degree in 1665, the University closed down as a precaution against the Great Plague. For the next two years Newton worked at home on calculus, optics and gravitation. He later continued his studies at Woolsthorpe Manor.

The popular tradition has it that Newton was sitting under an apple tree when an apple fell on his head, and that this made him understand that earthly and celestial gravitation are the same. A contemporary writer, William Stukeley, recorded in his Memoirs of Sir Isaac Newton's Life a conversation with Newton in Kensington on 15 April 1726, in which Newton recalled "when formerly, the notion of gravitation came into his mind. It was occasioned by the fall of an apple, as he sat in contemplative mood. Why should that apple always descend perpendicularly to the ground, thought he to himself. Why should it not go sideways or upwards, but constantly to the earth's centre." In similar terms, Voltaire wrote in his Essay on Epic Poetry (1727), "Sir Isaac Newton walking in his gardens, had the first thought of his system of gravitation, upon seeing an apple falling from a tree." These accounts are exaggerations of Newton's own tale about sitting by a window in his home (Woolsthorpe Manor) and watching an apple fall from a tree. It is now generally considered probable that even this story was invented by Newton in later life, to illustrate how he drew inspiration from everyday events.

Middle years

Mathematical research

A reputed descendent of Newton's apple tree, found in the Botanic Gardens in Cambridge, England.

Newton became a fellow of Trinity College in 1667. In the same year he circulated his findings in De Analysi per Aequationes Numeri Terminorum Infinitas (On Analysis by Infinite Series), and later in De methodis serierum et fluxionum (On the Methods of Series and Fluxions), whose title gave the name to his "method of fluxions".

Newton is generally credited as the discoverer of the binomial theorem, an essential step toward the development of modern analysis. Newton and Gottfried Leibniz developed the theory of calculus independently, using different notations. Although Newton had worked out his own method before Leibniz, the latter's notation and "Differential Method" were superior, and were generally adopted throughout the world. Though Newton belongs among the brightest scientists of his era, the last twenty-five years of his life were marred by a bitter dispute with Leibniz, whom he accused of plagiarism.

He was elected Lucasian professor of mathematics in 1669. Any fellow of Cambridge or Oxford had to be ordained at the time. 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 normal ordination requirement, and Charles II, whose permission was needed, accepted this argument. This prevented the conflict that would have occurred between his religious views and the orthodoxy of the church.

Optics

From 1670 to 1672 he lectured on optics. 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.

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 the colours we observe are the result of how objects interact with the incident already-coloured light, not the result of objects generating the colour. For more details, see Newton's theory of colour.

A replica of Newton's 6 inch reflecting telescope of 1672 for the Royal Society.

From this work he concluded that any refracting telescope would suffer from the dispersion of light into colours, and invented a reflecting telescope (today, known as a Newtonian telescope) to bypass that problem. By grinding his own mirrors, using Newton's rings to judge the quality of the optics for his telescopes, he was able to produce a superior instrument to the refracting telescope, due primarily to the wider diameter of the mirror. (Only later, as glasses with a variety of refractive properties became available, did achromatic lenses for refractors become feasible.) In 1671 the Royal Society asked for a demonstration of his reflecting telescope. 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. The two men remained enemies until Hooke's death.

In one experiment, to prove that colour perception is caused by pressure on the eye, Newton slid a darning needle around the side of his eye until he could poke at its rear side, dispassionately noting "white, darke & coloured circles" so long as he kept stirring with "ye bodkin."

Newton argued that light is composed of particles; thus he could not explain the diffraction of light. Later physicists instead favoured a wave explanation of light to account for diffraction. Today's quantum mechanics recognises a "wave-particle duality"; however photons bear very little semblance to Newton's corpuscles (e.g., corpuscles refracted by accelerating toward the denser medium).

Newton is believed to have been the first to explain precisely the formation of the rainbow from water droplets dispersed in the atmosphere in a rain shower. Figure 15 of Part II of Book One of the Opticks shows a perfect illustration of how this occurs.

In his Hypothesis of Light of 1675, Newton posited the existence of the ether to transmit forces between particles. Newton was in contact with Henry More, the Cambridge Platonist who was born in Grantham, on alchemy, and now his interest in the subject revived. 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." Newton's interest in alchemy cannot be isolated from his contributions to science.2 (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 wrote Opticks, in which he expounded his corpuscular theory of light. The book is also known for the first exposure of the idea of the interchangeability of mass and energy: "Gross bodies and light are convertible into one another...". Newton also constructed primitive form of a frictional electrostatic generator, using a glass globe (Optics, 8th Query).

Gravity and motion

For a detailed discussion on the writing of Principia, see the writing of Principia Mathematica.
Newton's own copy of his Principia, with hand written corrections for the second edition.

In 1679, Newton returned to his work on mechanics, i.e., gravitation and its effect on the orbits of planets, with reference to Kepler's laws of motion, and consulting with Hooke and Flamsteed on the subject. He published his results in De Motu Corporum (1684). This contained the beginnings of the laws of motion that would inform the Principia.

The Philosophiae Naturalis Principia Mathematica (now known as the Principia) was published on 5 July 16871) with encouragement and financial help from Edmond Halley. In this work Newton stated the three universal laws of motion that were not to be improved upon for more than two hundred years. He used the Latin word gravitas (weight) for the force that would become known as gravity, and defined the law of universal gravitation. In the same work he presented the first analytical determination, based on Boyle's law, of the speed of sound in air.

With the Principia, Newton became internationally recognised. He acquired a circle of admirers, including the Swiss-born mathematician Nicolas Fatio de Duillier, with whom he formed an intense relationship that lasted until 1693. The end of this friendship led Newton to a nervous breakdown.

Later life

File:Newtonshair.JPG
A lock of Newton's hair in Trinity College, Cambridge.

In the 1690s Newton wrote a number of religious tracts dealing with the literal interpretation of the Bible. Henry More's belief in the infinity of the universe and rejection of Cartesian dualism may have influenced Newton's religious ideas. A manuscript he sent to John Locke in which he disputed the existence of the Trinity was never published. Later works — The Chronology of Ancient Kingdoms Amended (1728) and Observations Upon the Prophecies of Daniel and the Apocalypse of St. John (1733) — were published after his death. He also devoted a great deal of time to alchemy (see above)2.

Newton was also a member of the Parliament of England from 1689 to 1690 and in 1701, but his only recorded comments were to complain about a cold draft in the chamber and request that the window be closed.

Newton moved to London to take up the post of warden of the Royal Mint in 1696, a position that he had obtained through the patronage of Charles Montagu, 1st Earl of Halifax, then Chancellor of the Exchequer. He took charge of England's great recoining, somewhat treading on the toes of Master Lucas (and finagling Edmond Halley into deputy comptroller of the temporary Chester branch). Newton became Master of the Mint upon Lucas' death in 1699. These appointments were intended as sinecures, but Newton took them seriously, exercising his power to reform the currency and punish clippers and counterfeiters. He retired from his Cambridge duties in 1701. Ironically, it was his work at the Mint, rather than his contributions to science, which earned him a knighthood. Newton was knighted by Queen Anne in 1705.

Newton was made President of the Royal Society in 1703 and an associate of the French Académie des Sciences. In his position at the Royal Society, Newton made an enemy of John Flamsteed, the Astronomer Royal, by attempting to steal his catalogue of observations.

Newton died in London and was buried in Westminster Abbey. It is believed Newton never had a romantic relationship, and he is said to have died a virgin. There is some speculation that Newton had Asperger syndrome, a form of autism. See People speculated to have been autistic. His niece, Catherine Barton Conduitt3, served as his hostess in social affairs at his house on Jermyn Street in London; he was her "very loving Uncle"4, according to his letter to her when she was recovering from smallpox.

Religious views

For a detailed discussion, please see Isaac Newton's religious views and Isaac Newton's occult studies
Isaac Newton (Bolton, Sarah K. Famous Men of Science. NY: Thomas Y. Crowell & Co., 1889)

The law of gravity became Newton's best-known discovery. He warned against using it to view the universe as a mere machine, like a great clock. He said, "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."

His scientific fame notwithstanding, the Bible was Newton's greatest passion. He devoted more time to the study of Scripture than to science, and said, "I have a fundamental belief in the Bible as the Word of God, written by those who were inspired. I study the Bible daily." Newton himself wrote works on textual criticism, most notably An Historical Account of Two Notable Corruptions of Scripture. He also attempted, unsuccessfully, to find hidden messages within the Bible (See Bible code).

Newton is often accused of being a unitarian and arian, and not believing in the church's doctrine of divine trinity. However, T.C. Pfizenmaier argued that he more likely held the Eastern Orthodox view of the Trinity rather than the Western one held by Roman Catholics, Anglicans and most Protestants.7 In his own day, he was also accused of being a Rosicrucian (as were many in the Royal Society and in the court of Charles II).Template:Fn

In his own lifetime, Newton wrote more on religion than he did on natural science. He believed in a rationally emanent world, but he rejected the hylozoism implicit in Leibniz and Baruch Spinoza. Thus, the ordered and dynamically informed universe could be understood, and must be understood, by an active reason, but this universe, to be perfect and ordained, had to be regular.

Newton's effect on religious thought

Newton and Robert Boyle’s mechanical philosophy was promoted by rationalist pamphleteers as a viable alternative to the pantheists and enthusiasts, and was accepted hesitantly by orthodox preachers as well as dissident preachers like the latitudinarians.Template:Fn Thus, the clarity and simplicity of science was seen as a way to combat the emotional and metaphysical superlatives of both superstitious enthusiasm and the threat of atheismTemplate:Fn, and, at the same time, the second wave of English deists used Newton's discoveries to demonstrate the possibility of a "Natural Religion."

The attacks made against pre-Enlightenment "magical thinking," and the mystical elements of Christianity, were given their foundation with Boyle’s mechanical conception of the universe. Newton gave Boyle’s ideas their completion through mathematical proofs, and more importantly was very successful in popularizing them.Template:Fn Newton refashioned the world governed by an interventionist God into a world crafted by a God that designs along rational and universal principles.Template:Fn These principles were available for all people to discover, allowed man to pursue his own aims fruitfully in this life, not the next, and to perfect himself with his own rational powers.Template:Fn The perceived ability of Newtonians to explain the world, both physical and social, through logical calculations alone is the crucial idea in the disenchantment of Christianity.Template:Fn

Newton saw God as the masterful creator whose existence could not be denied in the face of the grandeur of all creation.5'6'Template:Fn But the unforeseen theological consequence of his conception of God, as Leibniz pointed out, was that God was now entirely removed from the world’s affairs, since the need for intervention would only evidence some imperfection in God’s creation, something impossible for a perfect and omnipotent creator.Template:Fn Leibniz's theodicy cleared God from the responsibility for "l'origine du mal" by making God removed from participation in his creation. The understanding of the world was now brought down to the level of simple human reason, and humans, as Odo Marquard argued, became responsible for the correction and elimination of evil.Template:Fn

On the other hand, latitudinarian and Newtonian ideas taken too far resulted in the millenarians, a religious faction dedicated to the concept of a mechanical universe, but finding in it the same enthusiasm and mysticism that the Enlightenment had fought so hard to extinguish.Template:Fn

Newton versus the counterfeiters

Newton estimated that 20% of the coins taken in during The Great Recoinage were counterfeit. Counterfeiting was treason, punishable by death by drawing and quartering. As gruesome as the penalties were, the courts were not arbitrary or capricious. The rights of free men had a long tradition in England and the crown had to prove its case to a jury. The law also allowed for plea bargaining. Convictions of the most flagrant criminals could be maddeningly impossible to achieve. Newton was equal to the task.

He assembled facts and proved his theories with the same brilliance in law that he had shown in science. He gathered much of that evidence himself. Disguised, he hung out at bars and taverns. For all the barriers placed to prosecution, and separating the branches of government, English law still had strong, old customs of authority. Newton got himself made a justice of the peace. Between June 1698 and Christmas 1699, he conducted some 200 cross-examinations of witnesses, informers and suspects. He obtained the confessions he needed. While he could not resort to open torture, whatever means he did use must have been fearsome because Newton himself later ordered all records of these interrogations to be destroyed. However he did it, Newton won his convictions. In February 1699, he had ten prisoners waiting to be executed.

Newton's greatest triumph as the king's attorney was against William Chaloner. Chaloner was a rogue with a devious intelligence. He set up phony conspiracies of Catholics and then turned in the hapless conspirators whom he entrapped. Chaloner made himself rich enough to posture as a gentleman. Petitioning Parliament, Chaloner accused the Mint of providing tools to counterfeiters. (This charge was made also by others.) He proposed that he be allowed to inspect the Mint's processes in order to improve them. He petitioned Parliament to adopt his plans for a coinage that could not be counterfeited. All the time, he struck false coins, or so Newton eventually proved to a court of competent jurisdiction. On March 23, 1699, Chaloner was hanged, drawn, and quartered.

Enlightenment philosophes

Enlightenment philosophers chose a short history of scientific predecessors—Galileo, Boyle, and Newton principally—as the guides and guarantors of their applications of the singular concept of Nature and Natural Law to every physical and social field of the day. In this respect, the lessons of history and the social structures built upon it could be discarded.Template:Fn

It was Newton’s conception of the universe based upon Natural and rationally understandable laws that became the seed for Enlightenment ideology. Locke and Voltaire applied concepts of Natural Law to political systems advocating intrinsic rights; the physiocrats and Adam Smith applied Natural conceptions of psychology and self-interest to economic systems, and sociologists critiquing the current social order fit history into Natural models of progress.

Newton's legacy

Statue of Newton in the antechapel of Trinity College, Cambridge

Newton's laws of motion and gravity provided a basis for predicting a wide variety of different scientific or engineering situations, especially the motion of celestial bodies. His calculus proved vitally important to the development of further scientific theories. Finally, he unified many of the isolated physics facts that had been discovered earlier into a satisfying system of laws. Newton's conceptions of gravity and mechanics, though not entirely correct in light of Einstein's Theory of Relativity, still represent an enormous step in the evolution of human understanding of the universe. For this reason, he is generally considered one of history's greatest scientists, ranking alongside such figures as Einstein and Carl Friedrich Gauss.

Great Britain went on to an unofficial gold standard in 1717 when Newton, then Master of the Mint, established a fixed price of £3.17.10 ½d per standard (22 carat) troy ounce, equal to £4.4.11 ½d per fine ounce. Under the gold standard the value of the pound (measured in gold weight) remained largely constant until the beginning of the 20th century.

Newton is reputed to have invented the cat flap. This was said to be done so that he would not have to disrupt his optical experiments, conducted in a darkened room, to let his cat in or out.

Newtonmas is a holiday celebrated by some scientists as an alternative to Christmas, taking advantage of the fact that Newton's birthday falls on December 25.

Fictional appearances

Isaac Newton appears in many works of fiction. He is the hero of Rubrique-à-brac, a French comic strip by Marcel Gotlieb. An ongoing gag involves various depictions of the legend that he discovered the law of gravity due to an apple falling on his head. Newton also figures as a major character in Neal Stephenson's Baroque Cycle and in Philip Kerr's novel, Dark Matter.

Newton has a cameo role, along with Stephen Hawking and Albert Einstein, in a poker game in an episode of Star Trek: The Next Generation during season 6. Newton is notable in that scene for being the only scientist without a sense of humour. He also takes offence at the notion that the story of the apple would be fictitious. He also appears in an episode of Star Trek: Voyager where it is claimed that a member of the Q Continuum shook the tree he was sitting under, causing the apple to fall.

One of the more bizarre fictional apperances have been made in a Japanese animated show Vision of Escaflowne, where the main antagonist, Dornkirk, is revealed to be a 200+ year-old Isaac Newton.

Writings by Newton

Short Chronicle, The System of the World, Optical Lectures, Universal Arithmetic, The Chronology of Ancient Kingdoms, Amended and De mundi systemate were published posthumously in 1728.

Notes

  • Note 1: The remainder of the dates in this article follow the Gregorian calendar.
  • Note 2: Westfall (pp. 530–531) notes that Newton apparently abandoned his alchemical researches.
  • Note 3: Westfall, p. 44.
  • Note 4: Westfall, p. 595.
  • Note 5: Principia, Book III; cited in; Newton’s Philosophy of Nature: Selections from his writings, p. 42, ed. H.S. Thayer, Hafner Library of Classics, NY, 1953.
  • Note 6: A Short Scheme of the True Religion, manuscript quoted in Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton by Sir David Brewster, Edinburgh, 1850; cited in; ibid, p. 65.
  • Note 7: Pfizenmaier, T.C., "Was Isaac Newton an Arian?" Journal of the History of Ideas 68(1):57–80, 1997.
  • Template:Fnb Yates, Frances A. The Rosicrucian Enlightenment. London: Routledge and Kegan Paul, 1972.
  • Template:Fnb Jacob, Margaret C. The Newtonians and the English Revolution: 1689-1720. p28.
  • Template:Fnb Jacob, Margaret C. The Newtonians and the English Revolution: 1689-1720. p37 and p44.
  • Template:Fnb Westfall, Richard S. Science and Religion in Seventeenth-Century England. Yale University Press, New Haven: 1958. p200.
  • Template:Fnb Fitzpatrick, Martin. ed. Knud Haakonssen. “The Enlightenment, politics and providence: some Scottish and English comparisons.” Enlightenment and Religion: Rational Dissent in eighteenth-century Britain. Cambridge University Press, Cambridge: 1996. p64.
  • Template:Fnb Frankel, Charles. The Faith of Reason: The Idea of Progress in the French Enlightenment. King’s Crown Press, New York: 1948. p1.
  • Template:Fnb Germain, Gilbert G. A Discourse on Disenchantment: Reflections on Politics and Technology. p28.
  • Template:Fnb Webb, R.K. ed. Knud Haakonssen. “The emergence of Rational Dissent.” Enlightenment and Religion: Rational Dissent in eighteenth-century Britain. Cambridge University Press, Cambridge: 1996. p19.
  • Template:Fnb Westfall, Richard S. Science and Religion in Seventeenth-Century England. p201.
  • Template:Fnb Marquard, Odo. "Burdened and Disemburdened Man and the Flight into Unindictability," in Farewell to Matters of Principle. Robert M. Wallace trans. London: Oxford UP, 1989.
  • Template:Fnb Jacob, Margaret C. The Newtonians and the English Revolution: 1689-1720. p100-101.
  • Template:Fnb Jacob, Margaret C. The Newtonians and the English Revolution: 1689-1720. p61.
  • Template:Fnb Cassels, Alan. Ideology and International Relations in the Modern World. p2.

See also

Resources

References

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  • "Sir Isaac Newton". School of Mathematics and Statistics, University of St. Andrews, Scotland. March 8. {{cite web}}: Check date values in: |date= and |year= / |date= mismatch (help)
  • "The Newton Project". Imperial College London. March 8. {{cite web}}: Check date values in: |date= and |year= / |date= mismatch (help)
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Further reading

  • John Maynard Keynes, Essays in Biography, W W Norton & Co, 1963, paperback, ISBN 039300189X. Keynes had taken a close interest in Newton and owned many of Newton's private papers.
  • Isaac Newton, Papers and Letters in Natural Philosophy, edited by I. Bernard Cohen ISBN 0-674-46853-8 Harvard 1958,1978
  • Michael H. Hart, The 100, Carol Publishing Group, July 1992, paperback, 576 pages, ISBN 0806513500
  • Simmons, J, The giant book of scientists -- The 100 greatest minds of all time, Sydney: The Book Company, (1996)
  • Isaac Newton (1642-1727), The Principia: a new Translation, Guide by I. Bernard Cohen ISBN 0-520-08817-4 University of California 1999 Warning: common mistranslations exposed!
  • Berlinski, David, Newton's Gift:How Sir Isaac Newton Unlocked the System of our World, ISBN 0684843927 (hardback), also in paperback, Simon & Schuster, 2000
  • Stephen Hawking, ed. On the Shoulders of Giants, ISBN 0-7624-1348-5 Places selections from Newton's Principia in the context of selected writings by Copernicus, Kepler, Galileo and Einstein.
  • James Gleick, Isaac Newton, Knopf, 2003, hardcover, 288 pages, ISBN 0375422331
  • Harlow Shapley, S. Rapport, H. Wright, A Treasury of Science; "Newtonia" pp. 147-9; "Discoveries" pp. 150-4. Harper & Bros., New York, 1946.
  • William C. Dampier & M. Dampier, Readings in the Literature of Science, Harper & Row, New York, 1959.

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