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Isaac Newton
One of the Greatest Scientists of all Time
 
 
 
Dr Subodh Mahanti

 

 

If I have seen further it is by standing on the shoulders of giants.

Isaac Newton


Nature and Nature’s laws lay hid in night

God said, “Let Newton be ! “
And all was light.
Alexander Pope

Nature was to him an open book, whose letters he could read without effort. The conceptions which he used to reduce the material of experience to order seemed to flow spontaneously from experience itself, from the beautiful experiments which he ranged in order like playthings and describes with an affectionate wealth of detail. In one person, he combined the experimenter, the theorist, the mechanic and, not least, the artist in exposition. He stands before us strong, certain, and alone; his joy in creation and his minute precision are evident in every word and every figure.

Albert Einstein in his foreword to a twentieth century edition of Newton’s Opticks

 


Isaac Newton, one of the foremost scientific intellects of all time, single-handedly contributed more to the development of science than any other individual in history. It may not be exaggeration to state that Newton was the single most important contributor to the development of modern science. He surpassed the achievements made together by all the great scientific minds of antiquity by producing a scheme of the universe which was consistent, elegant, and intuitive.

Newton stated explicit principles of scientific methods which applied universally to all branches of science. His methodologies produced a neat balance between theoretical and experimental inquiry and between the mathematical and mechanical approaches. Newton mathematised the entire gamut of physical sciences. He reduced the study of the physical sciences to a rigorous, universal and rational procedure which marked the ushering in of the Age of Reason. The basic principles of scientific investigation stipulated by Newton have survived without any alteration until modern times.

Newton’s methodology was strictly logical. He presented his methodology as a set of four rules for scientific reasoning : 1) We are to admit no more causes of natural things such as are both true and sufficient to explain their appearances; 2) The same natural effects must be assigned to the same causes; 3) Qualities of bodies are to be extended as universal; and 4) Propositions deduced from observations of phenomena should be viewed as accurate until other phenomena contradict them. These four concise and universal rules for investigation were truly revolutionary. By their application Newton was able to unravel virtually all the unsolved problems of his day. Commenting on his approach to science once Newton wrote : “The best and safest way of philosophizing seems to be, first to enquire diligently into the properties of things and to establish those properties by experiments and then to proceed slowly to hypotheses for the explanation of them. For hypotheses should be employed only in explaining the properties of things, but not assumed in determining them; unless so far as they may furnish experiments.”

Newton’s methodologies led the natural philosophers to appreciate the “scientific method” – observation, generatlisation and experimentation – above all other methods of inquiry. Francois Marie Arouet de Voltair (1694-1778), the French writer and philosopher, said : “Newton taught men to examine, weigh, calculate and measure but never to conjecture … He saw, and made people see; but he did not put his fancies in place of truth.”

The scientific revolution that Galileo (1564-1642) had initiated at the beginning of the seventeenth century was triumphantly completed by Newton at the century’s end. Newton’s scientific work brought him great fame. He was idolised, almost deified, in his own lifetime. Newton was not right about everything. For example he thought that `absolute motion’ could exist, which Albert Einstein (1879-1955) later disproved with his theory of relativity. Newton was never on very cordial terms with any of his contemporaries. Since his childhood he remained a loner all his life. He did not marry. He was always slightly paranoid and unquestionably contentious. Newton quarreled often and pettily. His quarrels with Robert Hooke (1635-1703), Christiaan Huygens (1629-95), Gottfried Wilhelm Leinbniz (1646-1716) and John Flamsteed are much discussed episodes in the history of science. Newton encouraged and prompted his friends and followers to join the fray.

Newton was born on 25 December 1642 at a village Woolsthorpe in Lincolnshire in Eastern England. Here it is important to note that when Newton was born, the British Calendar was ten days ahead than the Gregorian Calendar. This is because though the Gregorian Calender was introduced in Catholic countries in 1582 but it was not applied in Britain until 1752.

His father, also Isaac Newton, who was a farmer, died a few months before Newton’s birth. Newton was born prematurely and christened Isaac in memory of his father. Newton’s mother Hannah remarried in 1645 and left him under the care of his maternal grandmother at Woolsthrope. After gaining the rudiments of education at the local school Newton joined the Grammar School at Grantham, where he lived with the family of an apothecary, called Mr. Clark. The Clarks were no ordinary apothecary’s family. Mrs. Clark’s brother Humphrey Babington was a Fellow of Trinity College who spent most of his time at Boothby Pagnell, near Grantham, where he was Rector. The School provided Newton a grounding in the classics mainly Latin with some Greek and a little mathematics. The knowledge of Latin proved to be very useful in Newton’s scientific career. In those days academics across Europe used to communicate in Latin. Many important scientific books were available only in Latin. At the school Newton was a lonely boy. He was not a very good student. Nobody paid much attention to him. One incident in school that had influence on his life was his fight with a larger lad. This lad was the school bully, who also happened to be first in studies as well. The fight ensued after Newton was punched by the bully. Newton fought back, he pushed the bully onto the ground and rubbed his face in the mud. The other students who were watching the fight cheered for Newton as they all hated the bully. Newton found that he could fight better than the bully and this made him think that he could do anything better than the bully. As a result he decided to pay attention to studies to compete. He stood first in his class. At school his greatest delights were solitary study and manufacturing mechanical devices. He made windmills, water-clocks, and sundials. It is said that he invented a four-wheel carriage which was to be moved by a rider. He also caused one of the earliest recorded UFO (Unidentified Flying Object) scares by flying a kite at night with a paper lantern attached to it.

After the death of her second husband in 1656, Newton’s mother came back to Woolsthorpe. Towards the end of 1659 Newton’s mother removed him from school so that he might prepare himself for managing the farm he would one day inherit from his mother. However, Newton proved to be no good in farming. He neglected his work in order to read book. On several occasions he was fined for allowing animals in his care to wander and damage other farmers’ crops. There is an interesting story linked to Newton during the period when he was supposed to practise farming. A steep hill is situated between Grantham and Woolsthorpe. It was a usual practice to dismount and lead one’s horse to the top of the hill before remounting. It is said that one day Newton arrived home with a book in one hand and the bridle in the other, his horse trotting behind him, as he had forgotten to remount. Throughout his life he had this habit of forgetfullness. There are many stories about his forgetfullness. In one story he had invited some of his friends to his house for dinner. They had the dinner and then went to the lounge. After an hour Newton jumped up and announced “we have talked long enough – let’s have dinner”. It was only after finding lot of bones and other leftovers, he did realise to his great embarrassment that they had already taken dinner.

His maternal uncle William Ayscough, Rector of Burton Coggles, wanted Newton to go Trinity College, Cambridge. Ayscoughs was a Cambridge graduate. Newton needed to prepare for getting admitted in Trinity College. So he needed to go back to his school. Henry Stockes, the schoolmaster of the Grammar School offered to take Newton into his own home, without being paid for lodging. In the autumn of 1660 Newton went back to school mainly to prepare for entrance to Cambridge.

He was admitted to Trinity College of the Cambridge University on July 1661. Newton was certainly benefited by the advice and influence of Babington. In those days young gentlemen used to be admitted to the Cambridge University at the tender age of 14 accompanied by a servant to look after them. But Newton entered the Trinity College at the lowest level, as a so-called subsizar, who paid for his keep by acting as a servant himself for the Fellows of the College and even for wealthy students. To be a subsizar was not at all a pleasant experience. Rather at its worst it could be extremely unpleasant. For Newton it was not so unpleasant. He was the servant to Humphrey Babington, who was seldom in residence in Cambridge and so Newton had few menial duties to perform. But at the same time Newton’s status as subsizar was not at all enjoyable.

Newton graduated in 1665. He had displayed no special brilliance. Nobody had an inkling that Newton would become the great unifier of the scientific revolution, drawing from the ideas of Nicolaus Copernicus (1473-1543), Johannes Kepler (1571-1630) and Galileo and others or that he would make great contribution to the fields of optics and mathematics. In 1665 the Great Plague hit London, virtually shutting that city down. Cambridge soon followed. The Cambridge University was temporarily closed. Some students alongwith their tutors moved to the nearby villages. Newton went to live at his mother’s farm in Lincolnshire. The farm was purchased by his grandfather Robert Newton. Newton stayed 18 months at Lincolnshire before he permanently returned to Cambridge in April 1667. It was a forced vacation. This period was Newton’s annus mirabilis (a year regarded as pivotal or crucial). Commenting on this period Newton said : “In those days (1665-67) I was in the prime of my age for invention and minded, Mathematics and Philosophy more than at any time since.” Here Newton began putting together some of his ideas. The results marked the beginning of a long and a fruitful career in science. It is during this forced vacation Newton laid the foundations for the calculus, a mathematical method of calculation that revolutionised scientists’ ability to handle complicated equations. It was also during this period that Newton noticed an apple falling to the ground. There is no evidence to indicate that the apple did hit him on the head as legend claims. Seeing the falling apple Newton started wondering whether the force that pulled the apple towards the Earth is the same force that kept the Moon in its orbit. It marked a major departure from earlier belief held by scientists followed by Aristotle, who insisted that the Earth and the heavens operated on two entirely different sets of laws. But Newton started thinking that there is only one set of universal laws and not two. At Lincolnshire, Newton also carried out a fascinating series of experiments with light.

The Cambridge University was among the best universities when it was founded in the thirteenth century. However, at Newton’s time Cambridge was not a very good place for learning particularly for learning science. Its learning was church-oriented. The only scientific professorship, the Lucasian Chair of Mathematics was established in 1663. Its first incumbent was Isaac Barrow, who was a Professor of Greek. Its only relevant courses were in theology and medicine. So Newton had to depend on his own study. Newton became so absorbed in his studies that often he would forget to eat and would stay up all night at his book. He did not care about his dress and hardly took a bath. He studied the writings of Galileo, Kepler, Descartes and Euclid among others. It is said that he turned to Euclid because he was bothered by his inability to comprehend certain diagram in a book on astrology which he had bought at a fair. However, he thought its propositions as self-evident and thus he put it aside as “trifling book”. He took it up again after being persuaded by his teacher, Isaac Barrow. He received a scholarship in April 1664 which ensured his stay at Cambridge till 1668. Newton received his BA in January 1665 and got his MA degree in 1668.

In 1667 Newton was elected a Fellow of the Trinity College and two years later he was appointed Lucasian Professor of Mathematics succeeding his teacher Dr.Barrow. The post of Lucasian Professor was one of the most desirable appointments in Cambridge. The professorship brought with it an income of 200 pounds a year with no tutorial responsibilities. It was a secure tenure for life. Its incumbent was to give only one course of lectures a year.

In 1672 Newton was elected a Fellow of the Royal Society of London and later that year he published his first scientific paper in the Philosophical Transactions of the Society describing his new theory of light and colour. The paper was titled “New Theory about Light and Colours.” In this paper Newton demonstrated that the ordinary white light was a mixture of the various colours of the spectrum. Though the paper was well received but two leading natural philosophers, Robert Hooke and Christiaan Huygens rejected Newton’s claim by stating that his theory was derived with certainty from experiments alone. Particularly they objected to what they took to be Newton’s attempt to prove by experiment alone that light consists in the motion of small particles or corpuscles rather than in the transmission of waves of pulses. By publishing this paper Newton started a lifelong feud with Hooke.

Newton was a mathematician of incomparable power. In 1696 the Swiss mathematician Johann Bernoulli (1667-1748) posed a problem to the mathematician of Europe, allowing then six months to solve. Newton solved the problem in single night and published it in it Transactions of the Royal Society. Though the paper did not bear Newton’s name but Bernouli was not fooled. He claimed to recognize the author as ‘the lion by his claw’. In 1716 the German mathematician Gottfried Wilhelm Leibniz issued a difficult problem. It is said that Leibniz had devised the complicated problem for the express purpose of stumping Newton. However, Newton solved the problem before going to bed after a day’s work at the Mint.

Newton discovered the generalised form of the bionomial theorem. He wrote about his discovery to Henry Oldenburg in 1676. He did not publish this discovery. It was later published by John Wallis (1616-1703) with due credit given to Newton. Newton laid the foundation for elementary differential and integral calculus. Calculus was also independently discovered by the German philosopher and mathematician Leibniz. However, Newton did not immediately publish it. His work on calculus, Methodis fluxionum (Method of Fluxions) composed between 1670 and 1671, was only published posthumously in 1736. Of course, Newton showed his unpublished works to his friends and colleagues. In fact in 1676 Newton deposited with Oldenburg his epistola prior (first letter) claiming discovery of his method of fluxions in an anagram. The terminology arose from his considering the path of a continuously moving body as a curve made by a continuously moving point. The moving point Newton called a fluent and its velocity he called a fluxion. He denoted fluxion by X and its acceleration as X. However, presently the notation used are that of Leibniz. On the other hand Leibniz published his own work on the differential and integral calculus in 1684 and he did not acknowledge any unpublished work of Newton though he had seen some Newtonian manuscripts on a visit to London in 1673. This started a bitter dispute of priority between Newton and Leibniz. The dispute began in 1700 when Leibniz objected the practice of the followers of Newton referring to him (Leibniz) as the `second inventor’ of the calculus. Leibniz applied to the Royal Society in 1712 to conduct an inquiry into the matter. At that time Newton was the President of the Royal Society. He appointed the committee, decided what evidence it should examine and actually drafted the report himself. What is more he used to refer this report the Commercium epistolicum (1713. On the Exchange of Letters) as an independent justification of his position. Newton’s behaviour was rather shameless. Leibniz and Newton bickered unbecomingly for some years as to who had the idea first. However, in this context it is worthwhile to note what Einstein had to say on this controversy. Einstein wrote : “The differential law is the only form which completely satisfies the modern physicist’s demand for causality. The clear conception of the differential law is one of Newton’s greatest intellectual achievements. It was not merely this conception that was needed but also a mathematical formalism, which existed in a rudimentary way but needed to acquire a systematic form. Newton found this also in the differential and the integral calculus. We need not consider the question whether Leibnitz hit upon the some mathematical methods independently of Newton or not. In any case it was absolutely necessary for Newton to perfect them, since they alone could provide him with the means of expressing his ideas.”

Newton’s masterpiece Philosophiae Principia Mathematica (Mathematical Principles of Natural Philosophy) is considered to be the greatest scientific work ever written. The book originally written in Latin was published in 1687. It did not appear in English until 1729, forty-two years after its original publication and two years after Newton’s death. The book is often referred to as Principia Mathemctica or simply the Principia. Newton was very reticent in publishing and he was extremely sensitive to criticism. It was Edmond Halley (1656-1742) who persuaded Newton to publish the Principia. Halley played an important role in its publication. When the Royal Society could not afford to finance its publication it decided that “Mr. Halley undertake the business of looking after it and printing it at his own charges”. Halley provided the necessary funds from his own pocket. He edited the text, corrected the proofs and saw it through the press.

The publication of Principia represented the culmination of the scientific revolution that had began with Copernicus a century and a half earlier. In this book Newton presented an overall scheme of the universe, one far more elegant and enlightening than any of his predecessors had devised.

Newton’s another famous prediction concerned comets. He stated that comets were not as mysterious as they appeared to be and like planets they also followerd elliptical path around the Sun. However, comet’s path was far more flattened and elongated than followed by the planets and which probably take them far beyond the edges of the solar system. Based on the Newton’s calculation Halley predicated that the comet sighed by him in 1682 (Halley’s comet) would return in 76 years in 1758 and it did return.

The book was divided into three parts. In Book I of Principia, Newton opened with definition of the three laws of motion, now known as Newton’s laws – laws of inertia, acceleration proportional to force and action and reaction. Newton’s first law of motion, which is also known as law of inertia, states that an object at rest tends to stay at rest and an object in motion tends to continue in motion at constant speed in a straight line. Newton second law states that the more force is placed on an object, the more it accelerates but the more heavier it is, the more it resists acceleration. For example it is easier to throw a lighter object than a heavier one. Newton’s third law states that for every action there is an equal and opposite reaction. For example a rocket exerts a downward push on the exhaust gases which push back it upward. And when the upward push of the exhaust gases exceeds the weight of the vehicle, the rocket rises off the launch pad in the air. It was Newton who first differentiated between the mass and the weight of an object. Often these two terms are used interchangeably in everyday language. The mass of a body is its resistance to acceleration or in other words a body’s mass is equivalent to its quantity of inertia. On the other hand the weight of a body is the gravitational force between it and another body. In Book II of Principia Newton presented new scientific philosophy which came to replace Cartesianism. The last part, Book III consisted of applications of the laws and conclusions derived in the first two sections. The Book III included an explanation for tides and a theory of lunar motion. Newton made some interesting projections. Newton had shown that the gravitational forces of the Earth’s various parts combined to form a sphere. But as the Earth spins around its axis, the additional force resulting from the spinning should prevent it to take up a perfect spherical shape there should be bulge at the equator. He even predicted the size of the bulge. In his life time efforts were made to verify the prediction but because of errors in calculation by mapmakers Newton appeared to be wrong. Today we know that Newton was right. In fact his predicted size of the bulge was accurate within one percent.

Newton’s work in physics and celestatial mechanics culminated in the theory of universal gravitation. Newton’s great insight of 1666 was to imagine that the Earth’s gravity extended to the Moon, counterbalancing in centrifugal force. From his law of centrifugal force and Kepler’s third law of planetary motion, Newton deduced that the centrifugal force of the moon or any planet must decreases as the inverse square of its distance from the centre of its motion. Newton’s law of universal gravitation states that every piece of matter attracts every other piece with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. Given the law of gravitation and the laws of motion Newton could explain a wide range of hitherto disparate phenomena such as eccentric orbits of comets, the courses of the tides and their major variation, the precession of the Earth’s axis and the perturbation of the moon by the gravity of the Sun. Newton’s one general law of nature and one system of mechanics reduced to order most of the known problems of astronomy and terrestrial physics.
Newton’s second great book Opticks was published in 1704, though it was completed in the mid-1690s. It is said that Newton had quietly waited to publish it until his arch rival Hook had died. In Opticks Newton observed that white light could be separated by a prism into a spectrum of different colours, each chracterised by a unique refractivity and proposed the corpuscular theory of light. While the Principia was a “hard book” in Newton’s own words, the Opticks was written in easily intelligible language and dealt with ideas, such as light and colour, that everyone could relate to.

In 1669 the first earl of Halifax Charles Montague, Chancellor of the Exchequer offered Newton the post of Warden of the Royal Mint. Newton, who wanted to leave Cambridge, readily accepted the offer. Newton’s appointment was confirmed on 19 March 1696 and he moved to London by the end of April. Montague while informing Newton of his appointment wrote that the post was `worth five or six hundred pounds (a year), and has not too much business, to require more attendance than you may spare’. But Newton took his work very seriously. As Warden he was the number two at the Mint. It was the Master of the Mint who was in charge. However, Thomas Neale, the Master of the Mint, was quite happy to leave all the work to Newton. It was Newton’s duty to pursue the counterfeiters and clippers of his day. Between June 1698 and Christmas of 1699 Newton interviewed 200 witnesses on 123 separate occasions and 27 counterfeiters were executed. At the end of 1699 Thomas Neale died and Newton succeeded him as the Master of the Mint. He held the post until he died. Newton supervised the introduction of a union coinage in 1707 following the union of kingdom of England and Scotland, the issue of new copper coins in 1718, the evaluation of the guinea to 21 shillings in 1717, and a general improvement in the assaying of the currency.

Newton had studied theology quite seriously. Newton strongly believed in the necessity of a God. His theological views are characterised by his belief that the beauty and regularity of the natural world could only “proceed from the counsel and dominion of an intelligent and powerful Being”. He thought that “the supreme God exists necessarily and by the same necessity he exists always and everywhere”. He believed that God periodically intervened to keep the universe going on track. He believed that the foundation of established religion in England was based on corrupted form of the original biblical texts. Further he thought that the concept of the Holy Trinity, placing Jesus Christ on equal footing with god was a false concept. This idea was known as Arianism, after Arius who established the doctrine. This kind of religious belief came in the way of Newton’s taking holy orders - a requisite condition for all Cambridge Fellows. And for Newton also a time came when without ordination he would not be able to continue the Fellowship. Loosing Fellowship meant he would also require to relinquish the Lucasian Chair. But in any case Newton would not take the holy orders because to him worshipping Christ as God would mean idolatry, a moral sin that would put his soul in peril. By the beginning of 1675 Newton was almost sure that he would have to part with Cambridge University. In fact he wrote to Henry Oldenburg, the then Secretary of the Royal Society, requesting him to be excused from paying his subscription to the Royal Society. He wrote, “I am to part with my Fellowship, and as my income contract, I find it will be convenient that I contract my expenses”.

Newton had only one chance that is to petition the king for dispensation from the requirement of ordination. So after obtaining permission of the then Master of Trinity Isaac Barrow Newton petitioned the King, Charles II. Newton sought such dispensation not for himself alone as a special case but for all Lucasian Professors. He argued that the requirement of ordination goes against the spirit of the bequest under which Henry Lucas had established the chair. It had a specific requirement that a holder of the post should not be active in the church. King Charles II, a patron of the Royal Society and lover of science, granted the dispensation in perpetuity, “to give all just encouragement to learned men who are and shall be elected to the said professorship”.

Throughout his life Newton displayed a deep interest in religion and alchemy. Newton spent much of his time in later part of his life in theological speculation, astrology and alchemical research. Newton wrote extensively on religious matters. Among his religious writings discovered after his death were 1000 manuscript pages to nearly 1.5 million words and two completed books. For obvious reasons he kept his writings secret. Much of his life was spent on deep studies of church history, the Bible and the chronology. He wanted to show that the text of the Bible had been corrupted by later Trinitarian editors and a similar corruption was introduced by Athanasius in the fourth century.

In Newton’s library were 138 books on alchemy and his own manuscripts on the subject contained more than 600,000 words. It cannot be said with certainty whether Newton was a genuine alchemist committed to dreams of the philosopher’s stone or his chemical interests led him to practise alchemy. He had established a chemical laboratory in Trinity College. Though he was very much interested in chemistry but he published very little on his chemical works. He published one brief work on chemistry, De nature acidorum (1710 ; On the Nature of Acids). There were also several passages devoted to chemistry scattered among the Queries that Newton added to his Optiks.

On being by asked by Halley that how he managed to make so many discoveries Newton said that he never relied an inspiration or serendipity to give him insight. Once he undertook a problem to solve Newton did not rest until he found out the answers -- he would think relentlessly and explore every angle during every available moment.

Newton became a Member of Parliament in 1689. In 1703, Newton was elected President of the Royal Society, a position he retained until his death. Newton was Knighted by Queen Anne in 1705. Newton was the first scientist to be honoured in this way. However, it is interesting to note that Newton was not Knighted for his scientific achievements.

Newton died on 20 March 1727 and he was buried in Westminister Abbey, on 28 March 1727. Voltair, who witnessed the burial ceremony, said that it was like “the funeral of a king who had done well by his subjects.”

The Latin inscription of Newton’s tom reads “ Mortals ! rejoice at so great an ornament to the human race !” Perhaps no one will disagree that the inscription is fully justified. Newton was also a human like us and this fact alone should challenge the rest of us to reach for height like his.

We would like to end this article by quoting what Einstein wrote on the occasion of the two hundredth anniversary of Newton’s death: “It is just two hundred years ago that Newton closed his eyes. We feel impelled at such a moment to remember this brilliant genius, who determined the course of western thought, research and practice like no one else before or since. Not only was he brilliant as an inventor of certain key methods, but he also had a unique command of the empirical material available in his day, and he was marvelously inventive as regards detailed mathematical and physical methods of proof. For all these reasons he deserves our deepest reverence. The figure of Newton has, however, an even greater importance than his genius warrants because destiny placed him at a turning point in the history of the human intellect. To see this vividly, we have to realise that before Newton there existed no self-contained system of physical causality which was somehow capable of representing any of the deeper features of the empirical world.”

For Further Reading

1. David Brewster, Memoirs of the Life, Writings and Discoveries of Sir Isaac Newton (2 vols.). Edinburgh:Thomas Constable, 1855.
2. E. B. Jourdain, Essays on the Life and Work of Newton. Chicao: Open Court, 1914.
3. Louis Trenchard More, Isaac Newton: Abiography. New york: Charles Scribenar’s Sons, 1934.
4. J. W. N. Sullivan, Isaac Newton,1642-1727. London: Macmillan, 1938.
5. E. N. da C. Andrade, Isaac Newton. London: Parish, 1950.
6. Gale E. Christianson. In the Presence of the Creator: Isaac Newton and His Times. New York: Free Press, 1984.
7. Frank E. Manuel. Portrait of Isaac Newton. Cambridge, Mass.: Harvard University Press, 1965.
8. Alexander Koyre. Newtonian Studies. Cambridge, Mass.: Harvard University Press, 1965.
9. D. T. Whiteside. The Mathematical Works of Isaac Newton (2 vols). New York: Johnson Reprint Corp., 1964.
10. Carl B. Boyer, The Concepts of the Calculus: A Critical and Historical Discussion of the Derivative and the Integral. New York: Columbia University Press, 1939.
11. A. R. Hall, Philosophers at War: The Quarrel between Newton and Leibniz. Cambridge: Cambridge University Press, 1980.
12. A. I. Sabra. Theories of light from Descartes to Newton. London: Oldbourne, 1967.
13. John Herivel. The Background to Newton’s `Principia’. Oxford; Oxford University Press, 1965.
14. B. J. T. Dobbs. The Foundations of Newton’s Alchemy: The Hunting of the Green Lyon. Cambridge: Cambridge University Press, 1975.
15. Frank E. Manuel. Isaac Newton, Historian. Cambridge, Mass.: Harvard University Press, 1963.
16. Frank E. Manuel. The Religion of Isaac Newton. Oxford : Oxford University Press, 1974.
17. Margret Jacob. The Newtonians and the nglish Revolution, 1869-1720. Ithaca, N.Y.: Cornell University Press, 1976.
18. Richard S. Westfall. The Life of Isaac Newton, Cambridge: Cambridge University Press, 1993