Search Results for Sir Isaac Newton


Biographies

  1. Newton biography
    • Sir Isaac Newton .
    • Isaac Newton's life can be divided into three quite distinct periods.
    • The third period (nearly as long as the other two combined) saw Newton as a highly paid government official in London with little further interest in mathematical research.
    • Isaac Newton was born in the manor house of Woolsthorpe, near Grantham in Lincolnshire.
    • (The Gregorian calendar was not adopted in England until 1752.) Isaac Newton came from a family of farmers but never knew his father, also named Isaac Newton, who died in October 1642, three months before his son was born.
    • Although Isaac's father owned property and animals which made him quite a wealthy man, he was completely uneducated and could not sign his own name.
    • Isaac's mother Hannah Ayscough remarried Barnabas Smith the minister of the church at North Witham, a nearby village, when Isaac was two years old.
    • Basically treated as an orphan, Isaac did not have a happy childhood.
    • His grandfather James Ayscough was never mentioned by Isaac in later life and the fact that James left nothing to Isaac in his will, made when the boy was ten years old, suggests that there was no love lost between the two.
    • There is no doubt that Isaac felt very bitter towards his mother and his step-father Barnabas Smith.
    • When examining his sins at age nineteen, Isaac listed:- .
    • Upon the death of his stepfather in 1653, Newton lived in an extended family consisting of his mother, his grandmother, one half-brother, and two half-sisters.
    • From shortly after this time Isaac began attending the Free Grammar School in Grantham.
    • Although this was only five miles from his home, Isaac lodged with the Clark family at Grantham.
    • Isaac was taken away from school but soon showed that he had no talent, or interest, in managing an estate.
    • An uncle, William Ayscough, decided that Isaac should prepare for entering university and, having persuaded his mother that this was the right thing to do, Isaac was allowed to return to the Free Grammar School in Grantham in 1660 to complete his school education.
    • This time he lodged with Stokes, who was the headmaster of the school, and it would appear that, despite suggestions that he had previously shown no academic promise, Isaac must have convinced some of those around him that he had academic promise.
    • Some evidence points to Stokes also persuading Isaac's mother to let him enter university, so it is likely that Isaac had shown more promise in his first spell at the school than the school reports suggest.
    • Another piece of evidence comes from Isaac's list of sins referred to above.
    • which tells us that Isaac must have had a passion for learning.
    • We know nothing about what Isaac learnt in preparation for university, but Stokes was an able man and almost certainly gave Isaac private coaching and a good grounding.
    • There is no evidence that he learnt any mathematics, but we cannot rule out Stokes introducing him to Euclid's Elements which he was well capable of teaching (although there is evidence mentioned below that Newton did not read Euclid before 1663).
    • Anecdotes abound about a mechanical ability which Isaac displayed at the school and stories are told of his skill in making models of machines, in particular of clocks and windmills.
    • Newton entered his uncle's old College, Trinity College Cambridge, on 5 June 1661.
    • Westfall (see [Never at Rest: A Biography of Isaac Newton (1990).',23)">23] or [The Life of Isaac Newton (Cambridge, 1993).',24)">24]) has suggested that Newton may have had Humphrey Babington, a distant relative who was a Fellow of Trinity, as his patron.
    • Newton's aim at Cambridge was a law degree.
    • Newton studied the philosophy of Descartes, Gassendi, Hobbes, and in particular Boyle.
    • It is a fascinating account of how Newton's ideas were already forming around 1664.
    • How Newton was introduced to the most advanced mathematical texts of his day is slightly less clear.
    • According to de Moivre, Newton's interest in mathematics began in the autumn of 1663 when he bought an astrology book at a fair in Cambridge and found that he could not understand the mathematics in it.
    • Returning to the beginning, Newton read the whole book with a new respect.
    • The new algebra and analytical geometry of Viete was read by Newton from Frans van Schooten's edition of Viete's collected works published in 1646.
    • Newton also studied Wallis's Algebra and it appears that his first original mathematical work came from his study of this text.
    • Newton made notes on Wallis's treatment of series but also devised his own proofs of the theorems writing:- .
    • It would be easy to think that Newton's talent began to emerge on the arrival of Barrow to the Lucasian chair at Cambridge in 1663 when he became a Fellow at Trinity College.
    • Certainly the date matches the beginnings of Newton's deep mathematical studies.
    • Despite some evidence that his progress had not been particularly good, Newton was elected a scholar on 28 April 1664 and received his bachelor's degree in April 1665.
    • There, in a period of less than two years, while Newton was still under 25 years old, he began revolutionary advances in mathematics, optics, physics, and astronomy.
    • While Newton remained at home he laid the foundations for differential and integral calculus, several years before its independent discovery by Leibniz.
    • Taking differentiation as the basic operation, Newton produced simple analytical methods that unified many separate techniques previously developed to solve apparently unrelated problems such as finding areas, tangents, the lengths of curves and the maxima and minima of functions.
    • Newton's De Methodis Serierum et Fluxionum was written in 1671 but Newton failed to get it published and it did not appear in print until John Colson produced an English translation in 1736.
    • When the University of Cambridge reopened after the plague in 1667, Newton put himself forward as a candidate for a fellowship.
    • In July 1669 Barrow tried to ensure that Newton's mathematical achievements became known to the world.
    • He sent Newton's text De Analysi to Collins in London writing:- .
    • [Newton] brought me the other day some papers, wherein he set down methods of calculating the dimensions of magnitudes like that of Mr Mercator concerning the hyperbola, but very general; as also of resolving equations; which I suppose will please you; and I shall send you them by the next.
    • Collins showed Brouncker, the President of the Royal Society, Newton's results (with the author's permission) but after this Newton requested that his manuscript be returned.
    • Collins could not give a detailed account but de Sluze and Gregory learnt something of Newton's work through Collins.
    • Barrow resigned the Lucasian chair in 1669 to devote himself to divinity, recommending that Newton (still only 27 years old) be appointed in his place.
    • Shortly after this Newton visited London and twice met with Collins but, as he wrote to Gregory:- .
    • Newton's first work as Lucasian Professor was on optics and this was the topic of his first lecture course begun in January 1670.
    • Every scientist since Aristotle had believed that white light was a basic single entity, but the chromatic aberration in a telescope lens convinced Newton otherwise.
    • When he passed a thin beam of sunlight through a glass prism Newton noted the spectrum of colours that was formed.
    • Newton was led by this reasoning to the erroneous conclusion that telescopes using refracting lenses would always suffer chromatic aberration.
    • In 1672 Newton was elected a fellow of the Royal Society after donating a reflecting telescope.
    • Also in 1672 Newton published his first scientific paper on light and colour in the Philosophical Transactions of the Royal Society.
    • The paper was generally well received but Hooke and Huygens objected to Newton's attempt to prove, by experiment alone, that light consists of the motion of small particles rather than waves.
    • The reception that his publication received did nothing to improve Newton's attitude to making his results known to the world.
    • However, perhaps because of Newton's already high reputation, his corpuscular theory reigned until the wave theory was revived in the 19th century.
    • Newton's relations with Hooke deteriorated further when, in 1675, Hooke claimed that Newton had stolen some of his optical results.
    • Although the two men made their peace with an exchange of polite letters, Newton turned in on himself and away from the Royal Society which he associated with Hooke as one of its leaders.
    • Newton's Opticks appeared in 1704.
    • 'Newton's rings' and .
    • Another argument, this time with the English Jesuits in Liege over his theory of colour, led to a violent exchange of letters, then in 1678 Newton appears to have suffered a nervous breakdown.
    • Newton's greatest achievement was his work in physics and celestial mechanics, which culminated in the theory of universal gravitation.
    • By 1666 Newton had early versions of his three laws of motion.
    • Newton's novel idea of 1666 was to imagine that the Earth's gravity influenced the Moon, counter- balancing its centrifugal force.
    • From his law of centrifugal force and Kepler's third law of planetary motion, Newton deduced the inverse-square law.
    • In 1679 Newton corresponded with Hooke who had written to Newton claiming:- .
    • After his 1679 correspondence with Hooke, Newton, by his own account, found a proof that Kepler's areal law was a consequence of centripetal forces, and he also showed that if the orbital curve is an ellipse under the action of central forces then the radial dependence of the force is inverse square with the distance from the centre.
    • asked Newton what orbit a body followed under an inverse square force, and Newton replied immediately that it would be an ellipse.
    • Halley persuaded Newton to write a full treatment of his new physics and its application to astronomy.
    • Over a year later (1687) Newton published the Philosophiae naturalis principia mathematica or Principia as it is always known.
    • Newton analysed the motion of bodies in resisting and non-resisting media under the action of centripetal forces.
    • Further generalisation led Newton to the law of universal gravitation:- .
    • Newton explained a wide range of previously unrelated phenomena: the eccentric orbits of comets, the tides and their variations, the precession of the Earth's axis, and motion of the Moon as perturbed by the gravity of the Sun.
    • This work made Newton an international leader in scientific research.
    • However this did not stop the universal admiration for Newton's technical expertise.
    • Newton was a staunch Protestant and strongly opposed to what he saw as an attack on the University of Cambridge.
    • When the King tried to insist that a Benedictine monk be given a degree without taking any examinations or swearing the required oaths, Newton wrote to the Vice-Chancellor:- .
    • The Vice-Chancellor took Newton's advice and was dismissed from his post.
    • However Newton continued to argue the case strongly preparing documents to be used by the University in its defence.
    • The University of Cambridge elected Newton, now famous for his strong defence of the university, as one of their two members to the Convention Parliament on 15 January 1689.
    • Newton was at the height of his standing - seen as a leader of the university and one of the most eminent mathematicians in the world.
    • After suffering a second nervous breakdown in 1693, Newton retired from research.
    • Newton himself blamed lack of sleep but this was almost certainly a symptom of the illness rather than the cause of it.
    • Newton decided to leave Cambridge to take up a government position in London becoming Warden of the Royal Mint in 1696 and Master in 1699.
    • As Master of the Mint, adding the income from his estates, we see that Newton became a very rich man.
    • Newton did not treat it as such and he made a strong contribution to the work of the Mint.
    • Given the rage that Newton had shown throughout his life when criticised, it is not surprising that he flew into an irrational temper directed against Leibniz.
    • Perhaps all that is worth relating here is how Newton used his position as President of the Royal Society.
    • Newton's assistant Whiston had seen his rage at first hand.
    • Newton was of the most fearful, cautious and suspicious temper that I ever knew.
    • A Poster of Isaac Newton .
    • John Maynard Keynes' Newton, the Man .
    • Newton's Arian beliefs .
    • Flamsteed v Newton .
    • Charles Bossut on Leibniz and Newton .
    • Newton's Principia Preface .
    • John Collins meets Isaac Newton .
    • Newton-Raphson method .
    • Honours awarded to Isaac Newton .
    • Lunar featuresCrater Newton .
    • Paris street namesRue Newton (16th Arrondissement) .
    • Famous Curves: Newton's diverging parabolas .
    • Famous Curves: Trident of Newton .
    • History Topics: Newton's bucket .
    • History Topics: Newton poetry .
    • The Newton Project (UK) .
    • The Newton Project - Canada .
    • Isaac Newton Institute Cambridge .
    • Kevin Brown (More about Newton's birthday) .
    • http://www-history.mcs.st-andrews.ac.uk/Biographies/Newton.html .

  2. Cotes biography
    • Both Newton and Whiston recommended Cotes for the Chair, as did Richard Bentley who was master of Trinity College.
    • For example Newton donated a clock which still survives at Trinity College.
    • Cotes himself wrote a letter to Newton concerning the eclipse in which he explained that his assistant had discovered a method to determine the mid-point of the eclipse and he [Correspondence of Sir Isaac Newton and Professor Cotes (1850).',3)">3]:- .
    • However, his mathematical abilities put him second only to Newton from his generation in England.
    • From 1709 until 1713 much of Cotes' time was taken up editing the second edition of Newton's Principia.
    • He did not simply proof-read the work, rather he conscientiously studied it, gently but persistently arguing points with Newton.
    • For example in [6] a discussion is considered which took place between Cotes and Newton in 1711 concerning the velocity of water flowing from a hole in a cylindrical vessel.
    • Newton gave the following rational approximations (we add decimal values to see their accuracy) .
    • However, toward the end of the task there are signs that they are cooling towards one another (see [Correspondence of Sir Isaac Newton and Professor Cotes (1850).',3)">3] for details of these letters).
    • In particular although Newton thanked Cotes in the first draft of a preface he wrote to this edition, he deleted these thanks for the final publication.
    • These were the methods of Newton which led to establishing how the basic forces of nature operated.
    • It contains (in the words that Cotes used himself in a letter to Newton [Correspondence of Sir Isaac Newton and Professor Cotes (1850).',3)">3]):- .
    • His substantial advances in the theory of logarithms, the integral calculus, in numerical methods particularly interpolation and table construction of integrals for eighteen classes of algebraic functions led Newton to say:- .
    • According to Edleston [Correspondence of Sir Isaac Newton and Professor Cotes (1850).',3)">3], Cotes died of a:- .
    • The second develops Newton's methods of interpolation and was particularly useful in studying orbits of comets.

  3. Maclaurin biography
    • The thesis, which developed Newton's theories, was written by a 14 year old boy at a time when such advanced ideas would only be familiar to a small number of the leading mathematicians.
    • Maclaurin had already shown himself a very strong advocate of the mathematical and physical ideas of Newton, so it was natural that they should meet during Maclaurin's visit to London.
    • It is surprising that some of Newton's biographers, for example A Rupert Hall in his 1992 biography, should declare that Maclaurin and Newton never met.
    • I received the greatest civility from [members of the Royal Society] and particularly from the great Sir Isaac Newton with whom I was very often.
    • Had he forgotten all about them; did he turn a deaf ear to all calls to return; was there something in him, akin to the impenetrable aloofness of Newton, which shut him off from his fellows and his duties at times of mental creativity.
    • The University of Edinburgh sought to appoint someone to a joint professorship with James Gregory and, on 21 August 1725, Newton wrote to Maclaurin offering his support in recommending him for appointment to the post (see [Dictionary of Scientific Biography (New York 1970-1990).
    • In November 1725 Newton wrote to John Campbell, the lord provost of Edinburgh, supporting Maclaurin's appointment (see [Dictionary of Scientific Biography (New York 1970-1990).
    • There is no evidence to suggest that Edinburgh took Newton up on his offer to contribute to Maclaurin's salary.
    • In 1742 Maclaurin published his 2 volume Treatise of fluxions, the first systematic exposition of Newton's methods written as a reply to Berkeley's attack on the calculus for its lack of rigorous foundations.
    • Maclaurin appealed to the geometrical methods of the ancient Greeks and to Archimedes' method of exhaustion in attempting to put Newton's calculus on a rigorous footing.
    • Another work Account of Sir Isaac Newton's discoveries was left incomplete on his death but was published in 1750.

  4. Robins biography
    • In London he was taught by Dr Henry Pemberton, who, at the time, was preparing the third edition of Newton's Principia for publication.
    • In addition to the Greek texts he read works by Fermat, Huygens, de Witt, Sluze, James Gregory, Barrow, Newton, Taylor and Cotes.
    • This paper gave a proof of a result by Isaac Newton on quadratures.
    • On his return to England he published A discourse concerning the nature and certainty of Sir Isaac Newton's method of fluxions and prime and ultimate ratios.
    • Some doubts having lately arisen concerning Sir Isaac Newton's doctrines of fluxions, and of prime and ultimate ratios; this treatise was written with design to give such an idea of both these subjects, as might clear them from uncertainty, without entering into the discussion of any particular objections.
    • He replied in the November part of The Present State of the Republick of Letters arguing that Robins had not faithfully represented the concept of limit as used by Newton.

  5. Emerson biography
    • To this all the noble and valuable discoveries of the last and present age are entirely owing: And by this method Sir Isaac Newton, the worthy inventor, determined and settled the system of the whole visible World.
    • Also in 1770 appeared two works on Newton's fluxions.
    • One was A short comment on Sir I Newton's Principia containing notes upon some difficult places of that excellent book.
    • The second of these works on fluxions was A Defence of Sir Isaac Newton against the objections that have been made to Several Parts of the Principia (1770).
    • In this work he answers objections made by Johann Bernoulli, Daniel Bernoulli and Leonhard Euler as well as defending Newton's right to be considered as the inventor of the "method of fluxions' rather than Leibniz.

  6. Wilkins biography
    • He aimed to [Founders of British science : John Wilkins, Robert Boyle, John Ray, Christopher Wren, Robert Hooke, Isaac Newton (London, 1960).',1)">1]:- .
    • Many at Cambridge regretted Wilkins' departure, particularly Isaac Barrow.
    • The Lord Brouncker, Mr Boyle, Mr Bruce, Sir Robert Moray, Sir Paule Neile, Dr Wilkins, Dr Goddard, Dr Petty, Mr Ball, Mr Rooke, Mr Wren, Mr Hill.
    • It is described in [Founders of British science : John Wilkins, Robert Boyle, John Ray, Christopher Wren, Robert Hooke, Isaac Newton (London, 1960).',1)">1] in the following way:- .
    • As to Wilkins' character, Aarsleff writes in [Founders of British science : John Wilkins, Robert Boyle, John Ray, Christopher Wren, Robert Hooke, Isaac Newton (London, 1960).',1)">1]:- .

  7. Jeans biography
    • Sir James Hopwood Jeans .
    • Jeans was awarded an Isaac Newton Studentship in astronomy and optics, then in 1901 he was elected a Fellow of Trinity.
    • The work examines what Jeans calls the 'mechanical age' from Newton to Einstein the 'new physics' of Planck, Rutherford, and Niels Bohr and 'From appearance to reality' with Bohr, Heisenberg, de Broglie, Schrodinger, and Dirac.

  8. Taylor biography
    • John Taylor was the son of Natheniel Taylor who was recorder of Colchester and a member representing Bedfordshire in Oliver Cromwell's Assembly, while Olivia Tempest was the daughter of Sir John Tempest.
    • Also in 1712 Taylor was appointed to the committee set up to adjudicate on whether the claim of Newton or of Leibniz to have invented the calculus was correct.
    • Returning to the paper, it is a mechanics paper which rests heavily on Newton's approach to the differential calculus.
    • It was, wrote Taylor, due to a comment that Machin made in Child's Coffeehouse when he had commented on using "Sir Isaac Newton's series" to solve Kepler's problem, and also using "Dr Halley's method of extracting roots" of polynomial equations.
    • James Gregory, Newton, Leibniz, Johann Bernoulli and de Moivre had all discovered variants of Taylor's Theorem.
    • The differences in Newton's ideas of Taylor series and those of Gregory are discussed in [Istor.-Mat.

  9. Zeeman biography
    • He served on the SERC Mathematics Committee from 1982 to 1985 and, in 1990, he chaired the committee which set up the Isaac Newton Institute in Cambridge.
    • He continues to serve on the Steering Committee for the Isaac Newton Institute.
    • On 2 October 2006 the London Mathematical Society and the Institute of Mathematics and its Applications announced that the 2006 David Crighton Medal for services to Mathematics and to the Mathematics Community was to be awarded to Professor Sir Christopher Zeeman, F.R.S.:- .
    • He chaired the inaugural Scientific Committee of the Newton Institute that oversaw its creation and chose the programmes during its first ten years.
    • These lectures led Sir Christopher to start the Royal Institution Mathematics Masterclasses for talented young people.

  10. Saunderson biography
    • The Lucasian professor of mathematics at Cambridge at that time was William Whiston who had been appointed to succeed Newton in 1703.
    • Roger Cotes, who was already working at Cambridge when Saunderson began teaching there, became the Plumian Professor of Astronomy and Experimental Philosophy in 1708 and, in the following year, he began editing a second edition of Newton's Principia.
    • As well as getting expert advice from Whiston and Cotes, Saunderson met Newton and was able to learn directly from him about certain difficult points in the text of the Principia.
    • Halley, of course, was a friend of Newton, as was de Moivre, Keill, Machin and Jones.
    • Although the main text is in English, there are included at the end Latin explanations of the main results from Newton's Principia.
    • Its full title is The Method of fluxions applied to a Select Number of Useful Problems, together with the Demonstration of Mr Cotes's forms of Fluents in the second part of his Logometria, the Analysis of the Problems in his Scholium Generale, and an Explanation of the Principal Propositions of Sir Isaac Newton's Philosophy.

  11. Cajori biography
    • After Cajori's death Sir Isaac Newton's "Mathematical principles" of Natural Philosophy and His System of the World was published in 1934.
    • Cajori makes very clear his aim in producing this edition of Newton's Principia which was to make the text readable to modern readers by replacing the archaic language used in the existing English translations of Newton's Latin text.
    • His "improved" language was based on a modernisation of the 1729 Motte translation - without reference to Newton's Latin edition - and contains numerous errors and deviations from the original meaning.
    • Hence, his presentation of Newton neither faithfully serves the modern reader nor the historian of science with regard to Newton's original thoughts.

  12. Hellins biography
    • Some of the greatest mathematicians that this kingdom ever produced, as Sir Isaac Newton, Dr Halley, Mr Cotes, and Mr Simpson, have thought it not beneath them to improve the construction of logarithms, which strongly argues the utility of those artificial numbers, and may suggest to us that the construction of them cannot be much further improved.
    • I answer, that argument, if it has any weight, operates equally against Sir Isaac Newton, Dr Halley, Mr Cotes, and Mr Simpson, and several other ingenious mathematicians; for logarithms were invented, and tables of them constructed, before their time; so that if I should be thought to have misemployed my time in improving the computation of these artificial numbers, I have some consolation in thinking that I have therein followed the example of the very respectable company just mentioned.

  13. De L'Hopital biography
    • Although others such as Huygens, Leibniz and Newton knew this, it was thought in Paris to be an important open question so l'Hopital, although probably one of the best mathematicians in France, realised he could learn much from Bernoulli.
    • He was also aware of Newton's contributions, writing:- .
    • I must here in justice own (as Mr Leibniz himself has done in 'Journal des Scavans' for August 1694) that the learned Sir Isaac Newton likewise discovered something like the Calculus Differentialis ..
    • The fact that this problem was solved independently by Newton, Leibniz and Jacob Bernoulli would put l'Hopital in very good company indeed if the solution was indeed due to him.

  14. Brodetsky biography
    • In 1910 Brodetsky was awarded the Isaac Newton Scholarship which enabled him to study at Leipzig for his doctorate.
    • On one occasion, he gave a lecture on Sir Isaac Newton in a room in the university constructed to seat an audience of 250, 400 turned up and were all accommodated, sitting or standing.

  15. McCrea biography
    • He specialised in those branches of mathematical physics that were stimulating exciting research at Cambridge, and after graduating he began research as one of the many pupils of R H Fowler FRS (later Sir Ralph Fowler) to whom he paid warm tribute on his centenary in 1980.
    • His talents were quickly appreciated at Cambridge and in 1927 he was awarded the Cambridge University Rayleigh Prize in Mathematics, a Trinity College Rouse Ball Senior Studentship, a Sheepshanks Exhibition in Astronomy, and an Isaac Newton Studentship.
    • We noted above that he was elected a fellow of the Royal Society of Edinburgh (proposed by Sir Edmund Taylor Whittaker, Sir Charles Galton Darwin, Edward T Copson, and Charles Glover Barkla) and he was awarded their Keith Medal 1939-41.

  16. Sampson biography
    • After two years as a lecturer in mathematics in London, Sampson returned to Cambridge in 1891 when he became the first holder of the Isaac Newton Studentship in Astronomy and Physical Optics.
    • We have mentioned several of these above, but let us also mention that he was elected a fellow of the Royal Society of Edinburgh on 4 December 1911 being proposed by Sir Frank Watson Dyson, Sir James Walker, Arthur Robinson, and James Gordon MacGregor.

  17. Molyneux Samuel biography
    • Samuel Molyneux's father was William Molyneux, a notable Irish astronomer and politician, and his mother was Lucy Domville, the youngest daughter of Sir William Domville, the attorney-general for Ireland.
    • Another chapter which was essentially due to Molyneux was entitled Sir Isaac Newton's Reflecting Telescope Made and Described by the Honourable Samuel Molyneux Esquire, and Presented by Him to His Majesty John V King of Portugal: with Other Kinds of Mechanisms for This and for Mr Gregory's Reflecting Telescope.

  18. Wiles biography
    • He filled what he thought were the remaining few gaps and gave a series of lectures at the Isaac Newton Institute in Cambridge ending on 23 June 1993.
    • In 2000, Andrew Wiles became "Sir Andrew Wiles" when he was made a Knight Commander of the Order of the British Empire by the Queen.
    • Sir Run Run Shaw, a leader of the Hong Kong media industry, established this Prize in 2002.

  19. Walsh biography
    • He became convinced that the differential calculus was a delusion; that Sir Isaac Newton was a shallow sciolist, if not an impostor; and that the universities and academics of Europe were engaged in the interested support of a system of error.
    • the falsehood of Newton's law of gravity.

  20. Penrose biography
    • This book is a record of a debate between the two at the Isaac Newton Institute of Mathematical Sciences at the University of Cambridge in 1994.
    • Sir Roger Penrose, OM, FRS has been awarded the Royal Society's Copley medal the world's oldest prize for scientific achievement for his exceptional contributions to geometry and mathematical physics.
    • Sir Roger, Emeritus Rouse Ball Professor of Mathematics at the University of Oxford, has made outstanding contributions to general relativity theory and cosmology, most notably for his work on black holes and the Big Bang.

  21. Lorenz Edward biography
    • profoundly influenced a wide range of basic sciences and brought about one of the most dramatic changes in mankind's view of nature since Sir Isaac Newton.

  22. Greaves biography
    • He continued to undertake research at Cambridge being Isaac Newton Student in 1921-3, and was elected a Fellow of St John's College in 1922.
    • He was elected a Fellow of the Royal Society of Edinburgh on 6 March 1939 having been proposed by James P Kendall, Max Born, Edmund G Dymond, Ruric W Wrigley, Edwin A Baker, and Sir E T Whittaker.

  23. Morgan William biography
    • who had been a pupil of the great Sir Isaac Newton.

  24. Goldstein biography
    • Based on his very successful undergraduate career, Goldstein was awarded the Isaac Newton Studentship to continue undertaking research in applied mathematics under Harold Jeffreys.
    • The Vice Chancellor of the university, Sir John Stopford, had persuaded the university authorities that these two appointments would "create at Manchester a dynamic and internationally renowned Department of Mathematics, interacting admirably with other units in the university".

  25. Cherry biography
    • However, his real love was mathematics and his godfather, Sir John MacFarland the Chancellor of the University of Melbourne, offered to lend him sufficient funds to study mathematics at the University of Cambridge in England.
    • The high quality of his work led to him receiving a Senior Scholarship and an Isaac Newton studentship.

  26. Hirst biography
    • Hirst read many works of literature, scientific texts and mathematics books such as Euclid's Elements, Hutton's Mathematics and Brewster's Life of Sir Isaac Newton.


History Topics

  1. Newton poetry
    • However, as a first step, I have collected some "Isaac Newton poetry".
    • Certainly in the English language there seem to be more poetic references to Newton than other mathematicians/scientists.
    • Many contemporary poets treated Newton as god-like and praised him accordingly.
    • Over the years, of course, there have been poets who have considered Newton to have destroyed the poetic view of the world.
    • For example, John Keats often proposed the toast, "Newton's health, and confusion to mathematics".
    • Others have chosen to write anti-Newton poetry for religious reasons or because they supported Leibniz.
    • Here are some examples of "Isaac Newton poetry", presented in chronological order beginning with the earliest: .
    • Had it not been for Halley, Newton's masterpiece, The Principia, may never have been written.
    • Newton unlocking Truth's close-fasten'd Chest, .
    • Newton dear to the Muse, in whose pure Breast .
    • Such was the Path immortal Newton trod, .
    • Mature in Thought, you Newton's Laws reduce .
    • James Thomson: A Poem Sacred to the Memory of Sir Isaac Newton (1727).
    • This Academy was a "Newtonian Institution" and Thomson's poems contain many references to Newton.
    • A Poem Sacred to the Memory of Sir Isaac Newton was written within weeks of Newton's death while Thomson was teaching at Watt's Academy: .
    • Shall the great soul of Newton quit this earth, .
    • When Newton rose, our philosophic sun! .
    • Let Newton, pure intelligence, whom God .
    • Below is an extract concerning Newton: .
    • To thee, great Newton! Britain's justest pride, .
    • Alexander Pope: Epitaph intended for Sir Isaac Newton, in Westminster Abbey (1730).
    • The following couplet may be the best-known of all the poetry associated with Newton: .
    • God said "Let Newton be" and all was light.
    • Newton arose; show'd how each planet moved ..
    • When mighty Newton the foundations laid, .
    • Here, awful Newton, the dissolving clouds .
    • Samuel Bowden: A Poem Sacred to the Memory of Sir Isaac Newton (1735).
    • For its own fav'rite Newton to explore.
    • Newton, th' All-wise Creator's works explores, .
    • Here is a short extract referring to Newton: .
    • See Newton chase conjecture's twilight ray, .
    • De Polignac, a Jesuit, argues for divine providence and against Newton's ideas.
    • Nor does the great Newton's famous system stand, .
    • Here is a "Newton extract": .
    • Here godlike Newton's all capacious mind .
    • Newton, immortal Newton rose; .
    • Though Newton's genius cloudless shone, .
    • Much more than Newton ever knew, .
    • Here is a short "Newton extract": .
    • Sagacious Newton lost with pond'ring thought .
    • Blake is famed, of course, for his famous painting "Newton", 1795: .
    • Reason and Newton, they are quite two things, .
    • Reason says 'Miracle', Newton says 'Doubt'.
    • Washed by the water-wheels of Newton.
    • This "Newton extract" is from Part V: .
    • How many a Newton, to whose passive ken .
    • Here is an extract referring to Newton: .
    • When Newton saw an apple fall, he found .
    • In which Sir Isaac Newton could disclose .
    • In this poem, Keats laments Newton having destroyed the poetry of the rainbow by reducing it to decomposed white light.
    • Keats is said to have often proposed a toast, " Confusion to the memory of Newton".
    • When asked to explain, he said, "Because Newton destroyed the poetry of the rainbow by reducing it to a prism? Ah, my dear old friend, you and I shall never see such days again!": .
    • The following extract is from Book III, Residence at Cambridge where Wordsworth looks at Newton's statue at Trinity College: .
    • Of Newton with his prism and silent face, .
    • http://www-history.mcs.st-andrews.ac.uk/HistTopics/Newton_poetry.html .

  2. Coffee houses
    • It was a common thing for meetings of the Royal Society to be continued in a social way at this coffee-house, the president, Sir Isaac Newton, being frequently of the parties.
    • So one of the gentlemen one might find in the Grecian Coffee House was Isaac Newton, where sometimes he met de Moivre.
    • Talking of Newton, de Moivre, Hooke and Wren brings us back to our main topic of mathematics in the coffee houses of London.
    • Customer 1: I'm told Sir, that coffee inspires a man in the mathematics.
    • Newton was also an Arian, but for fear that he would be dismissed (or worse) did not make his Arian views public.
    • But the most pathetic figure associated with its history is that of Abraham De Moivre, that French mathematician who became the friend of Newton and Leibniz.

  3. Greeks poetry
    • Having made a collection of poems which were about, or mentioned, Isaac Newton, I [EFR] looked for poems which were about, or mentioned, Euclid and Archimedes.
    • Wordsworth is the only poet in our collection who mentions Newton, Euclid and Archimedes in poems.
    • Perhaps the fact that he was a friend of Sir William Hamilton may explain the frequent mathematical references! Hamilton fancied himself as a poet and Wordsworth is famed for his sensible advice that Hamilton concentrate on his mathematics: .


Famous Curves

  1. Trident
    • Trident of Newton .
    • This curve was investigated by Newton and also by Descartes.
    • The name trident is due to Newton.
    • The curve occurs in Newton's study of cubics.
    • It is contained in his classification of cubic curves which appears in Curves by Sir Isaac Newtonin Lexicon Technicumby John Harris published in London in 1710.
    • Newton was the first to undertake such a systematic study of cubic equations and he classified them into 72 different cases.
    • The trident is the 66th species in his classification and Newton gives the graph essentially looking identical to the graph given above.
    • Newton states some properties of his trident.
    • Newton's classification of cubics was criticised by Euler because it lacked general general principle.

  2. Newtons
    • Newton's Diverging Parabolas .
    • Newton's classification of cubic curves appears in Curves by Sir Isaac Newton in Lexicon Technicum by John Harris published in London in 1710.
    • In this classification of cubics, Newton gives four classes of equation.
    • The third class of equations is the one given above which Newton divides into five species.
    • Of this third case Newton says: .
    • The case divides into five species and Newton gives a typical graph for each species.

  3. Serpentine
    • This curve was named and studied by Newton in 1701.
    • It is contained in his classification of cubic curves which appears in Curves by Sir Isaac Newton in Lexicon Technicumby John Harris published in London in 1710.
    • The incomparable Sir Isaac Newton gives this following Ennumeration of Geometrical Lines of the Third or Cubick Order; in which you have an admirable account of many Species of Curves which exceed the Conick-Sections, for they go no higher than the Quadratick or Second Order.
    • Newton shows that the curve f(x, y) = 0, where f(x, y) is a cubic, can be divided into one of four normal forms.


Societies etc

  1. Lucasian Chairs
    • 1664 Isaac Barrow .
    • 1669 Sir Isaac Newton .
    • 1798 Isaac Milner .
    • 1826 Sir George Airy .
    • 1849 Sir George Stokes .
    • 1903 Sir Joseph Larmor .
    • 1969 Sir M.

  2. Presidents of the Royal Society
    • 1680-1682 Sir Christopher Wren .
    • 1703-1727 Sir Isaac Newton .
    • 1871-1873 Sir George Biddell Airy .
    • 1885-1890 Sir George Gabriel Stokes .
    • 1890-1895 Lord Kelvin (Sir William Thomson) .
    • 1990-1995 Sir Michael Atiyah .


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  1. References for Newton
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    • R S Westfall, The achievement of Isaac Newton : an essay on the occasion of the three hundredth anniversary of the 'Principia', Math.
    • R S Westfall, Newton and the acceleration of gravity, Arch.
    • R S Westfall, Newton's marvelous years of discovery and their aftermath : myth versus manuscript, Isis 71 (256) (1980), 109-121.
    • R S Westfall, A note on Newton's demonstration of motion in ellipses, Arch.
    • R S Westfall, Huygens' rings and Newton's rings : Periodicity and seventeenth century optics, Ratio 10 (1968), 64-77.
    • D T Whiteside, The mathematical principles underlying Newton's Principia, Journal for the History of Astronomy 1 (1970), 118-119.
    • D T Whiteside, How forceful has a force proof to be? Newton's 'Principia', Book 1 : Corollary 1 to Propositions 11-13, Physis Riv.
    • D T Whiteside, Newton the mathematician, in Contemporary Newtonian research (Dordrecht-Boston, Mass., 1982), 109-127.
    • D T Whiteside, Kepler, Newton and Flamsteed on refraction through a 'regular aire' : the mathematical and the practical, Centaurus 24 (1980), 288-315.
    • D T Whiteside, Newton and dynamics, Bull.
    • D T Whiteside, Newton's lunar theory : from high hope to disenchantment, Vistas Astronom.
    • D T Whiteside, The mathematical principles underlying Newton's 'Principia mathematica', J.
    • D T Whiteside, Before the 'Principia' : the maturing of Newton's thoughts on dynamical astronomy, 1664-1684, J.
    • G J Whitrow, Newton's role in the history of mathematics, Notes and Records Roy.
    • E T Whittaker, Aristotle, Newton, Einstein, Proc.
    • E T Whittaker, Aristotle, Newton, Einstein, Philos.
    • A J Wojtcuk, Newton's childhood, in Newton and the new direction in science (Vatican City, 1988), 261-264.
    • H Wussing, Isaac Newton - Leben und Werk, NTM Schr.
    • I M Yaglom, Why was higher mathematics simultaneously discovered by Newton and Leibniz? (Russian), in Number and thought 6 (Moscow, 1983), 99-125.
    • K N Yan, A re-examination into Newton's definition of mass and Mach's criticism, Historia Sci.
    • K N Yan, On Isaac Newton's ideas of gravitation and God, Historia Sci.
    • A P Youschkevitch, Newton and the mathematical natural sciences (on the 300th anniversary of the 'Principia') (Russian), Mat.
    • A P Youschkevitch, Comparaison des conceptions de Leibniz et de Newton sur le calcul infinitsimal, in Leibniz in Paris (1672-1676) (Wiesbaden, 1978), 69-80.
    • M Yurkina, Newton's 'Principia' and the origin of the modern theory of the shape of the Earth (Russian), Istor.-Astronom.
    • http://www-history.mcs.st-andrews.ac.uk/References/Newton.html .

  2. References for Cotes
    • J Edleston (ed.), Correspondence of Sir Isaac Newton and Professor Cotes (1850).
    • D H Fowler, Newton, Cotes, and √√2 : a footnote to Newton's theory of the resistance of fluids.

  3. References for Jones
    • Lord Teignmouth, Memoirs of the Life, Writings and Correspondence of Sir William Jones (London, 1804).
    • D T Whiteside (ed.), I Newton, The mathematical works of Isaac Newton I (New York-London 1964).


Additional material

  1. John Maynard Keynes: 'Newton, the Man
    • John Maynard Keynes: Newton, the Man .
    • The Royal Society of London planned an event to celebrate the tercentenary of Isaac Newton's birth in 1942.
    • Keynes was fascinated by Newton's manuscripts and had been the first person to see some of the manuscript material by Newton which had been kept secret until his papers were sold in 1936.
    • Keynes' lecture, Newton, the man was delivered at the celebrations by his brother Geoffrey Keynes.
    • Newton, the Man .
    • It is with some diffidence that I try to speak to you in his own home of Newton as he was himself.
    • I believe that Newton was different from the conventional picture of him.
    • In the eighteenth century and since, Newton came to be thought of as the first and greatest of the modern age of scientists, a rationalist, one who taught us to think on the lines of cold and untinctured reason.
    • Newton was not the first of the age of reason.
    • Isaac Newton, a posthumous child bom with no father on Christmas Day, 1642, was the last wonderchild to whom the Magi could do sincere and appropriate homage.
    • Had there been time, I should have liked to read to you the contemporary record of the child Newton.
    • For in vulgar modern terms Newton was profoundly neurotic of a not unfamiliar type, but - I should say from the records - a most extreme example.
    • I believe that Newton could hold a problem in his mind for hours and days and weeks until it surrendered to him its secret.
    • 'Yes,' replied Halley, 'but how do you know that? Have you proved it?' Newton was taken aback - 'Why, I've known it for years', he replied.
    • Again, there is some evidence that Newton in preparing the Principia was held up almost to the last moment by lack of proof that you could treat a solid sphere as though all its mass was concentrated at the centre, and only hit on the proof a year before publication.
    • Certainly there can be no doubt that the peculiar geometrical form in which the exposition of the Principia is dressed up bears no resemblance at all to the mental processes by which Newton actually arrived at his conclusions.
    • This was Newton's garden.
    • At the top of this stairway stood his telescope - not to be confused with the observatory erected on the top of the Great Gate during Newton's lifetime (but after he had left Cambridge) for the use of Roger Cotes and Newton's successor, Whiston.
    • When he decided to prepare the Principia for publication he engaged a young kinsman, Humphrey Newton, to act as his amanuensis (the MS.
    • When Newton died Humphrey's son-in-law Conduitt wrote to him for his reminiscences, and among the papers I have is Humphrey's reply.
    • Let me not exaggerate through reaction against the other Newton myth which has been so sedulously created for the last two hundred years.
    • Very early in life Newton abandoned orthodox belief in the Trinity.
    • It may be that Newton fell under Socinian influences, but I think not.
    • For some of Newton's arguments, see our article Newton the Arian .
    • But this was a dreadful secret which Newton was at desperate pains to conceal all his life.
    • A hundred years later Sir David Brewster looked into the box.
    • Newton's extensive anti-Trinitarian pamphlets are, in my judgement, the most interesting of his unpublished papers.
    • Apart from his more serious affirmation of belief, I have a completed pamphlet showing up what Newton thought of the extreme dishonesty and falsification of records for which St Athanasius was responsible, in particular for his putting about the false calumny that Arius died in a privy.
    • It is a blot on Newton's record that he did not murmur a word when Whiston, his successor in the Lucasian Chair, was thrown out of his professorship and out of the University for publicly avowing opinions which Newton himself had secretly held for upwards of fifty years past.
    • At any rate, Newton was clearly an unbridled addict.
    • It is this with which he was occupied 'about 6 weeks at spring and 6 at the fall when the fire in the elaboratory scarcely went out' at the very years when he was composing the Principia - and about this he told Humphrey Newton not a word.
    • Newton has left behind him a vast mass of records of these studies.
    • It is utterly impossible to deny that it is wholly magical and wholly devoid of scientific value; and also impossible not to admit that Newton devoted years of work to it.
    • Some time it might be interesting, but not useful, for some student better equipped and more idle than I to work out Newton's exact relationship to the tradition and MSS.
    • In these mixed and extraordinary studies, with one foot in the Middle Ages and one foot treading a path for modern science, Newton spent the first phase of his life, the period of life in Trinity when he did all his real work.
    • Newton could not be Master of Trinity because he was a Unitarian and so not in Holy Orders.
    • Newton took this rejection very ill and prepared a long legalistic brief, which I possess, giving reasons why it was not unlawful for him to be accepted as Provost.
    • But, as ill-luck had it, Newton's nomination for the Provostship came at the moment when King's had decided to fight against the right of Crown nomination, a struggle in which the College was successful.
    • Newton was well qualified for any of these offices.
    • And when the turn of his life came and he put his books of magic back into the box, it was easy for him to drop the seventeenth century behind him and to evolve into the eighteenth-century figure which is the traditional Newton.
    • The breakdown probably lasted nearly two years, and from it emerged, slightly 'gaga', but still, no doubt, with one of the most powerful minds of England, the Sir Isaac Newton of tradition.
    • He set up house with his niece Catharine Barton, who was beyond reasonable doubt the mistress of his old and loyal friend Charles Montague, Earl of Halifax and Chancellor of the Exchequer, who had been one of Newton's intimate friends when he was an undergraduate at Trinity.
    • Newton puts on rather too much weight for his moderate height.
    • The Sir Isaac Newton of orthodox tradition - the eighteenth-century Sir Isaac, so remote from the child magician born in the first half of the seventeenth century - was being built up.
    • Voltaire returning from his trip to London was able to report of Sir Isaac - 'twas his peculiar felicity, not only to be born in a country of liberty, but in an Age when all scholastic impertinences were banished from the World.
    • Reason alone was cultivated and Mankind could only be his Pupil, not his Enemy.' Newton, whose secret heresies and scholastic superstitions it had been the study of a lifetime to conceal! .
    • So Newton's chest, with many hundreds of thousands of words of his unpublished writings, came to contain the 'Portsmouth Papers'.
    • http://www-history.mcs.st-andrews.ac.uk/Extras/Keynes_Newton.html .

  2. Science at St Andrews
    • The construction of the seven-figure tables involved far more than the devoted study of twenty years; it involved the imagination to lay bare, and then to organise, those concepts of relative motions and rates of changes that only became clear and distinct a hundred years later through the work of Newton and his contemporaries.
    • This was due to Sir Robert Moray who, according to tradition, had been a student in the University.
    • For six years (1668-1674) there worked in the College this man of genius who in an era of exceptional brilliancy was held to be second only to Isaac Newton.
    • On leaving St Andrews, James Gregory went to Edinburgh as her earliest mathematical professor, to be succeeded a year later, after his untimely death at the height of his powers, by his nephew, David, who subsequently in 1692 went to Oxford at the recommendation of Isaac Newton.
    • Meanwhile and independently, Newton, who was four years Gregory's junior, had devised and constructed a reflecting telescope in 1668, though it differed from Gregory's by directing the rays after the second reflexion into a path at right angles to the axis, the eye-piece being consequently set at the side and not at the end of the tube.
    • In Italy Gregory, inspired by the recent advances of the Italian and French schools, made his first discoveries in the differential and integral calculus, probably quite unaware that Barrow and Newton were doing the like at Cambridge.
    • The six years that Gregory spent at St Andrews were a period of great intellectual activity, enhanced at the end of the first year by news from Collins that a young pupil of Barrow's at Cambridge, Isaac Newton by name, was performing wonders in the analyticks.
    • In this way he learnt of Newton's telescope and thereupon entered into a friendly correspondence on the merits of the two patterns.
    • He received an occasional formula but no sustained account of Newton's mathematical advances.
    • 80 which contained Newton's own account of his experiments with the spectrum.
    • The misunderstanding and criticism that followed the publication of this epoch-making discovery had a deplorable effect upon Newton.
    • For Gregory withheld the revision, on learning from Collins that Newton had anticipated him.
    • He generously waited - and waited in vain - for Newton to break the silence.
    • How close Gregory and Newton were in mathematical thought may be judged from the fact that on one occasion independent statements of the same discovery - the infinite series for the inverse sine - crossed in the post.
    • What he and Newton were doing simultaneously at St Andrews and Cambridge was fundamentally to inaugurate a revolution in mathematics, comparable to that effected in arithmetic by the introduction into Europe of the Arabic numerals.
    • Little is known of Charles, but David left several interesting papers, including a copy of a very early unpublished work by his uncle David upon the history of fluxions prior to the celebrated controversy between Newton and Leibniz: and also a yearly record of the names of students attending the mathematical classes.
    • He was one of the first to give a formal proof of the binomial theorem that had been discovered independently by Newton and Gregory a century earlier.
    • He contributed to the history of gravitation as it was shaping under Colin Maclaurin, Lagrange and Laplace, on the foundation of Newton's Principia.
    • Others came to St Andrews with their reputation already made, such as David Brewster (1781-1868) Principal of the United College (1838-59) who brought a high repute in the study of light and its polarization, had in 1831 helped to found the British Association for the Advancement of Science, and who wrote a life of Isaac Newton.
    • The new physical laboratories were opened by Sir William Bragg in 1925, during the tenure of the Chair by Herbert Stanley Allen, who promoted and carried out research on the secondary spectrum of hydrogen and the band spectrum of water vapour.
    • Gregory had died at the height of his powers: Newton at the same age had not written the Principia.
    • In 1938, and, as a fitting sequel to the celebrations, an astronomer was appointed - Dr Findlay Freundlich, at the recommendation of Sir Arthur Eddington who had been the first to introduce into Britain the general theory of relativity.

  3. The Tercentenary of the birth of James Gregory
    • On Tuesday, 5th July 1938, at St Andrews, in the Upper Hall of the University Library, a Graduation Ceremonial took place, at which Sir James Irvine, F.R.S., Principal and Vice-Chancellor of the University, conferred the Honorary Degree of LL.D.
    • They made possible, fifty years later, that crowning achievement of the seventeenth century, the Principia of Isaac Newton.
    • Within those memorable years James Gregory lived and died, achieving in the brief span of his life a reputation among his peers second only to that of Newton.
    • Meanwhile, a young man working independently at Cambridge, Isaac Newton, four years junior to Gregory, had invented a reflecting telescope which was exhibited at the Royal Society in 1672 and brought fame to the maker.
    • The observer gazes directly into Gregory's and sideways into Newton's instrument.
    • He retaliated by inserting in his next book, the Exercitationes, a few pages which advanced this work of Huygens beyond all recognition: "I shall here try to bring the squaring of the circle and hyperbola to such perfection that Huygens will scarcely recognise his offspring." In this work Gregory crosses the Great Divide that separates mediaeval thought from the modern world: here also he is thinking the same thoughts as Isaac Newton, when as yet neither had heard of the other.
    • One of his friends was Sir Robert Moray, a founder of the Royal Society, a former graduate of St Andrews, a chemist, a mathematician, a student of music, a friend of the learned, and perhaps the most attractive Scot of his generation.
    • I would gladly hear Mr Newton's thoughts of it." This is the earliest recorded example of a diffraction grating.
    • It was here that Gregory first learnt, through a letter of Collins, about the geometrical methods of Barrow, the Lucasian Professor at Cambridge, and the analytics of his still more wonderful pupil, Isaac Newton, to whom Barrow relinquished his Chair.
    • Here Gregory also learnt of the fame that the reflecting telescope brought to Newton and of his remarkable discoveries in light, the breaking up of white light into colours.
    • Barrow and Newton had discovered the differential calculus, but within a month of receiving Barrow's book Gregory poured out such a volley of equations in his next letter that Collins was convinced beyond a doubt that Gregory had made the same discovery too.
    • These rough notes, written, who knows? in this very room, are the silent but inevitable witness giving Gregory the right to take his place with Barrow, Newton and Leibniz as a principal discoverer of the differential calculus: indeed in this one aspect of the subject he attained a result which neither of the others are known to have found.
    • like Moses Serpent that devoured the Serpents of the Egyptian Magi." Yet Gregory never published this, his crowning achievement: for on learning from Collins that Newton had in actual date anticipated him and modestly assuming that Newton had attained at least as far as he himself, Gregory decided to withhold his work until his young rival had published his own - which did not in fact take place until many years after the death of Gregory.
    • As he waited for Newton to break the silence Gregory turned once more to Astronomy.
    • The old letters, upon the backs of which he wrote his rough notes during the seven years spent at St Andrews and Edinburgh, passed into the possession of his family, and were carefully treasured: but after many years they were lost to be found again by Sir Peter Scott Lang in 1887, a successor two centuries later in the Chair of James Gregory, who bequeathed them to this Library about ten years ago.
    • The work was begun by Sir John Smith and continued by the present Librarian and myself.
    • Today, in this room where Gregory worked so long, we have their mathematical descendants, distinguished guests from the world of science, from the Cambridge of Newton, the Paris of Cassini, the Germany of Leibniz and the Flanders of Huygens, assembled in a Scotland where mathematics is still pursued for its beauty and its truth.

  4. Flamsteed v Newton
    • Flamsteed v Newton .
    • Isaac Newton needed astronomical data to give a full theory of the motion of the moon, something which he had left incomplete in the first edition of the Principia.
    • In the summer of 1694 Newton went by boat down the Thames to Greenwich for his first meeting with Flamsteed at the Royal Observatory.
    • Newton persuaded Flamsteed to give him 50 of his observations of the moon, and he also managed to get a promise of another 100 observations.
    • In return Flamsteed made Newton promise only to use them personally and not to make them public.
    • Continued pressure by Newton prised further observations from Flamsteed over the next months.
    • Newton promised Flamsteed fame if the observations were published along with his theory:- .
    • Soon Newton and Flamsteed grew to hate each other despite both realising that he needed the other.
    • When Flamsteed made public the fact that Newton was preparing a new edition of the Principia, Newton was furious:- .
    • In the end Halley published Newton's theory of the moon as a booklet entitled The famous Mr Isaac Newton's Theory of the Moon.
    • Later, as President of the Royal Society, Newton got control of the Royal Observatory and had Halley print Flamsteed's star catalogue without his knowledge.
    • I have had another contest with the President (Sir Isaac Newton) of the Royal Society, who had formed a plot to make my instruments theirs; and sent for me to a Committee, where only himself and two physicians (Dr Sloane, and another as little skilful as himself) were present.
    • I had resolved aforehand his knavish talk should not move me; showed him that all the instruments in the Observatory were my own; the mural arch and voluble quadrant having been made at my own charge, the rest purchased with my own money, except the sextant and two clocks, which were given me by Sir Jonas Moore, with Mr Towneley's micrometer, his gift, some years before I came to Greenwich.
    • http://www-history.mcs.st-andrews.ac.uk/Extras/Flamsteed_Newton.html .

  5. Nevil Maskelyne measures the Earth's density
    • If the attraction of gravity be exerted, as Sir Isaac Newton supposes, not only between the large bodies of the universe, but between the minutest particles of which these bodies are composed, or into which the mind can imagine them to be divided, acting universally according to that law by which the force which carries on the celestial motions is regulated; namely, that the accelerative force of each particle of matter, towards every other particle, decreases as the squares of the distances increase; it will necessarily follow, that every hill must, by its attraction, alter the direction of gravitation in heavy bodies in its neighbourhood, from what it would have been from the attraction of the earth alone, considered as bounded by a smooth and even surface.
    • Sir Isaac Newton gives us the first hint of such an attempt, in his popular Treatise of the System of the World, where he remarks, "That a mountain of a hemispherical figure, 3 miles high and 6 broad, will not, by its attraction, draw the plumb-line 2 minutes out of the perpendicular." It will appear, by a very easy calculation, that such a mountain would attract the plumb-line 1'18" from the perpendicular.
    • The law of the variation of this force, in the inverse ratio of the squares of the distances, as laid down by Sir Isaac Newton, is also confirmed by this experiment.
    • But now, by only supposing the mean density of the earth to be double that of the hill, which seems very probable from other considerations, the attraction of the hill will be reconciled to the general law of the variation of attraction in the inverse duplicate ratio of the distances, as deduced by Sir Isaac Newton from the comparison of the motion of the heavenly bodies with the force of gravity at the surface of the earth; and the analogy of nature will be preserved.

  6. Nevil Maskelyne measures the Earth's density
    • If the attraction of gravity be exerted, as Sir Isaac Newton supposes, not only between the large bodies of the universe, but between the minutest particles of which these bodies are composed, or into which the mind can imagine them to be divided, acting universally according to that law by which the force which carries on the celestial motions is regulated; namely, that the accelerative force of each particle of matter, towards every other particle, decreases as the squares of the distances increase; it will necessarily follow, that every hill must, by its attraction, alter the direction of gravitation in heavy bodies in its neighbourhood, from what it would have been from the attraction of the earth alone, considered as bounded by a smooth and even surface.
    • Sir Isaac Newton gives us the first hint of such an attempt, in his popular Treatise of the System of the World, where he remarks, "That a mountain of a hemispherical figure, 3 miles high and 6 broad, will not, by its attraction, draw the plumb-line 2 minutes out of the perpendicular." It will appear, by a very easy calculation, that such a mountain would attract the plumb-line 1'18" from the perpendicular.
    • The law of the variation of this force, in the inverse ratio of the squares of the distances, as laid down by Sir Isaac Newton, is also confirmed by this experiment.
    • But now, by only supposing the mean density of the earth to be double that of the hill, which seems very probable from other considerations, the attraction of the hill will be reconciled to the general law of the variation of attraction in the inverse duplicate ratio of the distances, as deduced by Sir Isaac Newton from the comparison of the motion of the heavenly bodies with the force of gravity at the surface of the earth; and the analogy of nature will be preserved.

  7. Turnbull lectures on Colin Maclaurin
    • He married a gentlewoman of the family of Cameron, and, of their three sons, John, the eldest, became a minister in the city of Glasgow, Daniel died young, after having signs of extraordinary genius, and Colin, who is the subject of this lecture, and whose bi-centenary we have just commemorated, became the most distinguished disciple of Isaac Newton.
    • But the greatest of the formative influences upon the life of young Maclaurin was that of Isaac Newton.
    • It was Halley who had persuaded Newton to write the Principia: and though the masterpiece had been before the world for thirty years, it was still a closed book to all but a handful of the acutest scholars.
    • Roger Cotes was the second, a young English scholar of whom Newton once wrote Had Cotes lived we might have known something.
    • He died in the year 1716 at the age of thirty-four and at the height of his powers: a brilliant mathematician and astronomer who was already acclaimed as a worthy successor to Newton at Trinity College, Cambridge.
    • How far he had developed in a grasp of the Newtonian philosophy, during the years of quiet preparation for his life work, we do not know: but we may suppose that through the influence at college of Robert Simson he had become acquainted with both the geometry and the natural philosophy of Newton, thereby receiving a grounding in these fields of mathematics that paved the way for his peculiar gifts in later years.
    • In the vacation of 1719 he visited London where he left his Geometria Organica to be printed and where he met Sir Isaac Newton.
    • Folkes (1690-1754), who eventually succeeded Newton as a President of the Royal Society, was an antiquary as well as a man of science - a choice youth of penetrating genius and master of the beauties of the best Roman and Greek writers.
    • Had he forgotten all about them; did he turn a deaf ear to all calls to return; was there something in him, akin to the impenetrable aloofness of Newton, which shut him off from his fellows and his duties at times of mental creativity? But a shock came which brought the travels to an end when his pupil was suddenly taken ill with a fever and died at Montpelier in southern France.
    • This Professor Gregory was the younger brother of David, the friend of Newton, and was the nephew of his more famous namesake James.
    • Long ago Newton had recommended David to the Chair of Mathematics at Edinburgh: now he did the same for Maclaurin.
    • Two years later Newton died.
    • The friendship which had grown between the ageing natural philosopher and his young disciple bore fruit in after years when Maclaurin wrote his work on Fluxions and also his account of Newton's philosophical discoveries.
    • The subjects ranged from Euclid and elementary algebra to conics, fluxions, probability and Newton's Principia.

  8. Turnbull lectures on Colin Maclaurin, Part 2
    • Maclaurin made two considerable contributions to the theory of higher plane curves ; the first was his Geometria Organica sive Descriptio Linearum Curvarum Universalis (London, 1720) with the imprimatur of Sir Isaac Newton, P.R.S., 1719.
    • The case n = 2, that of conic sections, had been well-nigh completely worked out by the ancients, although Newton added some notable new methods of generating the curves.
    • Newton himself considered the next case, that of cubic curves, n = 3, which led to a system of seventy-two varieties to which half a dozen more, that he had overlooked, were added by various later geometers, including Stirling, the friend of Maclaurin.
    • Newton was the first to give the organic description of curves up to cubics.
    • Maclaurin began by proving in his own way a theorem of Newton on the conic: given fixed points S and C, and the line AE, let two angles, PSQ and PCQ, of constant sizes, rotate about their vertices S and C.
    • Maclaurin makes this quite plain as the cases arise, by paying willing tribute to the discoveries of the ancients and to the more recent discoveries of Fermat, Nicol, Newton, to the spirals of Varignon, the conchoid of de la Hire, and the limacon of Pascal.
    • Maclaurin had one guiding principle to go on -- that which Newton suggested in the angular movements for the description of conics and cubics.
    • In this Maclaurin was fortunate, but he alone of all who followed Newton showed the true significance of the device.
    • One came from Newton and the other from Cotes.
    • From Newton, Maclaurin had learnt that when two straight lines PA, Pa meet a curve of order n in the points A, B, C ..
    • In the notation of fluxions Newton's theorem thereupon yielded the relation .
    • The book was written as a reply to a philosophical attack upon Newton's method of fluxions which Dr Berkeley, bishop of Cloyne, had made in a treatise entitled The Analyst (1734).
    • It was written in English and published at Edinburgh in 1742, and contained a mature and systematic account of Newton's fluxions, set out both in geometrical and in analytical form, with a wealth of applications and many novel discoveries.
    • One of the great passages in the book concerns the attraction of an ellipsoid, where Maclaurin successfully extended the work of Newton upon spherical attraction, and incidentally opened a new field of geometrical investigation by studying confocal conics.
    • Here Maclaurin expounds the calculus of variations by his geometrical and fluxional method, after first alluding to the early discoveries of Newton and James Bernoulli, on the solid of least resistance and the line of swiftest descent.
    • He continued the great work which Newton had begun, and to-day we are still indebted to him for the discoveries and the processes with which he has enriched our mathematical heritage.

  9. Gregory tercentenary
    • Principal Sir James C Irvine, who presided, extended a welcome to the guests.
    • It was at St Andrews, continued the Professor, that Gregory first learned, through a letter of Collins, about the geometrical methods of Barrow, the Lucasian Professor at Cambridge, and the analytics of his still more wonderful pupil, Isaac Newton, to whom Barrow relinquished his Chair.
    • It was there Gregory also learned of the fame that the reflecting telescope brought to Newton, and of his remarkable discoveries in light.
    • "These rough notes, written, who knows (?) in this very room, are the silent, but inevitable witness giving Gregory the right to take his place with Barrow, Newton, and Leibniz as a principal discoverer of the differential calculus"; indeed, in this one aspect of the subject he attained a result which neither of the others is known to have found.
    • Yet Gregory, never published this, his crowning achievement; for, on learning from Collins that Newton had in actual date anticipated him, and modestly assuming that Newton had attained as far as he himself, Gregory decided to withhold his work until his young rival had published his own, which did not, in fact, take place until many years after the death of Gregory.
    • As he waited for Newton to break the silence, Gregory turned once more to astronomy.
    • Professor Turnbull said that the old letters, upon the back of which Gregory wrote his rough notes during the seven years spent at St Andrews and Edinburgh, passed into the possession of his family, and were carefully treasured; but after many years they were lost, to be found again by Sir Peter Scott Lang, who, a successor two centuries later in the Chair of James Gregory, presented them to that Library.
    • degrees being conferred by Principal Sir James Irvine.
    • Addresses of congratulation were presented to Principal Sir James Irvine on behalf of the Royal Society of London, the Royal Society of Edinburgh, the University of Edinburgh, and the Edinburgh Mathematical Society.

  10. Mathematics and London Coffee Houses
    • Sir Isaac Newton, being frequently of the parties.
    • So one of the gentlemen one might find in the Grecian Coffee House was Isaac Newton, where sometimes he met de Moivre.
    • Talking of Newton, de Moivre, Hooke and Wren brings us back to our main topic of mathematics in the coffee houses of London.
    • Customer 1: I'm told Sir, that coffee inspires a man in the mathematics.
    • Newton was also an Arian, but for fear that he would be dismissed (or worse) did not make his Arian views public.
    • But the most pathetic figure associated with its history is that of Abraham De Moivre, that French mathematician who became the friend of Newton and Leibniz.

  11. Mathematics at Aberdeen 3
    • He extended ideas of Isaac Newton on curves generated by the intersections of rotating lines and did elaborate work on pedal curves and chains of such curves.
    • During the first of these he met Sir Isaac Newton, was elected Fellow of the Royal Society and made arrangements for the publication, in 1720, of his first major book Geometria Organica.
    • By November of the same year he was in Edinburgh, appointed conjunct professor with the ageing James Gregory, a post negotiated for him by Newton who had offered to pay twenty pounds a year towards his salary.
    • His numerous published works include books on fluxions, algebra and Newton's Philosophy.
    • To help and encourage beginners he published much expanded translations of two of Newton's tracts, on quadrature and series.
    • Interested students could go on to the Professor's optional third class of Advanced Algebra, Quadrature and Fluxions (Newton's approach to Calculus), with parts of Newton's Principles of Philosophy.

  12. Gibson History 9 - Colin Maclaurin
    • Shortly after his appointment he contributed two papers to the Philosophical Transactions the substance of which was incorporated in the Geometria Organica which appeared in 1720, Newton's Imprimatur being dated Nov.
    • It was a happy circumstance however that he was freed from the difficulties of the position by his appointment in 1725, on the recommendation of Newton, to the Chair of Mathematics in Edinburgh University.
    • Afterwards he prelects on Sir Isaac Newton's Principia and explains the direct and inverse method of fluxions.
    • Maclaurin's Account of Newton's Philosophical Discoveries, his Physical and Literary Essays, and his work on mathematical physics - some of it of great value - I can do nothing more than mention.
    • It passed through many editions and, while a good commentary on Newton's Arithmetica Universalis, it can hold its own as an excellent introduction to the subject - as that subject was understood by the best mathematicians, of his time.
    • He took an active part in the work of the new Society and contributed papers that were incorporated, according to Murdoch's statement, in the Treatise of Fluxions and in his Account of Newton's Philosophy.

  13. Florian Cajori on William Oughtred
    • It was during the second half of the seventeenth century that Sir Isaac Newton, surrounded by a group of great men - Wallis, Hooke, Barrow, Halley, Cotes - carried on his epoch-making researches in mathematics, astronomy, and physics.
    • Biographers of Sir Isaac Newton make particular mention of five mathematical books which he read while a young student at Cambridge, namely, Euclid's Elements, Descartes's Geometrie, Viete's Works, Van Schooten's Miscellanies, and Oughtred's Clavis mathematicae.

  14. The Edinburgh Mathematical Society: the first hundred years (1883-1983) Part 2
    • Tait was junior author with Sir William Thomson of the famous Mathematical Treatise on Natural Philosophy affectionately known as T and T'.
    • As Sir Edmund Whittaker wrote in his obituary of Knott, Tait 'had succeeded to the generalship of the quaternionites on the death of Hamilton and bequeathed it in turn to Knott.' .
    • No account of the Society would be complete without considerable mention being made of Sir Edmund Taylor Whittaker, who has already been referred to in this article more than once.
    • In later life he became an authority on the history of mathematics and, after his retirement in 1950, he edited the correspondence of Isaac Newton on behalf of the Royal Society.

  15. The St Andrews Schmidt-Cassegrain Telescope
    • In the meantime Isaac Newton, working independently, had constructed a reflecting telescope of a somewhat different pattern; the second Newtonian telescope to be made was presented to the Royal Society in 1672.
    • Sir Peter Redford Scott Lang who, from 1879 to 1921, was Regius Professor of Mathematics in St Andrews expressed the desire that a lectureship in astronomy should be founded at St Andrews, and that Baron Napier of Merchiston should be commemorated by the association of his name with the foundation.
    • Newton, on the other hand, used a plane secondary mirror placed obliquely so that it reflected the light sideways through an eyepiece set in the side of the tube near its upper end, a most inconvenient position for the observer.

  16. Percy MacMahon addresses the British Association in 1901
    • The members dined together twice annually, viz., on the second Friday in January in London in commemoration of the birth of Sir Isaac Newton (this feast frequently took place at the Black Swan, Brown's Lane, Spitalfields), and on the Second Friday in July 'at a convenient distance in the country in commemoration of the birth of the founder.' The second dinner frequently fell through because the members could not agree as to the locality.
    • The gravitation formula has been recognised from the time of Newton as ruling the dynamics of the heavens, and the exact agreement of the facts derived from observation with the simple theory has established astronomy as the most exact of all the departments of applied science.

  17. EMS obituary
    • With the notable exception of the late Sir Edmund Whittaker no one contributed more to giving our Society the status and esteem it possesses in the mathematical world than Herbert Westren Turnbull.
    • In 1921, Turnbull was appointed to the Regius Chair of Mathematics in St Andrews which had fallen vacant by the death of Sir Peter Redford Scott Lang.
    • Many mathematicians retire to a life of leisure but Turnbull retired in 1950 to edit, on behalf of the Royal Society, The Correspondence of Isaac Newton.

  18. Mathematical Works of Colin Maclaurin
    • An Account of Sir Isaac Newton's Philosophy, published (1748) by subscription by Patrick Murdoch for the benefit of Maclaurin's children, prefaced by a memoir of Maclaurin.

  19. Charles Tweedie on James Stirling
    • Very little is known regarding his stay in Venice and the date of his return to Britain; but his private letters show that when he took up residence in London he was on intimate terms of friendship with Sir Isaac Newton and other distinguished scholars in the capital.


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JOC/BS August 2001