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Isaac Newton

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Rebecca
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« Reply #30 on: August 22, 2007, 11:16:52 am »

Bernoulli's mathematical challenge

Newton's solution of the celebrated problems proposed by Johann Bernoulli and Leibniz deserves mention among his mathematical works. In June 1696 Bernoulli addressed a letter to the mathematicians of Europe challenging them to solve two problems—(1) to determine the brachistochrone between two given points not in the same vertical line, (2) to determine a curve such that, if a straight line drawn through a fixed point A meet it in two points P1, P2, then AP1m+AP2m [OCR garbled] will be constant. This challenge was first made in the Ada Lipsiensia for June 1696.

Six months were allowed by Bernoulli for the solution of the problem, and in the event of none being sent to him he promised to publish his own. The six months elapsed without any solution being produced; but he received a letter from Leibniz, stating that he had "cut the knot of the most beautiful of these problems," and requesting that the period for their solution should be extended to Christmas next; that the French and Italian mathematicians might have no reason to complain of the shortness of the period. Bernoulli adopted the suggestion, and publicly announced the postponement for the information of those who might not see the Ada Lipsiensia.

On January 29, 1697 Newton received from France two copies of the printed paper containing the problems, and on the following day he sent a solution of them to Montague, then president of the Royal Society. He announced that the curve required in the first problem must be a cycloid, and he gave a method of determining it. He solved also the second problem, and he showed that by the same method other curves might be found which shall cut off three or more segments having the like properties. Solutions were also obtained from Leibniz and the Marquis de l'Hôpital; and, although that of Newton was anonymous, yet Bernoulli recognized the author in his disguise; "tanquam," says he, "ex ungue leonem" (we know the lion by his claw).

In 1699 Newton's position as a mathematician and natural philosopher was recognized by the French Academy of Sciences. In that year the Academy was remodelled, and eight foreign associates were created. Leibniz, Domenico Guglielmini (1655—1710), Hartsoeker, and E. W. Tschirnhaus were appointed on February 4, James Bernoulli and John Bernoulli on February 14, and Newton and Ole Rømer on February 21.
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« Reply #31 on: August 22, 2007, 01:03:51 pm »

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« Reply #32 on: August 22, 2007, 01:04:54 pm »

End of professorship and presidency of the Royal Society

While Newton held the office of warden of the mint, he retained his chair of mathematics at Cambridge, and discharged the duties of the post, but shortly after he was promoted to be master of the mint he appointed Whiston his deputy with "the full profits of the place." Whiston began his astronomical lectures as Newton's deputy in January 1701. On December 10, 1701 Newton resigned his professorship, thereby at the same time resigning his fellowship at Trinity, which he had held with the Lucasian professorship since 1675 by virtue of the royal mandate. Whiston's claims to succeed Newton in the Lucasian chair were successfully supported by Newton himself.

On November 26, 1701 Newton was again elected one of the representatives of the university in parliament, but he retained his seat only until the dissolution in the following July. Newton does not seem to have been a candidate at this election, but at the next dissolution in 1705 he stood for the university. He was warmly supported by the residents, but being a Whig, he was opposed by the non-residents, and beaten by a large majority.

In the autumn of 1703 Lord Somers retired from the presidency of the Royal Society, and on November 30, 1703 Newton was elected to succeed him. Newton was annually re-elected to this honourable post during the remainder of his life. He held the office for 25 years, the longest term of office for any Royal Society president since except Sir Joseph Banks (at the time of writing, 2002). As president Newton was brought into close association with Prince George of Denmark, the queen's husband, who had been elected a fellow of the Royal Society. The prince had offered, on Newton's recommendation, to cover the expense of printing Flamsteed's observations—especially his catalogue of the stars. It was natural that the queen should form a high opinion of one whose merits had made such a deep impression on her husband. In April 1705, when the queen, the prince and the court were staying at the royal residence at Newmarket, they paid a visit to Cambridge, where they were the guests of Dr Bentley, the master of Trinity. Her Majesty went in state to the Regent House, where a congregation of the senate was held, and a number of honorary degrees conferred. Afterwards the queen held a court at Trinity Lodge, where (April 16, 1705) she conferred the order of knighthood upon Sir Isaac Newton.

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« Reply #33 on: August 22, 2007, 01:05:44 pm »

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« Reply #34 on: August 22, 2007, 01:06:32 pm »

Second edition of the Principia

As soon as the first edition of the Principia was published Newton began to prepare for a second. He was anxious to improve the work by additions to the theory of the motion of the moon and the planets. Dr Edleston, in his preface to Newton's correspondence with Cotes, justly remarks: "If Flamsteed the Astronomer-Royal had cordially co-operated with him in the humble capacity of an observer in the way that Newton pointed out and requested Of him... the lunar theory would, if its creator did not overrate his own powers, have been completely investigated, so far as he could do it, in the first few months of 1695, and a second edition of the Principia would probably have followed the execution of the task at no long interval."

Newton, however, could not get the information he wanted from Flamsteed, and after the spring of 1696 his time was occupied by his duties at the mint. Rumours, however, of his work, and of a new edition, were heard from time to time. In February 1700 Leibniz writes of Newton, "J'ai appris aussi (je ne sais où) qu'il donnera encore quelque chose sur le mouvement de la Lune: et on m'a dit aussi qu'il y aura une nouvelle édition de ses principes de la nature." (I have learnt - I forget from where - that he will give further details on the movements of the Moon: and I've also been told that there will be a new edition of his Principia).

Dr Bentley, the master of Trinity College, had for a long time urged Newton to give his consent to the republication of the Principia. In 1708 Newton's consent was obtained, but it was not till the spring of 1709 that he was prevailed upon to entrust the superintendence of it to a young mathematician of great promise, Roger Cotes, fellow of Trinity College, who had been recently appointed the first Plumian Professor of Astronomy and Experimental Philosophy. On May 21, 1709, after speaking to Newton, Bentley announced this arrangement to Cotes: "Sir Isaac Newton," he said, "will be glad to see you in June, and then put into your hands one part of his book corrected for the press." About the middle of July Cotes went to London, no doubt expecting to bring down with him to Cambridge the corrected portion of the Principia. Although Cotes was impatient to begin his work, it was nearly the end of September before the corrected copy was given to him.

During the printing of this edition a correspondence went on continuously between Newton and Cotes. On the 31st of March 1713, when the edition was nearly ready for publication, Newton wrote to Cotes: "I hear that Mr Bernoulli has sent a paper of 40 pages to be published in the Ada Leipsica relating to what I have written upon the curve lines described by projectiles in resisting media. And therein he partly makes observations upon what I have written & partly improves it. To prevent being blamed by him or others for any disingenuity in not acknowledging my oversights or slips in the first edition, I believe it will not be amiss to print next after the old Praefatio ad Lectorem, the following account of this new Edition.

"In hac secunda Principiorum Editione, multa sparsim emendantur & nonnulla adjiciuntur. In Libri primi Sect. ii Inventio viriuni quibus corpora in Orbibus datis revolvi possint, facilior redditur et amplior. In Libri secundi Sect. vii. Theoria resistentiac fluidorum accuratius investigatur & novis experimentis confirmatur. In Libro tertio Theoria Lunae & Praecessio Aequinoctiorum ex Principiis suis plenius deducuntur, et Theoria Cometarum pluribus et accuratius computatis Orbium exemplis confirmatur.

"28 Mar, 1713. I. N.

"If you write any further preface, I must not see it, for I find that I shall be examined about it. The cuts for ye Comet of 1680 & 1681 are printed off and will be sent to Dr Bently this week by the Carrier."

Newton's desire to avoid writing the preface seems to have come from a knowledge that Cotes was considering alluding to the dispute about the invention of fluxions. At last, about midsummer 1713, was published the long and impatiently expected second edition of the Principia, and; on July 27, Newton waited on Queen Anne, to present her with a copy of the new edition.

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« Reply #35 on: August 22, 2007, 01:07:34 pm »

The longitude problem

In 1714 the question of finding the longitude at sea, which had been looked upon as an important one for several years, was brought into prominence by a petition presented to the House of Commons by a number of captains of Her Majesty's ships and merchant ships and of London merchants. The petition was referred to a committee of the House, who called witnesses. Newton appeared before them and gave evidence. He stated that for determining the longitude at sea there had been several projects, true in theory but difficult to execute. He mentioned four:
1.   by a watch to keep time exactly
2.   by the eclipses of Jupiter's moons
3.   by the place of the moon
4.   by a new method proposed by Mr Ditton.
Newton criticized all the methods, pointing out their weak points, and it is due mainly to his evidence that the Committee brought in the report which was accepted by the House, and shortly afterwards was converted into a Bill, passed both Houses, and received the royal assent. The report ran "that it is the opinion of this committee that a reward be settled by Parliament upon such person or persons as shall discover a more certain and practicable method of ascertaining the longitude than any yet in practice; and the said reward be proportioned to the degree of exactness to which the said method shall reach."
Newton was a very popular visitor at the Court of George I. The Princess of Wales, Caroline of Ansbach, wife of George II, took every opportunity of conversing with him. Having one day been told by Sir Isaac that he had composed a new system of chronology while he was still resident at Cambridge, she requested him to give her a copy. He accordingly drew up an abstract of the system from his papers, and sent it to the Princess for her own private use; but he afterwards allowed a copy to be made for the Abbé Conti on the express understanding that it should not be communicated to any other person. The abbé, however, lent his copy to M Fréret, an antiquary at Paris, who translated it, and endeavoured to refute it. The translation was printed under the title Abrege de chronologie de M le Chevallier Newton, fait par lui-même et traduit sur le manuscrit anglais. Upon receiving a copy of this work, Sir Isaac Newton printed, in the Philosophical Transactions for 1725, a paper entitled "Remarks on the observations made on a Chronological Index of Sir Isaac Newton, translated into French by the observator, and published at Paris." In these remarks Sir Isaac charged the Abbé with a breach of promise, and gave a triumphant answer to the objections which Fréret had urged against his system. Father Souciet entered the field in defence of Fréret; and in consequence of this controversy Sir Isaac was induced to prepare his larger work, which was published in 1728, after his death, and entitled The Chronology of Ancient Kingdoms amended, to which is prefixed a short Chronicle from the First Memory of Kings in Europe to the Conquest of Persia by Alexander the Great.
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« Reply #36 on: August 22, 2007, 01:08:23 pm »

Theological studies

From an early period in life Newton paid great attention to theological studies, beginning his studies before 1690. That Newton was even then a powerful thinker was proved by his ability to attack the most difficult mathematical problems with success. For example in 1716 Leibniz, in a letter to the Abbe Conti, proposed a problem for solution "for the purpose of feeling the pulse of the English analysts". The problem was to find the orthogonal trajectories of a series of curves represented by a single equation. Newton received the problem at about 17:00 as he was returning from the mint, and though he was fatigued from work, he solved it later the same evening.

One of the most remarkable of Newton's theological works is his Historical Account of Two Notable Corruptions of the Scriptures, included in a letter to John Locke in November 1690. Sir Isaac was anxious for its publication but because his argument deprived the Trinitarians of two passages in favour of the Trinity, he became alarmed at the possible consequences. He therefore asked Locke, who was on the way to the continent, to have it translated into French and have it published there. Locke copied the manuscript and sent it to Jean Leclerc on April 11, 1691. On January 20, 1692 Leclerc announced his intention of publishing it in Latin. Upon hearing this Newton responded "to stop the translation and publication as soon as he could.. to suppress it". This was done, but Leclerc sent the manuscript to the library of the Remonstrants, and it was later published in London in 1754 under the title Two Letters from Isaac Newton to M le Clerc. This edition had many errors. Dr Horsley therefore published a genuine one, which is in the form of a single letter to a friend, and was taken from a manuscript in Sir Isaac's own hand.

Sir Isaac Newton also wrote Observation on the Prophecies of Daniel and the Apocalypse of St. John which was published in London in 1733. Another work Lexicon Propheticum published in 1737 was a dissertation on the sacred cubit of the Jews. He wrote four letters to Bently containing arguments for existence of a deity which were published by Cumberland, a nephew of Bently, in 1756. Newton also wrote a Church History and a History of Creation, Paradoxical Questions regarding Athanasius.

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« Reply #37 on: August 22, 2007, 01:09:21 pm »

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« Reply #38 on: August 22, 2007, 01:10:25 pm »

Alchemy

Newton devoted much of his time to the study of chemistry, a great number of his experiments still remain in manuscript. His Tabula Quantilatum et Graduum Caloris contains a comparative scale of temperature from that of melting ice to that of a small kitchen fire. He wrote another chemical paper De Natura Acidorum. Sir Isaac spent much time in the study of the alchemists including Jacob Boehme. In an earlier part of his life, Newton and a relation Dr Newton of Grantham had put up furnaces and had wrought for several months in quest of the philosophers tincture. Sir Isaac also studied the manuscripts of Flamsteed's Explication of Hieroglyphic Figures and William Yworth's Processus Mysterii Magnii Magni Philosophicus.
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« Reply #39 on: August 22, 2007, 01:11:35 pm »

Sir Isaac Newton's final years

In the last few years of Newton's life he was troubled by urinary incontinence probably due to a kidney stone. In January 1725 he was seized with violent cough and inflammation of the lungs which induced him to move to Kensington. In the next month he had a case of gout and then had an improvement of health. His duties from the mint were terminated and thus he seldom left home. On February 28, 1727 he went to London to preside at a meeting of the Royal Society but his health condition forced him to return to Kensington on March 4 when it was determined he had a kidney stone. He endured great suffering. On March 18 he became delirious around 6pm and stayed in that state until Monday March 20, 1727 when he died between one and two in the morning. His body was moved to London and on Tuesday, March 28 it lay in state in the Jerusalem Chamber in Westminster Abbey, then moved to his burial location in the Abbey. (Note: the date of Newton's death is March 20, 1726 in the "Old Style" Julian calendar and March 31, 1727 in the "New Style" Gregorian calendar).

His considerable liquid estate was divided equally between his eight half-nieces and half-nephews (three Pilkingtons, three Smiths and two Bartons (including Catherine Barton Conduitt). Woolsthorpe Manor passed to his heir-in-law, a John Newton ("God knows a poor representative of so great a man"), who, after six years of "****[fight]ing, horse racing, drinking and folly" was forced to mortgage and then sell the manor before dying in a drunken accident.
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« Reply #40 on: August 22, 2007, 01:13:31 pm »



Newton's grave in Westminster Abbey
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