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CONTENTS OF VOLUME II.
CHAPTER XIV.
History of the Infinitesimal Calculus — Archimedes — Pappus — Nappier — Edward Wright — Kepler's Treatise on Stereometry — Cavalieri's Geometria Indivisibilium — Roberval — Toricelli — Fermat — Walli's Arithmetica Infinitorum — Hudde — Gregory — Slusius — Newton's Discovery of Fluxions in 1655 — General Account of the Method, and of its Applications — His Analysis per Equationes, &c. — His Discoveries communicated to English and Foreign Mathematicians — The Method of Fluxions and Quadratures — Account of his other Mathematical writings — He solves the Problems proposed by Bernoulli and Leibnits — Leibnitz visits London, and corresponds with the English Mathematicians, and with Newton through Oldenburg — He discovers the Differential Calculus, and communicates it to Newton — Notice of Oldenburg — Celebrated Scholium respecting Fluxions in the Principia — Account of the changes upon it — Leibnitz's Manuscripts in Hanover,
CHAPTER XV.
Nicolas Facio de Duillier attacks Leibnitz — Leibnitz appeals to Newton — He reviews Newton's "Quadrature of Curves," and accuses him of Plagiarism — Newton's opinion of the Review — Dr. Keill defends Newton as the true inventor of Fluxions, and apparently retorts the charge of Plagiarism on Leibnitz, who complains to the Rojal Society — Keill explains his defence — The Royal Society approves of his explanation — Leibnitz calls Keill an upstart, and begs the Royal Society to silence him — the Society appoints a Committee to inquire into the Claims of Leibnitz and Newton — The Committee report to the Society, who publish the result in the "Commercium Epistolicum" — Instigated by Leibnitz, John Bernoulli attacks the Report, and asserts, in a private Letter to Leibnitz, that he was the first inventor of the new Calculus — Leibnitz circulates this Letter in a Charta Volans, and gives up Bernoulli as the author of it — Keill replies to this Letter, and attacks Bernoulli as its author, who solemnly
CHAPTER XVI.
Newton declines taking Orders — His Rooms in Trinity College — John Wickins his chamber-fellow — Letter from Mr. Nicolas Wickins, his Son — Dr. Humphrey Newton his Amanuensis from 1684-1689 — His two Letters to Conduitt — Newton's Speculations on the Theory of the Earth — James II. attacks the rights of the Charter-House, and sends an illegal Mandamus to the University of Cambridge — Newton one of the Delegates to resist this encroachment on its privileges — The Vice-Chancellor deposed — the object of the Deputation gained — Neglect of the Scottish Universities — Newton elected Member for Cambridge to the Convention Parliament — His habits of business — His letters to Dr. Covel — His acquaintance with Locke — His Theological inquiries — Locke exerts himself to procure for him some permanent appointment in King's College, the Charter-House, and the Mint — Failure of that attempt — Newton's disappointment — Ingratitude of his Country — Death of his Mother at Stamford — Writes an Account of Fluxions and Fluents for Wallis — His letter to Locke on multiplying Gold — Boyle's Recipes and Belief in Alchemy,
CHAPTER XVII.
Newton's health impaired — The Boyle Lectures by Bentley, who requests Newton's assistance — Newton's first Letter to Bentley on the Formation of the Sun and Planets — His second Letter — Rotation of the Planets the result of Divine power — His third Letter — Hypothesis of Matter evenly diffused — Letter of Bentley to Newton — Reply to it by Newton in a fourth Letter — Opinion of Plato examined — Supposed mental Illness of Newton ascribed to the burning of his MSS. — Referred to in the Letters of Huygens and Leibnitz — Made public by M. Biot — Mentioned in the Diary of Mr. De la Pryme — The story referred to disproved — Newton's Papers burnt before 1684 — Newton's Letter to Mr. Pepys — Letter of Mr. Pepys to Mr. Millington — Mr. Millington's reply — Mr. Pepys' second Letter to Mr. Millington — Newton solves a Problem in Chances — His Letter to Locke — Reply of Locke — Newton's Answer, explaining the cause of his Illness — His Critical Letter to Dr. Mill — His Mind never in a state of derangement, but fitted for the highest intellectual efforts,
CHAPTER XVIII.
Newton occupied with the Lunar Theory — His Correspondence with Flamsteed, the Astronomer-Royal — Newton's Letters to Flamsteed, published by Mr. Baily — Controversy which they occasioned — Flamsteed's Letter to Newton discovered recently — Character of Flamsteed, in reference to this Controversy — of Newton, and of Halley — all of them engaged, with different objects, in studying the Lunar Theory — Newton applies to Flamsteed for Observations on the Moon — and on the Refraction of the Atmosphere, which Flamsteed transmits to him — Analysis of their Correspondence — Flamsteed's bitterness against Halley — Differences between Newton and Flamsteed — Flamsteed's ill health interferes with his supplying Newton with Observations — Newton's impatience and expostulation with Flamsteed — Justification of Flamsteed — Biot ascribes Newton's Letter to mental illness — Refutation of this view of the subject — Newton never aflicted with any mental disorder,
CHAPTER XIX.
No mark of Natioual Gratitude conferred upon Newton — Friendship between him and Charles Montague, afterwards Earl of Halifax — Montague appointed Chancellor of the Exchequer in 1694 — He resolves upon a Recoinage — His Letter nominating Newton Warden of the Mint in 1696 — Newton appointed Master of the Mint when Montague was First Lord of the Treasury — His Report on the Coinage — Anecdote of his integrity when offered a bribe — He obtains for Halley the Deputy-Comptrollership of the Mint at Chester — Quarrels among the Officers there — Disturbances in the London Mint — New misunderstanding with Flamsteed — Remarkable Letter to him from Newton — Newton's conduct defended — The French Academy of Sciences remodelled — Newton elected one of the eight Foreign Associates — M. Geoffroy describes to Dr. Sloane the change in the Academy — Newton resigns his Professorship and Fellowship at Cambridge — Whiston appointed his Successor — Newton elected Member for the University in 1701, and President of the Royal Society in 1703 — Queen Anne confers upon him the honour of Knighthood in 1705 — Love-letter to Lady Norris — His Letter to his niece, Miss C. Barton — Account of Sir William and Lady Norris — Letters of Newton about standing for the University in 1705 — Letters of Halifax to Newton on that occasion — Newton and Godolphin defeated,
CHAPTER XX.
Sir Isaac is anxious to have the Greenwich Observations published — Flamsteed agrees, provided his expenses are paid — Prince George offers to pay the expense of publishing them — He appoints Sir Isaac and others Referees to manage the matter — Articles agreed upon between Flamsteed and the Referees — Differences arise, and delays in printing — The Prince
CHAPTER XXI.
Dissensions in the Royal Society — Dr. Sloane and Dr. Woodward — Letter to Newton on the subject — Dr. Woodward removed from the Council — Second edition of the Principia — Dr. Bentley's Letter to Newton about it — Delay of the work — Bentley's second Letter — Newton's Residences in London — Bentley announces to Newton the completion of the Second Edition — The Duke D'Aumont elected F.R.S. — Deslandes' account of a Dinner Party at Newton's — Origin of the Royal Observatory at Greenwich — Prince Menzikoff elected F.R.S. — Petition to Parliament for a Bill to promote the Discovery of the Longitude — Evidence of Newton — His Conduct misrepresented by Whiston and Biot — The Bill passes both Houses of Parliament — Dissensions in the Government — Offer of a Pension to Newton — Death of Queen Anne — Accession of George I. — Earl of Halifax Prime Minister — Death of Halifax — His Will — His affection for Miss Catherine Barton, Newton's Niece — Her intimacy with Swift — Her Character defended,
CHAPTER XXII.
Leibnitz attacks Newton's Philosophy — Newton's Reply — Leibnitz attacks the English philosophy as irreligious, in Letters to the Princess of Wales — The King requests Newton to defend himself — He claims the invention of Fluxions — Dr. Clarke defends the English philosophy — The dispute carried on through the Princess of Wales — Insincerity of Leibnitz — His Death — His Eloge by Fontenelle, who apologizes to Chamberlayne for a mistake adverse to Newton — Newton's Observations on the Eloge — Varignon reconciles Newton and John Bernoulli — Newton's Correspondence with Varignon, whose views are favourable to Leibnitz — Newton asks Varignon's Opinion on the Commercium — His Criticisms upon it — His Death — Correspondence between Newton and John Bernoulli — Montmort's Views on the Fluxionary Controversy — Nicolas Bernoulli's Letter to Newton — Letters of Dr. Smith, Dr. Derham, and Fontenelle, referred to,
CHAPTER XXIII.
The Princess of Wales obtains from Newton a manuscript Abstract of his System of Chronology — The Abbé Conti, at her request, is allowed to take a copy of it under promise of secrecy — He gives a copy to M. Freret of the French Academy, who writes a Refutation of it, and gives it to a Bookseller, who asks Newton's permission to print it — Newton neglects to answer two Letters on the subject — The Abstract and the Refutation of it printed — Newton reprobates the conduct of Conti, and defends his System — It is attacked by Father Souciet, and is defended by Halley — Sir Isaac's larger work on Chronology published after his death, and dedicated to the Queen by Mr. Conduitt — Pope assists in writing the Dedication — Opinions respecting the Chronology — Sir Isaac's Paper on the Form of the most Ancient Year — His unpublished Papers on the Julian Year, and the Reformation of the Calendar,
CHAPTEK XXIV.
Theological Writings of Newton — Their importance to Christianity — Motives to which they have been ascribed — Biot's opinion disproved — The date of Newton's theological writings fixed — His Letters to Locke on these subjects — History of his account of two corruptions of the Scriptures — His Observations on the Prophecies of Daniel, and on the Apocalypse — Abstract of his Historical Account of two corruptions of Scripture — His views adopted by the ablest Biblical Critics of modern times — His unpublished theological writings — Paradoxical Questions concerning Athanasius — His Irenicum or Ecclesiastical Polity tending to Peace — His Views on points of Trinitarian Doctrine — His Articles of Faith — His Plan for correcting the Romish tendencies of the Church of England— Coincidence of his Opinions with those of Locke — His Views on the Future Residence of the Blest — Opinions of Voltaire and Others — Napier, Boyle, Milton, and Locke, Students of the Scriptures — Analogy between the Book of Nature and that of Revelation — Letter of Dr. Morland to Newton
CHAPTER XXV.
Sir Isaac's early study of Chemistry — And of Alchemy, as shown in his Letter to Mr. Aston — His Experiments on the Metal for Reflecting Telescopes — His Chemical Pursuits between 1683 and 1687 — His Researches on the Quantities and Degrees of Heat, written after his illness in 1693 — His Experiments on the Rarefaction of Air, Water, and Linseed Oil — His Paper on the nature of Acids — The Results of his Chemical Researches, published among his Queries in his Optics — His Opinion on Fire and Flame — On Elective Attractions — Manuscript Works on Alchemy left among Sir Isaac's Papers — A belief in Alchemy prevalent in Newton's time — Boyle, Locke, and Newton studied Alchemy as a Science, others for fraudulent purposes,
CHAPTER XXVI.
Newton's first attack of ill health, and his recovery — History of his acquaintance with Dr. Pemberton, who superintends the third edition of the Principia — Their Correspondence — Improvements in the third edition — Change in the celebrated Scholium — And in the Scholium on the Motion of the Moon's Nodes— Demonstration of Machin and Pemberton — Publication of the third edition — Newton attacked with the Stone — Conduitt acts for him in the Mint — His Letter recommending Colin Maclaurin as Assistant to Gregory — His Liberality on this occasion — Maclaurin's Letter to Newton — Visit of the Abbé Alari to Newton — His acquaintance with Samuel Crell — He presides at the Royal Socieity on the 2d March — His last illness — And death on the 20th March 1717 — His Body lies in State — His Burial and Monument in Westminster Abbey — Statues and Pictures of him — His Property — His Descendants,
CHAPTER XXVII.
Permanence of Newton's Reputation — Character of his Genius — His manner of investigation similar to that used by Galileo — Error in ascribing his Discoveries to the use of the Methods recommended by Lord Bacon — The Pretensions of the Baconian Philosophy examined — Sir Isaac Newton's Social Character — His great Modety — The Simplicity of his Character — His Religious and Moral Character — His Hospitality and Mode of Life — His Generosity and Charity — His Personal Appearance — Statues and Pictures of him — Memorials and Recollections of him — His Manuscripts and Papers,
APPENDIX TO VOLUME II.