The first Idea of Gravity occurs to Newton in 1666—His first Speculations upon it—Interrupted by his Optical Experiments—He resumes the Subject in consequence of a Discussion with Doctor Hooke—He discovers the true Law of Gravity and the Cause of the Planetary Motions—Dr. Halley urges him to publish his Principia— His Principles of Natural Philosophy—Proceedings of the Royal Society on this Subject—The Principia appears in 1687—General Account of it, and of the Discoveries it contains—They meet with great Opposition, owing to the Prevalence of the Cartesian System— Account of the Reception and Progress of the Newtonian Philosophy in Foreign Countries—Account of its Progress and Establishment in England 140 CHAPTER XII. Doctrine of Infinite Quantities—Labours of Pappus—Kepler—Cavaleri— Roberval—Fermat—Wallis—Newton discovers the Binomial Theorem and the Doctrine of Fluxions in 1606—His Manuscript Work containing this Doctrine communicated to his Friends—His Treatise on Fluxions—His Mathematical Tracts—His Universal Arithmetic—His Methodus Differentialis—His Geometria Analytica—His Solution of the Problems proposed by Bernouilli and Leibnitz—Account of the celebrated Dispute respecting the Invention of Fluxions—Commercium Epistolicum—Report of the Royal Society—General View of the Controversy 168 CHAPTER XIII. James II. attacks the Privileges of the University of Cambridge-- Newton chosen one of the Delegates to resist this Encroachment—He is elected a Member of the Convention Parliament—Burning of his Manuscript—His supposed Derangement of Mind—View taken of this by foreign Philosophers—His Correspondence with Mr. Pepys and Mr. Locke at the time of his Illness—Mr. Millington’s Letter to Mr. Pepys on the subject of Newton’s Illness—Refutation of the Statement that he laboured under Mental Derangement 200 CHAPTER XIV. No Mark of National Gratitude conferred upon Newton—Friendship between him and Charles Montague, afterward Earl of Halifax—Mr. Montague appointed Chancellor of the Exchequer in 1694—He resolves upon a Recoinage—Nominates Mr. Newton Warden of the Mint in 1695— Mr. Newton appointed Master of the Mint in 1699—Notice of the Earl of Halifax—Mr. Newton elected Associate of the Academy of Sciences in 1699—Member for Cambridge in 1701—and President of the Royal Society in 1703—Queen Anne confers upon him the Honour of Knighthood in 1705—Second Edition of the Principia, edited by Cotes—His Conduct respecting Mr. Ditton’s Method of finding the Longitude 223 CHAPTER XV.