Dr. John Keill was the first person who publicly taught natural philosophy by experiments. Desaguliers informs us that this author “laid down very simple propositions, which he proved by experiments, and from these he deduced others more compound, which he still confirmed by experiments, till he had instructed his auditors in the laws of motion, the principles of hydrostatics and optics, and some of the chief propositions of Sir Isaac Newton concerning light and colours. He began these courses in Oxford about the year 1704 or 1705, and in that way introduced the love of the Newtonian philosophy.” When Dr. Keill left the university, Desaguliers began to teach the Newtonian philosophy by experiments. He commenced his lectures at Harthall in Oxford, in 1710, and delivered more than a hundred and twenty courses; and when he went to settle in London in 1713, he informs us that he found “the Newtonian philosophy generally received among persons of all ranks and professions, and even among the ladies by the help of experiments.” Such were the steps by which the Newtonian philosophy was established in Great Britain. From the time of the publication of the Principia, its mathematical doctrines formed a regular part of academical education; and before twenty years had elapsed, its physical truths were communicated to the public in popular lectures illustrated by experiments, and accommodated to the capacities of those who were not versed in mathematical knowledge. The Cartesian system, though it may have lingered for a while in the recesses of our universities, was soon overturned; and long before his death, Newton enjoyed the high satisfaction of seeing his philosophy triumphant in his native land. 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 1666—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._