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