TAYLOR, BROOK, a.celebrated English mathematician, was born at Edmonton, in Mid dlesex, Aug. 18, 1685, of a Puritan family of good position; entered St. John's college, Cambridge, in 1701, at a time when mathematical science was the prominent pursuit among the learned; took his degree of LL.B. in 1709; became a fellow of the Royal society in 1712, and its secretary in 1714, in which latter year he also took the degree of i LL.D. Though so young, he had become widely known in Britain and on the continent for great proficiency in mathematical knowledge, and power and versatility of mind, having already written various valuable treatises ou capillary action, on the vibration of a string, on music, etc. In 1716 he visited Paris, and was received with warm demon strations of regard by the French savans, who respected his ability and learning, and the prominent and distinguished part he had taken in the Leibnitzian controversy. On his return to England in 1717 he resumed his habits of severe study, but was forced by declining health to resign the secretaryship in 1718. For the next three years he wan
dered about, residing now on the continent, now in England. He died, Dec. 29,1731, at the age of 46. Besides his earlier works above mentioned, he contributed a series of able papers on higher algebra, dynamics, and general physics, published separately his Nethodus Incrementorum in 1715, and a Treatise on Linear Perspective, the first general exposition of this subject, in 1719. During the last ten years of his life he gaye him self up almost entirely to metaphysical and biblical studies. His Methodus Incremento rum contains, besides the famous "theorem" (see TAYLOR'S THEOREM), the first germs of the calculus of finite differences, various now common forms of infinitesimal series, with mechanical, physical, and algebraical applications. The chief use made by Taylor of his theorem is in a paper (1717) entitled "Method of Approximation to the Roots of Equations." The results of his investigations may be found in the Phil. Trans. (1713 23), and in his two works above mentioned.