TAYLOR, BROOK (1685-1731), English mathematician, was the son of John Taylor, of Bifrons House, Kent, was born at Edmonton in Middlesex on Aug. 18, 1685. He was educated at St. John's College, Cambridge, and studied mathematics under John Machin and John Keill. He obtained in 1708 a remarkable solution of the problem of the "centre of oscillation," which, how ever, remaining unpublished until May 1714 (Phil. Trans., vol.
xxviii. p. I I), his claim to priority was unjustly disputed by John Bernouilli. Taylor's Methodus Incrementorum Directa et lnversa (London, 1715) added a new branch to the higher mathematics, now designated the "calculus of finite differences." Among other ingenious applications, he used it to determine the form of move ment of a vibrating string, by him first successfully reduced to mechanical principles. The same work contained the celebrated formula known as "Taylor's theorem" (see CALCULUS, DIFFEREN TIAL), the importance of which remained unrecognized until 1772, when J. L. Lagrange realized its powers and termed it "le principal fondement du calcul differentiel." In his essay on Linear Perspective (London, 1715, revised ed. 1719) Taylor set forth the
true principles of the art in an original and more general form than any of his predecessors; but the work suffered from the brevity and obscurity which affected most of his writings.
Taylor was elected a fellow of the Royal Society early in 1712, sat in the same year on the committee for adjudicating the claims of Newton and Leibniz, and acted as secretary to the society from 1714 to 1718. From 1715 his studies took a philosophical and religious bent. Taylor died on Dec. 29, 1731, at Somerset House, and was buried at St. Ann's, Soho. As a mathematician, he was the only Englishman after Sir Isaac Newton and Roger Cotes capable of holding his own with the Bernouilli; but a great part of the effect of his demonstrations was lost through his failure to express his ideas fully and clearly. See also TAYLOR'S THEOREM.