# 1911 Encyclopædia Britannica/Taylor, Brook

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​TAYLOR, BROOK (1685–1731), English mathematician, was the son of John Taylor, of Bifrons House, Kent, by Olivia, daughter of Sir Nicholas Tempest, Bart., of Durham, and was born at Edmonton in Middlesex on the 18th of August 1685. He entered St John’s College, Cambridge, as a fellow-commoner in 1701, and took degrees of LL.B. and LL.D. respectively in 1709 and 1714. Having studied mathematics under John Machin and John Keill, he obtained in 1708 a remarkable solution of the problem of the “centre of oscillation,” which, however, remaining unpublished until May 1714 (Phil. Trans., vol. xxviii. p. 11), his claim to priority was unjustly disputed by John Bernoulli. Taylor’s Methodus Incrementorum Directa et Inversa (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 movement 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 Infinitesimal Calculus), the importance of which remained unrecognized until 1772, when J. L. Lagrange realized its powers and termed it “le principal fondement du calcul différentiel.”
In his essay on Linear Perspective (London, 1715) 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, and needed the elucidation bestowed on it in the treatises of Joshua Kirby (1754) and Daniel Fournier (1761).
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 Sir Isaac Newton and Gottfried Wilhelm Leibnitz, and acted as secretary to the society from the 13th of January 1714 to the 21st of October 1718. From 1715 his studies took a philosophical and religious bent. He corresponded, in that year, with the Comte de Montmort on the subject of Nicolas Malebranche’s tenets; and unfinished treatises, “On the Jewish Sacrifices” and “On the Lawfulness of Eating Blood,” written on his return from Aix-la-Chapelle in 1719, were afterwards found among his papers. His marriage in 1721 with Miss Brydges of Wallington, Surrey, led to an estrangement from his father, a person of somewhat morose temper, which terminated in 1723 after the death of the lady in giving birth to a son. The ensuing two years were spent by him with his family at Bifrons, and in 1725 he married, with the paternal approbation, Sabetta, daughter of Mr Sawbridge of Olantigh, Kent, who, by a strange fatality, died also in childbed in 1730; in this case, however, the infant, a daughter, survived. Taylor’s fragile health gave way; he fell into a decline, died on the 29th of December 1731, at Somerset House, and was buried at St Ann’s, Soho. By his father’s death in 1729 he had inherited the Bifrons estate. As a mathematician, he was the only Englishman after Sir Isaac Newton and Roger Cotes capable of holding his own with the Bernoullis; but a great part of the effect of his demonstrations was lost through his failure to express his ideas fully and clearly.
A posthumous work entitled Contemplatio Philosophica was printed for private circulation in 1793 by his grandson, Sir William Young, Bart., prefaced by a life of the author, and with an appendix containing letters addressed to him by Bolingbroke, Bossuet, &c. Several short papers by him were published in Phil. Trans., vols. xxvii. to xxxii., including accounts of some interesting experiments in magnetism and capillary attraction. He issued in 1719 an improved version of his work on perspective, with the title New Principles of Linear Perspective, revised by Colson in 1749, and printed again, with portrait and life of the author, in 1811. A French translation appeared in 1753 at Lyons. Taylor gave (Methodus Incrementorum, p. 108) the first satisfactory investigation of astronomical refraction.
See Watt, Bibliotheca Britannica; Hutton, Phil. and Math. Dictionary; Fétis, Biog. des Musiciens; Th. Thomson, Hist. of the R. Society, p. 302; Grant, Hist. Phys. Astronomy, p. 377; Marie, Hist. des Sciences, vii. p. 231; M. Cantor, Geschichte der Mathematik.