BARROW, ISAAC (1630-1677), English mathematician and divine, was educated at Charterhouse, Felsted, and St. Peter's college, Cambridge, where he studied literature, science, and philosophy. He travelled in France, Italy, and the Near East.
On his return, in 1659, to England he received ordination from Bishop Brownrig, and in 166o he was appointed to the Greek professorship at Cambridge. In July 1662 he was elected profes sor of geometry in Gresham college, on the recommendation of Dr. John Wilkins, master of Trinity college and afterwards bishop of Chester; and in May 1663 he was chosen a fellow of the Royal Society, at the first election made by the council after obtaining their charter. In 1664 he became first Lucasian professor of mathematics at Cambridge, resigning in 166g in favour of his pupil, Isaac Newton. His uncle gave him a small sinecure in Wales, and Dr. Seth Ward, bishop of Salisbury, conferred upon him a prebend in that church. In the year 167o he was created doctor in divinity by mandate ; and, upon the promotion of Dr. Pearson to the see of Chester, he was appointed to succeed him as master of Trinity college by the king's patent, Feb. 13, 1672. In Dr. Barrow was chosen vice-chancellor of the university.
By his English contemporaries Barrow was considered a mathe matician second only to Newton. He was undoubtedly a clear sighted and able mathematician, who handled admirably the severe geometrical method, and who in his Method of Tangents approxi mated to the course of reasoning by which Newton was afterwards led to the doctrine of ultimate ratios; he introduced the differen tial triangle, and was the first to observe explicitly the reciprocal relation between differentiation and integration. (See INFINITESI MAL CALCULUS.) His Sermons have long enjoyed a high reputa tion; they are weighty pieces of reasoning, elaborate in construction and ponderous in style.
His scientific works are very numerous. The most important are:— Euclid's Elements; Euclid's Data; Optical Lectures, read in the public school of Cambridge; Thirteen Geometrical Lectures; The Works of Archimedes, the Four Books of Apollonius's Conic Sections, and Theodosius's Spherics, explained in a New Method; A Lecture, in which Archimedes' Theorems of the Sphere and Cylinder are inves tigated and briefly demonstrated; Mathematical Lectures, read in the public schools of the University of Cambridge. The above were all written in Latin. His English works have been collected and published in four volumes folio.
See Ward, Lives of the Gresham Professors, and Whewell's biography prefixed to the gth vol. of Napier's edition of Barrow's Sermons.