BARROW, ISAAC

born 1630, London, Eng. died May 4, 1677, London English classical scholar, theologian, and mathematician who was the teacher of Isaac Newton. He developed a method of determining tangents that closely approached the methods of calculus, and he was first to recognize that the processes of integration and differentiation in calculus are inverse operations. Barrow's degree was granted in 1648, but his academic appointment was delayed because of political unrest during the Cromwellian period. He was ordained an Anglican minister in 1660 and became a professor of Greek at the University of Cambridge (166063). Two years later he was also appointed professor of geometry at Gresham College, London. Of his early works, which dealt primarily with ancient Greek mathematics, the most notable is his translation of Euclid's Elements: The Whole Fifteen Books (1660), which was reissued six times in the early 18th century. As Lucasian professor of mathematics at Cambridge (166369), he devoted much of his time to the preparation of three lecture series concerning optics (1669), geometry (1670), and mathematics (1683). These lectures contain most of his contributions to science and mathematics. His Lectiones Geometricae (1670; Geometrical Lectures) contained elements similar to the calculus later developed by Gottfried Leibniz of Germany, and it was known to both Leibniz and Newton. The association between Newton and Barrow has often been disputed. Newton was Barrow's pupil, he did attend some of Barrow's later lectures, and he was influenced to an uncertain extent. They worked together for a short time in 1669. In that year Barrow resigned his chair in favour of Newton and thereafter devoted himself to the study of divinity. In 1670 he became chaplain to Charles II, in 1673 was appointed master of Trinity College, Cambridge, and in 1675 was chosen vice chancellor of Cambridge.