William Neile

William Neile (1637 to 1670) was an English mathematician and a founder member of the Royal Society. His major mathematical work, the rectification of the semicubical parabola, was done when he was nineteen and published by John Wallis. By determining arc lengths of a curve given algebraically, extending to algebraic curves with Cartesian geometry a basic idea of differential geometry, it was a major advance toward what became infinitesimal calculus. His name also appears as Neil. Born at Bishopsthorpe, the eldest son of Sir Paul Neile, member of Parliament for Ripon and Newark, and grandson of Richard Neile, Archbishop of York, he entered Wadham College, Oxford, as a gentleman-commoner in 1652, where John Wilkins and Seth Ward taught him. In 1657 he became a student at the Middle Temple and gave his exact rectification, which he told William Brouncker, Christopher Wren and others at Gresham College about, and Wallis published it in De Cycloide in 1659. Hendrik van Heuraet found the general formula in 1659, and in 1673 Wallis asserted that Christiaan Huygens had slighted Neile's priority. Neile was elected a fellow of the Royal Society on 7 January 1663 and a member of its council in April 1666, and criticised the empiricist stance of other members in the debate on the theory of motion.