William Neile

William Neile (7 December 1637 – 24 August 1670) was an English mathematician and founder member of the Royal Society. His major mathematical work, the rectification of the semicubical parabola, was carried out when he was aged nineteen, and was published by John Wallis. By carrying out the determination of arc lengths on a curve given algebraically, in other words by extending to algebraic curves generally with Cartesian geometry a basic concept from differential geometry, it represented a major advance in what would become infinitesimal calculus. His name also appears as Neil.

Neile was born at Bishopsthorpe, the eldest son of Sir Paul Neile MP for Ripon and Newark. His grandfather was Richard Neile, the Archbishop of York. He entered Wadham College, Oxford as a gentleman-commoner in 1652, matriculating in 1655. He was taught by John Wilkins and Seth Ward.

In 1657, he became a student at the Middle Temple. In the same year he gave his exact rectification of the semicubical parabola and communicated his discovery to William Brouncker, Christopher Wren and others connected with Gresham College. His demonstration was published by Wallis in De Cycloide (1659). The general formula for rectification by definite integral was in effect discovered by Hendrik van Heuraet in 1659. In 1673 Wallis asserted that Christiaan Huyghens, who was advancing his own claim to have influenced Heuraet, was also slighting the priority of Neile.

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