William Neile, the eldest son of Sir Paul Neile, was born in York on 7 December 1637 in the palace of his grandfather Richard Neile, Archbishop of York. He died in White Waltham, Berkshire on 24 August 1670. ‘Deep melancholy,’ one observer recorded, ‘hastened his end through his love for a maid of honour, to marry whom he could not obtain his father's consent.’ In 1652 Neile entered Wadham College, Oxford, and although he took the trouble to matriculate in 1655, he never took a degree, leaving instead two years later to become a student at the Middle Temple. It was around that time that Neile discovered the cubical rectification of the parabola, which John Wallis published in his De cycloide (1659). Later that year Wallis also published William Brouncker's improvement of Neile's rectification. On 31 December, 1662 Neile was recommended by Robert Moray for membership of the Royal Society, and he was elected a week later. In 1666 Neile was elected to serve on the Council. For the most part, however, Neile resided in his father's house at White Waltham, devoting much of his time to astronomical observations in the observatory that his father had built there during the Interregnum.
From The Continuum Encyclopedia of British Philosophy in Oxford Reference.