Chapter II: JAMES GREGORY (1638-1675), Scottish mathematician, younger brother

of the preceding, was educated at the grammar school of Aberdeen and at Marischal College of that city. At an early period he manifested a strong inclination and capacity for mathematics and kindred sciences; and in 1663 he published his famous treatise _Optica promota_, in which he made known his great invention, the Gregorian reflecting telescope. About 1665 he went to the university of Padua, where he studied for some years, and in 1667 published _Vera circuli et hyperbolae quadratura_, in which he discussed infinite convergent series for the areas of the circle and hyperbola. In the following year he published also at Padua _Geometriae pars universalis_, in which he gave a series of rules for the rectification of curves and the mensuration of their solids of revolution. On his return to England in this year he was elected a fellow of the Royal Society; in 1669 he became professor of mathematics in the university of St Andrews; and in 1674 he was transferred to the chair of mathematics in Edinburgh. In October 1675, while showing the satellites of the planet Jupiter to some of his students through one of his telescopes, he was suddenly struck with blindness, and he died a few days afterwards.

He was also the author of _Exercitationes geometricae_ (1668), and, it
is alleged, of a satirical tract entitled _The Great and New Art of
Weighing Vanity_, intended to ridicule certain fallacies of a
contemporary writer on hydraulics, and published at Glasgow in 1672,
professedly by "Patrick Mathers, archbeadle of the university of St
Andrews."