1638 – James Gregory born in November at at Drumoak, Aberdeenshire, Scotland. He was a Scottish mathematician and astronomer. He was successively professor at the University of St Andrews and the University of Edinburgh.
1663 – He published his Optica Promota, in which the compact reflecting telescope known by his name, the Gregorian telescope, is described. The Gregorian telescope was the first practical reflecting telescope and remained the standard observing instrument for a century and a half.
1667 – He issued his Vera Circuli et Hyperbolae Quadratura, in which he showed how the areas of the circle and hyperbola could be obtained in the form of infinite convergent series. This work contains a remarkable geometrical proposition to the effect that the ratio of the area of any arbitrary sector of a circle to that of the inscribed or circumscribed regular polygons is not expressible by a finite number of terms.
1668 – His first book was reprinted with an appendix, Geometriae Pars, in which he explained how the volumes of solids of revolution could be determined.
1671 – He rediscovered the theorem that 14th century Indian mathematician Madhava of Sangamagrama had originally discovered, the arctangent series.
1675 – Died on October in Edinburgh.