In addition the first proof of the fundamental theorem of calculus and the discovery of the Taylor series can both be attributed to him. Nevertheless Gregory was effectively among the first to speculate about the existence of what are now termed transcendental numbers. Hence he inferred that the quadrature of the circle was impossible this was accepted by Montucla, but it is not conclusive, for it is conceivable that some particular sector might be squared, and this particular sector might be the whole circle. 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. In 1667, Gregory 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. He also described the method for using the transit of Venus to measure the distance of the Earth from the Sun, which was later advocated by Edmund Halley and adopted as the basis of the first effective measurement of the Astronomical Unit. In the Optica Promota, published in 1663, Gregory described his design for a reflecting telescope, the " Gregorian telescope". He died a few days later at the age of 36. Ībout a year after assuming the Chair of Mathematics at Edinburgh, James Gregory suffered a stroke while viewing the moons of Jupiter with his students. He was the grandfather of John Gregory (FRS 1756) uncle of David Gregorie (FRS 1692) and brother of David Gregory (1627–1720), an inventor. He had married Mary, daughter of George Jameson, painter, and widow of Peter Burnet of Elrick, Aberdeen their son James was Professor of Physics at King's College Aberdeen. He was successively professor at the University of St Andrews and the University of Edinburgh. Upon his return to London in 1668 he was elected a Fellow of the Royal Society, before travelling to St Andrews in late 1668 to take up his post as the first Regius Chair of Mathematics, a position created for him by Charles II, probably upon the request of Robert Moray. ![]() At Padua he lived in the house of his countryman James Caddenhead, the professor of philosophy, and he was taught by Stefano Angeli. In 1664 he departed for the University of Padua, in the Venetian Republic, passing through Flanders, Paris and Rome on his way. In 1663 he went to London, meeting John Collins and fellow Scot Robert Moray, one of the founders of the Royal Society. He was sent to Aberdeen Grammar School, and then to Marischal College, graduating in 1657. After his father's death in 1651 his elder brother David took over responsibility for his education. It was his mother who endowed Gregory with his appetite for geometry, her brother – Alexander Anderson – having been a pupil and editor of Viète. The youngest of the 3 children of John Gregory, an Episcopalian Church of Scotland minister, James was born in the manse at Drumoak, Aberdeenshire, and was initially educated at home by his mother, Janet Anderson. 2.2 Vera Circuli et Hyperbolae Quadratura.This is the theorem on which many of the subsequent calculations of approximations to the numerical value of π have been based. The result being true only if θ lie between -1/4 π and 1/4 π. In 1671, or perhaps earlier, he established the theorem that It was reprinted in 1668 with an appendix, Geometriae Pars, in which Gregory explained how the volumes of solids of revolution could be determined. This book contains also the earliest enunciation of the expansions in series of sin x, cos x, sin -1 x or arc sin x, and cos -1 x or arc cos x. In 1667 he issued his Vera Circuli et Hyperbolae Quadratura, in which he shewed how the areas of the circle and hyperbola could be obtained in the form of infinite convergent series, and here (I believe for the first time) we find a distinction drawn between convergent and divergent series. In 1660 he published his Optica Promota, in which the reflecting telescope known by his name is described. ![]() James Gregory, born at Drumoak near Aberdeen in 1638, and died at Edinburgh in October 1675, was successively professor at St. You should visit Browse Happy and update your internet browser today! The embedded audio player requires a modern internet browser.
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