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James Gregory (November 1638 - October 1675), was a Scottish mathematician and astronomer. He was born at Drumoak near Aberdeen, and died at Edinburgh. He was
successively professor at St. Andrews and Edinburgh.
In 1660 he published his Optica Promota, in which the compact reflecting telescope known by his name, the Gregorian telescope, is
described. The telescope design attracted the attention of several people in the scientific establishment: Robert Hooke, the Oxford physicist who eventually built the telescope, Sir Robert Moray, polymath and founding
member of the Royal Society and Isaac Newton, who was at work on a similar project of his own. Later, Gregory, who was and enthusiastic
supporter of Newton, carried on much friendly correspondence with him and incorporated his ideas into his own teaching, ideas
which at that time were controversial and considered quite revolutionary.
In 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. 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 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. It was reprinted in 1668 with an appendix, Geometriae
Pars, in which Gregory explained how the volumes of solids
of revolution could be determined.
In 1671, or perhaps earlier, he established the theorem that
- ,
the result being true only if θ lie between -(1/4)π and (1/4)π. This is a theorem on which subsequent
calculations of approximations to the numerical value of π have been based.
David Gregory was his nephew.
External link
MacTutor biography
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