James Gregory (astronomer and mathematician)
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- For other people with the same name, see James Gregory.
In 1663 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.
The Gregorian telescope was the first practical reflecting telescope and remained the standard observing instrument for a century and a half. However, the Gregorian telescope design is rarely used today, as other types of reflecting telescopes are known to be more efficient for standard applications.
Later, Gregory, who was an 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. Nevertheless Gregory was effectively among the first to speculate about the existence of what are now termed transcendental numbers. In addition the first proof of the Fundamental Theorem of Calculus and the discovery of the Taylor Series can both be attributed to him.
This book contains also the expansions in series of sin x, cos x, sin^(-1) x or arc sin x, and cos^(-1) x or arc cos x (The earliest enunciations of these expansions were made by Madhava in India in the 14th century). 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 rediscovered the theorem that 14th century Indian mathematician Madhava of Sangamagrama had originally discovered, the arctangent series
- [\theta = \tan \theta - (1/3) \tan^3 \theta + (1/5) \tan^5 \theta - \cdots,\,]
James Gregory discovered the diffraction grating by passing sunlight through a bird feather and observing the diffraction pattern produced. In particular he observed the splitting of sunlight into its component colours - this occurred a year after Newton had done the same with a prism and the phenomenon was still highly controversial.
The mathematician David Gregory was his nephew.
See also
- Colin Maclaurin
- Telescope
- Possible transmission of Kerala mathematics to Europe
External links
- John J. O'Connor and Edmund F. Robertson. [] at the MacTutor History of Mathematics archive.
- [Trinity College Dublin History of Mathematics]
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