Gregory

James Gregory

Born: Nov 1638 in Aberdeen, Scotland
Died: Oct 1675 in Edinburgh, Scotland

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James Gregory described the first practical reflecting telescope. He worked on using infinite convergent series to find the areas of the circle and hyperbola

In 1663 Gregory published Optica Promota which described the first practical reflecting telescope now called the Gregorian telescope. A primary concave parabolic mirror converges the light to one focus of a concave ellipsoidal mirror. Reflection of light rays from its surface converge to the ellipsoid's second focus which is behind the main mirror. There is a central hole in the main mirror through which the light passes. The tube of the Gregorian telescope is thus shorter than the sum of the focal lengths of the two mirrors.

In 1665 Gregory went to the University of Padua where he worked on using infinite convergent series to find the areas of the circle and hyperbola. In 1668 he published Geometricae Pars Universalis which found the areas under curves and the volumes of their solids of revolution.

Gregory was appointed professor at St Andrews in 1668 and became the first Professor of Mathematics at Edinburgh in 1674. He made important contributions in mathematics in addition to those described above. His mathematical work included infinite series expansions for

arc tan x, tan x, arc sec x

and he was one of the first to distinguish convergent and divergent series.

His series for arc tan x, discovered in 1671, yields, for x = 1,

pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...

This expansion for pi/4 was discovered independently by Leibniz in 1673.

References elsewhere in this archive:

There is a longer article on Gregory's time in St Andrews

Other Web sites:

Rice University, USA

References:

  1. Dictionary of Scientific Biography
  2. Biography in Encyclopaedia Britannica
  3. H W Turnbull, James Gregory Tercentenary Memorial Volume (London, 1939).
  4. A Malet, James Gregorie on Tangents and the 'Taylor' Rule for Series Expansions, Archive for History of Exact Sciences 46 (1993-94), 97-137.
  5. A Malet, Studies on James Gregorie (1638-1675) (PhD Thesis, Princeton, 1989).
  6. A D C Simpson, James Gregory and the reflecting telescope, Journal for the history of astronomy 43 (1992), 77-92. 
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