# James Gregory (mathematician)

James Gregory ( * November 1638 in Drumoak in Aberdeen, † October 1675 in Edinburgh) was a Scottish mathematician and astronomer. He found significant results of analysis or simultaneously with his contemporaries, but published little.

## Life and work

The pastor's son James Gregory was taught early on by his mother in mathematics and geometry. He attended the Marischal College, Aberdeen, where he mainly dealt to its conclusion in 1657 with astronomy and mathematical optics.

1663 Gregory published a book about his researches in optics, Optica Promota. In it he dealt with lenses, reflection, refraction, parallax and first used photometric methods for measuring distance. He also suggested to observe Venus transits for determining the astronomical unit, a proposal that was repeated later by Edmund Halley without mention of the priority Gregory. His most significant development was the description of an reflecting telescope, which directs with a secondary concave mirror, the reflected light of the primary parabolic mirror through a small hole in the primary mirror to the eyepiece. As Gregory telescope known, this design was used until the 19th century.

For his book he found while in 1663 a publisher in London, but no craftsman who could make the required mirror for his telescope. This should only ten years later Robert Hooke succeed.

From London he traveled in 1664 via Paris to Padua, where he worked on the calculation of circular and parabolic surfaces by infinite convergent series in collaboration with Stefano degli Angeli ( 1623-1697 ). There was 1667, the book Vera Circuli et hyperbolae quadratura in which he dealt with the basics of differential calculus and Geometriae pars universalis (1668 ), contains the first known proof of the fundamental theorem of calculus. In the same work, he determined the distance to Sirius by photometric comparison with Jupiter to 1.25 light-years instead of the current value of 8.6 LJ.

On his return to London in 1668 he was appointed a Fellow of the Royal Society and received in the same year a chair of mathematics at the University of St Andrews. It is certain that he knew the Taylor series of sine and cosine, and tangent of this summer. The latter opened up new avenues in the calculation of the circle number. A year later he married in St Andrews Jamesome Mary, the mother of two daughters and a son.

In St. Andrews followed by other significant achievements, such as in 1671, the independent discovery of the Taylor formula, the Brook Taylor himself only published in 1715. Many of these works can be found only in letters to colleagues, as Gregory after a plagiarism dispute with Christiaan Huygens very little published.

James Gregory discovered the diffraction of light by bird feathers and examined the diffraction pattern occurring.

After lengthy disputes with colleagues and the university management in St. Andrews, which at times even locked his salary, followed Gregory in 1674 a call to the newly established chair of mathematics at the University of Edinburgh. A year after his appointment he suffered in observing the moons of Jupiter a stroke, he died a few days later.

James Gregory was the grandfather of John Gregory and the uncle of the mathematician David Gregory.