GREGORY, James, one of the most eminent mathematicians of the seventeenth century, was a son of the reverend John Gregory, minister of Drumoak, in the county of Aberdeen, and was born at Aberdeen in 1638. His mother was a daughter of Mr David Anderson of Finzaugh, a gentleman who possessed a singular turn for mathematical and mechanical knowledge. Mathematical genius was indeed hereditary in the family of the Andersons, and from them it seems to have been transmitted to their descendants of the name of Gregory. Alexander Anderson, cousin-german of David Gregory above mentioned, was professor of mathematics at Paris in the beginning of the seventeenth century, and published there, Supplementum Apollonii Rhodii, 1612. The mother of James Gregory inherited the genius of her family; and observing in her son, whilst yet a child, a strong propensity to mathematics, she in-
structed him herself in the elements of that science. He received his education in the languages at the grammar-school of Aberdeen, and went through the usual course of academic studies in the Marischal College.
At the age of twenty-four he published his treatise, entitled Optica Promota, seu abditia Radiumum Reflexorum et Refractorum mysteria, geometrice enucleata; cui subnectitur appendix subtilissimorum Astronomia problematum resolutionem exhibens, London, 1663: a work of great genius, in which he gave the world an invention of his own, one of the most valuable of modern discoveries, namely, the construction of the reflecting telescope. This discovery immediately attracted the attention of mathematicians, both in our own and in foreign countries, all of whom were soon convinced of its great importance to the sciences of optics and astronomy. As the manner of placing the two specula upon the same axis appeared to Sir Isaac Newton to be attended with the disadvantage of losing the central rays of the larger speculum, he proposed an improvement on the instrument, by giving an oblique position to the smaller speculum, and placing the eye-glass in the side of the tube. But it is worth remarking, that the Newtonian construction of the instrument was abandoned for the original or Gregorian, which is now generally employed where the instrument is of a moderate size; though Sir William Herschel preferred the Newtonian form for the construction of those immense telescopes which he so successfully employed in observing the heavens.
The university of Padua being at this time in high repute for mathematical studies, James Gregory went thither soon after the publication of his first work; and, fixing his residence there for some years, he published, in 1667, Vera Circuli et Hyperboles Quadratura, in which he propounded another discovery of his own, the invention of an infinitely converging series for the areas of the circle and hyperbole. To this treatise, when republished in 1668, he added a new work, entitled Geometria Pars Universalis, inseriens quantitatum curvarum transformationi et mensurae, in which he is allowed to have shown, for the first time, a method for the transmutation of curves. These works engaged the notice, and procured the author the correspondence, of the greatest mathematicians of the age, Newton, Huygens, Halley, and Wallis; and as he was soon afterwards chosen a fellow of the Royal Society of London, he contributed to enrich the Philosophical Transactions by many excellent papers. Through this channel, in particular, he carried on a dispute with Huygens, on the occasion of his treatise on the Quadrature of the Circle and Hyperbole, to which that able mathematician had started some objections. It is unnecessary to enter into the particulars of this controversy; but, in the opinion of Leibnitz, who allows Mr Gregory the highest merit for his genius and discoveries, Huygens pointed out considerable deficiencies in the treatise above mentioned, and showed a much simpler method of attaining the end proposed.
In 1688 he published at London another work, entitled Exercitationes Geometricae, which contributed still further to extend his reputation. About this time he was elected professor of mathematics in the university of St Andrews: an office which he held for six years. During his residence there, he married (in 1669) Mary, the daughter of George Jameson, the celebrated painter, whom Mr Walpole has termed the Vandyke of Scotland, and who was a fellow disciple of that great artist in the school of Rubens at Antwerp. In 1674 he was called to Edinburgh to fill the chair of mathematics in that university; but he had held this place for little more than a year, when, in October 1675, being employed in showing the satellites of Jupiter through a telescope to some of his pupils, he was
suddenly struck with total blindness, and died a few days after, at the early age of thirty-seven.