GREGORY (James), one of the most eminent mathematicians of the last century, was a son of the Rev. Mr 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. This mathematical genius was hereditary in the family of the Andersons, and from them seems to have been transmitted to their descendants of the name of Gregory. Alexander Anderson, cousin german of the above-mentioned David, was professor of mathematics at Paris in the beginning of the 17th century, and published there in 1612, Supplementum Apollonii redivivus, &c. The mother of James Gregory inherited the genius of her family; and observing in her son, while yet a child, a strong propensity to mathematics, she instructed 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 academical studies in the Marischal college.
At the age of 24 he published his treatise, intitled Optica Promota, seu abditia radiorum reflexorum et refractorum mysteria, geometrice enucleata; cui subnectitur appendix subtilissimorum astronomie problematum resolutionum exhibens, London 1663: a work of great genius, in which he gave the world an invention of his own, and one of the most valuable of the modern discoveries, the construction of the reflecting telescope. This discovery immediately attracted the attention of the mathematicians, both of our own and of foreign countries, who were soon convinced of its great importance to the sciences of optics and astronomy. The manner of placing the two specula upon the same axis appearing 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 that instrument was long abandoned for the original or Gregorian, which is at this day universally employed where the instrument is of a moderate size; though Mr Herschel has preferred the Newtonian form for the construction of those immense telescopes, which of late years he has so successfully employed in observing the heavens.
The university of Padua being at that time in high reputation 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 Hyperbolas 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, intitled, Geometria pars universalis, interserviens quantitatum curvarum transmutationi et mensura; 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 Mr Gregory the correspondence, of the greatest mathematicians of the age, Newton, Huygens, Halley, and Wallis; and their author being soon after chosen a fellow of the royal society of London, contributed to enrich the Philosophical Transactions at that time by many excellent papers. Through this channel, in particular, he carried on a dispute with Mr Huygens, upon the occasion of his treatise on the quadrature of the circle and hyperbole, to which that able mathematician had started some objections. Of this controversy, it is unnecessary to enter into particulars. It is sufficient to say, that, in the opinion of Leibnitz, who allows Mr Gregory the highest merit for his genius and discoveries, Mr Huygens has pointed out, though not errors, some considerable deficiencies in the treatise above mentioned, and thrown a much simpler method of attaining the end in view.
In 1668, Mr James Gregory published at London another work, intitled, Exercitationes Geometricae, which contributed still to extend his reputation. About this time he was elected professor of mathematics in the university of St Andrew's; an office which he held for
Gregory. 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 fellow-disciple with 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. This place he had held 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 37.
He was a man of an acute and penetrating genius. His temper seems to have been warm, as appears from the conduct of his dispute with Mr Huygens; and, conscious perhaps of his own merits as a discoverer, he seems to have been jealous of losing any portion of his reputation by the improvements of others upon his inventions.