JAMES OREOORY, the first and most eminent, was son of the minister of Drumoak in Aberdeenshire, born at Aberdeeu 1638 or 1639, and educated at the university of that town. He went with credit through the usual studies, and showed a peculiar turn for mathematic& Especially he applied himself to optics ; and before the ego of twenty four had invented and published in his Optics Promote' a description of the reflecting telescope which bears his name, and still continues iu the most general use. About 1665 or 1666 he travelled to Italy, aud spent some years in prosecuting his studies at Padua. There in 1667 he published his method of expressing circular and hyperbolic areas by means of a converging series, which in tho next year he followed by a general method of measuring curved quantities, described by Montucla as a collection of curious and useful theorems for the trans formation and quadrature of curvilinear figures, the rectification of curves, the measurement of their solids of revolution, Ste., mostly characterised by great elegance, and generalised in a way peculiar to their author. Returning to Loudon about 1663, he was elected F.R.S., and soon after professor of mathematics at St. Audrews. That office he held until 1674, when he accepted the same chair in Edinburgh. In October 1675 ho was suddenly struck blind, and died within a few days, at the early age of thirty-six.
His character is thus described by Dr. Hutton (' Phil. and Math. Diet.') :—"James Gregory was a man of very acute and penetrating genius. His temper was in some degree an irritable one; and, couscious 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 on his inventions. He possessed one of the most amiable characters of a true philosopher, that of being content with his fortune iu his situation. But the most brilliant part of hie character is that of his mathematical genius as an inventor, which was of the first order." Dr. Hutton pro ceeds to give a list of his chief inventions, which follows here iu condensed form :—Reflecting Telescope, Burning Mirrors, Quadraturo of Circle and Hyperbola, Method for the Trsusformation of Curves, Demoustration that the Meridian Line is analogous to a scale of Logarithmic Tangents of the Half-Complements of the Latitude (on which the description of Mercator's Chart depends), Converging Series for making Logarithms, Solution of the Keplerian Problem, Geome trical Method of drawing Tangents to Curves, Rule for the Direct and Inverse Method. of Tangents, Various Series for expressing the Length
of Curves. It is said that on learoiug that Newton had discovered a general method of squaring all curves by infinite series, James Gregory applied himself to the subject, and arrived at a similar one. This he was strongly urged by his brother David to publish, but he very generously refused to do so, on the ground that, as he had been led to it by Newton's discovery, he was bound in honour to wait till Newton should publish his. His great powers as a geometrician were in some degree obscured by the length and intricacy of his methods. This fault however he wished partly to correct by the study of Newton's. His quadrature of the circle involved him in a dispute with Huygens, which led him to make improvements in his original method.
The following are James Gregory's works :—'Optica Promota, ste.; Loud., 1663; Vera Circuli et Hyperbolae Quadmtura,' Patay., 1667; 'Geometries Pars Uuiversalis,' Patsy., 1668 ; Exercitationee Geomo trim,' Lend., 1668 ; The Great and New Art of Weighing Vanity, &c.' Glasgow, 1772, published under the assumed name of Patrick Mothers, Archbeadlo to the University of St. Andrews; and detached papers and letters, published in the Philo& Trans. The Optics Promote,' and the tract on Weighing Vanity' (a silly satirical pro duction, the authorship of which is by no means certain), were reprinted at the expense of Baron Maseres, in a collection of tracts called Scrip toms Optici; London, 1823. There are copious extracts from James Gregory's works in the Commercium Epistolicum.'