GREGORY (Jarixs), professor of ma thematics, first in the university of St. An drews, and afterwards in that of Edin burgh, was one of the most eminent ma thematicians of the seventeenth century. He was a son of the Rev. John Gregory, minister of Drumoak, in the county of Aberdeen, and was born at Aberdeen, in November 1638. His mother was a daughter of Mr. David Anderson, of Fin zaugh, or Finshaugh ; a gentleman who possessed a singular turn for mathemati cal and mechanical knowledge. This mathematical genius was hereditary in the family of the Andersons, and from them it seems to have been transmitted to their descendants of the names of Gregory, Reid, &c. Alexander Anderson, cousin german of the said David, was professor of mathematics at Paris in the beginning of the 17th century, and published there several valuable and , ingenious works. The mother of James Gregory inherited the genius of her family ; and observ ing in her son, while yet a child, a strong propensity to mathematics, she instruct ed him herself in the elements of that science. His education in the languages he received at the grammar-school of Aberdeen, and went through the usual course of academical studies in the Ma rischal college ; but he was chiefly de lighted with philosophical researches, into which a new door had lately been opened by the key of the mathematics.
Galileo, Kepler, Des Cartes, &c. were the great masters of this new method; their works therefore became the princi pal study of young Gregory, who soon began to make improvements upon their discoveries in Optics. The first of these improvements was the invention of the reflecting telescope ; the construction of which instrument be published in his "Optics Promota," in 1663, at ttventy four years of age. This discovery soon attracted the attention of the mathemati cians, both of our own and of foreign countries, who immediately perceived its great importance to the sciences of op tics and astronomy. But the manner of placing the two specula upon the same axis appearing to Newton to be attended with the disadvantage of losing the cen tral rays of the larger speculum, he pro posed an improvement on the instrument, by giving an oblique position to the small er speculum, and placing the eye-glass in the side of the tube. It is observable, however, that the Newtonian construc tion of that instrument waslong abandon ed for the original, or Gregorian, which is now always used when the instrument is of a moderate size ; though Herschell has preferred the Newtonian form for the construction of those immense telescopes, which he has of late so successfully em ployed in observing the heavens.
About the year 1664, or 1665, coming to London, he became acquainted with Mr John Collins, who recommended him to the best optic glass-grinders there, to have his telescope executed. But as this
could not be done, for want of skill in the artist to grind a plate of metal for the object speculum into a true parabolic con. cave, which the design required, he was much discouraged with the disappoint. ment,and,after a few imperfect trials made with an ill-polished spherical one, which did not succeed to his wish, he dropped the pursuit, and resolved to make the tour of Italy, then the mart of mathemati cal learning, that he might prosecute his favourite study with greater advantage. And the University of Padua being at that time in high reputation for mathe matical studies, Mr. Gregory fixed his residence there for some years. Here it was that he published, in 1667, "Vera Circuli et Hyperbolae Quadratura;" in which he propounded another discovery of his own, the invention of an infinitely converging series for the areas of the cir cle and hyperbola. He sent home a copy of this work to his friend Mr. Collins, who communicated it to the Royal Society, where it met with the commendations of Lord Brounker and Dr. Wallis. He re printed it at Venice the following year, to which he added a new work, entitled "Geometrize Pars Universalis, inserviens Quantitatum Curvarum, Transmutationi et Mensurx ;" in which he is allowed to have shewn, 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, New ton, Huygens, Wallis, and others. An account of this piece was also read be fore the Royal Society, of which Mr. Gregory, being returned from his travels, was chosen a member the same year, and communicated to them an account of the controversy in Italy about the motion of the earth, which was denied by Riccioli, and his followers. Through this channel, in particular, he carried on a dispute with M. Huygens, on the occasion of his trea tise on the quadrature of the circle and hyperbola, to whin that great man had started some objections ; in the course of which our author produced some im provements of his series. But in this dispute it happened, as it generally does on such occasions, that the antagonists, though setting out with temper enough, yet grew too warm in the combat. This was the case here, especially on the side of Gregory, whose defence was, at his own request, inserted in the Philosophi cal Transactions. It is unnecessary to enter into particulars : suffice it there fore to say, that, in the opinion of Leib nitz, who allows Mr. Gregory the high est merit for his genius and discoveries, M. Huygens has pointed out, though not errors, some considerable deficiencies in the treatise above-mentioned, and shown a much simpler method of attaining the same end.