this lime in high repute for mathematical learning-, and Gregory repaired thither
from London, about the end of 1667, for the purpose of prosecuting his favourite
study. Here he published a Latin work on the areas of the circle and hyperbola, determined by an infinitely converging series; a second edition of which
he afterwards published at Venice, with an appendix on the transmutation of
curves. Mr Collins, who always showed himself zealous in Gregory's favour,
introduced this work to the notice of the Royal Society of London, of which he
was secretary. This work received the commendation of that distinguished nobleman lord Brounker, and Dr Wallis, the celebrated inventor of the arithmetic
of infinites. Gregory's attention was once more drawn to the squaring of curves,
by the method of converging series, on account of receiving an instance of the
case of the circle in a letter from his friend Collins, who informed him that
Newton had discovered a general method for all curves, mechanical and geometrical. Gregory speedily returned to Collins a method for the same purpose,
which he was advised by his brother David to publish. Gregory refused to do
this, and that from the most honourable motive : as Newton was the original inventor, he deemed it unfair to publish it, until Sir Isaac should give his method
to the public. Soon after, he returned to London, and from his celebrity as a
mathematician, he was chosen a fellow of the Royal Society. He read before the
society, the account of a dispute in Italy concerning the motion of the earth, which
Riciolli and his followers had denied, besides many other valuable communications. Huygens had attacked Gregory's method of quadrature in a journal of
that period, to which he replied in the Philosophical Transactions. The dispute
was carried on with great warmth by both, and from Gregory's defence it would
appear he was a man of warm temperament, but acute and penetrating genius. Of
the merits of either, in this dispute, it would be out of place here to enter into
detail. Leibnitz, who considered the subject with attention, and whose capacity
of discernment in such matters cannot be questioned, is of opinion, that although Huygens did not point out errors in the work of Gregory, yet he obtained some of the results by a much simpler method.
The small work "Exercitationes Geometricae," published by Gregory at London in 1668, consisted of twenty-six pages, containing however a good deal of important matter. No where do we learn more of the real private character of Gregory than in the preface and appendix to this little work. He speaks in explicit terms of his dispute with Huygens, complains of the injustice done him by that philosopher and some others of his contemporaries; and we are led to conclude from them, that he was a man who, from a consciousness of his own powers, was jealous of either a rival or improver of any invention or discovery with which he was connected. The same year in which he published this last work, he was chosen professor of mathematics in the university of St Andrews. The year following he married Miss Mary Jamieson, daughter of Mr George Jamieson, the painter whom Walpole has designated the Vandyke of Scotland. By his wife he had a son and two daughters. The son, James, was grandfather of Dr Gregory, author of the "Theoreticae Medicinae," and professor of the theory of medicine in the university of Edinburgh. James Gregory remained at St Andrews for six years, when he was called to fill the mathematical chair in the university of Edinburgh. During his residence at St Andrews, he wrote a satire on a work of Mr George Sinclair's, formerly professor of natural philosophy in Glasgow, but who had been dismissed on account of some political heresies. Dr Gregory did not live to enjoy the chair in Edinburgh more than one year; for returning home late one evening in October, 1675, after showing some of his students the satellites of Jupiter, he was suddenly struck blind, and three days afterwards expired. Thus, at the early age of thirty-seven, in the vigour
