In 1688, our author published at Lon don another work, entitled " Exercita tiones Geometricx," which contributed still much further to extend his reputa tion. About this time he was elected - Professor of Mathematics in the Univer sity of St. Andrews, an office which he held for six years. During his resi dence 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 An twerp.
In 1672, he published " The great and new Art of weighing Vanity : or a Dis covery of the Ignorance and Arrogance of the great and new Artist, in the pseu do-philosophical Writings. By H. Pa trick Mathers, Archbedal to the Univer sity of St. Andrews To which are an nexed some Tentamina de Motu Penduli et Projeetorum." Under this assumed name, our author wrote this little piece, to expose the ignorance of Mr. Sinclare, professor at Glasgow, in his hydrostatical writings, and in return for some ill usage of that author to a colleague of Mr. Gre gory's. The same year Newton, on his wonderful discoveries in the nature of light, having contrived a new reflecting telescope, and made several objections to Mr Gregory's, this gave birth to a dis pute between those two philosophers, which was carried on during this and the following year, in the most amicable man ner, on both sides ; Mr. Gregory defend ing his own construction, so far as to give his antagonist the whole honour of hav ing made the catoptric telescopes prefer able to the dioptric, and showing that the imperfections in these instruments were not so much owing to a defect in the ob ject speculum, as to the different retTan gibility of the rays"of light. In the course of this dispute our author described a burning concave mirror, which was ap proved by Newton, and is still in good esteem. Several letters that passed in this dispute . are printed by Dr. Desagu liers, in an appendix, to the English edi tion of Dr. David Gregory's" Elements of Catoptrics amd Dioptrics." In 1674, Mr. Gregory was called to Edinburgh, to fill the chair of mathema tics in that university. This place he had held but little more than a year, when, in October 1675, being employed in shewing 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, to the great loss of the mathematical world, at only 37 years of age.
As to his character, Mr. James Grego ry was a man of very acute and penetrat ing genius. His temper seems to have been warm, as appears from his conduct in the dispute with Huygens : and, con scious perhaps of his own merits as a dis coverer, he seems to have been jealous of losing any portion of his reputation by the improvements of others upon his in ventions. He possessed one of the most
amiable characters of a true philosoper, that of being content with his fortune in his situation. But the most brilliant part of his character is that of his mathemati cal genius as an inventor, which was of the first order; as will appear by the fol lowing list of his inventions and discove ries. Among many others may be reek oned his reflecting telescope ; burning concave mirror; quadrature of the circle and hyperbola, by an infinite converging series ; his method for the transformation of curves ; a geometrical demonstration of Lord Brounker's series for squaring the hyperbola ; his demonstration that the meridian line is analogous to a scale of logarithmic tangents of the half-com plements of the latitude : he also invent ed, and demonstrated geometrically, by help of the hyperbola, a very simple con verging series for making the logarithms : he sent to Mr Collins the solution of the famous Keplerian problem by an infinite series ; he discovered a method of draw ing tangents to curves geometrically, without any previous calculations; a rule for the direct and inverse method of tan gents, which stands upon the same prin ciple (of exhaustions) with that of flux ions, and differs not much from it in the manner and application; a series for the length of the arc of a circle, from the tangent, and vice versa. These, with others for measuring the length of the elliptic and hyperbolic curves, were sent to Mr. Collins, in return for some receiv ed from him of Newton's, in which he followed the elegant example of this au thor, in delivering his series in simple terms, independently of each other.— These, and other writings of our author, are mostly contained in the following works, viz.: 1. Optica Promota ; 4to. Lon don, 1663. 2. Vera Circuli et Hyperbo lx Quadratura, 4to. Padua, 1667 and 1668. 3. Geometrix Pars Universalis, 4to. Padua, 1668. 4. Exercitationes Geo metriem, 4to. London, 1668. 5. The great and new Art of weighing Vanity, Svo. Glasgow, 1672. The rest of his in ventions make the subject of several let ters and papers, printed either in the Phi los. Trans. vol. iii., the Commerc. Epis tol. Joh. Collins, et aliorum, 8vo. 1715, in the appendix to the English edition of Dr. David Gregory's Elements of Optics, 8vo. 1735, by Dr. Desaguliers, and some series in the Exercitatio Geometrica of the same author, 4to. 1684, Edinburgh ; as well as in his little piece on Practical Geometry.