In the year 1697, our author published, in the Phil. Transactions, a long paper On the properties of the catena ria or curve line, ormed by a heavy and flexible chain, hang ing freely from two points of suspension. The leading pro perties contained in this communication, had been pre viously discovered and published by Huygens, Leibnitz, and Bernoulli, but without demonstrations ; and Mr Grego ry proposed to himself to demonstrate these properties. An anonymous writer in the Leipsic Acts for February 1691, attacked this paper as destitute of originality. Dr Gre gory replied to this attack in the Phil. Trans. for 1699, and claimed as his own discovery the property ol the cate naria as being the true geometrical figure of an equilibrat ed arch. This discovery, however, had been previously made by Dr Hooke*.
The greatest of Dr Gregory's works, and that on which his fame must rest, appeared at Oxford in 1702, entitled Astronomice Physics et Geometric Elementa, Fol. In this valuable work, all the physical explanations are founded on the principles of the Newtonian philosophy; and the geometrical parts are either proved by reference to the writings of standard authors, or demonstrated by lemmas inserted in their proper places. A very admirable analysis of this work was given, apparently by Dr Halley, in the Phil. Trans. for 1703. Newton himself considered these elements as an excellent defence and exposition of his philosophy.
This work was followed, in 1703, with an edition of Euclid, entitled Euclidis quse supersunt omnia, Gr. et Lat. ex recensione Davidis Grcgorii, M. D. &c. It was pub lisfied in prosecutiom of a plan of Sir Henry Saville to print the works of the ancient mathematicians. It con tains the Elements; the Data ; two musical tracts ; the Optics and Catoptrics; the tract De Divisionibus ; and a fragment, De Levi et Ponderoso.
In the year 1704, Dr Gregory published, in the Philoso sophical Transactions, a paper on Cassini's Orbit of the Planets, in which he shcwed that the hypothetical curve proposed by that astronomer, is not consistent with the re ceived doctrines of astronomy.
After Dr Halley had been appointed to the Savilian professorship of Geometry in 1703, he embarked with Dr Gregory in the of Sir Henry Saville's plan, and had begun the publication of the Conics of Apollo nius ; but after having proceeded a short way in this un dertaking, he was seized with an illness of which he died, at Maidenhead in Berkshire, on the 10th of October 1710, in the 49th year of his age.
He left behind him four sons by his wife Elizabeth, daughter of Mr Oliphant of Langtown, to whom he was married in 1695. Among his manuscripts were found, .1 Short Treatise of the nature and Arithmetic of Logarithms. which was afterwards published in Dr Keill's translation ol Commandine's Euclid ; a Treatise of Practical Geometry, which was translated and published by Mr Maclaurin in 1745 ; and a commentary on the Principia, which Newton kept by him many years after the author's death. Sit Isaac had entrusted Gregory with a manuscript copy of the Principia for this purpose, and he availed himself ol the annotations of his friend in the second edition of that immortal work. A complete copy of these observations was presented, by the present Dr James Gregory, to the library of the University of Edinburgh, where it is care fully preserved. There are some paragraphs in this ma nuscript in the handwriting of Huygens, concerning his theory of light.
His wife, who survived him, erected an elegant monu ment to his memory in the church of St Mary, Oxford, with the following inscription : P. M.