He was also the author of _Exercitationes geometricae_ (1668), and, it is alleged, of a satirical tract entitled _The Great and New Art of Weighing Vanity_, intended to ridicule certain fallacies of a contemporary writer on hydraulics, and published at Glasgow in 1672, professedly by "Patrick Mathers, archbeadle of the university of St Andrews." III. DAVID GREGORY (1661-1708), son of David Gregory (1627-1720), was born in Aberdeen and educated partly in his native city and partly in Edinburgh, where he became professor of mathematics in 1683. From 1691 till his death he was Savilian professor of astronomy at Oxford. His principal works are _Exercitatio geometrica de dimensione figurarum_ (1684), _Catoptricae et dioptricae sphaericae elementa_ (1695), and _Astronomiae physicae et geometricae elementa_ (1702)--the last a work highly esteemed by Sir Isaac Newton, of whose system it is an illustration and a defence. _A Treatise on Practical Geometry_ which he left in manuscript was translated from the Latin and published in 1745. He was succeeded in the chair of mathematics in Edinburgh by bis brother James; another brother, Charles, was in 1707 appointed professor of mathematics in the university of St Andrews; and his eldest son, David (1696-1767), became professor of modern history at Oxford, and canon and subsequently dean of Christ Church. IV. JOHN GREGORY (1724-1773), Scottish physician, grandson of James Gregory (1638-1675) and youngest son of Dr James Gregory (d. 1731), professor of medicine in King's College, Aberdeen, was born at Aberdeen on the 3rd of June 1724. He received his early education at the grammar school of Aberdeen and at King's College in that city, and in 1741 he attended the medical classes at Edinburgh university. In 1745 he went to Leiden to complete his medical studies, and during his stay there he received without solicitation the degree of doctor of medicine from King's College, Aberdeen. On his return from Holland he was elected professor of philosophy at King's College, but in 1749 he resigned his professorship on account of its duties interfering too much with his private practice. In 1754 he proceeded to London, where he made the acquaintance of many persons of distinction, and the same year was chosen fellow of the Royal Society. On the death in November 1755 of his brother Dr James Gregory, who had succeeded his father as professor of medicine in King's College, Aberdeen, he was appointed to that office. In 1764 he removed to Edinburgh in the hope of obtaining a more extended field of practice as a physician, and in 1766 he was appointed professor of the practice of medicine in the university of Edinburgh, to whose eminence as a medical school he largely contributed. He died of gout on the 10th of February 1773.