STEWART, (the Rev. Dr. Merrnaw,) in biography, late professor of mathema tics in the University of Edinburgh, was the son of the Rev. Mr. Dugald Stewart, minister of Rothsay, in the Isle of Bute, and was born at that place in the year 1717. After having finished his course at the grammar school, being intended by his father for the church, he was sent to the University of Glasgow, and was enter. ed there as a student in 1734. His aca demical studies were prosecuted with diligence and success; and he was so happy as to be particularly distinguished by the friendship of Dr. Hutcheson, and Dr. Simson, the celebrated geometrician, under whom he made great progress in that science.
Mr. Stewart's views made it necessary for him to attend the lectures in the Uni versity of Edinburgh, in 1741; and that his mathematical studies might suffer no interruption, he was introduced by Dr. Simson to Mr. Maclaurin, who was then teaching both the geometry and the losophy of Newton, and under whom Mr. Stewart made that proficiency which was to be expected from the abilities of such a pupil, directed by those of so great a master. But the modern analysis, even when thus powerfully recommended, was not able to withdraw his attention from the relish of the ancient geometry, which he had imbibed under Dr. Simeon. He still kept up a regular correspondence with this gentleman, giving him an count of his progress, and of his ries in geometry, which were now both numerous and important, and receiving is return many curious communications with respect to the Loci Plani, and the Porisms of Euclid. Mr. Stewart pursued this latter subject in a different and new direction. In doing so, he was led to the discovery of certain curious and resting propositions which he published under the title of " General Theorems," in 1746. They were given without the monstrations; but they did not fail to place their discoverer at once among the geometricians of the first rank. The are, for the most part, Porisms, thou Mr. Stewart, careful not to anticipate e discoveries of his friend, gave them only the name of Theorems. They are among the most beautiful, as well as most gene ral propositions, known in the whole compass of geometry, and are perhaps only equalled by the remarkable locus to the circle in the second book of Apollo nius, or by the celebrated theorem of Mr. Cotes.
In September, 1747, he was elected pro. fessor of mathematics in the University of Edinburgh. The duties of this office gave a turn somewhat different to his mathematical pursuits, and led him to think of the most simple and elegant means of explaining those difficult propo sitions, which were hitherto only accessi ble to men deeply versed in the modern analysis. In doing this, he was pursuing the object, which of all others, he most ardently wished to attain, viz. the appli cation of geometry to such problems as the algebraic calculus alone bad been thought able to resolve. His solution of Kepler's problem was the first specimen of this kind which be gave to the world. This is founded on a general property of curves, which, though very simple, bad perhaps never been observed ; and by a most ingenious application of that pro perty, he shows how the approximation may be continued to any degree of &cm. racy, in a series of results which converge with great rapidity.
This solution appeared in the second vo lume of the Essays of the Philosophical Society of Edinburgh, for the year 1756. In the first volume of the same collection there are some other propositions of Mr. Stewart's, which are an extension of a cu rious theorem in the fourth book of Pap pus. They have a relation to the subject of Porisms, and one of them forms the nine. ty-first of Dr. Simson's Restoration.
He next published the "Tracts, Physi cal and Mathematical." In the first of these, Mr. Stewart lays down the doctrine of centripetal forces, in a series of propo sitions, demonstrated (if we admit the quadrature of curves) with the utmost rigour, and requiring no previous know ledge of the mathematics, except the ele ments of plane geometry, and of conic sections. The good order of these pro positions, added to the clearness and sim plicity of the demonstrations, renders this tract perhaps the best elementary treatise of physical astronomy that is any where to be found.