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Matthew Stewart FRS FRSE (28 June 1717 – 23 January 1785) was a Scottish mathematician and minister of religion.
He was born in Rothesay, on the Isle of Bute, in 1717, died at Catrine, Ayrshire, and is interred at Greyfriars Kirkyard in Edinburgh.
Educated at Rothesay Grammar School, Matthew Stewart entered the University of Glasgow in 1734 where he studied with the philosopher Francis Hutcheson and the mathematician Robert Simson, the latter with whom he studied ancient geometry. A close friendship developed between Simson and Stewart, in part because of their mutual admiration of Pappus of Alexandria, which resulted in many curious communications with respect to the De Locis Planis of Apollonius of Perga and the Porisms of Euclid over the years. This correspondence suggests that Stewart spent several weeks in Glasgow starting May 1743 assisting Robert Simson in the production of his Apollonii Pergaei locorum planorum libri II, which was published in 1749.
About the same time, his father, the Rev. Dugald Stewart, Minister of Rothesay, persuaded Matthew Stewart to enter the ministry. He was licensed by the Presbytery of Dunoon in May 1744, and became a minister at Roseneath, Dumbartonshire one year later.
Before entering the ministry, Stewart attended the lectures of Colin Maclaurin at the University of Edinburgh during the 1742-3 session. The chair became vacant by Maclaurin's death in 1746 and just over one year later Stewart left the ministry to become Professor of Mathematics. Publication of his best known work, Some General Theorems of Considerable use in the Higher Parts of Mathematics may have helped him secure the post. This book extended some ideas of Robert Simson and is best known for proposition II, or what is now known as Stewart's theorem, which relates measurements on a triangle to an additional line through a vertex. Stewart also provided a solution to Kepler's problem using geometrical methods in 1756, and a book describing planetary motion and the perturbation of one planet on another in 1761, along with a supplement on the distance between the sun and earth in 1763.
In 1772 his health began to deteriorate and his duties as professor at Edinburgh were initially shared, then taken over by his son Dugald Stewart, who later became a prominent Scottish philosopher.
He was the grandfather of the physician Patrick Miller (1782-1871) and of Colonel Matthew Stewart (c.1784-1851).