by E. I. Carlyle, rev. Niccol˜ Guicciardini

© Oxford University Press 2004 All rights reserved

**Stewart, Matthew** (1717-1785), mathematician, was born at Rothesay in the Isle of Bute on 28 June 1717, the second son of Dugald Stewart *(d.* 1753), minister of Rothesay, and his wife, Janet Bannatyne *(d.* 1761). He was the father of the much more famous Dugald Stewart, the leading Scottish philosopher of the early nineteenth century. Educated at the town grammar school, he entered Glasgow University in 1734. There he enjoyed the friendship of Francis Hutcheson (1694-1746) and of Robert Simson, the mathematician, to whom he owed his marked predilection for the Greek geometricians. The interest in the rediscovery of Greek geometry led Simson and Stewart to develop an extremely innovative approach, and in the nineteenth century Michel Chasles ranked the two among the most important contributors to the progress of geometry. In 1741 Stewart proceeded to Edinburgh University and studied under Colin MacLaurin but regularly corresponded with Simson on the subject of ancient geometrical methods. Simson was at that time engaged in restoring Euclid's porisms, and Stewart pursued the same subject in a different direction. In 1746 he published *Some General Theorems of Considerable Use in the Higher Parts of Mathematics.* Several of these theorems were in fact porisms, but Stewart avoided the name through fear of seeming to anticipate his friend.

On 6 May 1744 Stewart was licensed to preach by the presbytery of Dunoon, and on 9 May 1745, on the presentation of the duke of Argyll, he was ordained minister of Rosneath, Dunbartonshire, which charge, however, he resigned on being elected professor of mathematics at Edinburgh University in the beginning of September 1747, succeeding the recently deceased Colin MacLaurin. On 20 May 1750 he married Marjorie *(d.* 1771), the only daughter of Archibald Stewart, writer to the signet. Dugald Stewart was their only son to survive infancy.

In 1756 Stewart published, in the second volume of the *Essays and Observations* of the Royal Society of Edinburgh, a solution of the so-called 'Kepler's problem' (which required the determination of the area of a focal sector of the ellipse). In 1761, pursuing his plan of introducing the simplicity of ancient geometrical demonstrations into astronomic investigations, he published *Tracts, Physical and Mathematical, Containing an Explication of Several Points in Physical Astronomy,* in which he developed a treatment of centripetal forces in a series of propositions requiring only a knowledge of the elements of plane geometry and of conic sections. He even tried to deal (employing geometrical methods similar to those of Newton's *Principia mathematica)* with the difficult 'three body problem' (the study of the trajectories of three masses in mutual gravitational interaction) that had defeated many eighteenth-century mathematicians. A theorem in which he deduced the motion of the moon's apsides attained an accuracy far surpassing that reached by Newton. The result confirmed that arrived at through algebraical methods by Charles Walmesley in 1749. In 1763 Stewart issued a supplement entitled *The Distance of the Sun from the Earth Determined by the Theory of Gravity,* in which he computed the distance at 29,875 semi-diameters of the earth, a result whose inaccuracy was due to the difficulty of treating so complex a subject geometrically. The nature of his fault was first pointed out in 1769 by John Dawson in a pamphlet entitled *Four Propositions,* and in 1771 John Landen published an independent refutation of Stewart's conclusions.

In 1756 Stewart was created DD of Glasgow University. He was a founder member of the Royal Society of Edinburgh, being elected a fellow of the first meeting of its physical class on 3 November 1783. On 21 June 1764 he was elected a fellow of the Royal Society. In 1772 the failing state of his health compelled him to retire to his estate at Catrine in Ayrshire, and from then the duties of his mathematical professorship were performed by his son, Dugald, who in 1775 was elected joint professor. Stewart died on 23 January 1785.

E. I. CARLYLE, *rev.* NICCOLò GUICCIARDINI

**Sources **

J. Playfair, 'Memoir of Matthew Stewart', *Transactions of the Royal Society of Edinburgh,* 1/1 (1788), 57-76

M. Chasles, *Aperçu historique sur l'origine et le développement des méthodes en géométrie, particulièrement de celles qui se rapportent à la géométrie moderne* (1837)

R. V. Wallis and P. J. Wallis, eds., *Biobibliography of British mathematics and its applications,* 2 (1986)

M. Stewart, *Memoir of Dugald Stewart* (1838)

A. Bower, *The history of the University of Edinburgh,* 2 (1817), 357

T. Thomson, *History of the Royal Society from its institution to the end of the eighteenth century* (1812)

*Encyclopaedia Britannica,* 8th edn (1853-60), vol. 1, p. 695; vol. 4, p. 104

F. Bennet and M. Melrose, *Index of fellows of the Royal Society of Edinburgh: elected November 1783 - July 1883,* ed. H. Frew, rev. edn (1984)

Chambers, *Scots.* (1855)

parish register (baptisms), 5 July 1717, Rothesay

parish register (marriages), 20 May 1750, Edinburgh

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