by E. I. Carlyle, rev. Ian Tweddle

© Oxford University Press 2004 All rights reserved

**Simson, Robert** (1687-1768), mathematician, was born on 18 October 1687, probably the eldest of the seventeen children, all male, of John Simson *(d.* 1731), a Glasgow merchant, of Kirktonhall, West Kilbride, Ayrshire, and his wife, Agnes, daughter of Patrick Simson, minister of Renfrew. Thomas Simson was a younger brother. Robert Simson's name appears in the list of students matriculating in the fourth class at Glasgow University on 3 March 1701. Originally intended for the ministry, he studied under his maternal uncle, John Simson, professor of divinity, and first distinguished himself as a classical scholar. His interests then turned to mathematics, a subject which was in decline at Glasgow. Following the enforced resignation of the professor of mathematics, Robert Sinclair, Simson was nominated to this post on 8 March 1711. At that time he was spending a year in London pursuing his mathematical studies but after his return he was examined on 9 November 1711 and admitted to the professorship ten days later, having just graduated MA, on the 16th. About 1728 he became clerk to the university meeting and fulfilled both functions until he retired in 1761. In 1746 the University of St Andrews conferred on him the honorary degree of MD.

While in London, Simson made the acquaintance of several eminent mathematicians, among them Edmond Halley, whose influence perhaps reinforced his obsession with the works of the Greek geometers. He first directed his attention to Euclid's porisms, which are only known from the short account in the *Collectiones mathematicae* of Pappus of Alexandria. Although Pierre de Fermat claimed to have restored Euclid's work and Halley had edited the Greek text of the preface to the seventh book of Pappus, Simson was the first to throw real light on the matter. In a paper communicated in 1723 to the Royal Society by James Jurin, Simson restored two general propositions in which Pappus summed up several of the porisms *(PTRS,* 32, 1723, 330-40); his further work on the porisms was not published until after his death. In 1735 Simson published *Sectionum conicarum libri* V, which he partly intended as an introduction to the treatise by Apollonius of Perga on the subject; here Simson employed methods of pure geometry rather than algebra. In 1738 he completed the restoration of the 'Loci plani' of Apollonius, a task already attempted by Fermat before 1629 and by Francis Schooten in 1657; his conclusions were published in 1749 in a work entitled *Apollonii Pergaei locorum planorum libri II, restituti a R. Simson.* He next occupied himself with the restoration of the 'Sectio determinata' of Apollonius, which had already been the subject of some investigations by Alexander Anderson in 1612 and by Willebrord Snel in 1634; Simson's version was published posthumously. His most influential work was probably his definitive edition of Euclid's *Elements,* which he published in 1756. Both his Euclid and his *Conic Sections* ran through many editions and were translated into several languages.

In spite of his obsession with Greek geometry Simson was familiar with contemporary mathematics and included the elements of fluxionary calculus in his courses. There is an early manuscript of his dealing with inverse tangent series and their use in calculating π (U. Glas. L., MS. Gen. 1096), and in his paper 'An explication of an obscure passage in Albert Girard's commentary upon Simon Stevin's works' *(PTRS,* 48, 1754, 368-77) he used algebraic methods to discuss a limit involving Fibonacci numbers and an iterative process for finding square roots. Among his manuscripts now in Glasgow University Library are sixteen volumes of 'Adversaria on mathematical subjects, 1716-1767' (U. Glas. L., MS Gen. 256-71).

Simson appears to have been tall and of good stature. In spite of his great scholarship he was a modest, unassuming man who was very cautious in promoting his own work. He enjoyed good company and presided over the weekly meetings of a dining club that he had instituted. In his later years he complained of failing memory which inhibited his work. He had a special interest in botany, in which he was an acknowledged expert.

Simson never married. He died at the University of Glasgow on 1 October 1768 and was buried in the graveyard of Blackfriars Church. He bequeathed his extensive library to the University of Glasgow where it is still preserved as the Simson Collection. His manuscripts were left to his friend and colleague James Clow, professor of philosophy, with the request that he should put them in order and have them published. With financial support from Philip Stanhope, second Earl Stanhope, Clow published some of them in 1776 as Simson's *Opera quaedam reliqua.*

E. I. CARLYLE, *rev.* IAN TWEDDLE

**Sources **

W. Trail, *Account of the life and writings of Robert Simson* (1812)

*Encyclopaedia Britannica,* 3rd edn (1797), vol. 17, pp. 504-9

C. Innes, ed., *Munimenta alme Universitatis Glasguensis / Records of the University of Glasgow from its foundation till 1727,* 4 vols., Maitland Club, 72 (1854)

J. Coutts, *A history of the University of Glasgow* (1909)

D. Murray, *Memories of the old college of Glasgow: some chapters in the history of the university* (1927)

R. V. Wallis and P. J. Wallis, eds., *Biobibliography of British mathematics and its applications,* 2 (1986), 131-5

R. Alison, *The anecdotage of Glasgow* (1892), 116-17

J. M'Ure, *Glasghu facies: a view of the city of Glasgow,* ed. J. F. S. Gordon (1872), 330-31, 650-51

J. Strang, *Glasgow and its clubs* (1856), 2-24

J. Paterson, *History of the counties of Ayr and Wigton,* 3 (1866), 61-2, 365-8

I. Tweddle, 'John Machin and Robert Simson on inverse-tangent series for π', *Archive for History of Exact Sciences,* 42 (1991), 1-14

I. Tweddle, *Simson on porisms,* Sources in the History of Mathematics and Physical Sciences (2000)

**Archives **

CKS, corresp. with Lord Stanhope

RS

U. Glas., Archives and Business Records Centre

U. Glas. L.

**Likenesses **

P. de Nune, oils, 1746, University of Strathclyde, Glasgow, Collins Art Gallery

W. Cochrane, oils, 1769-70 (after P. de Nune, 1746), Hunterian Museum and Art Gallery, Glasgow

P. de Nune, oils, Royal Technical College, Glasgow

line engraving (after de Nune), NPG; repro. in Trail, *Account*

**Wealth at death **

£519 15s. excl. library bequeathed to University of Glasgow; also lands in Ayrshire, chiefly Kirktonhall and Knock Ewart: NA Scot., commissary of Glasgow testaments, vol. 64 (CC 9/7/67)

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