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Book of the Month

October 2008

Robert Simson

Part of a diagram from Simson's Conic Sections (17)

 Mathematical material

Glasgow: eighteenth century
MS Gen 1118 and other works

Robert Simson was born on 18 October 1687. He was Professor of Mathematics at the University of Glasgow from 1711 until 1761 and made a significant contribution to mathematical scholarship; his interest in early Greek geometers proved particularly influential. The Simson Collection in Glasgow University Library comprises 850 books, mainly mathematical and astronomical texts, which he bequeathed on his death in 1768. A number of manuscript items relating to Simson, including notebooks and letters, were received subsequently. A selection of these books and manuscripts are featured here.

Robert Simson was born in West Kilbride in Ayrshire, the son of a Glasgow merchant. He was educated at the University of Glasgow and graduated MA. It was originally intended that he train to become a religious minister but his interest turned to mathematics.


Portrait of Robert Simson in
MS Murray 660

Signature of Robert Simson in MS Gen 256


He went to London to pursue his studies and while there was nominated to a vacant post at Glasgow. He returned and was examined as to his suitability:

"Mr Robert Simson resolved the geometrical problems given him yesternight to the satisfaction of the Faculty after which he gave also a satisfying specimen of his skill in mathematicks & dexterity in teaching geometry and algebra, he also produced sufficient testimonials from ... the Professor of Astronomy at Oxford and from others in London well skilled in the mathematicks..."

Simson was admitted to the professorship in November 1711.
From 1728 he also held the office of Clerk of Senate at the University, the first person to do so.

Letter addressed to 'Professor Simson at Glasgow' (MS Murray 660)

MS Gen 1118: annotations to Pappus

Much of Simson's mathematical investigations related to his interest in the ancient Greek geometers, in particular, Euclid (born c 300 BC) and Apollonius of Perga (born c 240 BC). While in London, Simson had become acquainted with the astronomer Edmond Halley (1656-1742) who may have encouraged him in this area. Simson subsequently owned one of his publications, Edmundi Halleii astronomi dum viveret regii tabulae astronomicae: accedunt de usu tabularum praecepta (Ea5-a.2).

Knowledge of early work by the Greeks was largely due to later commentaries; these included writings by Pappus of Alexandria (fl AD 320). These were published in a Latin translation in the sixteenth century and, in turn, informed European mathematicians including Descartes (1596-1650), Pierre de Fermat (1601-1665) and Isaac Newton (1642-1727).


Title page of the sixteenth century Latin translation of the work of Pappus.
This is Simson's annotated copy. (MS Gen 1118)

Special Collections holds a number of copies of this translation,  Mathematicae Collectiones by Pappus. One is of particular interest as it belonged to Robert Simson and contains his handwritten annotations. Although Halley and Fermat had worked on Pappus, it was Simson who first explored the subject matter to a point of further understanding. His amendments to and developments of this text provide an interesting source for his work in this area. 

 Side by side: Simson's copy of a printed diagram, and his accompanying notes, interleaved in the book.
(MS Gen 1118)

Simson's annotations are extensive, ranging from comments or insertions at the side and foot of the page, to whole pages of notes interleaved with the book's original printed text.

One page of notes is headed 'Domi Mattheus Stewart Prop. 4. Lib. 4.'. Among Simson's personal manuscripts are letters between Simson and Matthew Stewart (1717-1785), the mathematical content of which includes work on finding the quadrature of the hyperbola and on porisms (MS Gen 146). 'Porisms' can be described as a proposition lying somewhere between a theorem (a statement to be proved) or a problem (a construction to be effected).   

A copy of Stewart's Propositiones geometricae, more veterum demonstratae, published in 1763, can also be found in Simson's library (Ea8-e.13).

(MS Gen 1118)

(MS Gen 1118)

Conic Sections (1735)

In 1735 Simson published his Sectionum conicarum libri V. This work provided an introduction to the treatise of Apollonius of Perga on the subject of conic sections. Copies of both the original Latin text (Bh3-f.2) and a later English translation (1775) (Bk9-g.6) can be found in the Old Library Collection, which comprises books acquired directly by the university before the end of the eighteenth century. A copy of Apollonii Pergaei: locorum planorum libri II (restituti a Roberto Simson) dated 1749 (Ea6-b.1) can also be found among Simson's personal library and bears further witness to his exploration of the work of this early mathematician. Here he restored Apollonius' lost treatise founded on the propositions given in the seventh book of Pappus.

Title page of Simson's publication on Conic Sections (Bh3-f.2)

The beginning of the text in the Conic Sections (Bh3-f.2)


Pull-out diagram from the Conic Sections (Bh3-f.2)

Euclid's Elements (1756)

Even more influential than the Conic Sections was Simson's definitive edition of Euclid's Elements, first published in 1756 in Latin. This work contained only the first six and the eleventh and twelfth books but the Data was added to the English version in 1762 (Bl8-g.20).  It became the standard text in England and, along with the Conic Sections, was produced in many editions, some posthumously. It was also translated into several languages. 

The university library houses several copies of this work both in the original Latin and translated into English. Some of these belong to the Old Library collection, already mentioned. Their presence elsewhere (including the Hunterian and Murray collections) perhaps further attests to their importance and popularity.


Simson's edition of Euclid's Elements, published in Latin in 1756 and printed
in Glasgow by Robert and Andrew Foulis.
(This copy is in the Murray collection: Mu55-c.3.
A copy in the Old Library collection is at Bn8-d.4)




Simson's bequest

Simson's bequest was mainly of mathematical and astronomical texts; spanning two centuries in date, these range from mid sixteenth century items to books published shortly before his death on 1 October 1768. A few of his own works were also included. A catalogue was drawn up which exists in several copies (MS Gen 1229, MS Gen 197 and Ea5-y.4). A borrowing register, with entries up to 1823, follows on from the rules regarding the administration of the collection (Ea5-b.1). 

The three rules governing the lending of books from the Simson collection, 1768 (Ea5-b.1)

Extract showing loans (and returns) during 1771 (Ea5-b.1)

A note attached to the borrowing register, giving
permission for books to be loaned to Mr Jackson.
The note is signed by George Jardine (1742-1827),
Professor of Greek and later of Logic. (Ea5-b.1)

Simson's manuscripts

James Clow, Professor of Philosophy at the university, was a friend of Simson's and an executor of his will. Simson left him his manuscripts and Clow published some of them in 1776 as Roberti Simsoni, Opera Quaedam reliqua ... (Ea5-b.2 and other copies).
In December 1784, "Professor James Clow informed a meeting of the Faculty that he would donate sixteen quarto volumes of the late Professor Simson's Adversaria to the library, as well as loose papers which had belonged to him."

Two of the sixteen volumes of
Simson's notebooks, titled
Adversaria, donated to the
library by Professor James
Clow (MS Gen 256-271)

Extract dated 12 March 1718, from volume A of Simson's Adversaria
(MS Gen 256)

As well as the Adversaria, the following manuscripts are identified as having been received from Clow: Simson's annotated copy of Pappus and a transcript of his notes on Pappus (MS Gen 1232). He may also have given MS Gen 1096 which are copies of two letters written by Simson to James Jurin (1684-1750). They demonstrate that Simson was well acquainted with developments in algebra and calculus, employing the methods of calculus to deal with inverse tangent series and their use in calculating the value of pi.

 Robert Simson, 18 October 1687 - 1 October 1768 (MS Murray 660)

The letters and papers on mathematical subjects which comprise MS Gen 196 include two letters from Simson to William Trail (1746-1831) who published a biography of Simson in 1812. He made use of Simson's books and manuscripts, which were in the university library by 1800. He also spoke to Simson's former colleagues and wrote of him:

"His manner of teaching was uncommonly clear, and engaging to young people; ... most of his scholars retained through life an affection and reverence for the Professor." Some of them, including Matthew Stewart, became distinguished mathematicians themselves.

In the twentieth century the library received further material relating to Simson. Within the Murray collection (received in 1928) there is a collection of letters to Simson written mainly by William Rouet (fl 1730-1767), another university colleague, from various European cities (MS Murray 660). In 1933, material relating to Simson, Stewart and Colin MacLaurin (1698-1746) was received via the then Professor of Mathematics, Thomas Murray MacRobert (MS Gen 146).

Although Robert Simson did not discover it, the Simson Line of a triangle is named for him. So too is the Simson Chair of Mathematics which was founded at the University in 1955.

The following have been useful in creating this article:

Carlyle, E I Simson, Robert (1687-1768), rev. Ian Tweddle, Oxford Dictionary of National Biography, Oxford University Press, 2004 [, accessed 16 Sept 2008]

Encyclopędia Britannica Online, articles on Pappus of Alexandria and Apollonius of Perga. Accessed 16 Sept 2008.

Innes, Cosmo Munimenta Alme Universitatis Glasguensis [Records of the University of Glasgow from its foundation until 1727] (1854) Sp Coll Mu21-a.53

Trail, William Account of the Life and Writings of Robert Simson, MD late Professor of Mathematics in the University of Glasgow (1812) Sp Coll Mu21-y.24

The University of Glasgow Story, entries for Robert Simson and James Clow. Accessed 16 Sept 2008.

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Based on an investigation by Anna Louise Mason (on placement August 2008)
Revised and prepared for the web by Sarah Hepworth October 2008