As he had had no formal training in the subject, Simson turned down the offer but agreed to take up the post a year later, during which time he would increase his knowledge of mathematics.

During this time he made valuable contacts with several prominent mathematicians, including John Caswell, James Jurin (secretary of the Royal Society), Humphrey Ditton and, most importantly, Edmond Halley.

He enjoyed good company and presided over the weekly meetings of a dining club that he had instituted … He had a special interest in botany, in which he was an acknowledged expert”.

He died, aged 80, in his college residence at Glasgow on 1 October 1768, and was interred in the Blackfriars Burying Ground (now known as Ramshorn Cemetery), where, in the south wall, is placed to his memory a plain marble tablet, with a highly and justly complimentary inscription”.

[10] The memorial, designed by Frederick Thomas Pilkington, is “a large octagonal monument with carved Egyptian details, topped with a ball finial”.

In 1749, was published Apollonii Pergaei locorum planorum libri II., a restoration of Apollonius's lost treatise, founded on the lemmas given in the seventh book of Pappus's Mathematical Collection.

This work, which contained only the first six and the eleventh and twelfth books, and to which, in its English version, he added the Data in 1762, was for long the standard text of Euclid in England.