The eldest son of John Simson of Kirktonhill in Ayrshire, he was intended for the church, but the bent of his mind was towards mathematics, and, when a prospect opened of his succeeding to the mathematical chair at the university of Glasgow, he proceeded to London for further study. After a year in London he returned to Glasgow, and in 1711 was appointed by the university to the professorship of mathematics, an office which he retained until 1761.
Simson's contributions to mathematical knowledge took the form of critical editions and commentaries on the works of the ancient geometers. The first of his published writings is a paper in the Philosophical Transactions (1723, vol. xl. p. 330) on Euclid's Porisms.
Then followed Sectionum conicarum libri V. (Edinburgh, 1735), a second edition of which, with additions, appeared in 1750. The first three books of this treatise were translated into English, and several times printed as The Elements of the Conic Sections. 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.
In 1756 appeared, both in Latin and in English, the first edition of his Euclid's Elements. 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.
After his death restorations of Apollonius's treatise De section determinata and of Euclid's treatise De Poritnatibus were printed for private circulation in 1776 at the expense of Earl Stanhope, in a volume with the title Roberti Simson opera quaedam reliqua. The volume contains also dissertations on Logarithms and on the Limits of Quantities and Ratios, and a few problems illustrative of the ancient geometrical analysis.
The pedal line of a triangle is sometimes called the Simson Line after him.
- Simson's line theorem by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
- Angle between two Simson's lines by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
- Simson's line
- Robert Simson's biography at MacTutor archive.
- W Trail, Life and Writings of Robert Simson (1812)
- C Hutton, Mathematical and Philosophical Dictionary (1815).