The first of Simson’s published writings is a paper in the Philosophical Transactions of the Royal Society of London (vol. xl. p. 330, 1723) on the subject of Euclid’s Porisms, the nature of which he was the first to elucidate (see 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, with the title The Elements of the Conic Sections. In 1749 was published Apollonii Pergaei Locorum Planorum Libri II. , a restoration of one of Apollonius’s lost treatises, 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, has become the standard text of Euclid in England. The additions and alterations which Simson made by way of restoring the text to its "original accuracy” are certainly not all of them improvements, and the notes he appended show with what an uncritical reverence he regarded the great geometers of antiquity. Two other works, restorations of Apollonius’s treatise Be Sectione Determinata and Euclid’s treatise De Porismatibus, which Simson was too distrustful of himself to publish during his lifetime, were printed for private circulation in 1776 at the expense of Earl Stanhope, in a volume with the title Roberti Simson, M.D Opera Quaedam Reliqua. The volume contains also two additional books De Sectione Determinata, two small dissertations on Logarithms and on the Limits of Quantities and Ratios, and a few problems illustrative of the ancient geometrical analysis. How far these restorations represent the lost originals will probably always be a matter of conjecture. The De Porismatibus certainly cannot be coextensive with Euclid’s three books; but, if it is only a restored fragment, the credit due to Simson’s perseverance and penetration in recovering from oblivion the nature and some of the contents of one of the most interesting treatises of antiquity will always be such as to keep his name in the remembrance of geometers.

SIMSON, William (1800-1847), portrait, landscape, and subject painter, was born at Dundee in 1800. He studied under Andrew Wilson at the Trustees’ Academy, Edinburgh, and his early pictures—landscape and marine subjects—were executed with great spirit and found a ready sale. He next turned his attention to figure painting, producing in 1829 the Twelfth of August, which was followed in 1830 by Sportsmen Regaling and a Highland Deerstalker. In the latter year he was elected a member of the Scottish Academy; and, having acquired some means by portrait-painting, he spent three years in Italy, and on his return in 1838 settled in London, where he exhibited his Camaldolese Monk Showing Relics, his Cimabue and Giotto, his Dutch Family, and his Columbus and his Child at the Convent of Santa Maria la Rabida. He died in London on the 29th of August 1847.

Simson is greatest as a landscapist; his Solway Moss—Sunset, exhibited in the Royal Scottish Academy of 1831 and now in the National Gallery, Edinburgh, ranks as one of the finest examples of the early Scottish school of landscape.

His elder brother George (1791-1862), portrait-painter, was also a member of the Royal Scottish Academy, and his younger brother David (d. 1874) practised as a landscape-painter.