Robert Simson (1687–1768) was a Scottish mathematician and chair of mathematics at the University of Glasgow. His work focused on restoring the existing partial versions of the ancient Greek geometers, such as Euclid and Apollonius. His restoration of Euclid’s *Elements* was especially influential. Images of a 1756 English first edition and an 1834 American edition of Simson’s *The Elements of Euclid* are available on *Convergence*.

The above portrait of Simson is from the frontispiece of his *Opera* and is one of the earliest images of the special academic gown worn by professors at the University of Glasgow.

*Opera*, published posthumously in 1776 by James Clow (Professor of Logic at Glasgow and Simson’s executor), contains four of Simson’s works which had not yet been published and an appendix. The title page can be seen below.

The next image is the section header page for the restoration by Simson of Apollonius’ *De Sectione Determinata* by using Pappus’ *Lemmata*. It was a work that Simson started early in his career and then completed in his later years.

*De Sectione Determinata* contains many problems like the one on page 71 pictured below, in which a number of points are given on a line, in this case 3, and another point is to be found that satisfies certain ratios.

According to William Trail, “the next, and certainly the most important portion of the posthumous volume, contains Dr. Simson’s discovery and illustration of the *Porisms* of Euclid.” [Trail 1812, p. 39] Porisms are “examples of Greek analysis which had been created to handle geometrical statements which fell between problems and theorems, such as classification of the properties of a geometrical locus.” [Ackerberg-Hastings 2000, p. 47] Below is the header page for this section of *Opera*.

The third work in *Opera* is *De Logarithmis* and may have been the last completed work of Simson. It is followed by *De Limitibus Quantitatum et Rationum*, the fourth part of Simson’s *Opera*. Although not complete, it was Simson’s attempt at a more rigorous treatment of fluxions than the one provided by Newton. The *Opera* concludes with an *Appendix* which contains samples of geometrical problems solved by Simson using methods of the ancient Greeks. Simson may not have intended these problems to have ever been published, but it was decided right before the *Opera *was printed to include a few examples.

A complete digital scan of the first edition of Simson’s *Opera Quaedam Reliqua*, call number QA3.S5 1776, can be found in the Linda Hall Library Digital Collections.

*Images in this article are courtesy of the Linda Hall Library of Science, Engineering & Technology and used with permission. The images may be downloaded and used for the purposes of research, teaching, and private study, provided the Linda Hall Library of Science, Engineering & Technology is credited as the source. For other uses, check out the LHL** Image Rights and Reproductions** policy.*

##### References

Ackerberg-Hastings, Amy. "Mathematics is a Gentleman's Art: Analysis and Synthesis in American College Geometry Teaching, 1790–1840." PhD diss., Iowa State University, 2000. DOI:10.31274/rtd-180813-13933.

Dickson, Neil. "Tradition and Humour: The Academic Dress of the University of Glasgow." *Transactions of the Burgon Society* 12 (2012). DOI: 10.4148/2475-7799.1097.

Dickson, Neil. Department of Mathematics, University of Glasgow. Email correspondence, October 2019.

Trail, William. *Account of the Life and Writings of Robert Simson, M.D.: Late Professor Mathematics in the University of Glasgow. *London, 1812.

Index to Mathematical Treasures