Mathematical Treasure: John Playfair’s Dissertation on the Progress of Mathematical and Physical Science

Like many of his mentors and contemporaries in Edinburgh—perhaps most notably William Robertson—John Playfair (1749–1819) maintained a lifelong interest in history. Since he served as the University of Edinburgh’s Professor of Mathematics from 1785 to 1805 and then was Professor of Natural Philosophy until his death, he paid particular attention to the development of mathematics and science both in Europe and in South Asia. When Archibald Constable and Macvey Napier began to prepare what became a six-volume Supplement to the already-venerable Encyclopaedia Britannica, Playfair was a natural choice to author a dissertation, or extended historical discourse, on “Exhibiting a General View of the Progress of Mathematical and Physical Science Since the Revival of Letters in Europe.” He completed the first half of the essay in 1816 for the second supplemental volume, but when he died in 1819, he had only reached Newton and Leibniz instead of the original goal of the present day. The second portion appeared in 1820 in the fourth supplemental volume.

Even though he was not able to complete it as he had planned, Playfair’s dissertation proved extremely popular with readers. In addition to being republished in various iterations of Encyclopaedia Britannica, it was reprinted in collections and booklets by other publishers, and it appeared in Playfair’s own Works, which were issued in four volumes in 1822. Pamphlets that appeared in the United States almost certainly were pirated, as was common then. Examples such as the 1820 Boston version shown below also illustrate how the set of dissertations (which included essays by Dugald Stewart, William Thomas Brande, and others) was reorganized and renumbered during the many reprintings, so that one such printing might not be internally consistent.

A full digitization of the copy owned by the New York Public Library is available at HathiTrust. Note that this version contains only the second part of Playfair’s dissertation; one copy of the full dissertation is owned by the University of Michigan and also available at HathiTrust. All of the National Library of Scotland’s copies of the Supplement to the Fourth, Fifth, and Sixth Editions of the Encyclopaedia Britannica are available at JSTOR, although they are not posted in chronological order.

To learn more about Playfair, see “Teaching Mathematics with Ephemera: John Playfair's Course Outline for Practical Mathematics,” “Mathematical Treasure: Playfair on Teaching Geometry” (both here in Convergence), and Amy Ackerberg-Hastings, “John Playfair on British Decline in Mathematics,” BSHM Bulletin 23, no. 2 (2008): 81–95.

Index of Mathematical Treasures