Best known for Elements of Geometry (1795) and Illustrations of the Huttonian Theory of the Earth (1802), University of Edinburgh mathematics and natural philosophy professor John Playfair (1748–1819) also wrote several dozen books, expository articles, and opinion pieces as individual publications or for Philosophical Transactions of the Royal Society of London, Transactions of the Royal Society of Edinburgh, and Edinburgh Review. Most of these works have been digitized and are readily available for study. In contrast, Playfair's 1793 Prospectus of a Course of Lectures on Some of the Practical Parts of the Mathematics has nearly disappeared, with as few as eight surviving copies. The paper considers what we can learn from this document, which consists of a nineteen-page list of potential topics. Despite its brevity, the Prospectus includes a number of themes and priorities that both echoed the activities of eighteenth-century European mathematicians and recurred throughout Playfair's writing and teaching.