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Abstract: Nicolas Vilant (1737–1807) was Regius Professor of Mathematics at St Andrews University in Scotland during 1765–1807. Plagued by ill health, he was unable to teach for much of this time, and employed a series of assistants. Well versed in the British analytical tradition, he was, like his contemporaries, largely unaware of developments in the rest of Europe. However, he was a mathematician of some skill, and his textbook The Elements of Mathematical Analysis, Abridged, for the Use of Students is of interest for his view of analysis. Though he was unable to complete a more comprehensive work for publication, many manuscripts survive in St Andrews University Library. Vilant’s book and manuscripts and the reception of his work are here examined. [Copyright &y& Elsevier]

Abstract: The mathematical work of James Glenie (1750–1817) was published at irregular intervals during a turbulent life. His ideas, mostly deriving from his time as an Assistant in Mathematics at St Andrews University in Scotland, were developed intermittently over a period of thirty-seven years. His mathematical achievements, underestimated by previous historians, were deeply rooted in Euclidean geometry and his own generalized theory of proportion. Among them are many new geometrical constructions and proofs, a novel demonstration of the binomial theorem, and an alternative approach to the differential calculus. [Copyright &y& Elsevier]