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.
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