 Interest in Budan's theorem has been revived because some further computational results are more easily deducible from it than from Fourier's version of the theorem.Budan's book was read across the English Channel; for example, Peter Barlow includes mention of it in his entry on "Approximation" in his "Dictionary" (1814), although grouping it with the method of Joseph-Louis Lagrange as being accurate, but of more theoretical interest than practical use.Budan's work on approximation was studied by Horner in preparing his celebrated article in the Philosophical Transactions of the Royal Society of London in 1819 that gave rise to the term Horner's method; Horner comments there and elsewhere on Budan's results, at first being sceptical of the value of Budan's work, but later warming to it.