MENGOLI, PIETRO. - Mathematician, b. at Bologna in 1626, d. there on 7 June 1686. He was a pupil of B. Cavalieri. Appointed parish priest in the same city, he combined with his priestly ministry a fruitful activity as a scholar of mathematical analysis.
He demonstrated the divergence of the harmonic series and found the sum of various arithmetic series. He was the first to regard the definite integral as the common limit of the upper integral and lower integral; however, he referred not, as is done today, to the upper and lower bounds of the integrand, but to the maximum and minimum values it assumes in each of the intervals into which the domain of integration is divided. This was because at that time attention was directed solely to continuous functions.
He also wrote a theory of logarithms and gave series expansions for them that could be used in the construction of tables.