MENGOLI, PIETRO. - Mathematician, b. in 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 his priestly ministry with an active pursuit of mathematical analysis.
He demonstrated the divergence of the harmonic series and found the sum of various arithmetic series. He was the first to consider the definite integral as the common limit of the upper integral and lower integral, though not, as is done today, with reference to the upper and lower bounds of the integrand function, but rather to the maximum and minimum assumed by this function in each of the intervals into which the domain of integration is divided. This was because at that time attention was focused solely on continuous functions.
He also wrote a theory of logarithms and provided series expansions for these that could be used in the construction of tables.