Novae quadraturae arithmeticae
Pietro Mengoli (1626, Bologna – June 7, 1686, Bologna) was an Italian mathematician and clergyman from Bologna, where he studied with Bonaventura Cavalieri at the University of Bologna, and succeeded him in 1647. He remained as professor there for the next 39 years of his life.
In 1644 it was Mengoli who first posed the famous Basel problem, solved in 1735 by Leonhard Euler.
He wrote a paper in 1650 in which he proved that the sum of the alternating harmonic series is equal to the natural logarithm of 2.
He also proved that the harmonic series does not converge, and provided a proof that Wallis' product for is correct.
- ^ Hofmann, Joseph Ehrenfried (1959). Classical Mathematics. Translated from the German Geschichte der Mathematik by Henrietta O. Midonick. New York: Philosophical Library Inc.