Pietro Mengoli was taught mathematics by Cavalieri at Bologna the studied for a doctorate in philosophy which was awarded by Bologna in 1650. Three years later he obtained a second doctorate in civil and canon law, also from Bologna.
When Cavalieri died, Mengoli was appointed to his chair at the University of Bologna. Mengoli was professor of arithmetic (1648-1649), professor of mechanics (1649-1668) and professor of mathematics (1668-1686). In addition to these posts he was also a parish priest in Bologna from 1660.
Mengoli used infinite series to good effect. He showed that the harmonic series does not converge and that the harmonic series with alternating signs converges to log(2). This series was also investigated by Nicolaus Mercator.
Mengoli wrote Novae quadraturae arithmeticae (1650) on infinite series, Geometriae speciosae elementa (1659) on limits, and Circolo (1672) where he found an infinite product expansion for p/2.
Other work by Mengoli included work on astronomy, work on refraction in the atmosphere and a book Speculazioni di musica (1670) on the theory of music.