Background
Pietro Mengoli was born in 1626 in Bologna, Papal States (now Emilia-Romagna, Italy).
Via Zamboni, 33, 40126 Bologna BO, Italy
Pietro Mengoli was taught mathematics by Cavalieri at the University of Bologna before he himself taught at Bologna from 1648. While he taught he studied for a doctorate in philosophy which was awarded by the University of Bologna in 1650. Continuing to study while he held chairs of mathematics, three years later he obtained a second doctorate in civil and canon law from Bologna. He was also ordained into the priesthood.
Via Zamboni, 33, 40126 Bologna BO, Italy
Pietro Mengoli was taught mathematics by Cavalieri at the University of Bologna before he himself taught at Bologna from 1648. While he taught he studied for a doctorate in philosophy which was awarded by the University of Bologna in 1650. Continuing to study while he held chairs of mathematics, three years later he obtained a second doctorate in civil and canon law from Bologna. He was also ordained into the priesthood.
clergyman educator mathematician scientist
Pietro Mengoli was born in 1626 in Bologna, Papal States (now Emilia-Romagna, Italy).
Pietro Mengoli was taught mathematics by Cavalieri at the University of Bologna before he himself taught at Bologna from 1648. While he taught he studied for a doctorate in philosophy which was awarded by the University of Bologna in 1650. Continuing to study while he held chairs of mathematics, three years later he obtained a second doctorate in civil and canon law from Bologna. He was also ordained into the priesthood.
After Cavalieri died in November 1647, Mengoli had been appointed to his chair at the University of Bologna. Mengoli held a number of chairs at the University of Bologna where he taught all his life. He was a professor of arithmetic from 1648 to 1649, then professor of mechanics from 1649 to 1668 and, finally, professor of mathematics from 1668 until his death in 1686. In addition to these chairs, he was also a priest in the parish of Santa Maria Maddelena in Bologna from 1660.
Mengoli used infinite series to good effect in Novae quadraturae arithmeticae, seu de additione fractionum published in Bologna in 1650, developing ideas that had first been investigated by Cataldi. He begins with the summation of geometric series, then shows that the harmonic series does not converge. In doing so he became the first person to prove that it was possible for a series whose terms tend to zero to be made larger than any given number. He also investigated the harmonic series with alternating signs which he proved converges to log(2). This series was also investigated by Nicolaus Mercator.
Mengoli also wrote Geometriae speciosae elementa (1659) on the limits of geometrical figures. This work is particularly interesting for it contains a definition of a definite integral in terms of the area of a plane figure rigorously given by constructing circumscribing and inscribing parallelograms which sum to equal limits. He defines limits of positive variable quantities using ideas that he had used in looking at limits of series. He called a positive variable quantity quasi-infinite if it could be made larger than any given number, quasi-nil if it could be made smaller than any given positive number, and quasi-a if it could be made smaller than any number greater than a and greater than any number less than a. By examining the limits of sums, products and quotients of variable quantities, Mengoli was setting up the basic rules if the calculus thirty years before Newton and Leibniz. Both of these were influenced by his contribution, in the case of Leibniz the influence was direct as he read Mengoli's work while in the case of Newton he knew of it indirectly through studying Wallis.
Other work by Mengoli included work on astronomy, work on refraction in the atmosphere and a book Speculazioni musicali (1670) on the theory of music.
A little-known aspect of Pietro Mengoli's mathematical activity is the difficulties he faced in trying to solve some problems in Diophantine analysis suggested by J. Ozanam. Mengoli's recently published correspondence shows that his insufficient familiarity with algebraic methods prevented him, as well as other Italian mathematicians of his time, from solving the so-called 'French' problems.
Mengoli was a Roman Catholic priest at Chiesa di Santa Maria Maddalena in Bologna.
Mengoli's mathematics was superficially conservative. He did not subscribe to the innovations of Torricelli, and his own discoveries were set out in abstruse Latin that made his works laborious to read. His books were nevertheless widely distributed in the seventeenth century, and were known to Collins, Wallis, and Leibniz; they were then almost forgotten so that Mengoli's work has been studied again only recently. His significance to the history of science lies in the transitional position of his mathematics, midway between Cavalieri's method of indivisibles and Newton's fluxions and Leibniz's differentials.
Mengoli criticized the theory of resonance set out by Galileo.
Mengoli's recently published correspondence reveals how he cherished his prestige as a scholar.
Being a Roman Catholic priest Pietro Mengoli was not married and had no children.