MENGOLI, PIETRO. - Mathematician, b. in Bologna in 1626, d. there on 7 June 1686. He was a disciple 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 consider the definite integral as the common limit of the upper integral and the lower integral, though referring not, as is done today, to the upper and lower bounds of the integrand function, but to the maximum and minimum that this assumes in each of the intervals into which the field of integration is divided. This was because at that time attention was directed only to continuous functions.

He also wrote a theory of logarithms and gave of these series expansions usable in the construction of tables.

Bibliography

BIBL.: G. Vacca, Sulle scoperte di P. M., in Rendiconti della R. Acc. dei Lincei, 5th series, 24 (1915), pp. 508-13, 617-20, with a list of his works.

Pietro Teofilato

@incollection{ec8_mengoli_pietro, author = {Teofilato, Pietro}, title = {Mengoli, pietro}, booktitle = {Enciclopedia Cattolica}, volume = {VIII}, pages = {683}, note = {Cited by column}, publisher = {Ente per l’Enciclopedia Cattolica e per il Libro Cattolico}, address = {Città del Vaticano}, year = {1952}, url = {https://azioneromana.com/article/mengoli-pietro} }

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Mengoli, Pietro

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