Mengoli, Pietro

1. Dates

Born: Bologna, 1625 (several sources says 1626)

Died: Bologna, 1686

Dateinfo: Birth Uncertain

Lifespan: 61

2. Father

Occupation: Unknown

Fantuzzi says only that Simone Mengoli was an honest and respectable citizen of Bologna.

No information on financial status.

3. Nationality

Birth: Italian

Career: Italian

Death: Italian

4. Education

Schooling: Bologna, Ph.D., Ll.D.

Mengoli studied mathematics with Cavalieri at Bologna. After Cavalieri's death Giovanni Antonio Rocca of Reggio guided his study of mathematics. He took a degree (this means a doctorate--Mengoli identified himself on title pages as "Doctor") in philosophy in 1650, and another (also a doctorate) in civil and canon law in 1653.

5. Religion

Affiliation: Catholic

Mengoli was ordained as a priest and served a parish in Bologna from 1660 to his death in 1686.

6. Scientific Disciplines

Primary: Mathematics

Subordinate: Astronomy, Music, Optics

Mengoli's mathematics was superficially conservative, and he was in fact quickly forgotten. Recently, however, he has been rediscovered and is increasingly recognized as a transition between Cavalieri's indivisibles and Leibniz's differentials.

Novae quadraturae arithmeticae, 1650, significantly extended early work in infinite series.

Geometriae speciosae elementa, 1659, contained a theory of limits.

Circolo, 1672, found the value of pi/2 as an infinite product. There were also other mathematical works.

Mengoli was also interested in astronomy. He wrote a book on atmospheric refraction, and he published one on musical theory.

7. Means of Support

Primary: Academia, Church Life

Mengoli succeeded Cavalieri in the chair at the university of Bologna, where he was a professor of arithmetic in 1648-9, professor of mechanics from 1649 to 68, and professor of mathematics from 1668 until his death in 1686. It is of interest to me that, although Mengoli and Montanari were professors of mathematics together at Bologna for fourteen years, neither is mentioned in accounts of the other.

He served as a parish priest in Bologna from 1660 until his death.

8. Patronage

Types: City Magistrate, Government Official, Eccesiastic Official, Court Official

Fantuzzi says that after Cavalieri's death Mengoli requested the chair from the Senate and received it. In 1649, a year after his original appointment at Bologna, Mengoli contributed a section on musical harmony to a volume for Senator Fantuzzi [sic] and Sig. Sulpizia Grimaldi, and in 1650 he published a Latin Elogio in praise of Sen. Paolo Fantuzzi (I assume the same Sen. Fantuzzi) on the occasion of his investiture as Confaliere.

Mengoli dedicated Via regia ad mathematicos ornata, 1655, to Queen Christina of Sweden.

He dedicated Speculazioni di musica, 1670, to Card. Azzolini.

He dedicated Circolo, 1672, to the Marquis Alessandro Fachinetti, Confaliere di Guistizia, and to the members of the government of Bologna. (I seem to recall from the case of Cavalieri, that reappointments in Bologna fell every four years. Mengoli's initial appointment as Professor of Mathematics was in 1668.

In 1676 he dedicated Novae quadraturae arithmeticae to the Senators of Bologna.

He dedicated Arithmetica, 1676, to Card. Leopoldo de' Medici.

9. Technological Involvement

Type: None

10. Scientific Societies

Memberships: None

Letters to Lorenzo Grimaldi are preserved in the Instituto of Bologna.

Sources

1. A. Agostini, "Pietro Mengoli," in Enciclopedia italiana, 22, 585.
2. E. Bortolotti, La storia della matematica nella università di Bologna, (Bologna, 1947), pp. 98-101, 137-8.
3. G. Eneström, "Zur Geschichte der unendlichen Reihen in die Mitte des siebzehnten Jahrhunderte," Bibliotheca mathematica, ser.
4. 3, 12 (1911-12), 135-48.
5. G. Vacca, "Sulle scoperte di Pietro Mengoli," Atti dell'Accademia nazionale dei Lincei. Rendiconti, ser. 5, 24.2 (Dec. 1915), 508-13.
6. G. Fantuzzi, Notizie degli scittori bolognesi, (Bologna, 1781- 94), 6, 9-11. P. Riccardi, Biblioteca matematica italiana, 1, 150-2.

Compiled by:

Richard S. Westfall

Department of History and Philosophy of Science

Indiana University

Note: the creators of the Galileo Project and this catalogue cannot answer email on geneological questions.