Cavalieri, Bonaventura

1. Dates

Born: Milano, c. 1598. Both Favaro and Abetti think he was born earlier.

Died: Bologna, 30 Nov. 1647

Dateinfo: Birth Uncertain

Lifespan: 49

2. Father

Occupation: Aristocrat

The father, also Bonaventura Cavalieri, was of a noble family that was not rich.

No clear information on financial status beyond the fact that they were not rich.

3. Nationality

Birth: Italy

Career: Italy

Death: Italy

4. Education

Schooling: Pisa

He studied theology in the monastery of San Gerolamo in Milan. Here Card. Federico Borromeo noted his intelligence; he wrote to Galileo introducing Cavalieri in 1617.

Through Benedetto Castelli, a lecturer in mathematics at Pisa, he was initiated in the study of geometry. He quickly absorbed the classical works in mathematics, demonstrating such exceptional aptitude that he sometimes substituted for his teacher at the University of Pisa.

I do not see any mention of any degree.

5. Religion

Affiliation: Catholic

He entered the Jesuate (sic) religious order in 1615.

6. Scientific Disciplines

Primary: Mathematics

Subordinate: Astronomy, Optics, Mechanics

He published eleven books beginning in 1632. Cavalieri's theory, as developed in his Geometria and in other works, related to an inquiry into infinitesimals. Cavalieri made a rational systematization of the method of indivisibles. His view of the indivisibles gave mathematicians a deeper conception of sets: it is not necessary that the elements of a set be assigned or assignable; rather it suffices that a precise criterion exist for determining whether or not an element belongs to the set.

He developed a general rule for the focal length of lenses and thought of a reflecting telescope.

He worked some on the problems of motion.

His appointment at Bologna virtually required that he involve himself somewhat with astronomy, and even astrology, in which he appears to have engaged only from necessity.

7. Means of Support

Primary: Church Life, Academia

Secondary: Schoolmastering

He was received into the minor order of the Jesuati in Milan in 1615, and in 1616 transferred to the Jesuati monastery in Pisa. In 1621 he was ordained a deacon to the Cardinal Federigo Borromeo.

Taught theology at the monastery of San Girolamo in Milan, 1620-1623.

Prior of St. Peter's at Lodi, 1623-1626.

Prior of the monastery of the Jesuati in Parma, 1626- 1629.

Prior of a convent of his own order in Bologna, 1629-

Professor of mathematics at the University of Bologna, 1629-1647.

When he was initially rejected for the chair in Bologna in 1619 because he was too young, he gave lessons in mathematics in Florence for a year--to Ascanio Piccolomini, to two nephews of Card. del Monte, and to other. Such lessons appear to have belonged to the entire period (1616- 19) of his study in Pisa. In Bologna he continued to give private lessons.

8. Patronage

Types: Scientist, Eccesiastic Official, Aristrocrat, City Magistrate

He was encouraged in his study by Benedetto Castelli. Castelli introduced him to Galileo, and he had Cavalieri substitute for him when Castelli had to be absent. Cavalieri tried to get the chair in Pisa when Castelli left for Rome, but the appointment went to Aggiunti.

The role of Card. Borromeo in Cavalieri's life is not wholly clear, but he kept popping up, and early he was clearly of importance.

Cavalieri owed his teaching position at Bologna to Galileo's influence with Marsili and Cardinals Aldobrandini and Ludovisi. Cavalieri asked Galileo to intervene on his behalf with the men above and with Margherita de' Medici, the wife of Odoardo Farnese. Galileo did so and the appointment went through. Marsili then became one of Cavalieri's strongest protectors.

Cavalieri dedicated a table of logs to the Senate of Bologna in 1632 when he was greatly concerned about his re- appointment--which then immediately followed. In gratitude he then published Lo specchio ustorio, also dedicated to the Senate. Favaro state that Cavalieri planned his publications to coincide with times when re-apointments would be necessary. Thus his last book, in 1646, Trattato della ruota planetaria perpetua, 1646, came with his last re-appointment--another work on astrology which he thought pleasing to the patricians of Bologna.

He dedicated a book on astrology (1639) to Card. Francesco Barberini.

About 1635 (or could this have been 1629?) Urban appointed Cavalieri as perpatual Prior of the Convent of Santa Maria della Mascarella in Bologna. (I think this was a house of the Jesuates.) Cavalieri never had anything to do with the convent; the appointment, engineered by Card. Giulio Sacchetti, the legate to Bologna, was intended to give him support for his work.

9. Technological Involvement

Types: Hydraulics, Applied Mathematics

Cavalieri constructed a hydraulic pump for his monastery; the Duke of Mantua apparently obtained one like it.

Cavalieri emphasized the practical use of logs (which he introduced into Italy) for various studies such as astronomy and geography. He published tables of logs, including logs of spherical trigonometric functions (for astronomers).

10. Scientific Societies

Memberships: None

Friendship and correspondence with Galileo. He wrote at least 112 letters to Galileo. Galileo said of Cavallieri, in his letter to Marsilli, "few, if any, since Archimedes, have delved as far and as deep into the science of geometry."

Friendship with Castelli, and correspondence with many of Galileo's circle--Marsili, Torricelli, Renieri, Viviani--and correspondence with Mersenne and Rocca.

It is reported of Stefano degli Angeli, who was a student of Cavalieri near the end of Cavalieri's life, when he was crippled with arthritis, that Angeli helped him with the "fatiguing difficulty" [faticoso disbrigo] of his correspondence.

Sources

1. A. Favaro, Amici e corrispondenti di Galileo, 3 vols. ed. Paolo Galluzzi, (Firenze, 1983), 3, 1247-1315.
2. G. Abetti, Amici e nemici di Galileo, (Milano, 1945), 195-210.
3. Dizionario biografico degli italiani, 22, 659.

Not Available and Not Consulted

1. U. D'Aviso, "Vita del P.Buonaventura Cavalieri" in Trattato della Sfera, (Rome, 1682).
2. G. Piola, Elogio di Bonaventura Cavalieri, (Milan, 1844).
3. A. Favaro, Bonaventura Cavalieri nello studio de Bologna, (Bologna, 1855).
4. P. Riccardi, Biblioteca matematica italiana, (Modena, 1870).
5. Fabroni, Historia Academiae Pisanae, 1, 267-301.
6. Bonaventura Cavalieri, Categgio, ed. Giovanna Baroncelli (Archivio della corrispondenza degli scienziati italiani), (Firenze: Olschki, 1987).
7. Enrico Giusti, B. Cavalieri and the Theory of Indivisibles, (1980).
8. Giovanna Baroncelli, "Bonaventura Cavalieri tra matematica e fisica," in M. Bucciantini and M. Torrini, eds. Geometria e atomismo nella scuola galileiana, (Firenze, 1992), pp. 67- 101.

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.