# Mathematician:Bonaventura Francesco Cavalieri

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## Mathematician

Italian mathematician who worked on optics and motion.

His approach to geometry was a precursor to integral calculus.

Introduced the logarithm to Italy.

A disciple of Galileo.

A member of the informal Académie Parisienne.

## Nationality

Italian

## History

- Born: 1598, Milan, Habsburg Empire (now Italy)
- 1615: Joined the religious order Jesuati in Milan, where he met and was greatly influenced by Galileo
- 1616: Transferred to the Jesuati monastery in Pisa
- 1619: Applied for the chair of mathematics in Bologna but considered too young
- 1621: Became a deacon and assistant to Cardinal Federico Borromeo at monastery in Milan
- 1623: Became prior of St Peter's at Lodi
- 1626: Went to the Gesuati monastery in Parma (note: not the Jesuits)
- 1629: Appointed to chair of mathematics at Bologna, where he taught mathematics till his death
- Died: 30 Nov 1647, Bologna, Papal States (now Italy)

## Theorems

- Cavalieri's Principle (also known to Zu Geng)

Results named for **Bonaventura Francesco Cavalieri** can be found here.

## Publications

*Lo Specchio Ustorio, overo, Trattato delle settioni coniche*(The Burning Mirror, or a Treatise on Conic Sections)- 1635:
*Geometria Indivisibilibus Continuorum Nova Quadam Ratione Promota**(Geometry, developed by a new method through the indivisibles of the continua)* *Exercitationes geometricae sex**Directorium Generale Uranometricum*- 1646:
*Trattato della ruota planetaria perpetua* *Tables of logarithms*

## Notable Quotes

*A line is made up of points like a string of beads; a plane area is made up of lines as a cloth is of threads; and a solid is made up of plane sections as a book is made up of pages.*

## Critical View

*I think sincerely that few men, if any, since Archimedes, have delved as far and as deep into the science of geometry ... he has discovered a new method for the study of mathematical truths; by it he proves in a shorter manner many of the theorems of Archimedes and other mathematicians.*

## Sources

- John J. O'Connor and Edmund F. Robertson: "Bonaventura Francesco Cavalieri": MacTutor History of Mathematics archive

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**Cavalieri's principle** - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.14$: Cavalieri ($\text {1598}$ – $\text {1647}$) - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Cavalieri, Bonaventura Francesco** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Cavalieri, Bonaventura Francesco** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Cavalieri, Bonaventura**