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{{redirect|Cavalerius|the lunar crater|Cavalerius (crater)}}
[[File:Bonaventura Cavalieri.jpeg|thumb|Bonaventura Francesco Cavalieri]]
[[File:IMG 4064 - Milano, Palazzo di Brera - Cavalieri, Bonaventura - Foto Giovanni Dall'Orto 19-jan 2007.jpg|thumb|Monument to Cavalieri in [[Milan]].]]
'''Bonaventura Francesco Cavalieri''' (in [[Latin]], '''Cavalerius''') (1598 &ndash; November 30, 1647) was an [[Italy|Italian]] [[mathematics|mathematician]].  He is known for his work on the problems of [[optics]] and [[motion (physics)|motion]], work on the precursors of [[infinitesimal calculus]], and the introduction of [[logarithms]] to Italy.  [[Cavalieri's principle]] in [[geometry]] partially anticipated [[integral calculus]].
 
== Life ==
Born in [[Milan]], Cavalieri studied [[theology]] in the [[monastery]] of San Gerolamo in Milan and [[geometry]] at the [[University of Pisa]] as a member of the [[Jesuates]] order.<ref>{{cite journal|last=Eves|first=Howard|date=1981, edition consulted 1998|title=Slicing it Thin|work=Mathematical Recreations: A Collection in Honour of Martin Gardner|pages=100|publisher=Dover}}</ref> He published eleven books, his first being published in 1632. He worked on the problems of [[optics]] and [[motion (physics)|motion]].  His [[astronomy|astronomical]] and [[astrology|astrological]] work remained marginal to these main interests, though his last book, ''Trattato della ruota planetaria perpetua'' (1646), was dedicated to the former.  He was introduced to [[Galileo Galilei]] through academic and ecclesiastical contacts.  [[Galileo]] exerted a strong influence on Cavalieri encouraging him to work on his new method and suggesting fruitful ideas, and Cavalieri would write at least 112 letters to Galileo.  Galileo said of Cavalieri, "few, if any, since [[Archimedes]], have delved as far and as deep into the science of geometry." He also benefited from the patronage of [[Cesare Marsili]].<ref>[http://galileo.rice.edu/Catalog/NewFiles/cavaleri.html Cavalieri, Bonaventura], at The Galileo Project</ref>
 
Cavalieri's first book was ''Lo Specchio Ustorio, overo, Trattato delle settioni coniche'', or ''The Burning Mirror, or a Treatise on Conic Sections''.<ref>[http://books.google.com/books?hl=en&lr=&id=ZX64AAAAIAAJ&oi=fnd&pg=PA1&dq=%22lo+specchio+ustorio%22&ots=CzX83kjdXO&sig=bZmh3XzXN2mWZdIa32OGlyypwEk Lo Specchio Ustorio, overo, Trattato delle settioni coniche]</ref>  In this book he developed the theory of mirrors shaped into [[parabola]]s, [[hyperbola]]s, and [[ellipse]]s, and various combinations of these mirrors.  The work was purely theoretical since the needed mirrors could not be constructed with the technologies of the time, a limitation well understood by Cavalieri.<ref>Stargazer, the Life and Times of the Telescope, by Fred Watson, [http://books.google.com/books?id=2LZZginzib4C&pg=PA134&dq=gregory+cassegrain+mersenne p. 135]</ref>
 
Building on the classic [[method of exhaustion]], Cavalieri developed a geometrical approach to calculus and published a treatise on the topic, ''Geometria indivisibilibus continuorum nova quadam ratione promota'' (''Geometry, developed by a new method through the indivisibles of the continua,'' 1635). In this work, an area is considered as constituted by an indefinite number of parallel segments and a volume as constituted by an indefinite number of parallel planar areas. Such elements are called indivisibles respectively of area and volume and provide the building blocks of Cavalieri's method. As an application, he computed the areas under the curves <math>y=x^n</math> – an early [[integral]] – which is known as [[Cavalieri's quadrature formula]].
 
 
Cavalieri is known  for [[Cavalieri's principle]], which states that the [[volume]]s of two objects are equal if the areas of their corresponding cross-sections are in all cases equal. Two cross-sections correspond if they are intersections of the body with planes equidistant from a chosen base plane.  (The same principle had been previously discovered by [[Zu Gengzhi]] (480&ndash;525) of [[China]].<ref name="needham volume 3 143">Needham, Joseph (1986). ''Science and Civilization in China: Volume 3; Mathematics and the Sciences of the Heavens and the Earth''. Taipei: Caves Books, Ltd. Page 143.) and was first documented in his book 'Zhui Su'(《[[:zh:缀术|缀术]]》). This principle was also worked out by [[Shen Kuo]] in the 11th century.</ref>)  Cavalieri developed a "method of the indivisibles," which he used to determine areas and volumes. It was a significant step on the way to modern [[infinitesimal calculus]].<ref>"[http://eom.springer.de/I/i050950.htm Infinitesimal calculus]", Encyclopaedia of Mathematics</ref>
 
Cavalieri also constructed a [[hydraulics|hydraulic pump]] for his monastery and published tables of [[logarithm]]s, emphasizing their practical use in the fields of astronomy and [[geography]].  He died at [[Bologna]].
 
Cavalieri takes place alongside [[Isaac Newton|Newton]], [[Gottfried Leibniz|Leibniz]], [[Blaise Pascal|Pascal]], [[John Wallis|Wallis]] and [[Colin Maclaurin|MacLaurin]] as one of those who in the  17th and 18th centuries "redefine[d] the mathematical object".<ref>{{fr icon}} [[Gilles-Gaston Granger]], ''Formes, opérations, objets'', Vrin, 1994, p. 365 [http://books.google.ca/books?id=EuIjwu5avPcC&pg=PA365&lpg=PA365#v=onepage&f=false Online quotation]</ref>
 
The [[lunar crater]] [[Cavalerius (crater)|Cavalerius]] is named for Cavalieri.
 
== Bibliography ==
* [http://books.google.ca/books?id=zRwAAAAAQAAJ&printsec=frontcover&hl=fr#v=onepage&q&f=false Elogj di Galileo Galilei e di Bonaventura Cavalieri] by Giuseppe Galeazzi, Milan, 1778
* [http://books.google.ca/books?id=I-eaNAAACAAJ&dq=%22Bonaventura+Cavalieri%22&hl=fr&sa=X&ei=eJMzT-XkHcT50gHK9P3WAg&redir_esc=y Bonaventura Cavalieri] by Antonio Favaro, vol. 31 of ''Amici e corrispondenti di Galileo Galilei'', C. Ferrari, 1915, 767 p.
 
==See also==
*[[List of Roman Catholic scientist-clerics]]
 
== Notes ==
<references/>
 
== References ==
*[http://galileo.rice.edu/Catalog/NewFiles/cavaleri.html The Galileo Project: Cavalieri]
 
==External links==
* Online texts by Cavalieri:
** {{la icon}} ''[http://echo.mpiwg-berlin.mpg.de/ECHOdocuView/ECHOzogiLib?url=/mpiwg/online/permanent/library/05TCTFNR/pageimg&start=1&pn=1&mode=imagepath Geometria Indivisibilibus]'' (Online 1653 edition, 543 p.)
** {{it icon}} '' [http://books.google.ca/books?id=ZX64AAAAIAAJ&ots=CzX83kjdXO&dq=%22lo%20specchio%20ustorio%22&lr&pg=PP5#v=onepage&q&f=false Lo specchio ustorio: overo, Trattato delle settioni coniche...]''
** {{la icon}} ''[http://books.google.ca/books?id=_742AAAAMAAJ&printsec=frontcover&sa=X&ei=vIwzT9O6Lau10AGFlNG7Ag&redir_esc=y#v=onepage&q&f=false Directorium generale uranometricum]''
** {{it icon}} ''[http://books.google.ca/books?id=zpIoAAAAcAAJ&hl=fr&pg=PR3#v=onepage&q&f=false Sfera astronomica]''
** {{it icon}} See also [[Wikisource]]
* Biographies:  
** {{MacTutor Biography|id=Cavalieri}}
** [http://www.bookrags.com/research/bonaventura-cavalieri-scit-03123/ Short biography on bookrags.com]
** {{la icon}} {{cite journal
| last1 = Fabroni
| first1 = Angelo
| authorlink1 = Angelo Fabroni| editor-first = | editor-link = | date =
| year = 1778
| title = Bonaventura Cavalerius
| journal = Vitae Italorum doctrina excellentium qui saeculis XVII. et XVIII. floruerunt | volume = I
| pages = 262–301
| location = Pisa | publisher =
| language = | format = | id =
| oclc = | pmid = | pmc = | bibcode = | doi =
| accessdate = 2012-02-08
| url = http://books.google.ca/books?id=wVkwAAAAYAAJ&pg=PA262#v=onepage&q&f=false
}}
* Modern mathematical or historical research:
** [http://eom.springer.de/I/i050950.htm Infinitesimal Calculus] On its historical development, in [[Encyclopaedia of Mathematics]], [[Michiel Hazewinkel]] ed.
** {{de icon}} [http://www.dividano.de/prinzip-von-cavalieri.html More information about the method of Cavalieri]
** [http://researchspace.csir.co.za/dspace/bitstream/10204/5267/1/Grobler5_2011.pdf Cavalieri Integration]
 
{{Authority control|VIAF=44324467}}
 
{{wikisourcelang|it|Autore:Bonaventura_Cavalieri|Bonaventura Cavalieri}}
 
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              = Cavalieri, Bonaventura
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Italian mathematician and astronomer
| DATE OF BIRTH    = 1598
| PLACE OF BIRTH    =
| DATE OF DEATH    = November 30, 1647
| PLACE OF DEATH    =
}}
{{DEFAULTSORT:Cavalieri, Bonaventura}}
[[Category:1598 births]]
[[Category:1647 deaths]]
[[Category:16th-century Italian mathematicians]]
[[Category:17th-century Italian mathematicians]]
[[Category:Italian astronomers]]
[[Category:University of Pisa alumni]]
[[Category:Roman Catholic cleric–scientists]]

Revision as of 08:22, 25 January 2014

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Bonaventura Francesco Cavalieri
Monument to Cavalieri in Milan.

Bonaventura Francesco Cavalieri (in Latin, Cavalerius) (1598 – November 30, 1647) was an Italian mathematician. He is known for his work on the problems of optics and motion, work on the precursors of infinitesimal calculus, and the introduction of logarithms to Italy. Cavalieri's principle in geometry partially anticipated integral calculus.

Life

Born in Milan, Cavalieri studied theology in the monastery of San Gerolamo in Milan and geometry at the University of Pisa as a member of the Jesuates order.[1] He published eleven books, his first being published in 1632. He worked on the problems of optics and motion. His astronomical and astrological work remained marginal to these main interests, though his last book, Trattato della ruota planetaria perpetua (1646), was dedicated to the former. He was introduced to Galileo Galilei through academic and ecclesiastical contacts. Galileo exerted a strong influence on Cavalieri encouraging him to work on his new method and suggesting fruitful ideas, and Cavalieri would write at least 112 letters to Galileo. Galileo said of Cavalieri, "few, if any, since Archimedes, have delved as far and as deep into the science of geometry." He also benefited from the patronage of Cesare Marsili.[2]

Cavalieri's first book was Lo Specchio Ustorio, overo, Trattato delle settioni coniche, or The Burning Mirror, or a Treatise on Conic Sections.[3] In this book he developed the theory of mirrors shaped into parabolas, hyperbolas, and ellipses, and various combinations of these mirrors. The work was purely theoretical since the needed mirrors could not be constructed with the technologies of the time, a limitation well understood by Cavalieri.[4]

Building on the classic method of exhaustion, Cavalieri developed a geometrical approach to calculus and published a treatise on the topic, Geometria indivisibilibus continuorum nova quadam ratione promota (Geometry, developed by a new method through the indivisibles of the continua, 1635). In this work, an area is considered as constituted by an indefinite number of parallel segments and a volume as constituted by an indefinite number of parallel planar areas. Such elements are called indivisibles respectively of area and volume and provide the building blocks of Cavalieri's method. As an application, he computed the areas under the curves – an early integral – which is known as Cavalieri's quadrature formula.


Cavalieri is known for Cavalieri's principle, which states that the volumes of two objects are equal if the areas of their corresponding cross-sections are in all cases equal. Two cross-sections correspond if they are intersections of the body with planes equidistant from a chosen base plane. (The same principle had been previously discovered by Zu Gengzhi (480–525) of China.[5]) Cavalieri developed a "method of the indivisibles," which he used to determine areas and volumes. It was a significant step on the way to modern infinitesimal calculus.[6]

Cavalieri also constructed a hydraulic pump for his monastery and published tables of logarithms, emphasizing their practical use in the fields of astronomy and geography. He died at Bologna.

Cavalieri takes place alongside Newton, Leibniz, Pascal, Wallis and MacLaurin as one of those who in the 17th and 18th centuries "redefine[d] the mathematical object".[7]

The lunar crater Cavalerius is named for Cavalieri.

Bibliography

See also

Notes

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  2. Cavalieri, Bonaventura, at The Galileo Project
  3. Lo Specchio Ustorio, overo, Trattato delle settioni coniche
  4. Stargazer, the Life and Times of the Telescope, by Fred Watson, p. 135
  5. Needham, Joseph (1986). Science and Civilization in China: Volume 3; Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd. Page 143.) and was first documented in his book 'Zhui Su'(《缀术》). This principle was also worked out by Shen Kuo in the 11th century.
  6. "Infinitesimal calculus", Encyclopaedia of Mathematics
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References

External links

  • Online texts by Cavalieri:
    • Template:La icon Geometria Indivisibilibus (Online 1653 edition, 543 p.)
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    • Template:La icon Directorium generale uranometricum
    • 59 year-old Osteopath Wesley from Sheet Harbour, has numerous interests including backgammon, property developers in singapore and kitchen chemistry. Finds travel an enlightening experience after setting up a journey to Central Zone of the Town of Angra do Heroismo best condo in singapore (pop over here) the Azores. Sfera astronomica
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  • Biographies:
    • Template:MacTutor Biography
    • Short biography on bookrags.com
    • Template:La icon One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

      In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

      Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

      Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

      A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

      The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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  • Modern mathematical or historical research:

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