Cavalieri's principle
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows:
* 2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in line segments of equal length, then the two regions have equal areas.
* 3-dimensional case: Suppose two regions in three-space (solids) are included between two parallel planes. If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes.
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Cavalieri's principle
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows:
* 2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in line segments of equal length, then the two regions have equal areas.
* 3-dimensional case: Suppose two regions in three-space (solids) are included between two parallel planes. If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes.
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Das Prinzip von Cavalieri (auc ...... aventura Cavalieri zurückgeht.
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El principio de Cavalieri (den ...... al así como de las integrales.
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En géométrie, la méthode des i ...... s après par Leibniz et Newton.
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In geometry, Cavalieri's princ ...... ut did not use infinitesimals.
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In matematica, il metodo degli ...... ezione e altezza piccolissima.
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O princípio de Cavalieri (a ba ...... mbém estão nessa mesma razão."
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Zasada Cavalieriego – metoda o ...... język współczesnej matematyki.
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Метод неделимых — возникшее в ...... nova quadam ratione promota).
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في الهندسة، مبدأ كافالييري، ال ...... لكن ليس القيم المتناهية الصغر.
@ar
カヴァリエリの原理（カヴァリエリのげんり、Cavalieri ...... という主張である。カヴァリエリは17世紀のイタリアの数学者。
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title
Cavalieri's Principle
urlname
CavalierisPrinciple
comment
Das Prinzip von Cavalieri (auc ...... aventura Cavalieri zurückgeht.
@de
El principio de Cavalieri (den ...... rpos. El enunciado podría ser:
@es
En géométrie, la méthode des i ...... s après par Leibniz et Newton.
@fr
In geometry, Cavalieri's princ ...... wo regions have equal volumes.
@en
In matematica, il metodo degli ...... so dalla diagonale . Prendendo
@it
O princípio de Cavalieri (a ba ...... oposição análoga para sólidos:
@pt
Zasada Cavalieriego – metoda o ...... te bryły mają równe objętości.
@pl
Метод неделимых — возникшее в ...... итие интегрального исчисления.
@ru
في الهندسة، مبدأ كافالييري، ال ...... وية، فإنّ للمجسّمين نفس الحجم.
@ar
カヴァリエリの原理（カヴァリエリのげんり、Cavalieri ...... という主張である。カヴァリエリは17世紀のイタリアの数学者。
@ja
label
Cavalieri's principle
@en
Metodo degli indivisibili
@it
Méthode des indivisibles
@fr
Principio de Cavalieri
@es
Princípio de Cavalieri
@pt
Prinzip von Cavalieri
@de
Zasada Cavalieriego
@pl
Метод неделимых
@ru
مبدأ كافالييري
@ar
カヴァリエリの原理
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