Everything about Bonaventura Cavalieri totally explained
Bonaventura Francesco Cavalieri (in
Latin,
Cavalerius) (
1598 -
November 30,
1647) was an
Italian mathematician 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're intersections of the body with planes equidistant from a chosen base plane. The principle was originally discovered by the 3rd century Chinese mathematician
Liu Hui in his commentary on
The Nine Chapters on the Mathematical Art. 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 (
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)).
Life
Born in
Milan, Cavalieri studied
theology in the
monastery of San Gerolamo in Milan and
geometry at the
University of Pisa. 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 through academic and ecclesiastical contacts. 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."
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Galileo exerted a strong influence on Cavalieri encouraging him to work on his new method and suggesting fruitful ideas. 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.
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.
The
lunar crater Cavalerius is named for the Latin name of Bonaventura Cavalieri.
Further Information
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