Coins illustrating Cavalieri's principle

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 are 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.^[1] 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 ([1]). Image File history File links Cavalieri's_principle. ... Image File history File links Cavalieri's_principle. ... Cavalerius is a prominent lunar impact crater that lies on the western edge of the Oceanus Procellarum lunar mare on the west part of the visible Moon. ... For other uses, see Latins and Latin (disambiguation). ... Events January 7 - Boris Godunov seizes the throne of Russia following the death of his brother-in-law, Tsar Feodor I. April 13 - Edict of Nantes - Henry IV of France grants French Huguenots equal rights with Catholics. ... is the 334th day of the year (335th in leap years) in the Gregorian calendar. ... 1647 (MDCXLVII) was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar (or a common year starting on Friday of the 10-day slower Julian calendar). ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... For other uses, see Volume (disambiguation). ... A possible likeness of Liu Hui on japanpostage stamp This is a Chinese name; the family name is 劉 (Liu) Liu Hui 劉徽 was a Chinese mathematician who lived in the 200s in the Wei Kingdom. ... The Nine Chapters on the Mathematical Art (九章算術) is a Chinese mathematics book, probably composed in the 1st century AD, but perhaps as early as 200 BC. This book is the earliest surviving mathematical text from China that has come down to us by being copied by scribes and (centuries later... Infinitesimal calculus is an area of mathematics pioneered by Gottfried Leibniz based on the concept of infinitesimals, as opposed to the calculus of Isaac Newton, which is based upon the concept of the limit. ...

Life

Monument to Cavalieri in Milan.

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. he also hit 396 homwruns in his major legue baseball carear, "few, if any, since Archimedes, have delved as far and as deep into the science of geometry."[2] For other uses, see Milan (disambiguation). ... For other uses, see Milan (disambiguation). ... Theology finds its scholars pursuing the understanding of and providing reasoned discourse of religion, spirituality and God or the gods. ... This article concerns the buildings occupied by monastics. ... For other uses, see Geometry (disambiguation). ... The University of Pisa (Italian Università di Pisa) is one of the most renowned Italian universities. ... For the book by Sir Isaac Newton, see Opticks. ... This article or section is in need of attention from an expert on the subject. ... For other uses, see Astronomy (disambiguation). ... Hand-coloured version of the anonymous Flammarion woodcut (1888). ... Galileo can refer to: Galileo Galilei, astronomer, philosopher, and physicist (1564 - 1642) the Galileo spacecraft, a NASA space probe that visited Jupiter and its moons the Galileo positioning system Life of Galileo, a play by Bertolt Brecht Galileo (1975) - screen adaptation of the play Life of Galileo by Bertolt Brecht... For other uses, see Archimedes (disambiguation). ...

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. Galileo can refer to: Galileo Galilei, astronomer, philosopher, and physicist (1564 - 1642) the Galileo spacecraft, a NASA space probe that visited Jupiter and its moons the Galileo positioning system Life of Galileo, a play by Bertolt Brecht Galileo (1975) - screen adaptation of the play Life of Galileo by Bertolt Brecht... The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. ...

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. Table of Hydraulics and Hydrostatics, from the 1728 Cyclopaedia. ... Look up logarithm in Wiktionary, the free dictionary. ... For the food product, see Bologna sausage. ...

The lunar crater Cavalerius is named for the Latin name of Bonaventura Cavalieri. Wikipedia does not yet have an article with this exact name. ... Cavalerius is a prominent lunar impact crater that lies on the western edge of the Oceanus Procellarum lunar mare on the west part of the visible Moon. ...

Notes

1. ^ Needham, Volume 3, 143.

References

• The Galileo Project: Cavalieri

External links

• O'Connor, John J. & Robertson, Edmund F., "Bonaventura Cavalieri", MacTutor History of Mathematics archive 
• Infinitesimal Calculus - , an article on its historical development, in Encyclopaedia of Mathematics, Michiel Hazewinkel ed.
• More informations about the method of Cavalieri