Article ID: CBB000930659

Fermat's Method of Quadrature (2008)

unapi

The Treatise on Quadrature of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, ? p x+m /ndx , or under a higher hyperbola, ? p x-m /ndx with the appropriate limits of integration in each casehas a second part which was mostly unnoticed by Fermat's contemporaries. This second part of the Treatise is obscure and difficult to read. In it Fermat reduced the quadrature of a great number of algebraic curves in implicit form to the quadrature of known curves: the higher parabolas and hyperbolas of the first part of the paper. Others, he reduced to the quadrature of the circle. We shall see how the clever use of two procedures, quite novel at the time: the change of variables and a particular case of the formula of integration by parts, provide Fermat with the necessary tools to squarequite easilyas well-known curves as the folium of Descartes, the cissoid of Diocles or the witch of Agnesi. Keywords : History of mathematics, quadratures, integration methods

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB000930659/

Similar Citations

Article Roshdi Rashed; (2013)
Descartes et l'infiniment petit (/isis/citation/CBB698670085/)

Book Roshdi Rashed; (2018)
Fermat et les débuts modernes de la géométrie (/isis/citation/CBB423365348/)

Article Heeffer, Albrecht; (2006)
The Logic of Disguise: Descartes' Discovery of the Law of Refraction (/isis/citation/CBB000772577/)

Article Barner, Klaus; (2001)
How old did Fermat become? (/isis/citation/CBB000100538/)

Article Stedall, Jacqueline; (2012)
John Wallis and the French: His Quarrels with Fermat, Pascal, Dulaurens, and Descartes (/isis/citation/CBB001251200/)

Book Bussotti, Paolo; (2006)
From Fermat to Gauss: Indefinite Descent and Methods of Reduction in Number Theory (/isis/citation/CBB000772063/)

Article Courgeau, Daniel; (2010)
Dispersion of Measurements in Demography (/isis/citation/CBB001021435/)

Article Rashed, Roshdi; (1999)
Pierre Fermat et les débuts modernes de l'analyse diophantiene (/isis/citation/CBB000330311/)

Article Blay, Michel; (1999)
Méthodes mathématiques et calcul de l'infini au temps de Fermat (/isis/citation/CBB000330316/)

Book Serfati, Michel; Descotes, Dominique; (2008)
Mathématiciens français du XVIIe siècle. Descartes, Fermat, Pascal (/isis/citation/CBB001022162/)

Article Ulrich Felgner; (2016)
Der Begriff der ‚Angleichung‘ (παρισότης, adaequatio) bei Diophant und Fermat (/isis/citation/CBB166694701/)

Essay Review Gispert, Hélène; (2000)
La capture du social dans les mathématques et leur histoire (/isis/citation/CBB000110358/)

Article Miyake, Katsuya; (1999)
Did Fermat See These Structures? (/isis/citation/CBB000330314/)

Article Marc Parmentier; (2015)
Leibniz et le virtuel (/isis/citation/CBB764317706/)

Article Roberts, Bryan W.; (2011)
How Galileo Dropped the Ball and Fermat Picked It Up (/isis/citation/CBB001211460/)

Article Rashed, Roshdi; (2001)
Fermat and Algebraic Geometry (/isis/citation/CBB000330303/)

Authors & Contributors
Rashed, Roshdi
Herreman, Alain
Felgner, U.
Stedall, Jacqueline Anne
Serfati, Michel
Roberts, Bryan W.
Concepts
Mathematics
Physics
Geometry
Algebra
Algebraic geometry
Mathematical analysis
Time Periods
17th century
18th century
19th century
Places
France
Great Britain
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment