A further analysis of Cardano’s main tool in the De Regula Aliza: on the origins of the splittings

Autor: Sara Confalonieri

Publikováno v: Archive for History of Exact Sciences. 72:303-352

In the framework of the De Regula Aliza (1570), Cardano paid much attention to the so-called splittings for the family of equations $$x^3 = a_1x + a_0$$ ; my previous article (Confalonieri in Arch Hist Exact Sci 69:257–289, 2015a) deals at length w

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::4cd1f8efffdbe02f2a0b122d0f032102
https://doi.org/10.1007/s00407-018-0209-z

The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations : Gerolamo Cardano's De Regula Aliza

Autor: Sara Confalonieri

Sara Confalonieri presents an overview of Cardano's mathematical treatises and, in particular, discusses the writings that deal with cubic equations. The author gives an insight into the latest of Cardano's algebraic works, the De Regula Aliza (1570)

Cardano’s earlier encounters with some general treatments of equations

Autor: Sara Confalonieri

Publikováno v: The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations ISBN: 9783658092740

In the Ars Magna, we have seen what were the most advanced strategies and methods at Cardano’s disposal to deal with equations. We have also remarked that his solving methods for cubic equations were supposedly strongly influenced by Tartaglia’s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::76a39a4d6cd010afff788cecee962573
https://doi.org/10.1007/978-3-658-09275-7_4

Putting in context Cardano’s works and mathematics

Autor: Sara Confalonieri

Publikováno v: The Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations ISBN: 9783658092740

This chapter is an introduction to Cardano’s works from both a nonmathematical and a mathematical viewpoint. In the following, I give an overview of Cardano’s mathematical treatises, including the few manuscripts still available, and discussing i

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3aec5c31501ce35f0a52494e69e368aa
https://doi.org/10.1007/978-3-658-09275-7_2

Effective solution of numerical equations in 19th-century engineering

Autor: Tournès, Dominique

Publikováno v: Numerical Solution of Equations in the 19th Century
Numerical Solution of Equations in the 19th Century, Sara Confalonieri, Jun 2019, Wuppertal, Germany

International audience; In 1876, the French engineer Léon-Louis Lalanne wrote about the solution of numerical equations that "finally it must be recognized that, while continuing to earn the admiration of geometers, the discoveries of Lagrange, Cauc

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::64ca947fcc0756a926fe5ddb14974e35
https://hal.archives-ouvertes.fr/hal-03138934