oai-hal-tel-00875863v3
type: Dataset
title: The telling of the unattainable attempt to avoid the {casus irreducibilis} for cubic equations: Cardano's {De Regula Aliza}. With a compared transcription of 1570 and 1663 editions and a partial English translation
description: Solving cubic equations by a formula that involves only the elementary operations of sum, product, and exponentiation of the coefficients is one of the greatest results in 16th century mathematics. This was achieved by Girolamo Cardano's Ars Magna in 1545. Still, a deep, substantial difference between the quadratic and the cubic formula exists: while the quadratic formula only involves imaginary numbers when all the solutions are imaginary too, it may happen that the cubic formula contains imaginary numbers, even when the three solutions are anyway all real (and different). This means that a scholar of the time could stumble upon numerical cubic equations of which he already knew three (real) solutions and the cubic formula of which actually contains square roots of negative numbers. This will be lately called the 'casus irreducibilis '. Cardano's De Regula Aliza (Basel, 1570) is (at least, partially) meant to try to overcome the problem entailed by it.
landing page: https://theses.hal.science/tel-00875863
keyword: aliza
keyword: cardan
keyword: cardano
keyword: cas-irreductible
keyword: casus-irreducibilis
keyword: cubic-equations
keyword: equations-cubiques
keyword: infoeu-reposemanticsdoctoralthesis
keyword: irreducible-case
keyword: mathmath-homathematics-mathhistory-and-overview-mathho
keyword: theses
issued: 2026-05-07T21:48:58.495560
modified: 2026-05-07T21:48:58.495564
language: en
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-tel-00875863v3/resource/7fe4263d-4022-4593-85a2-4a35f183ca77
type: Distribution
title: The telling of the unattainable attempt to avoid the {casus irreducibilis} for cubic equations: Cardano's {De Regula Aliza}. With a compared transcription of 1570 and 1663 editions and a partial English translation
format: HTML
access URL: https://theses.hal.science/tel-00875863
issued: 2026-05-07T21:48:58.506767
modified: 2026-05-07T21:48:58.478962