Download or read book The Telling of the Unattainable Attempt to Avoid the Casus Irreducibilis for Cubic Equations written by Sara Confalonieri and published by . This book was released on 2013 with total page 750 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ail 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 AJiza (Basel, 1570) is (at least, partially) meant to try to overcome the problem entailed by it. Its (partial) analysis is the heart of this dissertation.