Strategies to possibly overcome the casus irriducibilis: the De Regula Aliza

Abstract

We have two editions available of this treatise. The first one is the Hieronymi Cardani mediolanensis, civisque bononiensis, medici ac mathematici præclarissimi, de aliza regula, libellus, hoc est operi perfecti sui sive algebraicæ logisticæ, numeros recondita numerandi subtilitate, secundum geometricas quantitate inquirendis, necessaria coronis, nunc demum in lucem editæ. It dates back to 1570 and was printed in folio in Basel by Officina Henricpetrina together with the De Proportionibus and with the second edition of the Ars Magna. The second edition, which is shortly entitled De regula aliza libellus, is posthumous and placed in the fourth volume of the 1663 edition of Cardano’s Opera Omnia, printed in Lyon by Ioannis Antonii Huguetan and Marci Antonii Ravaud. Some miscalculations and typos are corrected and sometimes the punctuation is improved, but as a whole it contains no major change compared to the first edition.