Cardano's Ars Magna

Timeline

1. 1539–1544Milan · MilanIn Milan, Cardano obtained from Tartaglia a solution for a class of cubics lacking the quadratic term, and promised to keep it secret until Tartaglia published. He and Ferrari later extended the method to more cubic cases and to quartic equations; around 1543 he learned that del Ferro had discovered similar formulas earlier, and decided to publish.
2. 1545Nuremberg · NurembergThe first edition of Ars Magna appeared in 1545, giving geometric explanations and solution steps for various types of cubic and quartic equations in rhetorical form, and explicitly crediting Tartaglia, del Ferro, and Ferrari. The book discusses a division with sum ten and product forty, writing a solution containing negative radicals—an early record of imaginary numbers entering printed algebra.
3. 1546–1570Milan and the learned circles of northern Italy · ItalyTartaglia accused Cardano of breaking his oath of secrecy, and both sides along with Ferrari became embroiled in a public polemic. Nevertheless, Ars Magna made cubic and quartic root-finding common knowledge and inspired Bombelli and others to continue working with imaginary roots, becoming one of the starting points of modern equation theory.