Publication of Ars Magna

Timeline

1. 1539–1544Milan · MilanCardano obtained from Tartaglia a method for a class of depressed cubic equations and promised to keep it secret until Tartaglia published. He and his pupil Ferrari later extended the method to more cubic cases and to quartic equations; upon learning that Scipione del Ferro had discovered similar formulas earlier, he decided to publish and credited them by name in the book.
2. 1545Nuremberg · NurembergThe first edition of Ars Magna (Artis Magnae, sive de regulis algebraicis) appeared in Nuremberg, giving geometric explanations and root-finding steps for various cubic and quartic equations in rhetorical form. The cubic formula was thus first systematically made public; the book also discussed dividing a number into parts summing to ten and multiplying to forty, giving a solution involving negative radicals.
3. 1545–1548Milan / Venice · ItalyPublication brought the secret formulas into the public domain, and Tartaglia accused Cardano of perjury. Ferrari defended his master and invited a public contest. The dispute did not challenge the mathematical validity of the methods in the book, but made the priority of the cubic and quartic solutions the most famous controversy in 16th-century mathematics.