Cardano's "plagiarism"

There is a known story how Tartaglia (shown above) accused Cardano of “plagiarising” his results on cubic equations that Cardano published in Ars Magna in 1545.

It is easy to find out that the solution was first obtained by Scipione del Ferro, and his pupil Antonio Mario Fiore met Tartaglia in a mathematical disputation in 1535 (those were popular and provided good income for scholars). Tartaglia derived his solution during that disputation and considered it as a great treasure and did not want to disclose when later Cardano asked him. Finally, in March 1539, Tartaglia told Cardano the derivation in an encrypted poem and required that Cardano would never tell this secret anybody.

However, later Cardano and his pupil Ferrari found Ferro’s work in Bologna, kept by Ferro’s pupil and son-in-law Annibale Nave. Furthermore, Ferrari solved quartic equations under Cardano’s supervision. After that, Cardano decided that there was no point in keeping the cubic equations secret, and he published the whole research in Ars Magna, giving proper credit to both del Ferro and Tartaglia.

Tartaglia protested publicly, with great anger and insults. Ferrari decided to protect his teacher and challenged Tartaglia for a public disputation. On 10 August 1548, the disputation was set to discuss 31 problems that contestants posed to each other in previously sent letters, and they met in front of governor of Milan, who had been named judge. Ferrari was declared a winner.

Here is the chart for the disputation set for noon in Milan. The birthdate of Tartaglia is unknown – however, we know that Cardano’s ruler of ascendent is Venus, which is strong in this chart, and his ruler of 7th Mars is here in detriment. Also, transit Saturn forms a square with Cardano’s natal Sun, in retro motion – this means that in the last months his life was not easy due to the unfair accusations.

In fact, modern academics admit that Cardano’s publication of the cubic equation solution, with given credits to both authors (del Ferro and Tartaglia) and his pupil’s results on the quartic equations (also with proper credit), are one of the earliest examples of honest citation and fair research, which became well and widely known for the common benefit – and nowadays this solution is named “cardano formula”. Tartaglia wanted to keep it for himself, probably for a profit in disputations. Who was an honest scientist?