Re: [HM] The Tartaglia/Cardano controversy
Prof. Lueneburg (luene@mathematik.uni-kl.de)
Fri, 21 May 1999 09:35:15 +0200 (MESZ)
On Thur, May 20, Dr. John W. Dawson, Jr. wrote among other things:
>
> ................................ If Ferro made his discovery 20 years
> before Tartaglia and divulged it to his students, why did they not take
> advantage of that information and compete with Tartaglia in those
> mathematical competitions? ......................................
>
The plural "students" here is actually a dual. Annibale dalla Nave and
Anonio Maria Fiore got the information on the cubic from Scipione del
Ferro. Annibale dalla Nave was the son-in-law of del Ferro and his
successor as a professor of mathematics at the University of Bologna.
He was in the possession of del Ferro's papers Cardano and Ferrari saw
visiting Bologna.
Antonio Maria Fiore was the one who challenged Tartaglia. The thirty
problems he posed to Tartaglia were published by Tartaglia in Quesito
XXXI. They all lead to equations of the form x^3 + px = q except the
16th one which leads to the equation 14 + x = x^5 + 2x^3. One of the
side conditions seems to be corrupted. Replacing a certain cube root
by a square root in the side conditions, one gets the equation
14 + x = x^3 + 2x^2 with 2 as a solution. But this equation is also
of a different form.
Heinz Lueneburg