>TARTAGLIA says that Cardano had sworn not to publish the result. This is in
> his Quesiti. But Lodovico Ferrari, apostrophied by Tartaglia as "il suo
>creato",
> says in his second Cartello di sfida that he was also present in the
>house of
> Cardano in Milan when Cardano and Tartaglia were talking to each other and
> that Tartaglia were telling lies. So it is not clear whether Cardano ever
> swore an oath. Ferrari also mentions in this cartello that he and Cardano
> went to Bologna where they saw a note book of Ferro's with the solution of
> the equation of the first type. And, after all, the result is one that
>must be
> made public, it has to be known by all mathematicians. Cardano has no
>right to
> withhold it.
If you divide "all mathematicians" in the 16th century into two groups
a) the "professional" maestri d'abbaco and the different kinds of
mathematical practitioners and
b) the mathematical dilettanti
Tartaglia belongs to the first and Cardano to the second group.
Neither group shared the ideal intellectual socialism you pronouce as an
imperative to communicate every new and important mathematical result to
everybody. Of course, the second group depending on a reward system
consisting in personal reputation and if you will honour and by it in
social prestige was much closer to such an intellectual socialism, whereas
the members of the second group behaved like capitalist inventors who try
to exploit the economical possibilities inherent in their inventions as
much as possible.
The members of the first group did so because their income depended on the
possibility to sell their mathematical products to well paying clients who
ceased to come if these products where already available on the market in
printed form.
The members of the second group in general enjoyed a higher social status.
This holds especially for Cardano who explicitly considered his status so
much higher than that of Tartaglia that he feared a social disadvantage by
getting personally in touch with Tartaglia. Therefore he sent his "soldier"
Ferrari in order to do the job for him.
Cardano's publication behaviour - oath or not - served his own social needs
and violated the economical interests of Tartaglia.
Ivo Schneider