and that he should have dared to hint that
those which he (Cardan) had sent for solution were not his own, but the
property of Giovanni Colla. Cardan had found Colla to be a conceited fool,
and had dragged the conceit out of him--a process which he was now about
to repeat for the benefit of Messer Niccolo Tartaglia. The letter goes on
to contradict all Tartaglia's assertions by arguments which do not seem
entirely convincing, and the case is not made better by the abusive
passages interpolated here and there, and by the demonstration of certain
errors in Tartaglia's book on Artillery. In short a more injudicious
letter could not have been written by any man hoping to get a favour done
to him by the person addressed.

In the special matter of the problems which he sent to Tartaglia by the
bookseller Juan Antonio, Cardan made a beginning of that tricky and
crooked course which he followed too persistently all through this
particular business. In his letter he maintains with a show of indignation
that he had long known these questions, had known them in fact before
Colla knew how to count ten, implying by these words that he knew how to
solve them, while in reality all he knew about them was the fact that they
existed. Tartaglia in his answer is not to be moved from his belief, and
tells Cardan flatly that he is still convinced Giovanni Colla took the
questions to Milan, where he found no one able to solve them, not even
Messer Hieronimo Cardano, and that the mathematician last-named sent them
on by the bookseller for solution, as has been already related.

This letter of Tartaglia's bears the date of February 13, 1539, and after
reading it and digesting its contents, Cardan seems to have come to the
conclusion that he was not working in the right way to get possession of
this secret which he felt he must needs master, if he wanted his
forthcoming book to mark a new epoch in this History of Mathematics, and
that a change of tactics was necessary. Alfonso d'Avalos, Cardan's friend
and patron, was at this time the Governor of Milan. D'Avalos was a man of
science, as well as a soldier, and Cardan had already sent to him a copy
of Tartaglia's treatise on Artillery, deeming that a work of this kind
would not fail to interest him. In his first letter to Tartaglia he
mentions this fact, while picking holes in the writer's theories
concerning transmitted force and views on gravitation. This mention of the
name of D'Avalos, the mas