ion is shown by negative testimony in the _Judicium de
Cardano_, by Gabriel Naude.[106] In the course of his essay Naude lets it
be seen how thoroughly he dislikes the character of the man about whom he
writes. No evil disposition attributed to Cardan by himself or by his
enemies is left unnoticed, and a lengthy catalogue of his offences is set
down, but this list does not contain the particular sin of broken faith in
the matter of Tartaglia's rules. On the contrary, after abusing and
ridiculing a large portion of his work, Naude breaks out into almost
rhapsodical eulogy about Cardan's contributions to Mathematical science.
"Quis negabit librum de Proportionibus dignum esse, qui cum pulcherrimis
antiquorum inventis conferatur? Quis in Arithmetica non stupet, eum tot
difficultates superasse, quibus explicandis Villafrancus, Lucas de Burgo,
Stifelius, Tartalea, vix ac ne vix quidem pares esse potuissent?" It seems
hard to believe, after reading elsewhere the bitter assaults of
Naude,[107] that he would have neglected so tempting an opportunity of
darkening the shadows, if he himself had felt the slightest offence, or if
public opinion in the learned world was in any perceptible degree
scandalized by the disclosure made by the publication of the _Book of the
Great Art_.

This book was published at Nuremberg in 1545, and in its preface and
dedication Cardan fully acknowledges his obligations to Tartaglia and
Ferrari, with respect to the rules lately discussed, and gives a catalogue
of the former students of the Art, and attributes to each his particular
contribution to the mass of knowledge which he here presents to the world.
Leonardo da Pisa,[108] Fra Luca da Borgo, and Scipio Ferreo all receive
due credit for their work, and then Cardan goes on to speak of "my friend
Niccolo Tartaglia of Brescia, who, in his contest with Antonio Maria
Fiore, the pupil of Ferreo, elaborated this rule to assure him of victory,
a rule which he made known to me in answer to my many prayers." He goes on
to acknowledge other obligations to Tartaglia:[109] how the Brescian had
first taught him that algebraical discovery could be most effectively
advanced by geometrical demonstration, and how he himself had followed
this counsel, and had been careful to give the demonstration aforesaid for
every rule he laid down.

The _Book of the Great Art_ was not published till six years after Cardan
had become the sharer of Tartaglia's secret, which had thu