r on any spot which showed that Messer Hieronimo had broken
his oath, he found what must have been to him as a precious jewel, to wit
a mistake in reckoning, which he reported to Cardan in these words:

"In this process your excellency has made such a gross mistake that I am
amazed thereat, forasmuch as any man with half an eye must have seen
it--indeed, if you had not gone on to repeat it in divers examples, I
should have set it down to a mistake of the printer." After pointing out
to Cardan the blunders aforesaid, he concludes: "The whole of this work of
yours is ridiculous and inaccurate, a performance which makes me tremble
for your good name."[99]

Every succeeding page of Tartaglia's notes shows more and more clearly
that he was smarting under a sense of his own folly in having divulged his
secret. Night and day he brooded over his excess of confidence, and as
time went by he let his suspicions of Cardan grow into savage resentment.
His ears were open to every rumour which might pass from one class-room to
another. On July 10 a letter came to him from one Maphio of Bergamo, a
former pupil, telling how Cardan was about to publish certain new
mathematical rules in a book on Algebra, and hinting that in all
probability these rules would prove to be Tartaglia's, whereupon he at
once jumped to the conclusion that Maphio's gossip was the truth, and that
this book would make public the secret which Cardan had sworn to keep. He
left many of Cardan's letters unanswered; but at last he seems to have
found too strong the temptation to say something disagreeable; so, in
answer to a letter from Cardan containing a request for help in solving an
equation which had baffled his skill, Tartaglia wrote telling Cardan that
he had bungled in his application of the rule, and that he himself was now
very sorry he had ever confided the rule aforesaid to such a man. He ends
with further abuse of Cardan's _Practice of Arithmetic_, which he declares
to be merely a confused farrago of other men's knowledge,[100] and with a
remark which he probably intended to be a crowning insult. "I well
remember when I was at your house in Milan, that you told me you had never
tried to discover the rule of the _cosa_ and the _cubus_ equal to the
_numerus_ which was found out by me, because Fra Luca had declared it to
be impossible;[101] as if to say that, if you had set yourself to the task
you could have accomplished it, a thing which sets me off laughing