ch scant progress for so many years,
gave to this new process, about which Giovanni Colla was talking, an
extraordinary interest in the sight of all mathematical students;
wherefore when Cardan heard the report that Antonio Maria Fiore, Ferreo's
pupil, had been entrusted by his master with the secret of this new
process, and was about to hold a public disputation at Venice with Niccolo
Tartaglia, a mathematician of considerable repute, he fancied that
possibly there would be game about well worth the hunting.

Fiore had already challenged divers opponents of less weight in the other
towns of Italy, but now that he ventured to attack the well-known Brescian
student, mathematicians began to anticipate an encounter of more than
common interest. According to the custom of the time, a wager was laid on
the result of the contest, and it was settled as a preliminary that each
one of the competitors should ask of the other thirty questions. For
several weeks before the time fixed for the contest Tartaglia studied
hard; and such good use did he make of his time that, when the day of the
encounter came, he not only fathomed the formula upon which Fiore's hopes
were based, but, over and beyond this, elaborated two other cases of his
own which neither Fiore nor his master Ferreo had ever dreamt of.

The case which Ferreo had solved by some unknown process was the equation
_x^3 + px = q_, and the new forms of cubic equation which Tartaglia
elaborated were as follows: _x^3 + px^2 = q_: and _x^3 - px^2 = q_. Before
the date of the meeting, Tartaglia was assured that the victory would be
his, and Fiore was probably just as confident. Fiore put his questions,
all of which hinged upon the rule of Ferreo which Tartaglia had already
mastered, and these questions his opponent answered without difficulty;
but when the turn of the other side came, Tartaglia completely puzzled the
unfortunate Fiore, who managed indeed to solve one of Tartaglia's
questions, but not till after all his own had been answered. By this
triumph the fame of Tartaglia spread far and wide, and Jerome Cardan, in
consequence of the rumours of the Brescian's extraordinary skill, became
more anxious than ever to become a sharer in the wonderful secret by means
of which he had won his victory.

Cardan was still engaged in working up his lecture notes on Arithmetic
into the Treatise when this contest took place; but it was not till four
years later, in 1539, that he took any