ngaged in a contest with Antonio Maria
Fiore, the pupil of Ferreo, made out this same rule to help secure the
victory, and this rule he imparted to me after I had diligently besought
him thereanent. I, indeed, had been deceived by the words of Luca
Paciolus, who denied that there could be any general rule besides these
which he had published, so I was not moved to seek that which I despaired
of finding; but, having made myself master of Tartaglia's method of
demonstration, I understood how many other results might be attained; and,
having taken fresh courage, I worked these out, partly by myself and
partly by the aid of Ludovico Ferrari, a former pupil of mine. Now all the
discoveries made by the men aforesaid are here marked with their names.
Those unsigned were found out by me; and the demonstrations are all mine,
except three discovered by Mahomet and two by Ludovico."[91]

This is Cardan's account of the scheme and origin of his book, and the
succeeding pages will be mainly an amplification thereof. The earliest
work on Algebra used in Italy was a translation of the MS. treatise of
Mahommed ben Musa of Corasan, and next in order is a MS. written by a
certain Leonardo da Pisa in 1202. Leonardo was a trader, who had learned
the art during his voyages to Barbary, and his treatise and that of
Mahommed were the sole literature on the subject up to the year 1494, when
Fra Luca Pacioli da Borgo[92] brought out his volume treating of
Arithmetic and Algebra as well. This was the first printed work on the
subject.

After the invention of printing the interest in Algebra grew rapidly. From
the time of Leonardo to that of Fra Luca it had remained stationary. The
important fact that the resolution of all the cases of a problem may be
comprehended in a simple formula, which may be obtained from the solution
of one of its cases merely by a change of the signs, was not known, but in
1505 the Scipio Ferreo alluded to by Cardan, a Bolognese professor,
discovered the rule for the solution of one case of a compound cubic
equation. This was the discovery that Giovanni Colla announced when he
went to Milan in 1536.

Cardan was then working hard at his Arithmetic--which dealt also with
elementary Algebra--and he was naturally anxious to collect in its pages
every item of fresh knowledge in the sphere of mathematics which might
have been discovered since the publication of the last treatise. The fact
that Algebra as a science had made su