had found them out, whereupon he told me the name of the discoverer was
Scipio Ferreo of Bologna. 'And who else knows these rules?' I said. He
answered, 'Niccolo Tartaglia and Antonio Maria Fiore.' And indeed some
time later Tartaglia, when he came to Milan, explained them to me, though
unwillingly; and afterwards I myself, when working with Ludovico
Ferrari,[87] made a thorough study of the rules aforesaid. We devised
certain others, heretofore unnoticed, after we had made trial of these new
rules, and out of this material I put together my _Book of the Great
Art_."[88]

Before dealing with the events which led to the composition of the famous
work above-named, it may be permitted to take a rapid survey of the
condition of Algebra at the time when Cardan sat down to write. Up to the
beginning of the sixteenth century the knowledge of Algebra in Italy,
originally derived from Greek and Arabic sources, had made very little
progress, and the science had been developed no farther than to provide
for the solution of equations of the first or second degree.[89] In the
preface to the _Liber Artis Magnae_ Cardan writes:--"This art takes its
origin from a certain Mahomet, the son of Moses, an Arabian, a fact to
which Leonard the Pisan bears ample testimony. He left behind him four
rules, with his demonstrations of the same, which I duly ascribe to him in
their proper place. After a long interval of time, some student, whose
identity is uncertain, deduced from the original four rules three others,
which Luca Paciolus put with the original ones into his book. Then three
more were discovered from the original rules, also by some one unknown,
but these attracted very little notice though they were far more useful
than the others, seeing that they taught how to arrive at the value of the
_cubus_ and the _numerus_ and of the _cubus quadratus_.[90] But in recent
times Scipio Ferreo of Bologna discovered the rule of the _cubus_ and the
_res_ equal to the _numerus_ (_x^3 + px=q_), truly a beautiful and
admirable discovery. For this Algebraic art outdoes all other subtlety of
man, and outshines the clearest exposition mortal wit can achieve: a
heavenly gift indeed, and a test of the powers of a man's mind. So
excellent is it in itself that whosoever shall get possession thereof,
will be assured that no problem exists too difficult for him to
disentangle. As a rival of Ferreo, Niccolo Tartaglia of Brescia, my
friend, at that time when he e