when I
call to mind the fact that it is now two months since I informed you of
the blunders you made in the extraction of the cube root, which process is
one of the first to be taught to students who are beginning Algebra.
Wherefore, if after the lapse of all this time you have not been able to
find a remedy to set right this your mistake (which would have been an
easy matter enough), just consider whether in any case your powers could
have been equal to the discovery of the rule aforesaid."[102]

In this quarrel Messer Giovanni Colla had appeared as the herald of the
storm, when he carried to Milan in 1536 tidings of the discovery of the
new rule which had put Cardan on the alert, and now, as the crisis
approached, he again came upon the scene, figuring as unconscious and
indirect cause of the final catastrophe. On January 5, 1540, Cardan wrote
to Tartaglia, telling him that Colla had once more appeared in Milan, and
was boasting that he had found out certain new rules in Algebra. He went
on to suggest to his correspondent that they should unite their forces in
an attempt to fathom this asserted discovery of Colla's, but to this
letter Tartaglia vouchsafed no reply. In his diary it stands with a
superadded note, in which he remarks that he thinks as badly of Cardan as
of Colla, and that, as far as he is concerned, they may both of them go
whithersoever they will.[103]

Colla propounded divers questions to the Algebraists of Milan, and
amongst them was one involving the equation _x^4 + 6x^2 + 36 = 60x_, one
which he probably found in some Arabian treatise. Cardan tried all his
ingenuity over this combination without success, but his brilliant pupil,
Ludovico Ferrari, worked to better purpose, and succeeded at last in
solving it by adding to each side of the equation, arranged in a certain
fashion, some quadratic and simple quantities of which the square root
could be extracted.[104] Cardan seems to have been baffled by the fact
that the equation aforesaid could not be solved by the recently-discovered
rules, because it produced a bi-quadratic. This difficulty Ferrari
overcame, and, pursuing the subject, he discovered a general rule for the
solution of all bi-quadratics by means of a cubic equation. Cardan's
subsequent demonstration of this process is one of the masterpieces of the
_Book of the Great Art_. It is an example of the use of assuming a new
indeterminate quantity to introduce into an equation, thus anticipati