175 
I am indebted to Sig. F. Brioschi for politely forwarding 
to me, through this society, a copy of his interesting work, 
entitled, Sulla Risolvente cli Malfatti per le Equationi del 
Quinto Grado. From this work, which is printed in the 9th 
vol. of the Memoirs of the Royal Institute of Lombardy, I 
learn that Malfatti, in a Memoir published in 1771, in the 
Transactions of the Academy of Siena, entitled, De cequa- 
tionibus quadrato-cubicis disquisitio analytica , gives a dis- 
cussion of quintic equations which anticipates to some extent 
certain recent investigations on the subject. After having 
proposed and applied an original method for the solution of 
the lower equations, after having, that is, deduced from each 
equation another of one degree inferior, which he calls its 
resolvent (“ risolvente”), because the solution thereof leads 
to that of the given equation, Malfatti proceeds on the same 
method to deal with the equation of the fifth degree, and by a 
process of elimination arrives at the actual calculation of its 
resolvent. This resolvent he finds to be an equation of the 
sixth degree, that is, one degree higher than the proposed 
equation. Sig. Briosclii is unable to say certainly whether 
or not Malfatti expected this result, but he inclines to the 
opinion that Malfatti would scarcely have persisted in so 
laborious a calculation if he had not hoped that the final 
equation would be such as to help to a solution of the given 
one. While Malfatti was engaged upon this problem, 
Lagrange was publishing in the Berlin Memoirs (1770-71), 
his celebrated method for the general solution of equations, 
in which he bases the theory on the number of values which 
functions can take by permutation of the variables. Eight 
years later Ruffini gave to the world his Theory of Equations 
(published at Bologna), and accompanied it with a demon- 
stration of the impossibility of resolving by radicals any 
gejieral algebraic equation of a degree higher than the fourth. 
Malfatti at first entertained some doubts as to the validity of 
Ruffini’s demonstration, and in a Memoir published in the 
